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LA-13631-TThesis
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Etching of L102in
NF3 RF Plasma Glow Discharge
Los AlamosNATIONAL LABORATORY
LOSAlamos National Laboratory is operated by the University of Cal#orntifor the United States Departmentof Energy under contract W-7405-ENG-36.
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This thesis was accepted by the Department of Philosophy Engineering,the Llniversity of New Mexico, Albuquerque, New Mexico, in partialfulfillment of the requirements for the degree of Doctor of Philosophy.The text and illustrations are the independent work of the author andonly the front matter has been edited by the CIC-1 Writing and EditingStaff to confbrm with Department of Energy and Los Alamos NationalLuboratoy publication policies.
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L4-13631-TThesis
Issued: August 1999
Eiching of L102 in
NF3 RF Plasma Glow Discharge
John M. Veilleux
Los AlamosNATIONAL LABORATORY
Los Alamos, New Mexico 87545
Acknowledgments
I wish to thank Dr. Mohamed S. E1-Genk, my University and doctoral
advisor, who guided me during a verytrying time in my life, and helped me keep
this vision of a doctorate in mind. Mr. f-lamed Saber provided many important
observations and modeling insights to help me through an understanding of the
plasma reactions. Dr. E. Phil Chamberlain, my mentor at the Los Alamos National
Laboratory, guided me through the experimentation phase of my research, and
helped me really understand the meaning of applying science principles to an
observable.
I thank also Dr. Carter Munson and Dr. David Curtis of the Los Alamos
National Laboratory, who provided the overall technical direction and funding for
this work, as well as Dr. John Fitzpatrick, who provided guidance on the
chemistry of the plasma work. Special thanks are also due to the Chemical,
Science, And Technology Division’s Environmental Science and Waste
Technology Group (CST-7) for their continued funding of this waste
decontamination research project.
I thank also Catherine Auckland for her encouragement and patience who
made the process of pursuing a Ph.D. bearable.
This work was supported by CST-7 and CST-I 1, Los Alamos National
Laboratory, under the GRA program and by the Waste-Management Education
& Research Consortium under contract DE-FC-04-90AL-63805 to the Institute for
Space and Nuclear Power Studies.
v
Table of Contents
Acknowledgments .............................................................................................. v
Table of Contents ............................................................................................. vii
List of Figures .................................................................................................... ix
List of Tables ..................................................................................................... xi
Nomenclature...
.................................................................................................. X111
Abstract ............................................................................................................. xv
Chapter 1. Introduction ....................................................................................... 1
1.1. Previous Work on Radionuclide Etching .................................................... 11.2. Application of RF Glow Discharge for Waste Processing .......................... 21.3. Objectives of This Work .............................................................................21.4. Organization .............................................................................................. 3
Chapter 2. Background and Literature Search ................................................. 5
2.1.2.2.2.3.2.4.2.5.2.6.2.7.2.8.2.9.
Plasma Description .................................................................................... 5Plasma Models .......................................................................................... 6Major Species in the Bulk Plasma ............................................................. 7Transport of Reactive Species to a Surface ..............................................7Etch Concepts from Semiconductor Applications ...................................... 8Chemical Etching of U02 with F2 ............................................................... 9Uranium and Fluorine Chemistry and Thermodynamics .......................... 10Liquid Scintillation Counting (LSC) .......................................................... 10Analysis ................................................................................................... 11
Chapter 3. Experimental Setup ........................................................................ 14
3.1.3.2.3.3.3.4.3.5.3.6.3.7.3.8.3.9.
Plasma System ........................................................................................ 14Absorbed Power ...................................................................................... 18DC Sheath Voltage ..................................................................................22Pressure and Gas Flow ........................................................................... 23Stainless-Steel Planchettes ..................................................................... 26Sample Preparation ................................................................................. 27Liquid Scintillation Counter (LSC) ............................................................ 31Lower Limits of Detection ........................................................................ 37Activity Measurement of Plasma Processed Samples ............................. 39
vii
3.10. Temperature Measurements ................................................................ 423.11. Uncertainty in Measurements .............................................................. 433.12. Glow Discharge Obsewations ..............................................................47
Chapter 4. Results ............................................................................................. 52
4.1. The Etching Process ................................................................................ 524.2. Effect of Absorbed Power ........................................................................ 534.3. Effect of Plasma Gas Pressure ............................................................... 584.4. U02 Etch Rates ....................................................................................... 62
Chapter 5. CHEMKIN ....................................................................*.... .............*.. 64
5.4.5.2.5.3.5.4.5.5.5.6.5.7.5.8.
CHEMKIN Description ............................................................................. 64The CSTR Approximation ........................................................................ 66Plasma Reactions in CHEMKIN .............................................................. 67Surface Reactions ................................................................................... 71Thermodynamic Constants ...................................................................... 73CHEMKIN Validation ............................................................................... 73CHEMKIN Predictions for the Present Experiments ................................ 79Limitations on the Use of CHEMKIN ........................................................ 84
Chapter 6. U02 Etching And Application To Plutonium ................................. 85
6.1. The Plasma Species ................................................................................ 856.2. Reaction Model ........................................................................................ 87
6.3. Thermodynamic Analysis of Surface Etch Reactions .............................. 89
6.4. Volatile Surface Species .......................................................................... 94
6.5. Applications to Pu02 ................................................................................ 96
Chapter 7. Summary And Conclusions ......................................................... 100
Chapter 8. Recommendations for Continued Work ..................................... 103
8.1. Experiments with Depleted U02 ............................................................ 1038.2. Recovery system ................................................................................... 1048.3. in-Situ Measurements ............................................................................ 1048.4. Pu & PU02 work ..................................................................................... 104
Appendices ..................................................................................................... 105
Appendix A.Appendix B.Appendix C.Appendix D.Appendix E.
Properties ................................................................................ 106Experimental Details ................................................................ 115Data ......................................................................................... 138CHEMKIN ................................................................................ 150Analysis ................................................................................... 158
REFERENCES .........................................................................●............ .......... 171
...Vlll
List of Figures
Figure 1.Figure 2.Figure 3.Figure 4.Figure 5.Figure 6.Figure 7.Figure 8.Figure 9.Figure 10.Figure 11.Figure 12.Figure 13.Figure 14.Figure 15.Figure 16.Figure 17.Figure 18.Figure 19.Figure 20.Figure 21.Figure 22.Figure 23.Figure 24.Figure 25.Figure 26.Figure 27.Figure 28.Figure 29.Figure 30.Figure 31.Figure 32.Figure 33.Figure 34.Figure 35.Figure 36.Figure 37.Figure 38.Figure 39.Figure 40.Figure 41.Figure 42.Figure 43.
Transport of Plasma Species to the U02 Surface . ............................... 8RF Plasma Reactor& Recovery System ............................................ 16~lasma Test Chamberand Schematic of RF Antenna ....................... 16~lectrical Circuits . ............................................................................... 17Matching Network Power Equivalency. .............................................. 17~owered Electrode Voltage, No Plasma . ........................................... 20‘owered Electrode Voltage, With Plasma ..........................................2l4bsorbed Power vs NF3 Gas Flow Rate ............................................. 214bsorbed Plasma Power as Function of Transmitted Power. ............22Measured DC Sheath Voltage in Experiments . ................................ 23NF3 Gas Flow Rate in SCCM . .......................................................... 25Pressure Variation with Absorbed Power and Gas Flow. .................25Experimental Flow Rate vs. Manufacturer’s Correlation ................... 26Depleted Uranium Alpha Spectrum . .................................................29Uranyl Nitrate Hexahydrate Spectra by Liquid Scintillation. .............29Specification of Uranyl Nitrate Hexahydrate Solution. ...................... 30Liquid Scintillation Discriminator Setting ........................................... 35233UStandard Used To Calibrate the LSC Discriminator. ................35Alpha and Beta Detection Efficiencies. ............................................36Detection Efficiency Vs. Solution pH . ............................................... 36Lower Detection Limits. ....................................................................39Spectrum Analysis for Sample Count Rate . ..................................... 41Temperature Rise in Plasma Reactor . ............................................. 43Accuracy of the Measurements . .......................................................46Uncertainty in Measured Fraction of UOZ Etched .............................46Typical Plasma Operations. .............................................................47Glow Discharge Observations at 50 W Absorbed. ...........................48Fraction of U02 Etched in NF3 RF Plasma . ......................................53Power Effects on U02 Etching at 17 Pa . .......................................... 55Effect of Power on NR,~,Xat 17 Pa ................................................... 56Effect of Power on t at 17 Pa ........................................................... 56Power Effects on U02 Etching at 10.8 Pa ........................................57Power Effects on U02 Etching at 32.7 Pa ........................................ 57Power Effects on U02 Etching at 39.4 Pa ........................................ 58Pressure Effects on U02 Etching at 25 W ........................................ 59Pressure Effects on U02 Etching at 50 W ........................................6OPressure Effects on U02 Etching at 100 W ...................................... 60Pressure Effects on U02 Etching at 170 W .....................................6 IPressure Effects on U02 Etching . ....................................................6lInitial Etch Rate of U02 . ................................................................... 63Average Etch Rate at 17 Pa . ............................................................63Experimental Setup of Perrin et. al ................................................... 77Comparison of CHEMKIN with Si Etching Experiments. ..................78
ix
Figure 44.Figure 45.Figure 46.Figure 47.Figure 48.Figure 49.
..........
Maximum Variation in Rate Coefficient . ........................................... 78CHEMKIN Neutral Species Predictions at 17.0 Pa. ......................... 82CHEMKIN Ion Predictions at 17.0 Pa ...............................................82CHEMKIN Pressure Predictions . ...................................................... 83CHEMKIN Sensitivity with Flow Rate ............................................... 83Gibbs Free Energy of Formation for Uranium Fluorides/Oxyfluorides........................................................................................................... 92
Figure 50. Gibbs Reaction Energy, GR, for U02 Etching . .................................. 93Figure 51. Gibbs Reaction Energy, GR, for U Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Figure 52. Vapor Pressure of UFX Compounds . ................................................ 95Figure 53. Average Etch Rate ~ of UOZ Compared with PuOZ. ....................... 97Figure 54. Vapor Pressure of PUFGand UFGCompared .................................... 99Figure 55. Plutonium Compound Gibbs Free Energy of Formation ................... 99Figure B-1. RF Antenna . ..................................................................................ll6Figure B-2. Plasma Reactor and Recovery System. ....................................... 117Figure B-3. Inlet and Reactor Conditions .........................................................l2lFigure B-4. Experimental & Manufacturer’s Flow Calibration Data .................. 124Figure B-5. Rotameter Gas Flow Calibration ................................................... 125Figure B-6. Recovery System Flow and Throughput Characteristics ..............129Figure B-7. Recovery System Pressure Differential & Conductance ...............130Figure B-8. Effect of RF Power on Reactor Pressure ...................................... 133Figure B-9. Rotameter Setting During Plasma Operation ................................ 135Figure B-1 O. Plasma Extinguishing Pressure .................................................. 136Figure B-11. Type of Flow in Plasma Chamber . ............................................... 137Figure D-1. Determining the HF Partial Pressure ............................................ 153Figure D-2. Comparison of Chemkin and Experiment ..................................... 153Figure E-1. NF2 and NF3 Geometrical Cross Sections .................................... 160Figure E-2. Cross Section Correlation .............................................................l6lFigure E-3. Ion Energy Dependence on Cross Section . .................................. 163Figure E-4. Reaction Sequence of F Atoms and UOZ. .................................... 170Figure E-5. Reaction Sequence of F Atoms and U Metal . ............................... 170
x
List of Tables
Table 1.Table 2.Table 3.Table 4.Table 5.Table 6.Table 7.Table 8.Table 9.Table 10.Table 11.Table 12.Table 13.Table 14.Table 15.Table 16.Table 17.Table 18.Table 19.Table 20.Table 21.Table 22.Table 23.Table 24.Table 25.Table 26.Table 27.Table 28.
I,
1
I
Plasma Etch Modeling Mechanisms ................................................... 12Modeling Approaches .......................................................................... 13Characteristics of Plasma System ....................................................... 15VPPCorrelations with Pt,, Plasma Ignited. ............................................ 19Absorbed Power Correlation with Rotameter Setting, F (cm) .............. 20Planchetie Characteristics ...................................................................26Activity and Mass Parameters of Sample Solution ............................... 28Sample Specifications ......................................................................... 31Detection Limits of Depleted U02 Samples ......................................... 38
Measurement Uncertainties ............................................................... 45Equations and Related Error Functions .............................................49Plasma Observations ........................................................................5lU02 Plasma Processing Results at 17 Pa .........................................55Typical Output Parameters . ...............................................................65Species in NF3 Plasma . .....................................................................68Plasma Chemistry in CHEMKIN . ....................................................... 69Plasma Surface Reactions. ............................................................... 72Parameters of Perrin et. al. (1990) Experiments . .............................. 75CHEMKIN Species Consolidation. ....................................................75Perrin et. al. (1990) Experimental Data at 200 W .............................. 76CHEMKIN Parameters for the U02 Experiment . ............................... 79CHEMKIN Parameters at 17 Pa . .......................................................8OCalculated Mole Fractions of Plasma Species at 17 Pa . ................... 86Plasma Conditions at 17 Pa . ............................................................. 87Bonding Sites for Reaction with F Radicals . ......................................88Favorable Thermodynamic Reactions of U-O-F . ............................... 90Unfavorable Thermodynamic Reactions of U-O-F. ........................... 91SurFace Species Volatility Data. ........................................................96
Table A-1. Physical Properties Of Select Compounds ................................... 108Table A-2. Thermodynamic Properties Of Select Species .............................. 110Table A-3. Enthalpy and Gibbs Energy of Reaction for F Atom Reactions with
Uranium Fluorides and Oxyfluorides ............. ............................................ 112Table A-4.Table A-5.Table B-1.Table B-2.Table B-3.Table C-1.Table D-1.Table D-2.Table D-3.Table D-4.
Composition Of Stainless Steel ..................................................... 113Nuclear Properties Of Select Isotopes ........................................... 114Characteristics Of Plasma System .................................................ll6Plasma System Parts List . ............................................................. 118Stainless Steel Type 304 Sample Substrates ................................ 119Depleted UOP Experimental Data ..................................................l4OExperimental Mole Fractions & Pressure .......................................l52CHEMKIN Predictions, ~, for Perrin’s Experiment ........................ 154CHEMKIN Parameters for UOP Etching Experiment ...................... 154CHEMKIN Predicted Mole Fractions at 17 Pa for UOP Etching
Experiments . ............................................................................................. 155Table E-1.Table E-2.Table E-3.Table E-4.Table E-5.Table E-6.Table E-7.
Parameters for Etch Rate Calculation ............................................l59Physical Data on Select Species ................................................... 160Plasma Sheath Thickness and Ion Energy . ................................... 162Calculated Mole Fractions of Plasma Species at 17 Pa. ...............163Detailed Calculations for NF3 Ion ...................................................l64Energy From U02 Reactions with F Atoms .................................... 166Vapor Pressure Correlation ............................................................ 167
xii
Nomenclature
Symbol DefinitionA Activity (Bq); Specific activity (Bq/g) indicated by bar over A.Bc;
cddeEEAfFFOGGfGRHfHRJ
JOk
k~KckfKnKPLmMnNNA/v~NR,~aP
Pr%
Paa
Exponent of temperature, T, in Arrhenius kinetics relationship.Concentration (mol m-3).Alpha instrument count rate (counts/rein).Beta instrument count rate (counts per minute).Standard state concentration (1 mole/L)Dilution factor.Molecular diameter (m).Relative erro~ Electron chargeEnergy (J)Activation energy (kJ mol-f).Activity ratio of an isotope to the total activity.Flow rate (mol S-l).Inlet flow rate (mol s-l).Molar Production Rate (mol S-l).Gibbs free energy of formation (kJ moi-l).Gibbs free energy of reaction (kJ mol-f).Enthalpy of formation (kJ mol-l).Enthalpy of reaction (kJ mol-l).Etch rate (rein-l; ~m/min); Average etch rate indicated by bar over J.;Flux (m-z S-l)Initial etch rate (rein-l; pm/min).Boltzman’s Constant, 1.381x1 O-23 J K-l; Thermal Conductivity (Win-lK-l)
Reaction rate constant, (cnz3nzolecule~-1S-*, where n is the order of
the reaction.Backward (reverse) rate coefficient of a reaction.Equilibrium constant of a reaction with respect to concentration.Forward rate coefficient of a reaction.Knudsen number.Equilibrium constant of a reaction with respect to pressure.Thickness (m)Mass (kg).Molecular weight (g/mole).Number density (m-3)Number of atoms or molecules.Avogadro’s Number, 6.022xI 023 mol-l.Ratio of remaining to initial activity= (&-A)/AO.Asymptotic value of U02 activity fraction removed.Power absorbed (W).Pressure (Pa).Probability that a beta emission will be correctly counted inwindow.Probability that an alpha emission will be correctly countedalpha window .
...X111
the beta
in the
Symbol Definition
P“ Standard state pressure (1 Bar= 1x1O’ Pa)Pt, Power, Transmitted (W).Q Heat (W)R Gas Constant (8.3144 J mol-l K-l); Radius of glow discharge volume
(m)Rmax Maximum radius of glow discharge volume, equal to 25 cm.r Molar Production Rate per Unit Volume (mol S-ls Sheath thickness (m)s Cross sections! area (m*)SCCM Standard cubic centimeter per minute, gas flow
pressure.t Time (s); plasma process time; counting time;T Temperature (K)
Velocity (m/s): Volume (m3)Vs Sheath Voltage (V)x Mole fraction
GreekSymbol Definition
m-3).
rate at standard
half-life.
Pso
Y
Pv
BetaElectron temperature (in units of volts)Characteristic Etch Time (rein)Enthalpy (kJ mol-l)CountsDensity (kg m-3)Mean free path (m)Debye Length (m)Number of moles; Ratio of absorbed to transmitted powefiEfficiency.Specific gravity (kg m-3)Standard deviation; Cross section (m*)Sticking coefficient for a gaslwface reactantTotal mean counts; true mean of sampleViscosity (Pa-s)
SubscriptsSymbol Definitionb Bohm velocityc Critical level (for detection); Chamber (of plasma reactor)CR Combined chamber and recovery systemsD Qualitative level (for detection)e Electrons -! Ions
j Species numberInitial conditions
; Quantitative levelR Recovery system
(for detection)
xiv
ETCHING OF U02 IN NF3 RF PLASMA GLOW DISCHARGE
by
John M. Veilleux
Abstract
A series of room temperature, low pressure (10.8 to 40 Pa), low power (25
to 210 W) RF plasma glow discharge experiments with U02 were conducted to
demonstrate that plasma treatment is a viable method for decontaminating U02
from stainless steel substrates. Experiments were conducted using NF3 gas to
decontaminate depleted uranium dioxide from stainless-steel substrates.
Depleted U02 samples each containing 129.4 Bq were prepared from 100
microliter solutions of uranyi nitrate hexahydrate solution. The amorphous U02
in the samples had a relatively low density of 4.8 gm/cm3. Counting of the
depleted U02 on the substrate following plasma immersion was performed using
liquid scintillation counting with alpha/beta discrimination due to the presence of
confounding beta emitting daughter products, 2-h and 2~Pa. The alpha
emission peak from each sample was integrated using a gaussian and first order
polynomial fit to improve quantification. The uncertainties in the experimental
measurement of the etched material were estimated at about* 2Y0.
Results demonstrated that UOZ can be completely removed from
stainless-steel substrates after several minutes processing at under 200 W. At
180 W and 32.7 Pa gas pressure, over 99% of all U02 in the samples was
removed in just 17 minutes. The initial etch rate in the experiments ranged from
0.2 to 7.4 pm/min. Etching increased with the plasma absorbed power and feed
gas pressure in the range of 10.8 to 40 Pa. A different pressure effect on U02
etching was also noted below 50 W in which etching increased up to a maximum
pressure, -23 Pa, then decreased with further increases in pressure.
The U02 etching process was self-limiting as the etch rate decreased
exponentially with immersion time to the end point. The end point was defined in
xv
this work as when either all detectable U02 in the test sample was removed or
the etch rate became zero with U02 only partially removed. At both low and high
pressure, and low power (C 50 W), blocking occurred in which the end point was
reached before all U02 in the samples was completely removed.
A computer simulation, CHEMKIN, was applied to predict the NF3 plasma
species in the experiments. The code was validated first by comparing its
predictions of the NF3 plasma species with mass spectroscopy etching
experiments of silicon. The code predictions were within + 5% of the measured
species concentrations. The code predictions of plasma species in the U02
experiments were only applicable at 17 Pa because the assumption in the code
of a perfectly mixed plasma reactor was not met in the experimental chamber
except at 17 Pa.
The F
diffusing from
atom radicals were identified as the primary etchant species,
the bulk plasma to the UOZ surface and reacting to form a volatile
UF6, which desorbed into the gas phase to be pumped away. Ions created in the
plasma were too low in concentration to have a major effect on etching, but can
enhance the etch rate by removing non-volatile reaction products blocking the
reaction of F with U02.. The composition of these non-volatile products were
determined based on thermodynamic analysis and the electronic structure of
uranium. Analysis identified possible non-volatile products as the uranium
fluorides, UF2.~, and certain uranium oxyfluorides U02F, U02F2, UOF3, and UOF4
which form over the U02 sutiace. Successive reactions between these products
and F atoms lead to the formation of UFG. The UFG has a vapor pressure of 24
kPa, well above the operating pressure at the gas temperature (-300 K) of the
plasma, and, as a consequence, desorbs into the gas phase. The other
intermediate fluorides and oxyfluorides are solids and remain on the surface,
eventually slowing or blocking the etch reaction as they accumulate. These
results explain why when power was too low, the etch reactions completely
stopped before all detectable U02 could be fully etched. This is because the
rate of formation of the non-volatile products was higher that the removal rate,
xvi
allowing the accumulation of non-volatile products preventing diffusing F-atoms
to react with the U02, thus eventually slowing and blocking the reaction.
Comparison of U02 with previously measured PU02 etch rates showed
that the removal of U02 and PU02 were comparable and differences could be
accounted for by differences in experimental conditions. The chemistry and
reaction thermodynamics of U02 have many parallels to those of PU02, such as
similar vapor pressures at room temperature (24 vs. 14 kPa) and favorable
Gibbs free energy of formation of many species. These favorable parallels
suggest that similar kinetics will occur with PUOZ but that further experimentation
with PU02 etching should be continued over the power and pressure parameter
space.
xvii
CHAPTER 1. INTRODUCTION
The cost of decontamination, treatment, long term storage, and
monitoring of transuranic’ (TRU) waste in the United States in 1997 dollars has
been estimated at over $28,000/m3, compared to $1 ,800/m3 for low level
radioactive waste (Allen and Iiazelton, 1984). The total TRU volume exceeded
250,000 m3 in 1991 (Kisieleski et. al, 1994). Transuranic waste is defined to be
waste containing any alpha emitter with an atomic number greater than 92, a
half-life over 20 years, and an activity of 3700 Bqlg or greater. Plutonium and
americium waste contaminated objects are examples of transuranic waste, and
plasma treatment of such waste streams include contaminated glove-boxes and
high-value metallic objects such as ion sources. Other exampies of plasma
treatment applications are for enriched uranium recovefy from the cladding of
spent nuciear fuel (Kim et. al., 1999). The cost and safety of treating these
contaminated objects are a significant incentive to reduce the quantity of this
waste. Possible options include treatment to reclassify transuranic waste to low
level waste; volume reduction; or better yet a total or partial removal of the waste
from the metal object and full recovery of the radionuclides for subsequent
recycling or disposal. Unlike mechanical scrubbing and water jet techniques, RF
plasma is more effective for removal and recove~ of trace radionuclides from
surface crevices, can be operated remotely, and provides a better margin of
safety for the operator.
1.1. Previous Work on Radionuclide Etching
Eariy experiments performed in 1991 demonstrated the etching of
plutonium and plutonium oxide in fluorine based CFd02 RF plasma (Martz et. al.,
1991 ). They demonstrated PU02 average etch rates of -0.03 ~m/min at 50 W
and 26.7 Pa, and showed that Pu metal etching rates are lower than PUOZ by a
factor of 5 to 10. Their data also included pressure effects on Pu etching in the
range from 13 to 80 Pa, but the data were too few and had too much scatter to
confidently predict the relationship. The authors noted that their gravimetric
1
technique for measurement of mass loss during plasma processing was prone to
considerable error. Their PUOZ sample surface area exposed to plasma, varying
between 16.9 to 3.48 m2/g, were not well enough characterized to predict etch
rates with confidence. The authors also noted that their gravimetric technique for
measurement of mass loss during plasma processing was prone to consideiabie
error. Therefore, there was a need to continue this work to better quantify the
usefulness and limitations of using RF plasma glow discharge as an effective
decontamination technique for transuranic waste.
1.2. Application of RF Glow Discharge for Waste Processing
in an NF3 RF glow discharge, electrons are created which follow the RF
oscillations and collide with neutral particles to cause ionization, dissociation,
and other reactions. The most important species for etching are the creation of
atomic F radicals from NFs by electron collision. The F atoms then diffuse to the
surface where they react and volatilize contaminants, such as UO*. The
volatilized contaminants diffuse into the chamber where they are subsequently
pumped away, thus cleaning the underlying metal structure. The plasma, a
“quasi-neutral gas”, is in a highly non-equilibrium condition with neutral particles
near room temperature (- 298 K) while the electrons are at significantly elevated
temperatures, -50,000 K. Because the ionization fraction is small, typically c
0.001 Yo, the temperature experienced by objects in the plasma is room
temperature, and hence heating effects are minimal. As a result, plasma
cleaning can be accomplished without destroying the object to be
decontaminated.
1.3. Objectives of This Work
In this work, a series of single effect RF giow discharge experiments were
conducted with NFs gas to provide data on the dependence of the depleted
uranium dioxide (lJO*) etch rate from stainless steel surfaces on the absorbed
power and pressure. The power and pressure values were varied one at a time
and the etch rates of LJ02 from stainless steel surfaces were measured as a
2
function of immersion time. UOZ was used because it avoided the potential
inflexibil”ky and safety issues associated with experimentation with plutonium,
Provided data on the decontamination of U02 waste, provided procedures on
measurement techniques dealing with very small quantities of material, and
provided information on the physics of the processes. Unlike CFd02 plasma feed
gas used in other experiments (Martz et. al., 1991; Ianno et. al., 1981) , NFs
feed gas was chosen for plasma etching because it dissociates 10 to 25 times
faster and eliminates the possibility of forming carbon residues in the chamber
and on the surface of the sample, blocking the etching process. Consequently,
the U02 and NFs plasma data developed in this study can be applied to the
design of future experiments with plutonium because of similarities in the
chemistry including: similar oxidation states, similar volatility of the metal
hexafluoride, similar enthalpy of formation and Gibbs free energy of the
intermediate fluorides/oxyfluorides.
In these experiments, data were collected on the average etch rate of UOZ
as a function of the plasma immersion time, absorbed power, and gas pressure
at 17 Pa, the baseline case, with additional experiments conducted to establish
trends at both lower {10.8 Pa) and higher (31-40 Pa) pressures. Comparison of
the initial and the remaining radioactivity
etched during a certain immersion time.
develop a transient, multi-species diffusion
etching of U02 in the present experiments.
of tJ02 gave the average quantity
These results were also used to
model (E1-Genk et. al., 1999) for the
1.4. Organization
The organization of this paper follows with a background and literature
search. This chapter contains a description of the plasma and presents a
summary of the literature describing the plasma species, transport of species to
a surface, etch concepts that were advanced from studies in the silicon industry,
the chemistry and thermodynamics of uranium compounds, liquid scintillation
techniques, and data analysis references.
3
Chapter 3 describes the experimental setup. This chapter summarizes
the plasma system and operating parameters, describes how the uranium oxide
samples were prepared and characterized, describes the methods for quantifying
the remaining U02 following plasma immersion, and describes observations
related to the plasma glow discharge.
Chapter 4, Results, describes the baseline case (17 Pa, 50 W) to explain
the parameters used. This is followed by detailed data describing the power and
pressure variations on the amount of U02 etched. Finally, the etch rates are
calculated as a function of power and pressure.
The chapter on CHEMK!N, Chapter 5, describes the simulation code used
to determine the plasma species and their quantity as a function of power. The
chapter begins with a description of the code and modeling assumptions, and
describes the plasma chemistry, the surface chemistry, and thermodynamics.
Before applying the results to the present experiments, a validation was
performed and the results are described. The validation effort led to some
changes in the plasma chemistry and these were applied to the present
experimental setup which are described. Because of the approximations in the
code, application to the present experiments were limited to 17 Pa.
Chapter 6, Discussion and Application to PUOZ discusses the results of
UOZ etching and applies these results to PU02 using parallels in the chemistry
and thermodynamics. The self-limiting etching process with U02 is described in
terms of the formation of non-volatile surface species which block the reaction.
The parallels in the chemistry and thermodynamics of PU02 are investigated.
Chapter 7 summarizes the dissertation and draws conclusions. Finally,
Chapter 8 contains recommendations for future work in U02 etching, describes
improvements needed with the recove~ system, and, describes applications for
Pu and PU02 etching investigations.
CHAPTER 2. BACKGROUND AND LITERATURE SEARCH
Plasma processing experimentation in the semiconductor industry has
contributed to significant advances in the knowledge of the plasma and surface
chemist~ of the processes. Applications in the area of waste treatment and
decontamination, especially for radioactive waste on metallic substrates, has
received some emphasis. The first application to plutonium etching was reported
in 1991 (Martz et. al., 1991) and led the Los Alamos National Laborato~ in 1996
to continue this investigation with uranium, the subject of these experiments.
This chapter begins with a background on plasmas, focusing on how these
concepts may be applied toward decontamination of radionuclide contaminated
metals. It summarizes the literature search conducted to identify some of the
key etching concepts, provide data on species in the plasma, transport of
species to the contaminated surface, and etching
2.1. Plasma Description
A plasma is a collection of ionized and
concepts.
neutral particles and electrons
which, on the average, are electrically neutral (Lieberman & Lichtenberg, 1994;
Manes and Flamm, 1989; Dendy, 1993). A typical 13.56 MHz radio-frequency
(RF) glow discharge plasma drives highly mobile electrons to collide with neutral
gas atoms and molecules, resulting in ionization and dissociation of a gas, such
as NFs. There are many reactions occurring among the atoms, molecular
fragments, ions, and radicals of a plasma including recombination, electron
attachment, bimolecular collisions, and excitation reactions.
these effects is the creation of positive ions, negative ions, and
some of which are strongly reactive in a fluorine bearing gas,
The sum of all
neutral pa*icles,
such as F atom
radicals. A typical materials processing RF glow discharge plasma is
characterized by low-pressure (-0.1 to 140 Pa); weakly ionized (- 0.00170 of
total gas concentration); and containing 1014 to 1019 electrons per m3 with
energies in the 1 to 10 eV range, corresponding to electron temperatures of
11,600 to 116,000 K. The much heavier neutral and ionic constituents of this
plasma, unable to respond to the fast RF oscillations, retain thermal energies of
5-
- 0.026 eV, and therefore are at, or near, room temperature, -300 K.
Therefore, the RF glow discharge plasma is a highly non-equilibriufi thermal
system. The neutral species diffuse to surfaces where they “~n deposit their
energy (- 0.026 eV or 2.5 kJ/mole), adsorb, and react. A plasma sheath is
created at the plasma/wall/and plasma/electrode inte~aces of a chamber
because the RF driven discharge plasma acts like an RF diode. The RF
oscillations lead to the creation of a positive space charge buildup of ions near
surfaces, because the ions are unable to follow the rapid RF oscillation. This
creates strong electric fields in the sheath, directed from the plasma toward the
wall. Associated with this field is an effective DC voltage drop in the sheath
which accelerates ions into a surface, where they can deposit their energy,
enhancing surface reactions. The negative ionic species formed in
electronegative gases (Kouznetsov et. al, f 996), such as NF3, are the result of
electron attachment reactions that do not contribute to etching directly. These
negative ions are reflected at the plasma sheath and generally remain in the bulk
plasma; however, they affect the sheath thickness, the electron distribution, and
the F-atom concentration in a complicated way, and hence affect the overall
etching. Because the side wail area of a chamber is typically much larger than
the electrode surface area, the sheath voltage at the powered electrode is much
greater than the sheath voltage at the grounded walls. For this reason, samples
to be etched are often mounted on the powered electrode to achieve the
maximum ion bombardment effects.
2.2. Plasma Models
Models or a modeling approach was needed to provide estimates of the
plasma species and their concentrations. Several models were examined, as
tabulated in Table 2, and most were developed in support of semiconductor
applications. The CHEMKIN model was chosen as a result of this investigation
(Chapter 5). The model has an
been done with NF3, extensive
model was readily available.
extensive chemical reaction set, some work has
documentation is available, and the simulation
6
2.3. Major Species In the Bulk Plasma
As suggested by the. above plasma introduction, tie plasma is a
complicated mixture of many species. Mass spectroscopy inv~stigation of NF3
plasma species were conducted by a number of investigators’ (Pernn et. al.,
1990; Reese and Dibeler, 1956; Konuma and Bauser, 1993; Lui et. al., 1992;
Greenberg and Verdeyen, 1985; Honda and Brandt, 1984; Beattie, 1975; and
Weiner et. al., 1992). A database of 163 NF~02 reaction mechanisms, including
rate constants and activation energies, is available in the literature in support of
CHEMKIN (Meeks et. al., 1997; Meeks and Shon, 1995). Reported species
include: electrons; neutral species: F, F2, N, N2, N2F2, N2F4, N3, NF, NF2, NF3;
positive ions: F+, F2+, N+, N2+, NF+, NF2+, NF3+, N2F+; and negative ions: F2-,
F-.
2.4. Transport of Reactive Species to a Surface
For etching to take place, reactive bulk plasma species must be
transported to the surface containing the matefial to be etched (Lieberman and
Lichtenberg, 1991). The transport mechanisms are diffusion of
(Bird, 1960) and acceleration of ions through the plasma sheath
The concepts associated with the transport of reactive species
neutral species
to the material.
to a surface is
shown in Figure 1. Plasma neutral species, such as the highly reactive F atom
radicals, diffuse to the substrate sutiace with typical thermal velocity, vDti, and
adsorb to the surface via Van De Waals forces (physisorption) and
chemisorption (Lieberrnan and Lichtenberg, 1994). Positive ionic species, such
as F+ and NF2+, are accelerated through the negative potential of the plasma
sheath and attain much larger velocities, vAcc, determined by the potential
difference of the sheath, the velocity of the ions at the plasma sheath edge
(Bohm velocity), and collisions in the sheath. At the surFace, the ionic species
are rapidly neutralized because of the excess electrons present at the surface.
The surface chemistry is determined by chemical kinetics and the concentrations
of the reactive adsorbed species (Fogler, 1992; Levenspiei,
species, primarily fluorine, react to form a volatile product,
7
1972). These
usually a metal
fluoride, which desorbs into the bulk plasma to be pumped away. Thus, a
volatile radioactive contaminant ca~ be removed from a surface, leaving the
metallic substrate free of activity. If the sheath voltage is great enough (typically
500 to 1000 V), sputtering by energetic ions can also occur, causing the removal
of non-volatile species.
PIASMA REGIONN%Nfi+,Nfi F,~, F, etc.
(=+)‘+’
PlasmaSheath
i
Figure 1. Transport of Plasma Species to the U02 Surface.
2.5. Etch Concepts from Semiconductor Applications
Several review articles are available on general etch mechanisms, but
these are generally associated with silicon etching. Particularly extensive
reviews were conducted by Winters and associates (Winters and Cobum, 1992;
Winters et. al., 1983; Winters and Coburn, 1985), by Flamm and associates
(Flamm et. al., 1981; Flamm et. al., 1983) and others (Mauer et. al., 1978;
Zalm, 1986). In addition, a process similar to the oxidation of metals was
advanced for the fluorination of a surface (Babanov et. al., 1989; Cabrera and
Mott, 1949). Table 1 summarizes the etch mechanisms based on this review.
8
The etch mechanisms are divided into two types: , spontaneous (isotropic)
etching, and ion bombardment (anisotropic) assisted etching. The former is
called spontaneous because it relies on diffusion of the reactants with
subsequent chemical reaction to fofi the volatile product. It is considered
isotropic since it shows no preferential direction to etching. The latter, ion
bombardment, includes effects of energetic ions accelerated across the plasma
sheath to react with surface contaminants. It is anisotropic since the preferred
etch direction is along the ion path and hence, normal to the sheath. While the
concepts of isotropic and anisotropic etching are important for semiconductor
processing, they are not too important in the actinide etching described here.
However, spontaneous etching is important in that it permits etching in regions
inaccessible to plasma ions, such as inside crevices and pipe interiors.
Unlike UOZ etching, Si and SiOz etching with fluorine was found to result
in a constant etch rate. This effect was obsemed in plasma silicon etching with
NF3 (Stenger and Akiki, 1986), CFdOz (Donnelly et. al., 1984), and XeFz (Cobum
and Winters, 1979) gases. In U02 etching, the etch rate decreases with time,
as described in Chapter 6.
2.6. Chemical Etching of U02 with Fz
Etching in chemical reactors using elemental fluorine is also possible but
at temperatures above 700 K yielding etch rates of 1.3 micrometer/minute
(Iwasaki, 1968; Sakurai, 1974; Sazhin and Jeapes, 1997). Further, using F2
instead of NF3 for etching UOZ poses significant safety issues because limits are
0.1 ppm versus 10 ppm; Fz is very toxic compared to NFs; and short term Fz
gas ingestion can lead to death while NFs does not (MSDS for Fz and NFs).
Consequently, if Fz etching were used in place of plasma etching, a containment
chamber or facility would have to be built and high heat would have to be applied
to the substrate or gas to achieve the desired etch rate.
9
2.7. Uranium and Fluorine Chemistry and Thermodynamics
One of the eariier studies of uranium (and plutonium) I
fluorine: was performed at high temperature in a chel
(Vandenbussche, 1964). These experiments determined the etch
of U02, U03, U30& UOZF2, and UF4 with molecular fluorine.
experimentaiists have examined the fluorination of UOZ with F and
UF6 and the intermediate uranium oxyfluorides (Iwasaki, 1968; !
Machiels and Olander, 1977; Galkin and Zuev, 1984; Sazhin and
Lyman and Holland, 1987; Labaton and Johnson, 1959; Beattie
1985; Yahata and Iwasaki, 1964; and Souter and Andrews, 1997).
One of the most extensive reviews of the actinide chemi
uranium and its compounds, was published
Volume II contains an extensive listing of
prima~ sources include: Alberty and Silbey,
and Mossman, 1980; Cacace et. al., 1995;
et. al. 1980; Lide, 1993; Mallard, 1997;
Shackelford et. al., 1994; Venugopal et. al.,
in 1986 (Katz et. al.
thermodynamic prop
1997; Antony et. al.,
Hildenbrand and La!
Pearson, 1958; f
1992; Wagman et. :
Walker et. al., 1989. Included are the physical properties of select
compounds; thermodynamic properties to include enthalpy ar
energy of formation; Gibbs energy of reaction for select reactions;
stainless-steel; and nuclear properties. The properties used in
tabulated in Appendix A.
There are a number of excellent reference works on fluo
including: Simmons, 1950; Hinz et. al., 1980 (Gmelin); Lloyd, ~9;
Skoinik, 1976; Rosner and Allendorf, 197fi; Chen et. al., 1977; :
Sadeghi, 1991.
2.8. Liquid Scintillation Counting (LSC)
Development of the techniques for quantification of smal
uranium (-1 0-5 kg) was an important part of this research. The shl
10
alpha particle (Friedlander and Kennedy, 1949) in U02 results in self-shielding,
preventing an accurate activity measurement in surface counting devices, and
was an important consideration in choosing LSC (Chapter 3). The literature had
considerable data on using LSC to quantify alpha emitters: Bower et. al., 1994;
Passo and Kessler, 1992; Avila et. al., 1992; Pujol and Sanchez-Cabeza, 1997;
and Pates et. al., 1966. Because the UOZ samples had in-grown beta emitters,
calculating the lower limit of detection (Currie, 1968; Pastemack and Harley,
t 971) provided a means of quantifying the limits of LSC detection.
2.9. Analysis
Analysis of data, including error estimation, curve fitting to data, data
integration and differentiation, and counting statistics were necessary in the
evaluation of the spectral results and quantification (Bevington, 1969; Karen,
1997).
11
Table 1. Plasma Etch Modeling Mechanisms.
Type Of Etching Mechanism
Spontaneous or Isotropic Reactiie Species FluxTo SurfaceEtching
. DissociationEnergy
. Promoteadsorption
Precursor States
. Chemisorption
* Physisorption
Successive Fluorination(Mauer et. al. 1978, Flamm &Donnely 1981)
Field-~lsted Mechanism (Winters et. al. 1983)
* Theory Of Oxidation(Cabrera & Mott, 1949)
. Reduced ActivationEnergy
. Place Exchange Mechanism
Ion BombardmentAssisted Chemically Enhanced PhysicalSputtering(Mauer et. al.,Etching(Anisotropic 1978)Etching)
Damage Induced Chemical Sputtering(Flamm and Donnely,1981)
Surface inhibitors(Flamm and Donnely, 1981)
Field-Assisted Mechanisms(Winters et. al., 1983; Zalm,1986)(also cakd chemicalsputtering)
12
Table 2. Modeling Approaches.
Reference CommentsBarone & Graves,1995.Carter et. al., 1994.
Coltrin, et. al., 1996
Economou & Alkire,1988.
Kopalidis& Jome,1993
Martisovits&Zahoran, 1997
Meeks & Shon,1995.
Meeks et a!., 1997.
Moffat et. al., q991
Park & Economou,1991.
Shell, 1997.
Zawaideh & Kim,1987.
MolecularDynamicsSimulation.
MoiecularDynamicsSimulation.
Describesmethodology& equations used in Surface Chemkin. Does notconsiderionacceleration-only diffusing species.
Transportmodelwith diffusion& ion transport in a plug flow reactor.
Transportmodelwith diffusion& ion transport,one dimensional in parallelplate configuration.
Model for transportof neutral species. Transport of charged particlestosurfacesand their effects are not treated.
DevelopsCHEMKIN for use in plasma modelingwithetching. Determinesrate constantsvia solutionsto Boltzman equation. Gives Arrheniusfitstogas phase reactions. Develops governing equations, includingthesurface& plasma chemistry. No ion bombardmentmodeling.
Chemkin NF~02 plasma modeling for Si. Includesextensive chemisttyinthe plasmaalong with rate coeticients.
Continuouslystirredtank reactor approximationfor solvingkinetics&chemicalreactionsat surface. Uses surface Chemkin. No ionacceleration.
Transportmodelwith diffusion,no ion transport Parallel plate radialflowreactor.
Monte Carlo Simulation.Examines abstractive & dissociativeadsorptionwithvariousswfaca kineticsincluding surface diffusion,ad-layerordering,and weakly bound physiosorbed precursorstates.
Transport& Poissonequation solution that includesmost of theprocessesin plasma etching: physical sputtering,chemical etching,
,
enhanced physicalsputtering,enhanced chemical etching.
13
CHAPTER 3. EXPERIMENT SETUP
This chapter describes the experimental setup. Included; are the
descriptions of the plasma system, the method for determining the absorbed
power and sheath voltage, the NFs gas flow rate and resulting plasma pressure,
preparation and specification of the uranium oxide samples, the method
developed for achieving reproducible activity measurements of plasma
processed samples, and quantification of the uncertainty in the resulting
measurements. The chapter is concluded with a description of the visual
observations of the plasma during sample processing.
3.1. Plasma System
Experiments were
(Figure 2) with NFs gas
performed using a 13.56 M1-lz RF plasma system
to decontaminate depleted UOZ from the surface of
stainless-steel substrates. The system includes a vacuum chamber for
processing the samples and a fume hood mounted recove~ system for pumping
the chamber during processing. A power supply, matching network, and
electrical circuitry complete the system. Characteristics of the plasma system,
including room and fume hood flow rates, are summarized in Table 3. A detailed
equipment list and drawing of the plasma system is included in Appendix A.
A cubic (- 0.5 m per side) aluminum plasma chamber (Figure 3) with a
total internal volume of O.125-m3 and an internal surface area of 1.623 m2 was
used to process depleted uranium oxide samples in plasma. The RF powered
electrode surface area on which the UOZ samples were mounted measured
0.00203 m2. The volume and surface area were determined by measuring the
dimensions of all internal chamber and protuberances to the nearest centimeter.
A 6.5” x 0.5” thick quartz window provides an internal view of the plasma,
powered electrode, and sample. Details of the RF antenna are also depicted. A
5.08 cm diameter tray was mounted on the antenna holder and the 1.007 cm
diameter stainless steel U02 sample planchettes were placed on the 5.08 cm
14
tray. Under normal conditions, each plasma run was made with two U02
samples in the event one was lost due to experimental error or problems.
An attached fume hood mounted recovery system was used for pumping
the gas out of the chamber during plasma immersion experiments. Its total
volume, 0.0071 m3, was measured by expanding a known quantity of gas from
the plasma chamber. The recovery system was also designed to capture an
effluent radioactive gas by condensation in a liquid nitrogen cold trap, but this
feature was not used in the current experiments. A charcoal trap prevents pump
oil from back-streaming to the chamber and captures toxic gases created in the
plasma, such as F2, preventing escape to the environment. The final trap is the
pump oil itself, which captures any remaining uranium hexafluoride that gets
through the charcoal trap.
An RF20 power supply provides line, or transmitted power up to 2000 W,
an adjustable locally designed water-cooled matching network is used to
maintain zero reflected power during experiments, and a step-down voltage
divider with RF choke is used to measure the effective DC sheath voltage (Figure
4). Earlier experiments utilized a Zenith matching network and transmitted power
corrections were applied to normalize the data to the 1000W matching network.
This correction was done by equating the sheath voltage at varying transmitted
power at 50 cm gas flow rotameter setting and 17 Pa pressure (Figure 5).
Consequently, transmitted power values with the Heathkit matching network
were divided by 0.836 to make them equivalent to the 1000W matching network.
Table 3. Characteristics of Plasma System
Processing Chamber (Internal)Volume 0.125 m$Surface Area 1.623 m’
Recovery System Volume 0.0071 3
Powered Electrode Surface Area 0.00203 ~’
15
Plasma Chamber Recovery System
n13.56Mhzsupply aMatchingNetwork
nE!PiSam Ie
1, Ii
A EI JI-QxJ
1- Coid Trap Finger2- Charcoal Trap e3- Cold Trap Isolation Valves
Figure 2. RF Plasma Reactor& Recovery System.
ToRecoveryS@sm
SarOrneter
4
47 ●
[G “
f–w
49
Hei#lt47cm I
I\To NF3GasSu$ply
9;5
1
>
~~.n.ew % (b) SchematicofTest Chamber Rotsmetsr RF PlasmaAntenna(Wall-Anode) AllDimensions in centimeter (Cathode)
Figure 3. Plasma Test Chamber and Schematic of RF Antenna
RF-
4’L:’*’@DCvoltage
Dier
13.S6MHz
RF20 Plasma
PIasrnaEauivaleriI&wit
In out
IIRF Matchii t+awork DCVottagaDivider
EitherAHeathl&SA20600r tiFoHow+ng Cimuil
5 Turns.4- Da
‘“C” =“
Figure 4. Electrical Circuits.
---mu
100
Ptr.l+?athkii= 0.836*P@,,mw ~ Ii/
=/y--
I I
1t_\/d AAID / — I
I II III/ /6” i
Conditions
#/ /50 cm flow, 17 Pa
o0 50 100 150
RF-20 Transmitted Power, Pt, (W)
Figure 5. Matching Network Power Equivalency.
17
3.2. Absorbed Power
The power absorbed by the plasma was determined by a subtractive
power procedure (Horwitz, 1983; Godyak & Piejak, 1990) to eliminate the
necessity of measuring the voltage-current phase angle which would” have
required extremely precise and difficult measurements.
In the method, the peak-to-peak voltage at the RF antenna was measured
with and without a plasma. With no gas flow and chamber pressure of -0.5 Pa,
there was no plasma when RF power was applied. With these conditions, all
power losses occur in the matching network and lines. Next, a plasma was
initiated by flowing NFs gas and measuring the peak-to-peak voltage after the
chamber pressure had stabilized and with the reflected power adjusted to zero.
The power loss in this case is the sum of the matching network, lines, and
plasma losses. By comparing power with and without plasma at the identical
peak-to-peak voltage, the power absorbed by the plasma is the difference in
transmitted power with plasma and without plasma.
The antenna peak-to-peak voltage was measured with a Tektronix model
2225, 50 MHz oscilloscope coupled to a 1000:1 voltage divider between the
antenna and ground. The voltage divider used was similar to the one shown in
Figure 4 except that the choke was short circuited and the resistors were
replaced with a 10M series and 10K parallel resistor for a 1000:1 voltage
reduction. The first measurements without plasma were made with RF power
varying from zero to 550W. The antenna peak-to-peak RF voltage without
plasma is shown in Figure 6 and a least squares curve fit through the
experimental data points gives transmitted power as a function of the peak-to-
peak RF voltage (see figure for correlation). Next, measurements with a plasma
were taken of the antenna peak-to-peak voltage as a function of RF transmitted
power between 20 and 550 W at varying NF3 gas flow rates, based on the
Omega model S04-N082-03 rotameter settings of 20, 30,50, 80 and 100 cm. At
each gas flow and power setting, the reflected power was adjusted for a zero
value, and the peak-to-peak RF voltage measured after the pressure had
18
stabilized. Figure 7 shows the results of this experiment and the coefficients of
the least squares cuwe fits that relate the powered electrode peak-to-peak
voltage and transmitted power are tabulated in Table 4.
The absorbed plasma power, P, is then calculated at equal peak-to-peak
voltages as:
(1)
VPP is the antenna peak-to-peak voltage calculated with a plasma as
determined from the correlations shown in Figure 7 and Table 4. Next, the
transmitted power without plasma is calculated from the correlations shown in
Figure 6 using the values of VPPjust calculated. The results of this calculation
are shown in Figure 8, and the coefficients of the least squares curve fit through
the data are tabulated in Table 5. These correlations were then used to
determine the absorbed power from the transmitted power in the experimental
data.
Table 4. VPPCorrelations with Pti, Plasma Ignited.
Rotameter Coefficient of Coeilicient of ConstaSetting Pt: Ptr nt
( ) a, (VW_*) b, (V W-l)fro -5.284 5.92180 -3.586 5.005 689.350 -2.975x1 0-3 4.895 696.730 -2.878x1 0-3 5.155 655.020 -3.480x103 5.708 589.3
A secondary correlation for fraction of power absorbed, q, defined as the
ratio of absorbed, P, to transmitted, P@,power, was determined as a function of
transmitted power and pressure (Figure 9). This correlation was found to be
useful in providing an estimate of the absorbed power. The transmitted power
varies slowly with pressure and a least squares fit (inseit, Figure 9) gives the
pressure term in equation (2). From a physical view, the data suggests that as
transmitted power increases, fewer molecules are avaiiable to absorb the power,
so the ratio decreases. As the transmitted power decreases below - 100 W,
19
insufficient power is available for ionization and dissociation, and consequently
the power ratio drops.
~=;=o.42/l-~-]+tr(l.oo~lo-5P3-l.89~(2)
. L -1
Table 5. Absorbed Power Correlation with Rotameter Setting, F (cm)
P,, (W) Coefficient of FZ Coefficient of F Constant-..a, (W cm-2) b, (W cm-l) c, (w)
500 -0.008209 2.008 132.7400 -0.01031 1.776 103.7240 -0.005567 0.7583 78.37120 +8.828x104 -0.1203 53.45100 +().001812 -0.2354 46.8272 +0.003006 -0.3796 35.1550 +0.003624 -0.4511 25.56
No Plasma
600 v
400 ‘
200 “
Pf, = 5.376E-5 V; - 0.009878 VPP
o~no 1000 2000 3000 4000
Antenna Peak-Peak Voltage, VPP (V)
Figure 6. Powered Electrode Voltage, No Plasma.
20
3000
2000
1000
0
300
200
100
0
With Pfasma
Vw = ap~+bpr + c
See text for coefficients
o 200 400 600
Transmitted RF Power, P& (W)
Figure 7. Powered Electrode Voltage, With Plasma.
20 40 60 80 100 120
NF~ Flow Setting, F (cm)
Figure 8. Absorbed Power vs NF3 Gas Flow Rate.
21
:1■
&-‘--Q-—-—.—-—-—-—-
40 E~--
=; +3------------ ----- -----:-//_————_ ———— —. ——.
~ g?1
Q !
30 -
20 -
10 -
j’”FEEm_‘g
1
m
o 10.8
❑ 27.031.0
: 35.4■ 39.4Pa
- Jv
- -
* Praaaum Correlation
- -
-w m m *-1
nt1 I Preaaure, p(Pa)11 t I I i
“o 100 200 300 400 500
Transmitted Power, Ptr (W)
Figure 9. Absorbed Plasma Power as Function of Transmitted Power.
3.3. DC Sheath Voltage
During the experiments, absorbed power varied from 25 to 210 W and
resulted in DC equivalent sheath voltages ranging from 0.1 to 500 V,
respectively. Figure 10 shows that the sheath voltage depends on pressure;
the higher the pressure at constant power, the lower the sheath voltage.
The sheath voltage was measured across both sheaths (the powered
electrode sheath and the ground sheath) and the plasma (Figure 4). The voltage
drop across an RF plasma is quite small and thus the total voltage drop is
approximated as that due to the sheaths (Lieberman and Lichtenberg, 1994, p.
333). Because the areas of the powered eiectrode, S, in the experimental
system is 20.3 cm2 and that of the grounded wall is f 6025 cm2, the sheath
voltages will be highly asymmetric, with most of the voltage drop occurring on the
powered electrode according to equation (3) (Lieberman and Litchtenberg, 1994,
p. 370). For example, at 50 W absorbed power and 17 Pa, the measured voltage
is –142 V. Based on equation (3), the voltage across the grounded wail
22
becomes negligibly small, 8x1 0+ V. Therefore, the sheath voltage can be
assumed to be across the powered eleatrode sheath.
o
-1oo~
>*ci- -200
g5>c -300
z
2u)
-400
-500
$(3)
tbsorbed Power
Iw
24 ■
39
m
100#
168
210 ❑
10 20 30 40
Pressure, p (Pa)
Figure 10. Measured DC Sheath Voltage in Experiments.
3.4. Pressure and Gas Flow
For the conditions of these experiments, the NFs gas flow rate was
operated between 3 and 18.5 SCCM, resulting in plasma gas pressures varying
between 10.8 to 40 Pa, respectively, using the recove~ system vacuum
forepump. The following paragraphs describe the flow and pressure in the
system under varying power settings.
Pressure was controlled by adjusting the inlet gas flow indication, in
centimeter, using a rotameter, Omega model S04-N082-03. Manufacturer’s flow
23
correlation (Omega, 1995) with pressure was used to determine the gas flow rate
in standard cubic centimeter per minute (SCCM), which is the flow rate
converted to standard conditions at To, = 298 K and pO = one atmosphere
pressure (STP). The true flow rate of gas, in SCCM, is determined from the
manufacturer’s flow rate for air at STP, (SCCMh, the specific gravity of the gas
relative to air, ps (2.46 for NFs), the gas temperature, T, and the gas pressure, p,
in the chamber. With the gas temperature - 298K, the temperature dependence
cancels and the true flow depends directly on the square root of the pressure as
shown by Equation (4). The true flow rate in SCCM for NFs gas flow is shown in
Figure 11.
J(Scckf)o = ~, T p,—— (4)SC(34 TOp’ “
The chamber pressure varied with absorbed power and rotameter setting,
as shown in Figure 12. As power was appiied, the pressure increased aimost
instantaneousiy from the base pressure, reflecting the dissociation of NFs
moiecuies and an increase in totai number of moles of gas. This data was used
to determine the approximate flow meter setting to achieve a desired pressure.
The rotameter is an instrument designed to set flow conditions, rather
than to measure the actuai flow rate, and that is the manner it was used in these
experiments. Care was taken to set the flow conditions identically for aii
experiments. This inciuded verifyhg that the reguiated outiet pressure was 20
psig and that aii the vaives between the gas suppiy and the vacuum chamber,
except the rotameter adjustment valve, were fuiiy open. in order to verify the
volumetric gas flow, experiments were conducted (Appendix B) to determine the
true flow. The manufacturer’s correlations were found to reflect the true flow
rates over most of the range of pressures used, except at rota meter flow settings
above -90 cm, for which the manufacturer’s flow rates were understated (Figure
13).
24
NF~ Gas25
20
15
10
5
\(
40
30
20
10
0
Omega Model S04-N082-03T=298K
Rotameter SettingF=150cm
ggz=:80
50
30
20
10
Figure 11. NF~
20 30 40
Pressure, p (Pa)
Gas Flow Rate in SCCM.
< Solid lines are least squares fit throughthe experimental data.
v v. w 30v v v v
mv
n 20c1 u n
Rotameter Model: S04-N082-03
o 50 100 150 200 250
RF Absorbed Power, P (W)
Figure 12. Pressure Variation with Absorbed Power and Gas Flow.
25
0.0025
0.0020
0.0015
0.0010
0.0005
00 50
50
40
30
20
10
n
30co
Rotameter Flow Setting, F (cm)
Figure 13. Experimental Flow Rate vs.
Stainless-Steel Planchettes
Manufacturer’s Correlation.
A total of 12 stainless steel planchettes were machined from stock 304
material. Each planchette was measured with a vernier caliper and weighted
prior to first use. The characteristics are shown in Table 6, where the
uncertainties
planchettes.
are the standard deviations of the measurements from the 12
Detailed specifications are included in Appendix B.
Table 6. Planchette Characteristics
Characteristics Value
Mass (g) 0.5373 & 0.0019
Internal Diameter (cm) 1.007.+ 0.002
internal Depth (cm) 0.146 t 0.006
internal Surface Area (cm*) 0.796 ~ 0.(303
26
3.6. Sample Preparation
Depleted U02 in test samples were prepared by heating and flaming
solutions of uranyl nitrate hexahydrate pipetted in 100 PI increments into
cylindrically shaped 1.007-cm diameter stainless steel planchettes. The
following paragraphs describe the preparation and specification of the samples,
including the planchettes.
The depleted
U02(NQ~.6H20, was
uranyi nitrate hexahydrate, chemical formula
prepared in a 1M HN03 solution. To determine the atom
ratio of the various alpha emitting species in the solution, a small quantity was
diluted by a factor of 100:~ and electroplated onto a one-inch diameter stainless
steel wafer. Dilution and electroplating was necessary to achieve a uniformly
thin layer on the wafer that would yield a resolved spectrum. The alpha energy
spectrum, Figure 14, verified that the main alpha emitting isotopic components of
this solution were 23%, 2%, and a trace amount of 235U. These results were
obtained by counting the electroplated sample for 4000 minutes in a silicon solid
state alpha spectrum analyzer with multichannel analyzer and data multiplexer
connected to a DEC VAX computer. Table 7 summarizes the activity and atom
(or mass) ratios. The activity ratios, fj, j = 2%, 235U,and 2%J, were obtained by
first subtracting the background from the overall energy spectrum, summing the
counts under each of the three peaks (238U,235U, and 2%J) to obtain the total
counts, then taking the ratios of counts under each peak to the total counts. The
mass ratios were calculated by taking the ratio of the product of the activity ratio
and the half-life of the isotope to the sum of the products as shown in equation
(5):
(mass_ ratio), =fi(L,2)J
Zfi(h),
,j =B8 U,235U,~3 U. (5)
J
Liquid scintillation spectra of the uranyl nitrate alpha and beta emissions
alpha channelsare shown in Figure 15. The alpha spectrum was taken from the
27
while the beta spectrum was taken from the beta channels of the Packard 2550
counter. Comparing the observed spectra with a spectral atlas (Cross et. al.,
1983), the beta spectrum in this solution was attributed to the -h and 2MPa(m)
daughters of *MU. The emission peak in the beta spectrum near channel 245
was attributed to mislabeling of alpha emissions as beta in the counter. it should
be noted that the alpha emission energy peak in liquid scintillation counting is
\ower by a factor of at least 10 from the tme peak energy because the light
scintillation from the cocktail is measured rather than the alpha energy itself
(Passo and Kessler, 1992). As an example for calculating the instrument alpha
count rate, the liquid scintillation alpha peak for all uranium isotopes was
integrated using the procedures described in paragraph 3.9 and divided by the
count time to give the count rate. The count rate was then corrected for
alphalbeta misidentification, equation (15), and the activity calculated using
equation (16). The beta activity was calculated by integrating the beta spectrum
over the entire energy range (O to 2000 keV) except that alpha/beta corrections
were not applied, primarily because beta quantification was not needed in the
analysis.
Varying the volume of uranyl nitrate solution from 10 to 100 pi, counting
the alpha and beta emissions by liquid scintillation, and taking the slope of the
resultant curve provided the activity per unit volume of solution shown in Figure
16 and summarized in Table 7.
Table 7. Activity and Mass Parameters of Sample Solution
Isotope Activity Ratio, f Mass RatioSpecific Activity
(Ba/ul\To#al U 1.000 1.00000 1.294
u 0.895 0.99949 1.158:5U 0.102 0.00001 0.132
0.003 0.00050 0.0042~#, 2wPa (Beta) NA NA 2.153
28
Depleted Uranium a-Spectrum
% Count Time: 4000 Minutes150 ‘
100 ‘
50 -
235\
u*
234u
4.0 4.2 4.4 4.6 4.8 5.0
Energy (MeV)
Figure 14. Depleted Uranium Alpha Spectrum.
6000
4000
2000
0
Figure
.
1
II
Packard Model 2550TFUAB with CJPDiscrimination
o 150 300 450
Channel Number
fl5. Uranyl Nitrate Hexahydrate Spectra by Liquid Scintillation.
29
250
200
150
100
50
0
I
I !kdeted Uranvl Nitrate Hexalwdrate SoIution~ = 1.294* 0.020 Bq/@ ‘
I
A = 1.158 f 0.017 Bq/pl
A~ 2.153 f 0.042 Bq/wl
o 20 40 60 80 100
Volume (~1)
Figure 16. Specification of Uranyl Nitrate Hexahydrate Solution.
From the specifications in Table 7, the molar and mass conce
the solution can be determined. Let ~U be the specific activity t
uranium content (= 1.294 Bq/pi), j the isotope, fj the activity ratio of
total U, mj the mass of isotope j, Mj the molecular weight of j, ~j the m
the number of atoms or molecules containing j, NA Avogadro’s nun
volume of uranyl nitrate in the sample, and \ the half-life of j. Becal
the mass is due to 238U (0.99949), then the total number
total mass, m, is approximately equal to the mass of 238U.
of uranium to a compound, the mass of the compound is
of moles,
To conve
the mass
times the ratio of their molecular weights. The results are tabulated in
N, 2“ Vfjtl~,=~=~=
J~ NA 121(2)‘
~=~~, ‘~238U*
J
30
xm= mjZmn8u, (8)J
(9)
In preparing the samples for these experiments, 100 y] of uranyl nitrate
solution was pipetted onto a planchetie, heated on a hot plate to dryness, then
flamed until the stainless steel planchette turned red hot. The deposited U@
generally contained extensive voids, evident when viewed under a 200x
microscope. The density of the deposited material was calculated by filling one
stainless steel planchette with concentrated uranyl nitrate solution, prepared by
evaporating 20 ml of the original solution to near dryness. The planchette was
re-characterized because plasma processing during the course of these
experiments changed the depth and mass. With each 100 @ pipetted into the
planchette, the solution was converted to amorphous U02 by drying then flaming
the sample. In the final step, the UOZ in the sample was overfilled then filed to
make the UQ flush with the planchette’s top edge. The resulting amorphous
UOZ was weighted and its mass divided by the volume to determine its density.
The calculated density, with voids, was 4800 * 600 kg/m3 (Table 8).
Table 8. Sample Specifications
Parameter Value
Solution, UOZ(N03)2.6HZ0Molar Concentration of U (mol/L) 0.39 * 0.02Mass Concentration of U (g/L) 93.1 A 3.6
UOZ from 100 PI of SolutionDensity, p (kg/m3) 4800 ~ 600Mass, m (kg) 1.06 X 10”5Number of Molecules. N 2.36 X 1019
3.7. Liquid Scintillation Counter [LSC)
The original approach for determining the amount of radionuclides
removed following plasma processing was a gravirnetric technique of weighing
dried uranyl nitrate solution before and after processing. This approach was
unsatisfactory because the hydroscopic dry uranyl nitrate prevented accurate
31
and reproducible mass measurements, which did not significantly improve when
the uranyl nitrate was first converted to U02. The next method tried was simple
alpha counting of the surface of deposited U02, but alpha patilcie self-shielding
(Friedlander, 1949) prevented accurate measurement of the total activity of
samples. Liquid scintillation counting was therefore implemented in the present
experiments for alpha counting of the UOZ test samples (Passo and Kessler,
1992; Bower et. al., 1994).
The depleted uranium samples had significant beta activity as a result of
the ingrown daughter products of thorium and protactinium. As long as sufficient
quantities of uranium alpha emitters were in the sample, the beta activity could
be differentiated from the alpha activity. However, as the plasma etched away
the uranium (and any other volatile metal) leaving behind a significant portion of
the non-voiatiie metals, especially the beta emitting 2~h and 2wPa, beta activity
became a significant fraction of the total activity, preventing accurate counting or
even detetilon of the underlying alpha activity. Consequently, beta and alpha
discrimination was essential for quantifying uranium samples having appreciable
beta emitters when the alpha activity was comparatively small. The choice was
to remove the confounding beta emitters from the sample, or to utilize an
instrument capable of differentiating alpha from beta emitters. The choice was
the Packard Model 2550TFUAB liquid scintillation counter (LSC) for the
measurements, primarily because the daughters would have grown back during
the course of the experiments.
Liquid scintillation counters work on the principle of exchange of
radioactive particle kinetic energy to a fluor molecule in a liquid scintillation
cocktail, such as UitimaGoldw AB. The fluor molecule is activated to an
unstable higher energy state from which it is subsequently de-excited with the
emission of a photon. Since the radioactive material is surrounded by the fluor,
the liquid scintillation counter is a 47cdetection system. The photon impinging on
the photornultiplier tube is detected as a signal pulse. Electronic coincidence
circuits are included to minimize noise activated pulses. Alpha particles are
32
typically detected with near 100% eficiency while higher energy beta particles,
such as the beta isotopes in these samples, are detected with 95% efficiency.
I The 1009’o efficiency for alpha particles is achieved because they “have a
significantly greater energy transfer per unit distan6e traveled than do beta
particles. However, this effect also results in the loss of alpha particle energy
resolution and they appear as a single broad spectral peak at approximately one
tenth of their true energy—that is, in the hundreds of keV. This is the basis of all
liquid scintillation devices used for alpha quantifkation (Passo and Kessler,
1992).
The liquid scintillation counter, Packard Model 2550TFUAB, incorporates a
multichannel analyzer with a pulse decay analysis (PDA) circuit for differentiating
between alpha and beta particle generated light pulses originating from the
phosphor in the liquid scintillation cocktail. The design of the PDA uses the fact
that light scintillation originating from beta particles have a much shorter lifetime
than those emanating from alpha particles. To use this feature, the alphalbeta
discriminator level must be adjusted to minimize the misidentification of the two
particles.
Figure 17 shows the results of setting the discriminator level to minimize
the misidentification of alpha and beta emissions. The ideal setting was 115
giving an misidentification error of 2%. To generate this curve, a Iocaily prepared
pure uranium alpha emitter consisting of only 233Uand ‘*U uranyl nitrate in a 1.0
M nitric acid solution with a specific alpha activity of 2.977 Bq/microliter
determined from the LSC spectrum was used to generate the alpha counts as a
function of discriminator setting (Figure 18). The beta activity was less than
0.0058 Bq/microliter, indicating that most beta emitters were removed during the
preparation process. A Packard 14C beta emitter standard containing 2150 Bq
on 2/1/93 was used for the beta counts as a function of discriminator setting.
Activity correction for time elapsed since the solutions were standardized was not
necessary because the half-life is several thousand years. The counter’s alpha
33
and beta detection efficiencies (Figure 19) at a discriminator setthg of 115 were
determined to be 100% and 95.5%, respectively.
Quenching, or loss of counting efficiency with variation of the pH of the
uranyl nitrate solution, was an important parameter because of the desire’ to
prevent the solution from precipitating and to maximize the quantity of the
sample used for counting accuracy (Pulol and Sanchez-Cabeza, 1997). Nine
samples each consisting of 100 microliters of uranyl nitrate solution were dried
and the precipitate dissolved in nitric acid of varying molarity (0.01, 0.05, 0.1 and
0.2 M). Each sample’s pH was measured with an Orion model 920A pH meter
calibrated with buffers per manufacturer’s specifications. A 6 ml aliquot of
solution was then added to 14 ml of lJltimaGold AB cocktail and counted for 60
minutes. The resulting activity was compared to the expected activity to
determine the efficiency, taking into account the aliquot size and dilution factor.
The resulting activity versus pH is shown in Figure 20. The alpha counter
efficiency remained near 100% in the pH range 1.0 to 2.0, dropping significantly
for pH less than 1.0. Beta particle quenching increased with pH, but since the
prima~ interest was in alpha quantification, this effect had no impact on these
experiments. Above pH -2.5, precipitation of the uranyl nitrate in the cocktail
can occur, resulting in significant loss of counts.
34
80
60
40
20
0
t
Discriminator 115Error 2°A
t 1 I
3Packard Model 2550 TFUAB
.=. ‘. =.❑,
\ \ \ x“
Beta ‘ “n,
Mislabeled ‘\\\
1‘bndards:
14Cfor Beta
t 2% for Alphat
\\\
‘n,II
/
/\\\\\\
/
9V11GIEUG11GU\\\n 1
t “=1.0’ i-----n-LJ , n. n n I
o 50 100 150 200
Alpha/Beta Discriminator
Figure 17. Liquid Scintillation Discriminator Setting.
10000 \ I
. . . 120untTime: 300 min I
1000
100
10
1
Lti(.J4
=:
232 0u
i nil 1 INU,\Lli t 12.5 5.0 7.5
Energy (MeV)
Figure 18. 2% Standard Used To Calibrate the LSC Discriminator.
35
J
100
80
60
40
200
100
90
nw
n n mb
Alpha +3 ----R ?
r“/ I \
//
Beta,’,el
//
Packard Model2550 TFVAB
50 100 150
Alpha/Beta Discriminator
Figure 19. Alpha and Beta Detection Efficiencies.
200
r la. 1 6 ?
o
“B’. $ 0 0\ o 0 Alpha-..
13--..n-.-
•1 -----13 -n
Beta
0
I I I
Packard Model 2550 TR/AB
UltimaGoldm AB Cocktail80
‘1.0 1.5 2.0
Uranyl Nitrate Solution PI-I
Figure 20. Detection Efficiency Vs. Solution pH.
36
3.8. Lower Limits of Detection
Lower limits of detection were quantified for the Packard liquid scintillation
counter with the uranyl nitrate solutions because the interfering beta emitters
could confound the measurements. Detection limits were evaluated based on
three increasingly stringent detection levels: the critical level of detection, ~;
the qualitative level of detection, Ao; and the quantitative level of detection, ~
(Currie, 1968) and assuming that type I and II errors were both equal at 5%. A
type I error is the probability that radioactivity is obsewed when in fact it isn’t
present while a type II error is the probability of not obsetiing radioactivity when
in fact it exits. The critical level identifies the ability to detect the presence of a
signal, a binafy decision. The qualitative level identifies the ability to quantify the
signal with the specified value of the type !1 error. The quantitative level
identifies the ability to detect and to measure the signal with a high degree of
confidence.
Consider the case of a “blank” sample consisting only of background
radiation and interfering nuclides. The total mean counts from the blank, W, is
given by the sum of the mean counts from the background, W, and the
interfering nuclides, ~. The mean counts from the background were measured
using an LSC vial containing 6 ml of de-ionized water in 14 ml of Packard
UitimaGoldm AB liquid scintillation cocktail. The average alpha emissions taken
over three separate measurements of 60 minutes each was 0.1015
counts/second. The mean counts from the interfering nuclides were the beta
emitters from 2~h and 2%Pa daughters of 2mU that appeared in the alpha
window of the liquid scintillation counter (i.e., the mislabeled beta activity). The
total counts from this source, assuming that these emitters were not etched away
during plasma processing, is given by:
37
{n the above equation, px (2%) is the probability that a beta decay will
appear in the alpha window of the LSC, qP (0.955) is the counter eficiency for
beta activity, AP (2.153 Bq/pl) is ~he specific atiivity of beta emitte~ (Figure 16),
V (100 @) is the volume of the depleted uranyl n“-te in the sample before
plasma processing, and t is the instrument count time, typically 60 minutes. The
three activity limits of detection, with the alpha detection efficiency, q. -1.0, are
given by
Ac=~&,
AD = #.71 + 4.65A],
A,=;{l+[l+fi]}.
(12)
(13)
(14)
The activity for lower limits of detection for the Packard model 2550
TR/AB for the uranyl nitrate samples used in these experiments are plotted in
Figure 21 and the detection limits with 60 minutes count time is summarized in
Table 9. in the experimental results, the quantity of interest is NR, the ratio of
activity removed to the initial activity of the sample, 129.4 Bq. Thus, the LSC can
detect up to the hl~ limit, or 1 – A/l 29.4. For example, at the critical level, the
minimum detection level is 0.08 Bq. The equivalent UOZ etched ratio that can be
detected, ~R, is 0.99938. Consequently, the Packard model 2550 TR/AB liquid
scintillation counter can be used to detect the removal of all but 0.00062 fraction
of the initial U02.
Table 9. Detection Limits of Depleted UOZ Samples
Criteria Activity NR Limit(Ba)
Critical 0.08 0.99938Qualitative 0.16 0.99876Quantitative 0.50 0.99614
38
—
10
1
0.1
0.01
Packard Model 2550 TR/AB
A~
t
o 50 100 150 200
Counting time (Nlin)
Figure 21. Lower Detection Limits.
3.9. Activity Measurement of Plasma Processed Samples
Quantification of the samples’ activity following plasma immersion was
performed by first dissolving the plasma processed UOZ in hot 3M HNOS. The
surface activity of the pfanchette following this procedure was at or ~below
background.
To keep the solution pH in the range between 1.0 and 1.5 for LSC
counting, the 3M solution was evaporated to dryness and then dissolved in 0.05
M nitric acid before adding the solution to a LSC cocktaiL This had the effect of
keeping the pH in a narrow band above 1 but below 1.5. Several samples over
several weeks of data taking were verified to be in this range using pH paper.
With this procedure, it was possible to count all the dissolved uranium rather
than taking aliquot fraction of solution, thereby reducing the dilution factor from
-40 to 1 and significantly reducing the error from this source. Typical volumes
added to the liquid scintillation vials included - 6 ml of solution with 14 ml of
39
UltimaGold AB cocktail. Deionized distilled water was used for makeup volume
,. as needed to keep the total liquid scintillation volume at 20 ml.
All solutions were counted in LSC and the resulting spectrum was
integrated over the alpha peak to obtain the raw counts per minute. Figure 22
shows a typical alpha spectrum from a sample processed in plasma for 255
minutes at a power of 49.6 W absorbed and 17.3 Pa. The first peak is from the
beta activity that falls within the alpha window. The second peak is due to alpha
emissions. The procedure developed was to fit a gaussian and a first order
polynomial to the region of the cume that includes the entire alpha peak
(Bevington, 1969). From the least squares fit, the parameters of the gaussian
were plotted and the resulting cuwe integrated to give the total counts under the
gaussian peak, hence under the alpha peak. In the example shown, the counts
were 46483 yielding a count rate of 775 counts per minute (cpm). A program,
EasyPlot (Karen, 1997), was used to perform the cuwe fit and integration. This
procedure removed both the activity contribution from the beta emitters and the
background. For comparison, the LSC reported count rate using fixed energy
windows (channels 100 to 400) was 1211 cpm, which would have resulted in a
significant error.
40
600
400
200
0
255 rein, 49.6W, 17.3 Pa -
- LSC Spectrum Data
o 150 300 450
Channel, x
Figure 22. Spectrum Analysis for Sample Count Rate.
The raw counts obtained from LSC were next corrected for alpha and beta
mislabeling. The following terms apply C= the alpha count rate determined by
the gaussian fit, Cp the background corrected beta count rate reported by LSC
summed over all channels, pab the probability that an alpha emission appears in
the beta window, and pPa the probability that a beta emission appears in the
alpha window. The two latter probabilities are 0.02 in the present experiments.
Therefore, pap = 1- pwand PM = 1- pp~.The correction becomes:
C = C= + P.pc. - P#fXc/l =c=(2-pJ-cJh-Pbb). (15) ‘
To calculate the activity, A, from the count rate, C, requires corrections for
the dilution factor, d, and the alpha instrument efficiency, q= (-t). The dilution
factor in all later experiments was -1 because all the solution was included in the
LSC measurement. Earlier experiments were based on aliquots of the solution,
measured either volumetrically or gravimetricaily. The volumetric procedure
used ratios of volumes of original solution to the aiiquot for comparison, resulting
41
in d -40 along w“th significant errors. The resulting activity was calculated from
the relationship:
A=C~. (16)??a
The activity of uranium removed from the substrate surface normalized to
the initial activity, ~R, is defined from the activity obtained from equation (16) and
the initial activity of the UOZ sample before plasma processing, A., of 129.4 Bq
from Table 3, on
NR=l-~.4
3.10. Temperature Measurements
(17)
The temperature rise inside the plasma was monitored for a few cases, all
at 17 Pa and 50W absorbed power. These measurements were made at the
completion of plasma processing with power off and the system brought up to
atmospheric pressure via a nitrogen gas purge. The purpose was to verify that
the temperature during plasma processing remained near room temperature.
The measurements were made with an Omega l-fH81 meter with a type K
Inconel overbraided ceramic fiber insulated thermocouple, Omega model XCIB-
K-2-2. The bead welded exposed junction helped assure that temperature
rapidly reached equilibrium. Measurements were made of the ambient gas at
the center of the reactor, on the surface of the powered electrode, and on the
interior of the aluminum reactor wall. Ali measurements were made within -5
minutes of shutdown. Temperature comparisons with the ambient temperature
outside the reactor are shown in Figure 23. The wall and interior air temperature
rise was less than -5 K, while the temperature of the powered electrode rose 30
to 45 K, depending on the plasma immersion time. These results confirm that
the temperature inside the plasma remain near room temperature during plasma
processing although the temperature of the samples rise about 30-45 K above
ambient.
42
o Powered Electrode
40
20
0
00
/’ o
0
:~ Temperature after power shutdown
I Intefior Chamber Wal}
[-
a /.—-— -—.
7 IM—Chamber Ambient Air
o 50 100 150
Plasma Processing Time (rein)
Figure 23. Temperature Rise in Plasma Reactor.
3.11. Uncertainty in Measurements
Accuracy and precision of the measurements were estimated. Accuracy
was assessed from iiquid scintillation measurements of 15 samples of uranyl
nitrate with varying volumes between 25 and 100 microliters each converted to
U02 by the method previously described but without plasma processing. These
samples were obtained over the course of the experiments. The intent was to
verify that the initial activity could be recovered. The results are depicted in
Figure 24 indicating that on average, 97% of the original uranyl nitrate activity .
was recovered by the liquid scintillation process described earlier.
The precision, or uncertainty in determining the fraction of UOZ etched,
~R, was ~ 2.0 % (Figure 25) which included uncertainties due to: counting
statistics; isotope activity ratio; activity of the initial solution; pipette volume; mass
measurement; ratio of aiiquot to total sample solution; counter efficiency;
planchette area; and aipha/beta
uncertainties were large occurred
misidentification. The cases for which the
when the plasma immersion time was less
43
than 30 minutes, or the absorbed power was less than 40 W, or when pressure
was too low (- 10.8 Pa) or too high (- 40 Pa). The “following paragraphs
describe how these estimates were made. I
The uncertainty or standard deviation, cfG, or the reiatiW? error, eG, of a
function G are functions of the individual measurements, xi
uncertainties, 0=,, or relative errors, ei. They are calculated
(Bevington, 1969):
)G= G(x1,x2,... ,
~: =~(;:c=j)2 f1
6GeG =?.
Applying equation (19) to the functions, NR A, etc. resulted
functions tabulated in Table 11. Al! radioactive source standards
and their
as follows
(18)
(19)
(20)
in the error
and known
constants (molecular weight, counting time, half-life, Avogadro’s Number) were
assumed to be error free.
The uncertainty in the observable are tabulated
uncertainty in the counter efficiency was determined for
in Table 10. The
the least accurate
counter used, the surface alpha scintillation counter, which provided a worke
case error for LSC counting. A known 239Pusource was counted and the reiative
counter el%ciency error was determined by the relationship shown in Tabie 11.
Manufacturer’s specifications used the largest error reported for the range of
these experiments. These included uncertainties for a graduated cylinder,
Eppendorf pipette, and Mettlar balance. The uncertainty in plasma processing
time varied with power. Below 250 W, the power was applied or removed
immediately and an uncertainty of - 10 seconds was taken as an average error.
Above 250 W, application of power was siowiy ramped to the desired value
which vaned from -2 minutes below 500 W, and -5 minutes above 500 W.
These ramp times were taken as the uncertainties. The isotopic ratio error
44
applied Poisson counting statistics using the relationship noted in Table 11. The
value shown was based on the alpha energy spectrum used to determine the
isotopic ratios. The uncertainty in the diameter of the stainless-steel planchette
was based on the measured standard deviation from all 12 planchettes. The
probabilities of an alpha emission being counted in the alpha window, and the
probability of a beta emission being counted in the beta window were based on
the 2% incorrect identification of alpha and beta emissions (Figure 17).
The counter uncertainty was calculated for each datum applying Poisson
(Bevington, 1969) counting statistics, Equation (21). In this approach, the
uncertainty, ax, in the total counts, Z, in the appropriate alpha or beta window is
related to the counting time, t, and the measured instrument count rate, C. or CP.
Since the counting time was determined by the liquid scintillation counter’s
internal clock, its error was negligible in comparison to the counting emor. Thus,
IfOz= x, (21)
Table 10. Measurement Uncertainties
(22)
Symbol Description
Counter efficiency~V Graduated cylinder volume accuracyf Isotopic ratio
Mettler Balance AccuracyYP Pipette volume accuracy (Eppendo~dP Planchette diameter~ Piasma immersion time (depends on
power)O~p S 250W
250c P< 500W500< Ps1200W
pa= probability an alpha counted in alphawindow
pPp probability beta counted in beta window
2,, Specific activity of uranyl nitrate solution
Relative Absolute UnitsError, e Error, o for a0.015 -
0.2 ml0.032 -
0.2 mg0.016 -
0.016 cm
10 s
2 min5 min
0.98 0.01
0.98 0.010.015 –
45
1.05
1.00
0.95
0.90
1
.-—
Recovery: 97%
I
-J-—.
L Activity recovered, A, of original uranyl nitratesoltiion, AO,following conversion to U02,
dissolving in HNO~, and LSC Counting.
5 10
Test Sample Number
Figure 24. Accuracy of the Measurements.
15
50 I
40
30
20
10
Relative Error Distribution in NR
Most Probably Error 0.02
i
Figure 25.
0.2 0.4 0.6 0.8 1.0
Relative Error, e~R
Uncertainty in Measured Fraction of UOZ Etched.
46
3.12. G!ow Discharge Observations
For typical etch operations, the NF3 gas flow was started and the pressure
allowed to stabilize before RF power was applied. Power application resulted in
an increase in pressure and sheath voltage, as shown in Figure 26. The
pressure increase was due to the dissociation of the NF3 and a net increase in
moles of gas created. After about 7 minutes, both pressure and sheath voltage
had stabilized, and therefore the zero reference for the plasma immersion time
was set at seven minutes for all experiments. At the end of the desired plasma
immersion time, RF power was removed which caused a drop in pressure to
below initial conditions. When power is removed, dissociation stops while the
gas flow continues. Recombination reactions, both in the chamber volume and
on surfaces, result in a net decrease in moles of gas, leading to pressure below
the initial pressure. After 4 to 5 minutes, pressure had increased to the initial
pressure, reflecting a return to the initial conditions.
25 ~
I RF On Sheath Voltage RF Off;\~e. ------- ----- ____1 i
20
NF~ On
at- 20 minq5 . –.—
III1
I
‘E!!!H—.—-—.—-—- —- —.-— ,~_–
I ---4 ~ Time to stabilize ;VI I
hlF~Off
at -66 min—-—
120
60
40
0o 50
Plasma Process Time (Min)
Figure 26. Typical Plasma Operations.
The glow discharge in the chamber during processing had a magenta
tinge. The glow was brightest near the antenna at all pressures, filled the entire
chamber in the vicinity of 17 Pa, and was brightest in the range 17 to 35 Pa. At
47
higher pressure and low power, the glow region shrunk towards the antenna and
was surrounded by a dark region extending from the grounded walls of the
chamber to the glow discharge edge. As power increased, the glow region
expanded outward from the antenna, eventually filling the entire chamber as
power increased further. Figure 27 and Table 12 shows the glow discharge
region as a function of pressure at 50 W. The radius of the glow discharge
volume, R, ranges from O at the center of the RF antenna to the maximum
radius, R~a, at the test chamber wall. At 7.5 Pa, the glow region radius, R, is -
11 cm, and the volume increases as pressure increases. At 16.4 Pa, the glow
discharge fills the entire volume and this continues to above 17 Pa. At -23 Pa,
the glow region starts to shrink again, becoming -18 cm in radius at 25.7 pa and
continuing to shrink until at 41.3 Pa, the glow is veiy small and the brightness
has decreased significantly. The glow is brightest at 16.4 through 35.2 Pa, and
decreases in brightness at either extreme of pressure. The sheath around the
cathode RF antenna remained bright at all pressures except the lowest (7.5 Pa)
and the highest pressure (41.3 Pa) and the visual thickness of the sheath also
varied with pressure.
I R=-llan
1
(a) 7.5 Pa (c) 16.4Pa 1
(d) 25.7 Pa (e) 35.2 Pa (f) 41.3 Pa
Figure 27. Glow Discharge Observations at 50 W Absorbed.
48
Table 11. Equations and Related Error Functions.
Name Relationship Error
Activity Ratio RemovedlvR N~=l-~
“b
Alpha or Beta Countc,+ O~J=(7 =
Rate, Cj, i = ~ or ~.2’) J_Xj
Count Rate, C c = Ca -t-(l-paa)ca –(l–ppfl)cfl ~c =(Count correction appliesonly for liquid UCscintillation)
ec. —c
Activity, A(tP) ~ d&(fp)= eA=[edY+(e,Y+(ec)’ +kf,)+(e,}]’2
7Initial Activity of sample, ~ Z/LAll = ) +(d’ +(’, Y]”o
L’
Plasma Process Time, tP t~ 0.1667e =—, for O< PS250 Watts
IF tp
e = ~ , for 250< P S 500 Watts‘P P
e = ~ , for 500< P S 1200 Watts1P P
49
Table 11. Equations and Related Error Functions.
Name Relationship Error
Dilution Factor, d v“
Jr
2
(Based on volumetric d = ~a“,
e~ = i- e~P~method),
Dilution Factor, d (mg - mO)1/2
(Based on gravimetric(m,. –mO)2 +(mg - mgo)2 +(mg –mo)*
‘=(mg-mg~) (7” = Crmmethod) (mg - row)’
o~ed=—
dDilution Factor, d d=l cr~=e~=O(Based on counting entire
sample)
Counter 13fficiency, q x–B ~ d-(Used error for surface q = Af =
v Atalpha counter which gavea relative error much ~=m
larger than LSC)v x-B
Isotopic Ratio, f f = Counts of ~in spectra over
r
fcounts of all others in spectra % = ( f)– l-i-
x
Jl+fef =
fx
Area of Planchettes, S nd2 dd = diameter s=~ (SS=-j-ad
50
Table 12. Plasma Observations
Pressure Sheath Sheath Bulk Plasma Plasma Plasma Plasma Color(Pa) Voltage Brightness* Radius (cm) Brightness* Brightness*
(v) (Center) ?4R7.5 -266 8 11 5 3 purple13,3 -235 10 22 6 5 purple/magenta16.4 -173 10 25 7 7 magenta25.7 -127 10 18 8 5 intense
magenta35.2 -55 10 10 8 5 intense
magenta41,3 -5 7 5 4 2 weak magenta
*Subjective brightness scale, range O (dark) to 10 (brightest).
51
CHAPTER 4. RESULTS
The experimental results presented in this section are taken from over
250 plasma etching experiments (Appendix C). First, the etching process is
described in terms of an example that describes the parameters used for
analysis. Next, the experimental data on the effects of power and pressure on
the initial and average etch rates are presented and discussed.
4.1. The Etching Process
The measured activity of the uranium dioxide removed from the substrate
surface normalized to the initial activity of the sample, NR, is plotted in Figure 28
versus plasma immersion time. The data closely follows an exponential function
of the form
iv, = ivR,m (l-e-q (23)
In the above equation, NR,ma is the asymptotic fraction of UOZ etched at
the end-point, t is the plasma immersion time, and r is the characteristic etch
time. The end-point, as defined in this work, is when all detectable U02 in the
sample has been etched or the etch rate becomes almost zero, with UOZ in the
sample only partially removed. The plasma immersion time was corrected by
seven minutes to account for the time
pressure and sheath voltage. In the
determined from least squares fit to
respectively.
needed for the plasma to reach steady
figure, the values of NR,_ and ~, as
the data, are 0.96 and 52.7 minutes,
The U02 etch rate, J(t), can be expressed, based on equation (23), as:
()dN NRm :=Je:J(t)=&= - e o“
T(24)
In the above equation, the term (NR,~~/~ ), or Jo, is the initial etch rate at t
= O, (0.0182 rein-l), and is shown in Figure 28 as the slope to the curve for NR
versus t at t = O. Conversion of the etch rate in rein-l to thickness or mass of the
sample etched per unit time is described in Appendix E. The etch rate J(t)
52
approaches almost zero after -4 characteristic etch times and occurs at 210
minutes in this example. ~ The self-limiting nature of the etch process is
demonstrated in the above two equations by the term (1-e-z). This term
represents the blocking effect of the U02 surface during” processing to further
reaction with the atomic F generated in the bulk plasma to form a volatile UF6.
The blocking term varies from unity at t = Oto zero at the end-point.
_ ‘R.max J!_-—+--* —-Un d
-./JT = 52.7
< —.II
NR = fll~s(l - e-)
I
b
Initial Etch Rate, JO= 0.0182 rein-l (0.5 ~m/min)
#
.% .’I ❑17 Pa
50 wt
‘o 100 200 300
Plasma Process Time, t (Min)
Figure 28. Fraction of UOz Etched in NF3 RF Plasma.
4.2. Effect of Absorbed Power
Figure 29 shows the U02 etch data taken at 17 Pa, while the absorbed
power was varied from 25 to 210 W. The corresponding values of /V~,~~ and ~
are summarized in Table 13, al~ng with the initial etch rates, Jo. Except for 25 W,
all the UOZ in the samples was etched to the underlying substrate given enough
time in the plasma. The characteristic etch time varied from 52.7 minutes at 50
W to 8.9 minutes at 210 W. Three samples (not shown) were processed in
53
The trend of the results at 10.8 Pa was similar (Figure 32), except that at
both 25 and 50 W, NR,~= did not approach 1.0, a complete removal of the UOZ
before blocking occurred. This shows that even though the sheath voltage
increased from -140 V at 17 Pa to -176 V at 10.8 Pa (Chapter 3), the higher
energy resulting from ions accelerating through the higher sheath potential was
not enough to maintain the etch reactions. The fraction etched decreased as
pressure decreased from 17 Pa to 10.8 Pa, implying that the F atom
concentration decreased. As power increased above 100 W, however, NR,m=
reached 0.96 with ~ decreasing to -30 minutes.
plasma for 24 hours at 50 W, and there was no detectable UOZ left in any of the
samples. Over 99% of the initial U02 was removed at 210 W afier 37 minutes.
At 25 W, fU~,ma did not reach one (i.e., full removal), indicating that complete
removal of detectable U02 could not be achieved at the end-point. The initial
etch rate, Jo, in the present experiments varied from 0.22 to 3.11 microns per
minute, depending on the values of the gas pressure and the absorbed power in
the plasma. These data show that increasing the absorbed power increased
hl~,~a and decreased t, thus increasing Jo, the initial etch rate.
After four characteristic etch times, either ail UOZ was removed or the etch
rate reached zero. This is demonstrated in Figure 30 and Figure 31 which
depicts the length of time needed to achieve the value of h&/,mx shown in Table
d3. NR,~a approaches 1.0 above 50 W, but is significantly reduced below 50 W.
The figures also show that there is little incentive to process beyond four
characteristic times, with little improvement realized at five characteristic
processing times.
The highest fractions etched were realized at 32.7 Pa (Figure 33) with
NR,mx approaching one (complete Uoz removal) and z approaching less than 10
minutes. At 25 W, etch results were similar to the lower pressure results, with
‘ Detectableas definedin Chapter3 forthe criticaldetedlon level.54
blocking occurring before U02 could be completely removed. At 180 W, over
999’o of the U02 was removed in just 17 minutes.
,
At 39.4 Pa (Figure 34), NR,~a at 50 W was less than unity. These results
are similar to the case at 10.8 Pa, suggesting that the combination of pressure
and power needs to be optimized to achieve the
pressure is either too high or too low for the
decreases.
1.0
2K
Oa 0“83‘5c 0.60.=oCOk 0.4w2~u 0.2
o’
Table 13. U02 Plasma Processing
highest etched fractions. If the
power used, the etch fraction
Results at 17 Pa.
Absorbed NR<.m r Initial Etch Rate JoPower (W) (rein) (rein-’) (pmlmin)
25 0.54 68.0 0.0079 0.2250 0.96 52.7 0.0182 0.50100 0.98 28.0 0.0350 0.97168 0.97 12.3 0.0789 2.18210 1.00 8.9 0.1124 3.11
-.—-~-—-—.—-—-—-—--t+ -—-—-—-—-n a
[i?/ ‘210 ~ u w
168 AAl 00~o 50
f?
‘v’ v vv v
v
@!J
100 200 300
Plasma Process Time, t (Min)
Figure 29. Power Effects on U02 Etching at 17 Pa.
55
21OW
0.5 Lo 100 200 300 400
Plasma Processing Time, t, to Achieve /VR~~X(rein)
Figure 30. Effect of Power on NR,m.. at 17 Pa
60
45
30
15
“o 100 200
Plasma Process Time, t, to Achieve
300
N~,~=(min)
400
Figure 31. Effect of Power on ~ at 17 Pa
56
2“
1.0
0.8
0.6
0.4
0.2
0
.—-— -—-— .— -—-— -—-— - —-— .I
o
]10.8 Pal
o 100 200 300
Plasma Process Time, t (Min)
Figure 32. Power Effects on U02 Etching at 10.8 Pa
1.0
0.8
0.6
0.4
0.2
n
-—-— -—-— -—-— .— -—-—- —-
132.7 Pal
-.0 100 200 300
Plasma Process Time, t (Min)
Figure 33. Power Effects on UOz Etching at 32.7 Pa
57
1.0
0.8
0.6
0.4
0.2
0
[
P=50W
o 30 60 90 120
Plasma Process Time, t (Min)
Figure 34. Power Effects on U02 Etching at 39.4 Pa
4.3. Effect of Plasma Gas Pressure
The pressure effects at 25 W of A/~ versus plasma processing time are
shown in Figure 35. At this power setting, the complete removal of U02 was not
achieved at any pressure. But 17 Pa yielded the highest etch fraction, ~R,~~ =
0.54. At both 10.8 and 31 Pa, the amount etched decreased compared to 17
Pa.
At 50 W and 17 Pa, NR,~~Xapproached 1, indicating the complete removal
of U02 (Figure 36). But at both 10.8 and 39.4 Pa, complete removal of U02 was
not achieved, with similar results at both pressures.
At 100 W, complete remova} of U02 was achieved at all pressures
between 10.8 and 39.4 Pa (Figure 37) with characteristic etch times ranging from
70 to 14.1 minutes as pressure increased. At 170 W (Figure 38), similar results
were achieved but with significantly faster characteristic etch times ranging from
30.5 to 3.7 minutes.
58
To summarize the pressure variation data, increasing the NF3 gas
pressure increased the amount etched, /V~, up to a peak pressure, then the
amount etched decreased as summarized in Figure 39. Above 50 W, ~R
increased monotonically with pressure in the pressure range examined. In
principle, the F atom concentration should decrease with increasing pressure at
constant power because fewer NF3 molecules will dissociate and some F atoms
will recombine to F2 in the plasma and on the chamber walls (Hinz et. al., 1980).
However, in our plasma reactor, the brightening of the glow near the antenna
and the shrinking glow region implied that the effective plasma volume
decreased while ionization increased closer to the antenna. Hence, as pressure
increased, the actual F atom density increased. This effect continued up to a
maximum pressure, then the F atom density decreased, as suggested by the
decreasing amount etched as pressure increased further. In the region where
etching increased monotonically with pressure, the highest etch fractions were
achieved. For example, at 32.7 Pa and 100 W, 99% of the UOZ was removed in
just 17 minutes, compared to 37 minutes at 17 Pa and 210 W.
.— - —-—. — -—- —.— -—-—- —-— -—-—-—-
b .
0 100 200 300
Plasma Process Time, t (Min)
Figure 35. Pressure Effects on U02 Etching at 25 W.
59
1.00
0.75
0.50
0.25
1--- —- —- —-.–- +- —-*–- —-- —-o-1
wQ
o
n
—10.8
u50 w
-.0
1.00
0.75
0.50
0.25
0
100 200
Plasma Process Time, t (Min)
Figure 36. Pressure Effects on U02 Etching at 50 W.
300
a .— -—-—-—- —-—-
R.4
I.w!!!l
50 100 150 200 250
Plasma Process Time, t (Min)
Figure 37. Pressure Effects on U02 Etching at 100 W.
60
1.00
0.75
0.50
0.25
.-
170 WI
o 30 60 90 120
Plasma Process Time, t (Min)
Figure 38. Pressure Effects on UOZ Etching at 170 W
1.0
0.8
0.6
0.4
0.2
00
.- —-— -—.—- —-— -A
c1
t = 53 min
10 20 30
Pressure (Pa)
Figure 39. Pressure Effects on U02
61
40
Etching.
50
4.4. U02 Etch Rates
Figure 40 shows the experimental initial etch rate, $, at 17 Pa and the
trends at other pressures. In developing this chart, some data which did not
include sufficient data points to establish t+~= with reasonable confidence were
not included, such as the high and low pressure data at 25 W. In addition, the
units used for equation (24) were converted to micrometers per minute by
multiplying by the factor 27.64 (Appendix E). These results may be converted to
milligrams per minute by multiplying equation (24) by the factor 13.56.
The baseline data at 17 Pa shows that the initial etch rate increased from
0.2 to 3.1 pm/min as absorbed power increased from 25 W to 210 W. Increasing
pressure generally increased the etch rate, to 7.4 ~m/min at 32.7 Pa and 180
W. When power was set too low for a given pressure, the etch rate also dropped
as indicated by the 39.4 Pa data points. Decreasing pressure (e.g., to 10.8 Pa)
generally resulted in a lower etch rate and this effect was related to the
decreasing brightness of the glow discharge near the antenna, and hence lower
F atom concentration in the bulk plasma.
The average etch rate, ~, needed to compare these results with the
reported PuG average etch rates (Martz et. al., 1991), was obtained by
integrating equation (24) as shown below:
(25)
The average etch rate at 17 Pa is plotted in Figure 41 as a function of
power for values oft/z = O, 2, and 4 where the latter value represents the etching
end point. The experimental etch data for th va~ing between 3.5 to 4.5 is also
plotted showing good agreement between prediction and experiment. the
62
average etch rates at the end point ranged from 0.1 to 0.7 pmlmin between 50
and 200 W. The equivalent mass etch rate is also shown for comparison.
0.1
0.01L J
10
1
0.1
50 100 150 200
resorbedPcYw3r(w)
Figure 40. Initial Etch Rate of UOZ. ~
Experimental Data, 35s U, s 45
8
00, ~o 50 100
Power
Figure 43. Average Etch
150 200
Rate at 17 Pa.
10
1
D.1
1
0.1
0.01
63
CHAPTER 5. CHEMKIN
To understand the physics of the etching process, it was necessary to
determine the type and concentrations of the reactive plasma species in an N~
plasma, including those that react with the UG to form gaseous UF6. Such a
determination was made using an existing RF piasma discharge code,
CHEMKIN Ill: A Fortran Chemical Kinetics Package For The Analysis Of Gas-
Phase Chemical And Plasma Kinetics. CHEMKIN had been previously applied
to silicon etching in CF~02 and NF~02 plasmas with good results (Meeks et. al.,
1997; Meeks and Shon, 1995). The following discussion describes the
CHEMKIN code, the code validation, and the code predictions for the present
experiments.
5.1. CHEMKIN Description
CHEMKINti, a chemical kinetics code developed by Sandia National
Laboratory, is a collection of modules for modeling chemically reacting flows in
chemical reactors and in RF glow discharge plasma. It consists of a number of
Fortran modules or subroutines, data files, script example problems, and
documents to facilitate the modeling of chemical kinetics. It models the chemical
kinetics of reactions in the gas phase and at a gas/solid interface to include the
transport and interactions of ions, molecules, and radicals. Three basic
modules used to model the present experiments were Cl-lEMKIN, SURFACE
CHEMKIN, and AURORA. The AURORA module was selected because it
modeled the plasma as a continuously stirred tank reactor (CSTR) which most
closely approached the experimental conditions of these experiments at 17 Pa.
A utility, FITDAT, was also available to generate thermodynamic polynomial
coefficients in the form needed by CHEMKIN and SURFACE CHEMKIN to carry
out the calculations.
i CHEMKIN is availabie from Reaction Design, 11436 Sorrento Valley Road: San Diego, California92121, Tel: (649) 550-1920
64
The CHEMKIN module (Kee et. al., 1996) solves elementary gas-phase
chemical kinetics, including multi-fluid plasma systems that may not be in
thermal equilibrium. The SURFACE CI-IEMKIN module (Coltrin et. al., 1996)
solves problems involving elementary heterogeneous and gas-phase chemical
kinetics in the presence of a solid surface. SURFACE CHEMKIN was used in
conjunction with CHEMKIN to model the NFs plasma reactions in the present
experiments, but not to determine the etch rate. The AURORA module (Meeks
et. al., 1996) predicts the steady state or time averaged properties (density,
molecular weight, flow rates, etc.) of well-mixed plasma systems and predicts the
ion, electron, and neutral species concentrations in the bulk plasma. It applies
the continuously stirred tank reactor (CSTR) approximation. The module
characteristics are specified by a reactor volume, residence time or mass flow
rate, heat loss or gas temperature, surface area, surface temperature, incoming
gas temperature and mixture, and net power deposition into the plasma. The
module runs in conjunction with CHEMKIN and SURFACE CHEMKIN. Typical
output parameters from CI-IEMKIN are summarized inTable 14.
Table 14. Typical Output Parameters,
Parameter
Mass flow rateTemperature: gas, ions, electronsPressureMean densityMean molecular weightMean volumetric flow rateSCCMResidence timeMole fraction of each speciesConcentration of each speciesMolar flow rate of each speciesMass flow rate of each speciesVolumetric flow rate of each speciesSCCM of each speciesSurface site fractions (etching)Bulk site fractions (etchina)
65
5.2. The CSTR Approximation
Cha@cterization of the plasma reactor and recovery system in terms of,
pressure and flow of gaseous products is determined from the mole balance
Consider a chamber whose volume, V,continuity equation (Fogler, ” 1992). ‘
contains gases whose total pressure is p, has an inlet flow of to moles of
species j per unit time, t, and an outlet flow of ~ moles per unit time. The
applied RF power causes some of the gas to dissociate while other processes
cause species to undergo other reactions, including recombination, for a net
molar production rate of species j, ~. The net production of moles of species j in
the chamber is the partial derivative of the number of moles of species j,qj. The
mole balance then becomes
F,O-F,+G,=Zd
(26)
The Aurora module for a plasma assumes steady state, so the
partial derivative becomes zero. Assuming no surface production of species
(i.e., no etching), the
formation of species
becomes:
F,. - F+jrjdv=o.
production rate, Gj, is the integral of
j per unit volume, f, and the mole
the molar rate of
balance equation
(27)
The CSTR approximation implies that within the volume, all the species
are perfectly mixed and the outlet conditions are identical to the conditions inside
V. Thus, the integrai becomes simply the product of f and V, and, after
rearranging, becomes:
Fjo -F,v= (28)
–r, “
Equation (28) is the design equation of the CSTR approximation (Fogler,
1992). Essentially, this approximation reduces all the differential equations to a
system of linear algebraic equations, greatly simplifyhg the solution of the
plasma chemistry. It will be shown below that this approximation results in the
66
need to restrict the use of CHEMKIN to conditions at 17 Pa in the present
experiments.
5.3. Plasma Reactions in CHEMKIN
Mass spectroscopy investigation of NE plasma species were conducted
by a number of investigators (Perrin et. al., 1990; Reese and Dibeler, 1956;
Konuma and Bauser, 1993; Greenberg and Verdeyen, 1985; Honda and Brandt,
1984). h&F2 was identified by excimer laser photolysis of NE (Weiner et. al.,
1992) and ~ radicals by laser-induced fluorescence (Lui et. al., 1992). The...
cracking pat,temlt’ of NF3 by electron bombardment was measured by mass
spectroscopy (Beattie, 1975). The species identified are listed inTable 15. The
fact that not all species were identified by all the experimentaiists is only
indicative of the instrument and focus of the experimentalists’ work. CHEMK}N
includes all the species observed, except ~F+ which only Konuma and Bauser
(1993) observed and F2-which only Reese and Dibeler (1956) observed .
The plasma reaction set for CHEMKIN (Table 16) was obtained from
Sandia (Meeks, Private Communication, 1998) using their N~02 reaction set
(Meeks et. al., 1997). All reactions involving oxygen, and all but four typical
electron-neutral excitation reactions for N6, N2, N, and FZ were removed since
these reactions were not of interest for the bulk plasma and doing so improved
the computer processing time considerably. Reaction #35 was added for NF and
NF2 reactions with NF2 (Du and Setser, 1993). Based on the validation work
discussed below, the rate coefficients for reaction #17 was decreased by a factor
of 10 in order to increase NFs dissociation while reaction numbers f 2, 14, 15,
and 16 were increased by a factor of 10 and reaction #36 was added to bring the
N2 and N concentrations into agreement with the experimental work of Perrin et.
al. (1990).
‘“A cracking patternk definedas the fragmentsof a molecule that form when the parentmoleculeis exposed to an ionizationsource, but withoutthe presence of a plasma.
67
%i
Definitions and units used in Table 16 are summarized below
Units:
EXCI:
REV:
TDEP/E/:
Molecules, cm3, seconds, Kelvin.
Electron energy loss per collision (eV) due to excitationreactions.
Signifies that the reverse reaction rate values to followare to be used rather than equilibrium values.
Reaction depends on the temperature of the specieswithin the slash marks, in this case the electrontemperature (as opposed to the gas temperature).
The forward rate coefficient, kf is given by equation (29) and is the
defining equation for the constants given in the tabie. EA/R has units of K; EA is
the activation energy in kJ/mole; R is the gas constant (8.3144 J mol-l IC1); B,
the exponent of the temperature, is dimensionless; T is the temperature (K); and
~, the reaction rate constant, has units of (cwz’nzolecule~-]s-’, where n is the
order of the reaction, varying between O and 3. The reverse rate coefficient,
when it applies, is calculated from the REV keyword value or, when REV is not
given, from equilibrium kinetics (Appendix D).
(/)EA R-—
kf = koTBe T(29)
Table 16. Plasma Chemistry in CHEMKIN.
Reaction Type of Reaction b B EJR Keywords10NIZATION/DISSOCIATION/ATTACHMENTREACTIONS
1 E+ NF3~ NF3++2E 7.39E-34 5 38t11TDEPIEt
2 E+ NF.3+NF~++2E+F 2.25E40 6.46 34184TDEPIEI
3 E+NF3 ~NF+ +2E+2F 3.93E-6311.0439849TDEP/E/
4 E+NF2+ NF2++2E 2.21E-33 4.94 31902TDEP/E/
5 E+ NF+NF++2E 1.94E-42 6.8 33586TDEP/E/
6 E+ N2+N2++2E 2.56E-43 7.07 31481TDEP/E/
7 E+ N+ N++2E 5.11E-37 5.78 47602TDEP/E/
69
Tabie 16. Plasma Chemistry in CHEtvlKIN.
Reaction Type of Reaction b B EJR Keywords8 E+ F2j F~++2E
9 E+ F+ F++2E
10 E+NFs~NFZ+F+E
11 E+ NF3+NF+2F+E
12 E+ NF2+NF+F+E
13 E+ NF2+N+2F+E
f4 E+ NF~N+F+E
15 E+ N2F2+2N+2F+E
16 E+ NpF.+~2N+4F+E
17 E+NF3sNF2+F-
18 E+ F*+ F+ F-
RECOMBINATIONREACTIONS
t9 E+ N+~N
20 E+N2+~N+N
21 E+ N2++N2
BIMOLECULAR & 3RD BODYREACTIONS
22 N+ N+ Me Nz+M
23 NF2+M@NF+F+M
24 NFP+NFP+M~NzF4+M
25 i=+F+ M@ F2+M
26 NFz+FP@NF3+F
27 NF+NF@N2+F+F
28 NF+NFe F2+N2
29 NF+N2F2eNF2+N2+F
30 NF + NF2 ~ N2F2+F
31 NF2+N@F+F+N2
32 NF2+Ne NF+NF
33 NFz+F+M@NF3+M
34 F+ N3QNF+N2
35 NF+NF2e N~+3F
36 NFP+ NF2@ N2+4F
ION-IONMUTUALNEUTRALIZATIONREACTIONS
37 F-+ NF~+~ 2F+ NF2
38 F.+ NFZ+~ 2F+ NF
39 F-+NF+ aF+NF
40 F-+N2+ ● F+Nz
41 F-+N+ +F+N
42 F-+F2+ +F+F2
43 F-+F+ ~F+F
CHARGETRANSFERREACTIONS
1.64E4
2.24E-47
2.06E-17
1.35E-30
1.57E-16
1.69E-23
1.57E-16
2.28E-16
2.28E-16
1.49E-09
1.02E-05
2.25E-O?
2.25E-01
2.25E-01
1.41E-32
1.26E-09
1.50E-32
2.80E-34
3.00E-14
6.88E-11
4.00E-12
2.00E-12
3.75E-12
1.40E-11
3.00E-12
1.03E-30
5.80E-11
2.75E-15
1.50E-32
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
7.25 32663TDEP/E/ ;
7.81 34076TDEP/E/
1.72 37274TDEP/W
4.45 34210TOEP/E/
1.& 27565TOEP/E/(ko=10-original)
2.99 37652TDEPIEI
1.84 27565TDEP/E/(IQ=10*01’i9inaI)
1.7 36391TDEP/E/(ko=10=original)
1.7 36391TDEP/E/(ko=10*onginal)
-0.14 3751TDEP/E/(ko=O.10*original)
-0.9 1082TDEP/E/
-2.5 0 TDEPIEi
-2.5 0 TDEP/E/
-2.5 0 TDEP/E/
o 0 REVI 3.163E-07-0.5113200.f
O 25700
0 0
0 0 REV17.600E-12O. 14300.I
o 4860
0 1251
0 0
0 0
0 187
0 95
0 0
0 0 REV13.98OE-10O. 16417.I
o 0
0 3095(Added,Du&Setser,1993)
o 0 (Added,k= k,m24)
o 0
0 0
0 0
0 0
0 0
0 0
0 0
70
Table 16. Plasma Chemistry in CHEMKIN.
Reaction Type of Reaction b B EJR Keywords44 F++l=z~Fz++F 9.7OE-10
45 F++N ~N+ +F 1.04E-09
46 F+ + NF3~ NF3++F 1.16E-09
47 F++ NFa NF++F 1.23E-09
48 F+ + NF2~ NF2++ F 1.30E-09
49 F2++N ~N++F2 9.37E-10
50
51
52
53
54
55
56
57
58
59
60
61
F2++ NF3~ NF3++ F2
F2++ NF ~ NF++ F2
F2++ NF2~ NF2++ F2
N2++N aN+ +N2
Nz++ NF3● NF3++ N2
N2++ NF ~ NF++ N2
N# + NF2● NFz++ N2
N+ + NF3● NF3++ N
N++ NF~NF++N
N+ + NF2~ NFz++ N
NF++ NFZ~ NF2++ NF
F++ N2=N2++F
1.04E-09
l.ll E-09
1.17E-09
9.37E-10
1.04E-09
l.ll E-09
1.17E-09
9.7OE-10
1.03E-09
1.08E-09
9.I5E-10
9.7OE-10
o
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
“oo0
0
0
0
0
0
0
0
0
0
0
0
0
EXCITATIONREACTIONS(TYPICAL)
62 E+ NF3+E+NF3 3.42E-21
63 E+ N2+N2+E 2.02E-34
64 E+ N~N+E 1.25E-39
65 E+ F2+F2+E a 1.09E-51
2.52 33296E)(CU7.70/ TOEP/E/
5.29 36200EXC1/13.00/ TOEP/E/
6.07 38618EXC1/13.70/TDEP/E
8.54 37389EXC1/13.06/TOEP/E/
5.4. Surface Reactions
The surface reactions modeled are the wall fluorination, ion wall
recombination, and, for the validation case, the fluorine reactions with surface
silicon (Table 17). Etch reactions for U02 were not modeled since the objective
was to determine reactive species concentrations in the bulk plasma (and
therefore at the plasma/sheath interface) for input to another model (E1-Genk et.
al., 1999). The constant, y, is defined as a sticking coefficient when the keyword
“STICK” is used and as a correction to the BOHM velocity when the keyword
“BOHM” is used. The sticking coefficient is a dimensionless quantity defined as
the reaction rate divided
the reaction (Meeks et.
by the incoming flux of species, and is the probability of
al., 1996, p. 83; Coltrin et. al., 1996). The BOHM
71
correction is an approximate method of correcting for transport conditions to the
surfa~e, accounting for the ion density gradient which affects the transport of
ions near the walls (Meeks et. al., 1996, page 83). The keyword needed in the
CHEMKIN input file is included in Table 17.
Table 17. Plasma Surface Reactions.
Type Reactions YFluorination of Aluminum Walls (STICK KEYWORD)
F + AL(s) + /@) 1“
F + ALF(s) ~ ALF2(S) 1F + ALF2(s) ~ ALF3(s) 1F2 + AL(s) + ALF2(s) 1F2 + ALF(s) S ALF3(s) 1
Ionic Wall Recombination (BOHM KEYWORD)F++E~F 0.4F2++E+F2 0.4N++E~N 0.4N2++E+N2 0.4NF++E~ NF 0.4NF2+ + E ~ NF2 0.4NF3+ + E * NF3 0.4
Silicon Etch Reactions (For Validation with Perrinonly) (STICK KEYWORD)
F + Si(s) * SiF(s) 1F + SiF(s) S SiF2(s) .01F + SiF2(s) ● Sil%(s) 1F + SiF3(s) + Si(b) ~ SiF4 1
The fluorination reactions with the chamber walls have sticking
coefficients (STICK KEYWORD) of 1.0 because passivation of the aluminum
wall sutiace is fast, requiring less than 60 seconds in a fluorine bearing plasma
(Mayumi et. al., 1990) to form AIFs (Miller and McCluskey, 1991). The
intermediate fluorination reactions were developed based on the concept of
successive reactions of a diffusing F or Fz atom (Mauer et. al. 1978, Flamm &
Donnely 1981).
Ion recombination reactions will occur on the side walis of the chamber
with much greater occurrence than on the powered electrode, because the area
of the wall is much greater than that of the powered electrode. The resulting
72
highly asymmetric discharge means that the voltage drop through this sheath is
only on the order of a coupie of volts (L’ieberman and Lichtenberg, 1994, p. 370).
Because the implementation of AURORA provides only a single value for the ion
energy loss through a sheath, the grounded wall sheath potential (2 V) was
applied. in addition, the BOHM coefficient adjustment of 0.4 (Table 17) was
applied based on values suggested by Sandia (Meeks et. al., 1996, page 83).
For silicon fluoride reactions, the sticking coefficients (STICK KEYWORD)
for all but the reaction leading to SiFz were set to 1.0. There were two reasons
for this approach: (1) to maintain the successive fluorination step sequence
from Si to the volatile SiF4 (Mauer et. al. 1978, Flamm & Donnely 1981); and (2)
to modify only a single reaction as the rate limiting step. This seiection was
somewhat arbitrary because the objective was to generate the experimentally
observed SiFA and the intermediates were not necessary. Consequently, the
sticking coefficient was adjusted until a value of 0.01 resulted in the value
reported by Perrin et. al.(1 990).
5.5. Thermodynamic Constants
CHEMKIN contains a thermodynamic database with values of specific
heat at constant pressure, enthalpy, and entropy as a function of temperature.
The ionic species thermodynamic data not in the database were obtained from
Sandia (Meeks and Veilieux, 1998) and are listed in Appendix D.
5.6. CHEMKIN Validation
Only one source of NF3 plasma mass spectroscopy data was found that
provided the data needed to make a species quantity comparison with
predictions from CHEMKIN (Perrin et. al., 1990). In that experiment, the
concentrations of the neutral plasma species were determined by combining
mass spectroscopy data with relative ionization probabilities. In cases where
data was lacking (e.g., N2Fg), the authors were able to estimate the quantities
from the total system pressures and the partial pressures of the other gases.
They conducted their investigations at 50, 100, fl50, 200, and 300 W but only at
73
200 W did they provide total system pressure from which to estimate the partial
pressure of ‘othefl species. Their experiment consisted of a heated plasma
“box” inside a larger chamber. The plasma was created inside the “box” whose
‘heated interior side-walls contained the silicon. The plasma species and etch
products flowed out of the “box” toward the pump and the mass spectrometer,
resulting in recombination reactions within the outer chamber and walls during
the transport (Figure 42). As a result of this transport, ions and short-lived
species would be expected to recombine, and consequently Perrin et. al. (1990)
only measured NFs, Nz, SiFA, certain species which they attributed to N2F4, and
other gases, including HF. The HF came from a plasma-deposited film of SiHA
used to coat the interior of the plasma box prior to NF3 etching. The etch
process was monitored by laser reflectomet~.
Table 18 summarizes the plasma “box” parameters (Perrin et. al., 1990)
that were modeled in CHEMKIN. Dimensions of the outer chamber were not
available. Because of the recombination during transport to the mass
spectrometer, in comparing CHEMKIN, we assumed that only the long lived
species would retain their identify and that ions and short lived species would be
transformed into their parent species as summarized in Table 19. Consequently,
the mole fractions of the parent species are the sum of the mole fractions of the
individual plasma species listed. The contributions to the “Other” category
includes F and Fz. The authors did not observe Fz (or F) until after the silicon
etch end point was reached. At that point, the Fz mole fraction increased from -
0 to over 0.36, indicating that silicon was no longer consuming F atoms. In their
experiment, any excess F would react with H and other impurities. Therefore, all
F and F2 species predicted by CHEMKIN were included with “other parent
species.
74
Table 18. Parameters of Pernn et. al. (1990) Experiments.
Item Value
Volume (ma)
Area (m2)
Power (W)
Pressure, no plasma (Pa)
Pressure, plasma (Pa)
Flow (SCCM)
Wall Temperature (K)
Si Crystal Dimension (m)
Si Site Concentration (mole/m2)
Al Crystal Dimension (m)
Al Site Concentration (mole/m2)
0.0128
0.4480
200
10
12
140
575
5.43xlo-’0
5.63x10~
4.04xlo-’0
4.05XI 0-5
Table 19. CHEMKIN Species Consolidation.
Long Lived Plasma SpeciesParent SpeciesNF3 NF3N2 N, N2, N3, N+, N2+SiF4 SiFAOther NF2, NF, N2F2, N2F4, F2, F, F+, F2+, NF+, NF2+, NF3+, F-
The comparison of experimental results (Perrin et. al., 1990) with
CHEMKIN was best performed in terms of mole fractions, xj, of species j, and so
the conversion of measured concentration ratios was made from the relationship
shown in equation (23). Here, pj is the partial pressure of species j, p is the total
pressure with plasma (12 Pa), p. is the total pressure without plasma (1 O Pa),
and Cj/Co is the concentration ratio reported by Perrin et. al. (1990) in their figure
8. The results of this conversion are tabulated in Table 20.
P,
[1
CJ Pox,=—= — — (30)
P cop”
75
Table 20. Pernn et. al. (1990) Experimental Data at 200 W.
Species c$c~ 3NFs 0.253 0.211N2 0.315 0.262SiF4 0.408 0.340Other (HF, N2F4) 0,224 0.187TOTAL 1.200 1.000
Several iterations were performed starting with the original CHEMKIN
chemistry reaction set (Table 16), and adjustments were made to the reaction
rate constant value, ~, until the experimental mole fractions for all the species
were in agreement. Because there are many interactions in the chemistry which
could alter the results in unexpected ways, the changes to the rate coefficients,
k, were kept to within one standard deviation of the expected error of the original
reaction set k value. For example, in reaction #l 7, the electron attachment
reaction was reported to have a k-value (Miller et. al., 199S):
3477*695
k = (1’i 4)x10-12~ Tcm 3 (31)
s – molecule ‘
The values of k reported in the original CHEMKIN data set (Meeks et. al.,
1997), as well as 0.1 and 10 times the k values, were bounded at 298K within
the error bars of (EA/R), ~ 695 K, of the original rate coefficient for reaction 17, as
demonstrated in Figure 44. The rate coefficient reported by Miller et. al. (1995)
was a factor of 1000 less than the original (Meeks et. al., 1997), further
supporting a reduction of the rate coefficient. But because of the constraints on
the allowed modifications, the final value of k selected was 0.1 times the original.
The next change in the k-values was for the quantities of N, N2, and N2F4,
whose predicted mole fractions were too low with the original set (Meeks et. al.,
1997). Applying the same limitations as described above, values for the rate
constant, k. (see Equation (29)), for reactions #12, 14, 15, and 16 were each
increased by a factor of 10, and reactions 35 and 36 were added. The two latter
reactions were added because they had been reported in the literature (Du &
Setser, 1993).
76
The final result was an overall error in the mole fractions of the reported
neutral species NF3, N2, SiF4, and all others of less than A 5.3%, as shown in
Figure 43. The worst case relative error for any of the parent species was t 5.3
%. A detailed listing of CHEMKIN predicted mole fractions of the NFs plasma
species is included in Appendix D. These results suggest that the CSTR
approximation inherent in the AURORA module of CHEMKIN is suited to the
experimental conditions of the Perrin et. al. (1990) experiment. However, even
here there were anomalies. Perrin et. al. (1990) reported that the etch rate
increased with pressure between 12 and 15 Pa, then decreased between 15
and 35 Pa. These results, whose trend was confirmed with the present
experimental data, demonstrate that AURORA can only be applied to cases
where the CSTR approximation can be applied.
Estimates of the species partial pressures were made (Appendix D), but
without knowing the partial pressures of the “other” species, accurate
comparisons with CHEMKIN were not possible except at 200 W.
hJF3Gas inlet
t
HeatedWalls .
Cold ~Walls
I MassSpectrometer
I
Plasma4
Box
I I
Iu kTypical GasDiffusion Pathto Mass spec.
- pump
Figure 42. Experimental Setup of Perrin et. al.
77
co.-2
Ii
0.5
0.4
0.3
0.2
0.1
0
Figure
I o-”
10-’3
10-’5
10-’7
10-’9
piq ,5;K a’NF. Plasm hamber Conditions
200 W, 12 Pa, 140 SCCM
NF31
N2
43. Comparison of CHEMKIN with Si Etching Experiments.
~E3Reaction #17:
e+ NF3+. NF2+F-
2.5 3.0
k+= 1.49x1 0-8T a“14e-(3751*g5w
k.= 1.49x104 T 4“14e-3751m(Meeks et. al., 1997)
k-= 1.49x10-%0”14e-(3751- ‘g5)n
/Miller et. al., 1995
3.5 4.0 4.5 5.0
1Ooorr
Figure 44. Maximum Variation in Rate Coet%cient.
78
5.7. CHEMKIN Predictions for the Present Experiments
With the set of final plasma chemistry reactions defined above,
predictions of the mole fractions of the various species of the NFs plasma for the
conditions of the U02 experiments were evaluated, but under conditions of no
etching. Consequently, the surface reactions (Table 17) were implemented with
only the ionic and wali fluorination reactions. The objective was to obtain the
reactive species concentrations at the plasma sheath interFace for use in another
simulation (E1-Genk et. al., 1999). Because of the CSTR approximation inherent
in the CHEMKIN modeling, the CHEMKIN mole fraction predictions for these
experiments are given only for 17 Pa (see paragraph 5.8) with Appendix D
containing detailed mole fraction data.
The CHEMKIN input parameters describing the U02 experimental plasma
conditions are tabulated in Table 21. Most of the parameters are self-
explanatory. Power was allowed to vary from 25 to 250W absorbed. The
volumetric flow rate, in SCCM, was set in CHEMKIN to the flow rate determined
from manufacturer’s calibration correlation needed to achieve 17 Pa at the power
specified. The heat transfer coefficient, 1486 W m-2 S-l, produced a neutral gas
temperature that remained nearly constant over the range of power (Table 22).
Table 21. CHEMKIN Parameters for the UOZ Experiment.
Item Value
Volume (m~) 0.125
Area (m2) 1.604Power (W) 25 to 250Pressure, plasma (Pa) 17
Flow (SCCM) 5.34 to 5.7
Ambient Temperature 298(K)H [W m-2 S-l} 1486
The predicted effect of power on the major neutral species mole fractions
are shown in Figure 45. Neutral species not shown had mole fractions less than
0.001. As power increased, predicted NF3 dissociation and F atom mole fraction
79
Table 22. CHEMKIN Parameters at 17 Pa.
Power (W) SCCM Neutral Gas Electron(cm3/min) Temperature (K) Temperature (eV)
25 5.71 298.1 5.615075100125150
175200225250
5.675.635.595.555.515.465.425.385.34
298.2298.3298.3298.4298.5298.6298.6298.7298.8
5.215.014.874.774.684.604.534.464.38
both increased. The increasing F atom concentration with power is in agreement
with the experimentally observed increasing etch rate with power. The predicted
ion mole fractions are shown in Figure 46, with the negative F ions having the
highest predicted mole fraction, approaching 1.8 x 10-5 at 200 W. ionic species
not shown had mole fractions less than 10+. The NFs inlet flow rate, in SCCM;
the electron temperature, in eV; and the neutral gas temperature, in K, are
tabulated in Table 22. The inlet flow rate variations reflect the experimental
pressure variation with power previously discussed. Predicted mole fractions of
all species are tabulated in Appendix D.
The predicted effect of pressure, at constant power, is demonstrated in
Figure 47 for F and NFs species, indicating that the F atom concentration is
predicted to decrease with increasing pressure as the NF3 concentration
increases. Since F atoms are the primary etchant species (see Chapter 6), this
would indicate that the etch rate shotild decrease with increasing pressure, a
conclusion that is not observed for all experimental conditions. For example,
below -50 W, the etch rate increased with pressure until a peak pressure -23
Pa was reached, then decreased. CHEMKIN predicts the decrease, but not the
increasing and peak pressure. Above - 50 W, the experimental etch rate
increased throughout the pressure range 10.8 to 40 Pa, never reaching a peak.
These results indicate that the CSTR approximation cannot be applied under all
80
conditions. Above 17 Pa, the plasma glow region, hence the effective plasma
volume, decreased, an aspect that is not modeled ~th the CSTR approximation.
‘ Below t 7 Pa, the glow volume region also decreased, again suggesting that the
CSTR assumptions are not met. Only at 17 Pa was the glow visually uniform,
suggesting that 17 Pa is the only pressure region in which CHEMKIN can be
applied.
Several variations were investigated to understand the sensitivity of
various parameters, including fiow variations between manufacturer’s and
experimental flow measurements, and variation in heat transfer coefficients. The
inlet flow rate variation of NF3, in SCCM, differed slightly between manufacturer’s
flow correlation and experimentally measured values. These differences were
inconsequential at all pressures, as demonstrated (Figure 48) for NFs neutrals
and ions at 10.8 Pa, for which pressure the greatest variations occurred. Several
variations in heat transfer coefficient were also investigated. Under adiabatic
conditions, CHEMKIN predicted that the plasma temperature would increase to
well above 1000 K, a situation which did not occur experimentally. Finally, a heat
transfer coefficient equal to 7.53 W m-2 S-l yielded a wall temperature equal to
the experimentally measured temperature at 50 W and 17 Pa (Chapter 3). This
condition resulted in a neutral gas temperature varying from 300 to 311 K in the
power range 25 to 250 W, which appears reasonable. Between 1486 and 7.53
W m-2 S-l, mole fractions of NF3 varied from 0.796 to 0.799 while F mole fractions
varied from 0.150 to 0.153, respectively. However, because of insufficient
temperature data throughout the pressure and power range, operation at near
constant gas temperature obtained at the higher heat transfer coefficient was
used.
CHEMKIN predicted that NF3 and F-atoms are the predominant species in
the NFs bulk plasma. The F atom mole fraction increased with power as the NFs
mole fraction decreased. However, the predicted pressure variation at constant
power did not follow the experimental variation in etch rate because the CSTR
approximation did not apply throughout the pressure range.
81
4L
F
c 0.1 :0.=umLal62 0.01 :
EEl
0.001 I 1 I !
o“ 50 100 150 200 250
Power (W)
Figure 45. CHEMKIN Neutral Species Predictions at 17.0 Pa.
I t i 44
w
104 ( I I I
o 100
Power (W)
Figure 46. CHEMKIN Ion Predictions
82
200
at 17.0 Pa.
0.02
O.ofl
0.005
0.002
0.001
0.0005
10°
10-2
104
10 20 30 40
Pressure (Pa)
Figure 47. CHEMKIN Pressure Predictions.
NF3
‘- ~-- 5-- $-- G--
1O*t I
o 50 100 150 200 250
Power (W)
Figure 48. CHEMKIN Sensitivity with Flow Rate
83
5.8. Limitations on the Use of CHEMKIN
The CSTR approximation applies to the plasma
experiments only to a degree, and this was only
conditions of these U021
determined after many
comparisons of the CHEMKIN predictions with the present etching results. The
problem was that the concentration of species in the test chamber for U02
etching was not uniform at all pressure and power levels used, as noted in the
experimental chamber observations in Chapter 3. The glow, which is
representative of a convolution of species density, electron distribution, and
cross section for electron impact (Lieberman and Lichtenberg, 1994, p.254), was
brightest near the antenna at all pressures, filled the entire chamber at 17 Pa,
and was brighter at 17 Pa than at 10.8 Pa in the power range used. At higher or
lower pressures, the glow region shrunk towards the antenna, and was
surrounded by a dark region extending from the grounded walls of the chamber
to the edge of the glow discharge. As power increased, the volume of the glow
discharge region expanded outward from the antenna, eventually filling the entire
volume at high enough power.
completely uniform throughout
ranges used in the experiments.
These observations imply that mixing was not
the test chamber for all pressure and power
The CSTR approximation appears valid only near 17 Pa at all powers where the
glow fills the chamber but has intensity variations. CHEMKIN provides the
correct trends of the effect of changing power, but not of pressure, primarily
because the effective plasma volume is not constant, as required by the CSTR
approximation. CHEMKIN predicted that the F atoms are a major constituent of
the plasma, which is confirmed experimentally (Perrin et.al., 1990; Pelletier,
1987; and Flamm et. al., 1981); that F atoms increase with powe~ and that F
atoms decrease with pressure. The power variation is correct, but the pressure
variation is not. To conclude, CHEMKIN provides useful data in species
predictions and quantities, but must be used with care when extrapolating the
results. In these experiments, CHEMKIN provided useful data at 17 Pa, but not
at other pressures because the CSTR approximation did not hold.
84
CHAPTER 6.
The self-limiting
U02 ETCHING ANDPLUTONIUM
nature of U02 etching
APPLICATION TO
was demonstrated by the
experimental results of chapter 4. The nature of this self-limiting process is
reviewed in this chapter and likely causes identified. First, the plasma species
are examined to determine the etchant species. Next, thermodynamic
assessment of reaction products identify likely candidates that form non-volatile
products that block or slow the etchant reactions with U02 to form a volatile UFe.
These results are extended to plutonium based on similarities in the chemistry
and thermodynamics.
6.1. The Plasma Species
The plasma species and mole fractions predicted by the CHEMKIN code
(Chapter 5) are summarized in Table 23. The most abundant species are NFs
and F atoms, but F is the reactive radical which reacts with U02 to produce the
volatile UFG. Fluoride volatile products were also produced in silicon etching
experiments with fluorine bearing gases (Pelletier, 1987; Flamm et. al. 1981).
NF3 is non-reactive at the experimental temperature (- 300 K) and the other
plasma species are too low in concentration to be a significant factor. The F
atom concentration increases with power as also demonstrated by the increasing
experimental etch rate of U02 with power. The F atoms created in the plasma
diffuse to the U02 surface where they react with U02 to produce UF6. The
accumulation of UFG molecules in the sheath slow the flux of F atoms to the
surface, reducing the effective F atom diffusion coefficient by as much as 1570
(E1-Genk et. al., 1999), further blocking or slowing the reaction of U02 to UF6 with
plasma immersion time.
85
Table 23. Calculated Mole Fractions of Plasma Species at 17 Pa.
Species 50 w 100W
NF3 I 0.80 0.61F 0.15 0.31N2 0.03 0.06F2 0.01 0.02NF2 0.01 0.01
NzF4 2.1 E-04 8.3E-05N 3.3E-07 8.2E-07N2F2 1.6E-09 7.OE-10
NF 2.3E-12 3.OE-12N3 5.2E-57 7.1 E-57Electrons 1.7E-09 6.7E-09
F- 6.6E-06 1.1 E-05ions 6.6E-06 1.1 E-05
The ions, while too few in number to contribute significantly to the etching
process, deposit energy on the sutface, enhancing the reaction processes by
removing non-volatile products from the UOZ surface. For example, the sample
substrate temperature in the UOZ etching experiments rose -40 K above ambient
compared to only 4 K at the walls of the chamber. The relatively high
temperature rise of the sample resuited mostly from ion bombardment.
Exothermic reactions of UOZ and F atoms deposit at most 62 J of heat in 30
minutes of plasma processing at 50 W RF compared to 680 J from ion
bombardment (Appendix E). Hence, most of the temperature increase will be
from ion bombardment. The ions, in traversing the sheath, will suffer collisions
since their mean free path is a factor of -5 to 10 smaller than the sheath
thickness (Appendix E). Consequently, the energy deposited will be less than
the sheath voltage, but still high enough to break bonds and heat the surface
(Table 24). The sheath voltage was obtained from experimental measurements
(Chapter 3), the electron energy and neutral gas temperature were obtained from
CHENIKIN predictions (Chapter 5), and the ion energy was calculated as shown
in Appendix E.
86
Blocking of the etch reactions can arise during the reaction steps leading
to the formation of UF6Ythus requiring an understanding of the etch mechanism.
Table 24. Plasma Conditions at 17 Pa.
Parameter 50 w IoowSheath Voltage (V) -142 -261Electron Energy (eV) 5.21 4.87Neutral Temperature (K) 298.2 298.3Sheath Thickness (cm) 0.14 0.16NFs Ion Energy (eV) ?1.3 17.9
NF3 Ion Energy (kJ/mol) 1087 1731
6.2. Reaction Model
Since F atom radicals are the predominant reactive species in the plasma,
reactions of adsorbed F and U02 are the initiating events leading to the
formation of a uranium fluoride gas. Because U forms in the III-VI oxidation
states (Jacob et. al., 1980), compounds UF3 through UF6 and the oxyfiuorides of
uranium are the ones likely to form. The reaction mechanism to produce UFtj is
quite complex and therefore a model for the reaction of adsorbed F atoms with
UOZ was developed to simplify the chemistry. This model combines aspects of
electronic valence orbitals of uranium, probability theory, and thermodynamic
Gibbs free energy heats of formation and reaction as described below.
Before UF6 appears from the starting material, UOZ several intermediate
compounds of the fluorides and oxyfluorides of uranium will form. The highly
reactive F atom radicals will diffuse to the surface and adsorb to U02 surface
sites via physisorped van der Waals forces and chemisorption (Lieberman and
Lichtenberg, 1985). Reactions will occur with UOZ molecular sites to form
products of U-O-F, where U-O-F indicates several possible compounds involving
all three atoms. Taking the possibie combinations of U, O, and F atoms to fill the
electronic valence structure of the U atom (Alberty and Silbey, 1997, Table 10-3)
leads to several species including the oxyfiuorides and fluorides shown in Table
25. Several restrictions were applied to the reactions including: reactions can
87
only proceed in a direction to increase the complexity of the molecule (i.e., no
dissociation reactions); only one U atom per molecule (i.e., U308 not
considered); no reactions with desorbed oxygen were considered; and bonding
with F occurs first with the outermost U valence orbital before the inner orbital.
The electronic structure shown in Table 25 for U depicts the bonds in order of
decreasing binding energy where, for example, the 6d1 electron will bind before
the 7s2 electrons.
Table 25. Bonding Sites for Reaction with F Radicals.
U O F Species Electronic MaximumStructure Bonding Sites
100U [Rn]5fJ7sz6d1 1101UF [Rn]5f~7s2 2102UF2 [Rn]5~7s1 1103UF3 [Rn]5~ 2I04UF4 [Rn]5? 2105UF5 [Rn]5f7 1I06UF6 [Rn] oIlouo [Rn]5f37s1 1lIIUOF [Rn]5f3 21 1 2 UOF2 [Rn]5~ 21 1 3 UOF3 [Rn]5f1 11 1 4 UOF4 [Rn] 2120U02 [Rn]5? 21 2 1 U02F [Rn]5f3 21 2 2 UOZFZ [Rn] 2
Next, the concept of probability of reactions of one or more F atoms with a
molecule was applied. Binary reaction probability suggests that the likelihood of
one F atom reacting with a U-O-F molecule is greater than two F atoms reacting
tith a similar molecule at the same time, and these probabilities are much more
likely than three F atoms reacting with another similar molecule at the same time.
This means, for example, that the probability of U02 reacting to form U02F is
greater than the probability of U02 retaining its identity until two F atoms interact
to suddenly produce U02F2. Thus, it is more likely that the sequence will be
UOZ to U02F to U02F2. Based on this assumption, reactions with up to two F
atoms reacting at a time were examined. The actual number of F atoms that can
88
bind was also limited by the number of electrons in the outetiost electronic
orbital. Forexample, tithe 6d'otii@l isavailable, then only one bonding site will
be created. The results of this calculation are depicted in Table 25 as maximum
bonding sites. For UF3, UOF, and U02F, the maximum number of bonding sites
were limited to two atoms although the 5f-orbitai indicates three electrons are
available (5f3). In the case of compounds with fully saturated bonds (i.e., all
vaience band eiectrons of U are bound), such as UOF4 and U02F2, reaction is
assumed to be the abstraction of oxygen and thus the maximum number of
nearest neighbor F atoms is assumed to be two. UF6 undergoes no further
reaction and so the number of bonding sites is zero. Consequently, the number
of F atoms reacting were iimited to the maximum number of bonding sites, and
these resuits were used in assessing a sutiace etch reaction mechanism.
6.3. Thermodynamic Analysis of SurFace Etch Reactions
in Figure 49, the Gibbs free energy of formation is piotted for each of the
uranium species iisted in Tabie 25. This figure provides an indication of which
species are iikeiy to form from the starling material, U02, shown with a horizontal
iine. Species above the iine require energy whiie those beiow the iine can
spontaneousiy react. For exampie, from UOZ approximately 1000 kJ/moie is
needed to form U and reiease the 02. The piasma environment containing
energetic ions bombarding the surface (Tabie 24) and exothermic surface
reactions provide more than enough energy to form any of these products. As a
result, U02 may dissociate into U and 02. Consequently, reactions of F with both
U02 and U as the starting materiai were anaiyzed to determine the surface
species, based on favorabie Gibbs energy of reaction, GR, and restricting
reacting F atom radicais to the number of bonding sites. Standard state
conditions (298 K, 1 Bar) were appiied since the majority neutrai piasma gas
species are near room temperature and pressure corrections are negligible,
<0.075 kJ/moie (Appendix E).
A thermodynamic anaiysis of aii combinations of U-O-F reactions was
performed based on the maximum number of bonding sites shown in Tabie 25
89
(Appendix E). A value of the Gibbs free energy of reaction, GR that is negative
is indicative of a reaction that can proceed spontaneously in the direction
indicated by the chemical reaction equation until equilibrium renditions for
products and reactants are met. Table 26 contains a listing of all favorable
(negative G~) thermodynamic reactions evaluated while Table 27 contains a
listing of all unfavorable (positive GR) thermodynamic reactions evaluated. The
table also includes the reaction enthalpy, which is positive for endothermic
reactions and negative for exothermic reactions.
Table 26. Favorable Thermodynamic Reactions of U-O-F.
No. Reaction HR* GR* .kJ mol-l kJ mol-’
2F + UF ~ UF3 -1618.8 -1485.61
234567891011121314151617181920212223242526
2F + UOF -3 UOF3F + UC)F + UOF2
F + UF2 + UF32F+UOF~UF3+02F+U+UF22F + UF3 ~ UF52F + U02 + UOZFZF+ LJF-+ UF2
F+ UO~UOF2F + UOF2 ● UOF4
F + UF3 + UF4F + U02 ~ UOZF2F + U02F2 + UF4 +022F + UF4 ~ UF62F + UOF2 ~ UF4 + OF + UOF3 ~ UOF4F + UOF2 ● UOF3F + U02F ~ UOZFZ
F + UF4 + UF52F + U02F2 ● UOF4 + OF + UF5 + UFtj(s)2F + U02F ~ UF3 + OzF+lJ+lJF2F + UOF4 ~ UFG+ O2F + UOZF ● UOF3 + O
-1124.8-1040.4-1050.4-867.6-689.8-731.8-727.3-568.4-644.4-578.4-487.4-292.9-415.3-396.2-314.6-494.0-84.4
-434.4-244.0-180.7-201.4-362.3-121.4-182.0-121.1
-1223.0-979.5-870.1-809.1-749.8-660.6-650.1-615.5-599.1-519.0-449.3-427.1-387.3-368.4-278.9-275.4-243.5-223.0-211.0-164.0-161.9-161.0-134.3-133.1-111.6-35.427 F + UOF3 ~ UF4 +-0 -230.2
90
The surface products obtained from thermodynamically favorable
reactions (e.g., negative G~) starting with U02 is shown in Figure 50. Reactions
involving a single F atom are shown as solid lines while reactions requiring two F
atoms are shown as dashed lines, where the former indicates a greater
probability of occurrence. Two products, U02F2 and U02F, have GR values of -
650 and 427 kJ/mole, respectively, but because UOZF requires a single F atom,
it has a higher likelihood of forming. From UOZF, the likely path is to U02F2.
From there, two F atoms are required to continue the reaction, but the path to
UF4 is more likely than to UOF4 because of the former path’s larger negative
value of GR. From UF4, the most probable sequence is to UF5 then UF6. Other
reactants requiring two F atoms to proceed are possible, resulting, for example,
in UF3 and UOF3, but the reaction products obtained from single F atom
reactions are favored. By exception, the species that were not
thermodynamically favored (i.e., had positive GR values in reactions of F with U
or U02) included UO, UOF, and UOFZ. Consequently, the likely reaction
products formed from F radicals and UOZ are the uranium fluorides, UFM, and
the uranium oxyfiuorides: UOZF, UOZF2, UOFS, and UOF4.
Table 27. Unfavorable Thermodynamic Reactions of U-O-F.
No. Reaction m“ GR”kJ mot-’ kJ mol-’
1 F+ UOF4+UF5+0 19.4 28.82 F+ UOF+UI=2+0 182.8 61.03 F + U02F2 ~ UF3 + 02 72.0 62.04 F+lJO~lJF+O 106.8 77.55 F + U02F ~ UOFZ + O -36.7 132.06 F+UOFZ~UFS+O 172.8 170.47 F+lJO~F+lJ +0 228.0 212.08 F+ UOF4+UF4+F+0 263,8 240.19 F + U02F2 ~ UOF3 + O 313.0 248.010 2F + U02 ~ UF2 + 02 395.2 282.011 F+ U02F2 +UOF2+O+F 398.0 355.012 F+ U02+UOF+0 710.8 684.413 F + U02F ~ UFZ + Oz 688.1 709.114 F+U02 ~UF +02 963.6 897.515 F+ UOF2+UF2+O+F 1223.2 1040.5
91
The reaction mechanism starting with U is shown in Figure 51. There is a
single path from U to UF but because the GR values of succeeding reactions are
significantly more negative, thermodynamics implies that UF will not remain on
the surface, but react to form UFZ then sequentially to UF3, UF4, UF5, and UF6.
The reaction from UF to UF2 or UF3 is probably vety fast, since no stable
uranium compounds in the first oxidation state are known (Bierrnan et. al., 1983).
Other paths requiring two F atoms are possible as indicated by the dashed line,
but less probable than the first reaction sequence. The reaction path from U to
UF6 is essentially a single path compared to the U02 mechanism with several
parallel paths.
0
-500g
F3 -1000x
&-1500
-2000
Uoe —. %
u Y‘F \ UOF T=298K
\ @ ‘Fz UOZF\, /p–
-?I
u I\ UF~ 3 U02F,
UOFZ‘-%UOF UOFg
3 &—UF4 % UF~
UF~ ‘-e
-2500 ~ I200 240 280 320 360
Molecular Weight (g/mole)
Figure 49. Gibbs Free Energy of Formation for Uranium Fluorides/Oxyfiuorides.
92
I Surface ReactionsRea~onGMMFreeEnergy,G R(Wmok)at288K
IJ(<=2 i
--’-% UOF4-------:33-- ----uF6III -211
~% ~ uo F2- -s~’- - u ~ -162
Ii
~ UF5 b UF6\
-223 \-373
XF + lj~\
449.----.----ElJF6
427 I / 45 *,*
t~
U02F--’~ UF&- ----- ---- ---->UF6\ --\ ~ ~61
X-112 -A\
‘h -275UOF3 ~
Sotid Lines: requires 1 F atomDashed lines: requires 2 F atoms
UF5 “62 * UF6
UOF4 = - + UF6
Figure 50. Gibbs Reaction Energy, GR, for U02 Etching.
Surface Reactions
)C<=2
ReactionGibbsFreeEnergy,GR(IcJmoie)at 298K
xF+U-661
r ---- ---- - T
1“-134
UFIit
Figure 51.
.I ‘\
-1486 J \ -617---- ---- - ---- ---- - *
Solid Lines: requires 1 F atomDashed lines: requires 2 F atoms
Gibbs Reaction Energy, GR for U Etching.
UF6
UF6
93
6.4. Volatile Surface Species
The volatility of the sutiace species will indicate which will ciesorb into the
gas phase and which will likely remain on the surface, blocking the reaction.
Figure 52 shows a, plot of the vapor pressure of the available data while Table 28
extrapolates the vapor pressure to 298K, and includes melting point data. While
the vapor pressure is defined as an equilibrium process of like compounds in the
gas and condensed phase, the vapor pressure provides an indication of whether
the material will remain in the condensed phase on the surface, or whether it will
vaporize. The vapor pressure correlations used are fisted in Appendix E. Since
the experimental operating pressure varies from 10.8 to 40 Pa at --298 K, the
vapor pressure must be compared at these conditions. The 24 kPa vapor
pressure of UFG (Lange and Forker, 1967) at 298 K (Figure 52) is well above the
operating pressures in the experiments, and therefore UFEiwill desorb into the
piasma. The vapor pressures of the known uranium fluorides (UF5, UF4, and
UFS) at 298 K are severai orders of magnitude iower than the piasma operating
pressures and these species wili remain in the condensed phase (Katz et. ai,
‘1986(a); Jacob et. ai. 1980). UF and UF2 vapor pressure data is unavailable.
However, the bond dissociation of these two compounds are on the
bond dissociation energy of UFA and much greater than the bond
energy of UF5 (Hiidenbrand and Lau, 1992), suggesting that
pressures are aiso much iess than the chamber operating pressure.
ai, 1986) and U02 (Ohse, 1979) both have high meiting points and
order of the
dissociation
their vapor
U (Katz et.
measurable
vapor pressures oniy above 1480 K
sutiace at the operating pressures
oxyfiuoride U02F2 has a measurable
and so both wiii remain as soiids on the
and temperatures of the piasma. The
vapor pressure oniy above 900 K and the
UOF4 vapor pressure is iower by a factor of neariy 10 (Lau et. ai., 1985);
consequently, both wiii also remain as soiids on the surface. Vapor pressure
data on the remaining oxyfiuorides, UOZF and UOFS, were not avaiiabie;
however, extrapolating the trends in the oxyfiuoride species (Tabie 28) suggests
that U02F and UOF3 vapor pressures shouid be between UOF4 and U02F2. If
this is the case, then U02F and UOF3 wiii aiso remain in the condensed phase at
94
298 K. From this analysis, it is concluded that UF6 is the only species with a
vapor pressure above the plasma operating pressure at - 300 K, and will
therefore desorb into the gas phase.
106‘UFG(a) UF~(C)
Operating - U02(
102Region
UOzF2(e)
10-2
~;f/ ~
/—UOF4(e)
U (b) References
104 uF~(b)a. Lange& Forker,1967b. Katz et. al., 1986 Vol. L
UF4(C)c. Jacobet. al., 1980d. Ohse et. al., 1979e. l-au et. al., 1985
10-’0300 1000 2000 3000
Temperature (K)
Figure 52. Vapor Pressure of UFX Compounds.
Therefore, it is argued that the non-volatile products likely to form over the
U02 surface are the uranium fluorides, UF2.5, and the uranium oxyfiuorides:
U02F, U02F2, UOF3, and UOF4. UF may form, but will immediately be converted
to UF2 or higher fluoride. These non-volatile products account for the blocking
effect previously discussed. If power is too low or pressure too high, conditions
at the surface may be such that these compounds slow and eventually stop the
reaction of F and U02. The blocking effect may be minimized by operating with a
pressure/power combination that optimizes the F atom concentration and the ion
energy to increase the removal of non-volatile deposits. This is supported by the
present experimental results (Chapter 4).
95
Table 28. Surface Species Volatility Data.
Species Vapor Pressure Melting Referenceat 300K Point
(Pa) (K)uFfj 24000 337 Lange and Forker, 1967 (p. 1450)UF5 2.7x1 0-11 673 Katz et. al. 1986 (Vol. 1,p.308)UF4 5X1020 1233 Jacob et. al. 1980 (p. 27)UF3 <<1 1273 Jacob et. al. 1980 (p 6)UF2 * * See discussionUF * * See discussionu <<1 1406 Katz e. al. 1986 (Vol. 1,p. 228),
UO* <<1 3148 Ohse et. al. 1979U02F ● * See discussionU02F2 <<1 Lau et. al. 1985UOF3 <<1 * See discussionUOF4 << I Lau et. al. 1985
6.5.
were
Applications to PU02
The average etch rates of U02 determined from the present experiments
compared with the reported etch rate of PU02 in a CFd02 RF plasma
(Martz et. al., 1991) operated at 50 W and 26.7 Pa, as shown in Figure 53 (see
Chapter 4 for definitions). Unlike the detailed U02 etch data, the PU02
measurements are only available at a single power and pressure, thus
significantly limiting the ability to compare the results. A t.h = 4 value for U02
provides a reasonable comparison to the PuO* etch rate since NR will have
nearly reached the asymptotic value, NR,~~X. At 50 W absorbed power, the
average etch rate at the end-point was 0.108 pm/min for UO* and 0.030 pm/min
for PU02, a factor of 3.6 times slower for PU02.
Experimental differences may account for some or all the differences
between the U02 and the reported PuOZ etch rates: pressure (17 vs. 26.7 Pa),
etching gas (NF3 vs. CF~02), and uncertainties in the gravimetric method the
authors used. Pressure differences can lead to significant etch rate differences
as found in U02 etching, and similar results are expected for PU02. The gas
used could be a significant factor because NF3 dissociates 10 to 25 times faster
than CF402, increasing the available F atom radicals responsible for etching
96
(Ianno et. al., 1981). The reported gravirnetric technique for measuring mass
loss was prone to considerable error (Martz et. al., 1991) which would be
improved if the quantification methods developed here were applied. These
factors taken together suggest that the etch rate differences may be due more to
experimental conditions than to the differences in chemistry.
10
1
0.1
0.01
1 0 ExperimentalData. 35s ths45 th=o
U0217 Pa for U02
826.7 Pa for PuOZ
● PU02
Io 50 100 150 200
Power
Figure 53. Average Etch Rate ~ of U02 Compared with PUOZ
The vapor pressure of PuFG at 298 K is 14 kPa (Weinstock et. al., 1959),
comparable to 24 kPa for UF6 (Figure 54). Consequently, at the pressures of the
experiment, the PuF6 will desorb from the surface. The intermediate compounds
PUFIA are all solids at room temperature (Katz et. al., 1986 (a)), comparable to
the tJF2.5 intermediates, and will remain on the surface in the solid phase.
Although there is some evidence that PuF5 exists, it had not been isolated and
thermodynamic data was not available for this compound.
The thermodynamics of the PU02 and Pu fluorides (Figure 55) are similar
to that of the U02 system (Figure 49), suggesting surface chemistry similar to
that of U02. The major difference with the U kinetics is the reaction from PuF4 to
97
PuF6, where an equilibrium condition exists as suggested by the neariy equal ~
values for the two compounds. The equilibrium rate constant, ~, as calculated
from the favorab)e Gibbs reaction energy of -95.6 kJ/mole (Aiberty and Silbey,
1997) for reacting PuF4 with two absorbed F atoms high}y favors the reaction to
PuFEi as indicated by the large ~
reactions of PU02 with adsorbed
PuFEi in an RF plasma system.
Kp = e-% =5.7X1016 .
value in Equation (32). Consequently, etching
plasma F atoms are also expected to go to
(32)
The above results suggest that PUOZ etching rates should be comparable
to that of UOZ, with similar constraints on etching due to the self-limiting etching
process and the formation of non-volatile compounds. The differences in
reported etch rates between PUOZ and UOZ etching may be due entirely to
experimental differences. Furthermore, increasing power and pressure will most
likely increase PUOZ etching, much like U02 etching increases with power and
pressure.
98
106
105
104
1)
2)Lange & Forker, p. 1450, 1967.Weinstock et. al., 1959.
103250 270 290 310 330
Temperature (K)
Figure 54. Vapor Pressure of PuF6 and UFGCompared.
350
Pu Uo
T=298Ku UF
nPU02 \
•1U02
UOF2PuFA+ 2F e W6,
G~ = -95.6 kJ/mo! UF4UF5
‘G, Estimated PuF~ Not Observed-2500 ‘
200 240 280 320 360
Molecular Weight (g/mole)
Figure 55. Plutonium Compound Gibbs Free Energy of Formation.
99
CHAPTER 7. SUMMARY AND CONCLUSIONS
A series of single effect, RF plasma, glow discharge experiments were
conducted using NF3 gas to decontaminate depleted uranium dioxide from
stainless-steel substrates. In the experiments, the plasma absorbed power was
varied from 25 to 210 W, the pressure from 10.8 to 40 Pa, and the NF3 flow rate
from 3 to 18.5 SCCM. Depleted U02 samples each containing 129.4 Bq were
prepared from 100 microliter solutions of uranyl nitrate hexahydrate solution.
Quantification of the remaining uranium foilowing plasma immersion was
performed with liquid scintillation counting with alpha/beta discrimination,
spectral counting was adjusted by gaussian and first order polynomial fits, and
the resulting measurement uncertainties were A 2~0.
Results demonstrated that U02 can be completely removed from
stainless-steel substrates after several minutes processing at under 100 W with
initial etch rates ranging from 0.2 to 7.4 pm/min. At 180 W and 32.7 Pa gas
pressure, over 99% of all U02 was removed in just 17 minutes. The data showed
that etching increased with power in the range of 10.8 to 40 Pa. A pressure
effect was also noted below 50 W in which the etching increased up to a
maximum pressure, -23 Pa, then decreased with further increases in pressure.
The etching process was self-limiting and decreased exponentially with
immersion time to the end point, which is defined as the point where either all
UOZ is removed or the etch rate becomes zero. At both low and high pressure,
and low power (< 50 W), the end point was reached before all U02 was
completely removed.
A computer simulation, CHEMKiN, was applied to predict the NF3 plasma
species in these experiments. The code was validated by comparison with
experimental mass spectroscopy measurements of NF3 plasma etching of
silicon. The code predictions were within t 570 of the measured species
concentrations. The code predictions of plasma species in the U02 experiments
were only applicable at 17Pa where the plasma volume filled the entire test
100
chamber and
species.
F atom
intensity variations suggested adequate mixing of the plasma
raditils are the primary etchant species, diffusing from the bulk
plasma to the surface, adsorbing to the surface, and reacting with UOZ to form a
volatile UF6, which desorbs into the gas phase to be pumped away. Ions created
in the plasma were too low in concentration to have a major effect on etching.
However, because they are accelerated through the plasma sheath, they can
deliver considerable energy to break chemical bonds on the U02 surface and
thereby enhance the primary etching process.
A primary etch mechanism, based on thermodynamic arguments, was
identified in which F atom radicals react with U02 to form non-volatile products,
including uranium fluorides, UF2.5, and uranium o@uorides, U02F, U02F2,
UOF3, and UOFg over the U02 surface. Successive reactions with adsorbed F
atoms lead to UF6. The UF6 has a vapor pressure of 24 kPa, well above the
operating pressure at the gas temperature (-300 K) of the plasma, and, as a
consequence, desorbs into the gas phase. The other intermediate fluonides and
oxyfluorides are solids and remain on the surface, eventually slowing or blocking
the etch reaction as they accumulate. When power was too low, the reactions
completely stopped before all detectable U02 could be fully etched. The
accumulation of desorbing UF6 near the U02 surface reduces the diffusion
coefficient of F atom radicals in the sheath, further slowing the reaction
processes and hence the etch rate.
The PU02 experimental etch rate data were comparable to the U02 etch
rates measured in these experiments. The chemist~ and thermodynamics of
PU02 have many parallels
temperature (24 vs. 14 kPa)
many intermediate species.
with U02: similar vapor pressures at room
and favorable Gibbs free energy of formation of
Some of the uncertainties include incomplete
knowledge of the thermodynamics, no counterpart to UF5, and an apparent
equilibrium condition between PuF4 and PuF6 not observed in the uranium
101
system. The U02 etch results indicate improving etch rates with power and
pressure, and a similar effect would be expected with PuOZ. The’ favorable
parallels suggest that further experimentation with PUOZ etching should be
continued to quantify the physics of the processes over the power and pressure
parameter space.
These results demonstrated that the RF plasma glow discharge is a viable
method for decontaminating UOZ from stainiess steel substrates. The results
further show that the RF plasma glow discharge has potential application to
transuranic waste, including Pu and PuOZ.
102
CHAPTER 8. RECOMMENDATIONS FOR CONTINUED WORK
8.1. Experiments with Depleted U02
Early experiments with depleted UOP were conducted to determine the
ability of an NF3 RF plasma to etch radionuclides from the interior of aluminum
pipes. The preliminary results (Veilleux et. al., 1997) indicated that pipes with an
L/D (length to diameter) of 15.7 showed that contaminant removal exceeded
99.9Y0. However, these results were prelimina~, based on analysis at 50 W and
17 Pa only, and used quantification methods prone to considerable error, such
as surface alpha probes and gravimetric methods. Therefore, there is a need to
repeat these experiments with the quantification methods developed in the
present experiments using varying L/D pipes to quantify the effect of diameter on
the etch rate, as well as power and pressure effects.
The present experiments were conducted with an NFs plasma. While NFs
dissociates 10 to 25 times faster than CFd02 gas, NF3 is considerably more
expensive than CF~02. Therefore, there would be utility in comparing directly
the etch rates in different gases.
Experimental quantification of plasma and surface species would provide
information regarding all reactant species. Mass spectrometric sampling inside
the plasma coupied with actinometry would provide valuabie species
identification and quantity.
A smaii number of early experiments were conducted with high specific
activity 233U to determine monoiayer thickness effects on the decontamination
rate. It was found that the iast layer of U02 was extremeiy d’tilcuit to remove,
and is possibiy associated with the strong chemical bonds that can form between
uranium and the metaiiic eiements of stainiess steei, especially nickei. However,
not enough experiments were conducted provide a good statistical base.
Experiments with varying power and pressure are needed to better quantify the
preliminary resuits.
103
8.2. Recovery system
Early experiments were conducted to determine the ability of the recovery
system cold trap to capture the UF6 removed from surfaces and to quantify the
results. These preliminary resuits suggested that at least 5070 of the initial U02
was captured, but the data base is small and the statistics poor. In addition, the
quantification methods used at the time were not good enough to obtain
statistically reliabie results. Capture of effluent gases in the recovery system and
species quantification by Fourier transformed infrared (FTIR) spectroscopy will
provide a method of performing a mass balance of etched species, and provide
a means of determining if UFG is deposited along recovery system components
or remains in the gas phase.
8.3. In-Situ Measurements
Measurements of temperature of the substrate as a function of power and
pressure would provide significantly improved kinetics data for the reactions to
better determine the activation energy of the reactions. In tumi this data would
be very useful in designing future etching systems and to assess scale-up of the
vacuum chamber and recovery system. In the current experiments, this was not
possible because the proper equipment was not available to assure safe
operation.
8.4. Pu & PUOZ work
The early experiments conducted with PUOZ and Pu metal were based on
essentially a single data point for power and pressure. A range of experiments
are needed to better quantify the etch rate over the parameter space of power
and pressure, much like was done with the U02 experiments. Fairly large
quantities of PU02 and Pu will be required since bulk metal etch rates are
needed, not just monolayer thickness. Therefore, these experiments will need to
be performed in a Nuclear Class II category facility.
104
APPENDICES
~pendix A Properties ;●...............................0.......................*......................... 106
Appendix B. Experimental Details ................................................................. ‘1’t5
Appendix C. Data ............................................................................................ 138
Appendix D. CHEMKIN ............ ...................=................................................... 150
Appendix E. Analysis ..................................................................................... 158
105
A’1.
were:
1958,
AZ.
APPENDIX A. PROPERTIES
Physical Properties
The physical properties are tabulated in Table A-1 and the data sources
Alberty & Silbey 1997, Katz et. al. 1986, Shackelford et. al. 1994, Pearson
and Lide 1993.
Thermodynamic Properties
The thermodynamic properties of select elements and compounds are
tabulated in Table A-2. The values are at standard state (1 bar, 298.15K).
References are to: Aiberty and Silbey, 1997; Antony et. al., 1995; Cacace et.
al., 1995; Hildenbrand and Lau, 1991; Hinz et. al., 1980; Katz et. al., 1986 (b);
Lide, 1993; Mallard, 1997; Venugopal et. al., 1992; and; Wagman et. al.,
1982.
A.3. Enthalpy and Gibbs Energy Of Reaction
The Enthalpy, H, and Gibbs, G, reaction energy are determined by
summing the respective formation energies of products and reactants according
to Equation (A-1) or (A-2). Here, v, is the stoichiometric coefficient of the species
j and is positive for products and negative for reactants. Hj is the enthalpy of
formation for species j, Gj is the Gibbs energy of formation for species j.
Elements have a zero Gibbs energy of formation at all temperatures. Because
the corrections for temperature and pressure are small in the range of the
experiments (Appendix E), Gibbs energies of formation at standard state are
given.
G, =~v,G, (A-1 )
HR = ~V,H1 (A-2)J
The reaction enthaipy and Gibbs energy in kJ/mole are summarized in
Table A-3 for reactions with possible uranium compounds that can form from
U02. In general, reactions with up to three adsorbed F atoms were aliowed and
106
where more are shown, such a reaction is a summary reaction incorporating
several intermediate steps. A negative enthalpy indicates an exotherrnic
reaction while a positive value indicates an endothermic reaction. A negative
Gibbs reaction energy indicates that the reaction is thermodynamically possible
but doesn’t say anything about the rate of reaction. A positive Gibbs reaction
energy indicates that the reaction is not thermodynamically favorable. The
reaction could still occur, but energy at least equal to GR is required. The energy
may be available from previous reactions, if the reaction in question is a
successive reaction.
A4. Properties Of Stainless Steel
The composition of stainless steel is taken from Lide 1994, p. 12-27 and
tabulated in Tabie A-4.
lL5. Nuclear Properties
The nuclear properties of seiect isotopes are tabuiated in Tabie A-5. The
data is taken from Shieien 1992 and Waiker et. ai. 1989. A description of the
iattice types maybe found a text on Soiid State Physics (e.g, Dekker, 1963).
107
Table A-1. Physical Properties Of Select Compounds
Item
AhAlAr
ECr-alpha
F
F2
FezNFezOsFe-alphaFeF2FeFsFeO
l===H20 (gas)HzO(liquid)HeHF (gas)NN2
N2F
N2F2
l====NFNF2NF3PU(s)-AlphaPuF3(S)PuF4(S)PuF6(g)
MW (g/mol)
28.t27.C39,$
52.C19.[38.(
125,7159,755.t93,(
112.671.s18.[18.(4.[
20.(14.(28.(47.(66.[
104.(20.:33.(52.(71.(
242,1296,’315.:353.(
Density MP (C) BP (C) LatticeType Latticea Latticeb Latticec 1St Atomic Electron Bond(g/cm3) (A) (A) (A) Ionization Radius(pm) Affinity(eV) Dissociation
Potential Energy(eV) (kJ/mol)
1.16E-03 3.392.70 660.4 2467.0 cubic 4.04 0.44
15.8 65.9cubic 2.88 0.67
1,69E-03 -219.6 -188.1 17,4 39.6 3.415.7 2.96 157.0
6.35 200.05.27 1565.0 hex-R 5,03
bcc 2.87 7.9 122,74.09 1000.03.52 1000.0 4.25.70 1369.0 1.49
5.14E-03 0.0 100.01.00 0.0 100.0
24.6 29.1-83.1 19.5
14.5 52.11.25E-03 -209.9 -195.6 15.6 949.6
12.811.9 87.921.6 35.412.0 261.911.6 145.6 1.7 275.0
2.96E-03 -206.6 -128.8 13,0 156.8 238.319.86 641.0 3232.0 monoclinic 6.18 4,62 10,96 176.49.32 1425.0 trigonal(LaF3) 7.09 7.257.05 1037.0 monoclinic(C2/c) 12.60 10,57 6.28
50.8 62.3 orthorhombic(Prima) 9.95 9.02 5.26●
108
Table A-1. Physical Properties Of Select Compounds
Item MW (g/mol) Density MP(C) BP(C) LatticeType Latticea Latticeb Latticec 1S! Atomic Electron Bond(g/cm3) (A) (A) (A) Ionization Radius(pm) Affinity(eV) Dissociation
Potential Energy(eV) (kJ/mol)
PuF6(S) 353.0 4.86 50.8 62.3 orthorhombic(Prima) 9.95 9.02 5.26PU02(s) 276.0 11.46 fcc(Fm3m) 5.40Si 28.1 2.33 1410.0 2355.0cubic(Fd3m),diamond 5.43 5.43 5,43 1.39Ss (304) 54.9 7.90 1425.0 /-
U (gas) 238,0U (s-alpha) 238.0 19.05 1132.3 3616.0orihorhombic 2,85 5.86 4,95 4.0 177.5Uo860212 10.00 fctetragonal 5.36 5,55UZOS 8.35 orthorhombic 8.29 31.71 6.73UsFeOIO orthorhombic 6.51 7.53 16.14U308 842.1 8.41 trigonal 6.81 4,14U308(s) 642.1 8.39 1150.0 orthorhombic(C2mm) 6.72 11.96 4.15U6F13 17,70 tetragonalbc 10.31 5.24UF3(S) 295.0 8,95 1140.0 trigonal 7.18 7.35 1.5UF4(S) 314.0 673 960.0 monoclinic(C2/c) 12,60 10.79 8.37 1.7UFS(s-alpha) 333.0 5.81 400.0 tetragonal(14/m) 6.51 4,46 5.9 299.1UFS(s-beta) 333.0 6.47 tetragonal(142d) 11.46 5.20 5.9UF6(9) 352.0 1.90 64.0 56.2 14.4
UFg(S) 352.0 5.06 64.0 56,2 orthorhombic(Prima) 9.90 6.96 5.22 14.4UFez 13.21 fcc(Fm3m) 7.06Uo 14.10 BI (Fm3M) 4.93U02 (cr) 270.0 !0,96 2875.0 fcc(Fm3m) 5.47UOZ(NOS)Z*2HZ0 430.1U02(N03)2*6H20 502.1 2.81 60.2 116.0orthorhombic(cmc2) 13.06 6.02 11.45LJ0233 pseudocubic 5.41UOZFZ 346.0 6.37 rhombohedral(R3m) 5.76UOS(Beta) 7.15 orthorhombic 13.01 10,72 7.51U03 (s) 286,0 7.80 650.0 orthorhombic(Fddd) 9.81 19.93 9.71
109
Table A-2 Thermodynamic Properties Of Select Species
species State H: Gf” s“ Cp” RefkJmoi_l kJmol-1 JK1morl J K1 morl
AIF 9 -258.2 -283.7 215.0 31.9 Lidep. 5-5
PJF2 ,9 -694.5 -704.4 264.2 45.9 JANAF,ref. 53
AIF3 c -1510.4 -1431.1 66.5 75.1 JANAF,ref.53
AIF3 9 -1209.3 -1192.7 276.7 62.2 JANAF,ref.53
F 9 79.4 62.3 158.8 22.7 Lide1993
F- ~9 -255.4 -242.6 I Wagmanet. al. 1982F+ 19 1766.4 1678.1 Wagmanet. al. 1982
F2 19 0.0 0.0 202.8 31.3 Lide1993
F2(ads) ads 6.6 Lide1993
Ffi 9 24.7 41.9 247.41 43.3 Wagmanet. al. 1982
F2& 9 18.0 17.1 I Wagmanet. al. 1982
Fe c 0.0 0.0 27.3 25.1lWagmanet. al. 1982
Fe203 c -824.2 -742.2 87.4 103.9
FeF2 c -711.3 -668.6 87.0 68.1 Wagmanet. al. 1982
FeO(Wustite) c -266.3 -245.1 57.5 48.1 Wagmanet. al. 1982
FO 9 109.0 105.0 216.8 30.5 Wagmanet. al. 1982
H@ 9 -241.8 -228.6 188.8 33.6 Lide1993
H20 I -285.8 -237.1 70.0 75.3 Ltie 1993
HF 9 -273.3 -275.4 173.8 Licie1993
N 9 472.7 455.5 153.3 20.8 Lide1993
N2 9 0.0 0.0 191.6 29.1 L* 1993
N2F 9 1214.2 1153.5 Cacaceet. al. 1995
IN2F2 66.0 Wagmanet. al.1982
N2F2 g (trans) 82.0 77.9 Wagmanet. al. 1982
N2F4 $1 -6.4 79.9 301.2 79.2Lide1993p.514
N3 9 413.0 345.8 225.5 40.7ChemkinPolynomialFfi
iNF 9 248.9 164.7 2?5.3 30.4 ?dlailafd1997,Lide1993
INF2 9 43.1 57.8 249.4 41.0 Lide1993
NF3 9 -132.1 -90.6 260.8 53.4 Lde 1993
NiUQ c -2556.0 -2616.5 202.9 Katzet. al. 1986
NiU3010 c -3942.0 4348.7 358.0 Katzet. al. 1986
,0 19 249.2 231.7 161.1 21.9 tide 1993
0- 9 101.6 96.5 Wagmanet. al. 1982
p+ 9 1568.8 1490.4 Wagmanet. al. 1982
!02 9 0.0 0.0 205.1 29.4 Alberty.and Silbey1997
103 9 142.7 163.2 238.9 39.2 Albetty.and Silbey1997
~Pu-a c 0.0 0.0 54.5 31.2 Katzet. al. 1986
\PuF 9 -116.0 -190.5 250.0 33.0 Katzet. al. 1986
1PuF2 9 -615.0 -703.6 297.0 51.0 Katzet.al.1987
PuF3 9 -1163.0 -1158.0 336.0 72.0 Katzet. al. 1987
lPuF3 c -1585.7 -1516.4 126.1 92.6 Katzet. al. 1986~PuF4 9 -1443.0 -1416.0 368.0 Katzet. al. 1987
110
Table A-2 Thermodynamic Properties Of Select Species
species state H: G“ s“ h“ Refk.Jmor’ kJ mol-1 JK1morl J K1 morl
PuF4 c -1846.0 -1753.0 147.3 116.2Katzet.al. 1986t
PUF6 c -1662.0 -1728.0 222.0 167.0Katzet. al. 1988
PUF6 9 -1813.0 -1724.0 369.1 129.4 Katzet. al. 1986
PU02 c -1056.2 -998.0 66.1 66.3 Katzet. al. 1966
PuOF c -1139.0 -1082.1 92.0 Katzet.al. 1987
Ss (304) s 0.0 0.0 25.2 Katzet.al. 1966
u c,a 0.0 0.0 50.2 27.7 Katzet.al. 1986
u 9 536.0 491.0 199.7 23.7 Kak et.al. 1987
U2N3 C,p -736.0 -755.4 65 54.2Katzet.al.1966
UF 9 42.0 -72.0 252.0 37.9 Katzet. al. 1986
UF2 9 -53?.0 $25.2 316.0 56.0 Katzet. al. 1986
UF3 9 -1059.0 -1006.1 Katzet. al. 1986
UF3 c -1502.0 -1433.0 123.4 95.1 Katzet.al. 1986
UF4 9 -1599.0 -1519.1 Katzet. al. 1986
UF4 c -1910.0 -1820.0 151.7 116.0Katzet. ai. 1986
UF5 9 -1937.0 -1887.0 386.0 111.0 Katzet. al. 1986
UF5 c, a -2075.0 -1969.0 200.0 132.0 Katzet.al. 1986
UF6 9 -2147.4 -2063.8 377.8 129.6 Katzet. al. 1986
UF6(s) c -2197.0 -2068.6 227.8 166.8Katzet.al. 4986
UFS2 c -32.2 Katzet. al. 1986
UFe2 c -19.9 [Antonyet al 1995
UN c -290.8 -266 62.631 47.8 Katz;Venugopalet al 1992
UNQ c -37.91 Antonyetal1995
uNi5 c -39.5 Antonyet al 1995
Uo 9 21.0 20.0 Wagmanet.al. 1982
U02 c -1085.0 -1031.8 77.0 63.6 Katzet.al. 1986
U02F 19 -996.0 -1094.1 329.0 68.0 Katzet. al. 1986
U02F c -1298.5 -1396.6 329.0 68.0 Katzet.al. 1986
U02F2 c -1653.5 -1557.3 135.6 103.2Katzet. al. 1986
U02F2 9 -1351.0 -1246.9 -349.0 86.0 Katzet. al. 1986
U02F3 c Assumesameas U02F2
U03 c,a -1217.5 -1140.6 99.4 81.8 Katzet,al. 1986
UOF 9 -544.0 -516.8 Katzet. al. 1986
UOF2 c -1505.0 -1434.0 119.0 Katz et. al. 1986UOF2 9 -1117.0 -1217.2 336.0 79.0 Katz et. al. 1986
9 -1510.0 -1615.2 353.0 89.o Katz et. al, 1986c -1924.6 -1828.4 Katz et. al, 1986
‘ Valuenotgiveninref.,assumesvalueis0.95 timesenthalpy.- Valuenotgiveninref.,determinefromH andCp.- Valuenotgiveninref.,assumedequalto gas phasevalueminusdifferenceingastosolidvalueforU02F2.
111
Table A-3. Enthalpy and Gibbs Energy of Reaction for F Atom Reactions withUranium Fluorides and @41uondes
Reaction HR GRkJ mol-’ kJ mol-1
F+ U+IJF2F + lJF + lJl=3
F+ UF--+ UF2F + UF2 + UF32F + UF3~ UF5F + UF3 + UF42F + UF4 ~ UF6F + UF4 -+ UF5F + UF5 -+ UFe(s)F+ U()~UF+OF+ IJO + F+lJ +0F+lJOalJOFF+ UOF+UF2+(32F + UOF ~ lJOF~F + UOF + U0F22F+lJOFalJF3+oF+ UOFZ~UF3+02F + UOF2 ~ UOF42F + UOF2 ● UF4 + OF + UOF2 ~ UOF3F+ UOF2+UF2+O+FF + UOF3 -3 UOF4F + UOF3 ●UF4 + OF + UOF4 ~UF5 + OF+ UOF4+UF4+F+02F + UOF4 ~UF6 + O2F + U02 + U02F22F + UOZ aUFZ + OzF+ U02+UOF+0F -I-U02 ~U02FF+ U02+UF+02F + U02F aUOFZ + OF + U02F ●UOZFZF + U02F +UFZ + 022F + U02F ~UF3 + Oz2F + U02F aUOF3 + OF + U02F2 -+ UF3 + 02F + U02F2 + UOF3 + O
F+ U02F2+UOF2+O+F2F + U02F2 + UF4 + 02
-121.4 -134.3-1618.8
-568.4-1050.4
-731.8-487.4-396.2-244.0-201.4106.8228.0
-644.4182.8
-1124.8-1040.4
-867.6172.8
-578.4-314.6
-84.41223.2-494.0-230.2
19.4263.8
-182.0-727.3395.2710.8
-292.9963.6-36.7
-434.4688.1
-362.3-121.1
72.0313.0398.0
-415.3
-1485.6-615.5-870.1-660.6-449.3-368.4-211.0-161.9
77.5212.0
-599.161.0
-1223.0-979.5-809.1170.4
-519.0-278.9-243.51040.5-275.4
-35.428.8
240.1-333.1-650.1282.0684.4
-427.1897.5132.0
-223.0709.1
-161.0-111.6
62.0248.0355.0
-387.3
112
Table A-3. Enthalpy and Gibbs Energy of Reaction for F Atom Reactions with,, Uranium Fluorides and Oxyfiuorides
Reaction HR GRkJ mol-l kJ mol-1
2F + U02F2 ●UOF4 + O -180.7 -164.0
Table A-4 Composition Of Stainiess Steel
M Composition Composition Totai Per 1000(g/moi) (%) (304) 9
c 12.0 0.08!/0 0.0008 0.o’1 0.17Mn 54.9 2.00% 0.0200 1.10 19.95P 31.0 0.0570 0.0005 0.01 0.25s 32.1 0.30% 0.0003 0.01 0.17Si 28.1 1.00?40 0.0100 0.28 5.10Cr 52.0 18 to 20?40 0.2000 10.40 188.84Ni 58.7 8 to 12?40 0.1200 7.04 127.89Fe 55.8 Remainder 0.6485 36.21 657.61TOTAL 1 55.07 1000.00
143
Table A-5 Nuclear Properties Of Select Isotopes
Isotope MW (g/mol) Half-L& Max Alpha Max Beta Max(yr) Energy Energy Electron (B:ig)
(MeV) (MeV) Energy(MeV)
‘3Ac 225.02 0.0274 2.15E+1814c
2tiCm‘lFr%d2wPa2’2P02’3P02’6P0*PU239PU
“Ra‘ORn‘kh‘%h
‘u‘u‘u‘u
14.00
244.06221.01147.92
234.04211.99212.99216.00238.05239.05224.02220.01
228.03234.04232.04233.04234.04238.05
573018.11
9.1 E-0675
2.2E-069.6E-091.3E-1 14.8E-09
87.7424065
0.009971.7E-06
1.9130.06603
721.59E+052.47E+054.47E+09
5.81
3.18
5.505.16
5.324.824.774.20
0.16 1.65E+14
2.99E+156.56E+211.19E+15
2.29 2.54E+226.48E+244.76E+27
1.29E+25
6.34E+142.30E+125.92E+183.45E+223.03E+16
0.19 0.0910 8.56E+170.1086 7.92E+140.0767 3.57E+110.1004 2.29E+110.0895 1.24E+07
114
APPENDIX B. EXPERIMENTAL DETAILS
B.f. Equipment Diagram& Parts List
A detailed parts diagram of the recovery system combined with a block
diagram of the plasma reactor region is depicted in Figure B-2. The length, width,
and height are the nominal internal dimensions of the chamber reactor. The
chamber volume, Vc, includes volumes of protuberances of the interior of the
plasma chamber and was measured to an accuracy of 1 cm. The surface area
is the internal surface areas of all metallic protuberances and each dimension
was measured to an accuracy of 1 cm.
The recovery system volume, VR = 0.0071 m3, was determined by
expanding a quantity of gas at pressure pc from the plasma chamber (volume
V=) into the combined voiumes (VcR = VC + VR) and pressure pcF7and using
Boyle’s law, pcVc = pcRVcR. Since both pressures were measured, Vc is known,
the moles of gas remains constant before and after expansion, and temperature
remains constant, VR is calculated from:
~R _ Pcvc y_— . cPCR
(B-1)
The dimensions of the powered electrode was determined from the
surface area of a 2“ diameter stainless steel hoider on which the samples were
placed. The RF antenna is shown in Figure B-1.
Fume hood linear flow rate was obtained from design specifications of the
fume hood with the window open as specified on the hood. Room air flow was
similarly obtained from building design information for exhaust air, divided by
dimensions of the room in which the experimental chamber is located.
Dimensional characteristics of the plasma system are summarized in
Table B-1. Table B-2 is a detailed parts iist of the system.
115
Table B-1. Characteristics Of Plasma System.
Plasma Reactor Internal DimensionsLength (m), width (m), height (m) 0.047x0.047x0.049Volume (m3) 0.125Surface Area (m*) 1.623
Recovery System (mJ) 71XIO+Powered Electrode (m*) 20.3xI 04Fume Hood (ft rein-’) 145Room Air Flow (ft3 rein-’) 47500
RF Plasma Antenna
r
IStainlessSteel Rod1.50mm thi*-
PianchetteHolder
i
‘6cm —
Figure B-1. RF Antenna.
116
Plasma Chamber & Recovery System.—
‘\
-10--.—
Oa\
M’I’ _
A-------~5?-”- ~ :
m1=
“J”’” -
.. . .—---- ~w,*
““”iv)I L3Epc-Y--- “
1-+-g&?y#&=--+- ~,_-.—————
.-
1- F-
—. ———.. ---1l\ , ,..., “Od.-,’w0F.Jq -y ~ ,
I “------’” l_+-,_.,F_ pm 1----- ——.-——7-
F_—-
?F,
m. --— ,~
*S
/Fume Hood
Figure B-2. Plasma Reactor and Recovery System.
117....-
Table B-2. Plasma System Parts List.
!plasmaSyatem_tfa&Meter i , 1b% system hmpmtes a detailedpa~ &t of the recovery system and rrta@ ~nts of fhqplasrra chanber.
3
~Al parts are ~ Corporationunless otherwise specified II{
i
\ ftem : page S PN fXmcriptiOn*:;
1 84 4030028tww,90deg 1. ________________ .. .*: 218 420002~BoredFlangew/2tappedholes 1;2a:
—. -..——1/4”toIL?’adaptor,SS 1;
3’—.-
:I@proB.%HValve If4: 122BA-00010B2B Baratrco Ressure Transducer, Type122A/10mTom 1!—.-= .
MS FtRCIC BaratronI%ess (hntrciier~!-.
5: 195 W)OOl 6utterftyVtie ,.
6a 84 403002 Eb/ ,90 dq 1:~.
50 140007 DoubleSided Flanoe.blank ,:
21. .—
66—
404002 Tee 1+
22 88 730003 %ge adaptor D31seai-wo ,:—.—23, .–.
80 720003‘Mf Nppk?,KF—.
1:——— .. —. —.. ——.. .—... ———... -—
25 Dcwnx, 1“ lDforCaldTrap.l!Ybng, we&dtoitern20 ;:—...— -.—.-.. ... . .———-—-.. -...-. -..—.- ......... .. -——
26 122BA-00010625 BaratronRessure Transducer, Typel 22A/1000Torr-’
1,...——.—.... . . . ..—. .-. =--...... . . . . . . . . . . .. . . . . .. .. . . ._, __ ,---- .—_...—._“,.,..... .. . . .... . . .. .._Ns KF-GIBWS l-channel PWdnital readout 1:...—-----.-...._.. __. _..—.—.-....—-.—.-—.._.. ... .. ... . . - .. ..—.. .—.__._,._ . ...______ .-..—.. . ....—._._4 _________ .__.
27’ 1/4”to 1/2”adaptor, SS 1—----------- . . ..— -—-. . . ... .. . ..-..---—-— .——...——28
. . ..---. —..—— -218 -__._4~~I~-.,*ed ~n9e w ~ ~pped h~s ____–– —-...-..1:
_.- ——.. ____29 tWpro SS-4H Vatue 1
30--—-—— .—-.—
195 360001’ButterfivVatve 1-j
--..———--.—.31a 62 402002 “N@e - —
;1;
33 199 431006 hblacular Sieve, CarbonTrap 1:—.34
——58 730003 FbrIw Adaptor, ti to NWO 1:
—.—— . ..- —... —- —- ——— —.35 175 310074; KF Rght Angk Valve 1
———- ——-—. ~36
—.—.—- ...-213 441117 K150 .SSflexibkehose 2.
>—.—--.———— .“... . ..—.. —. —- --- —..—..———.-—. ..--z—.37 GRX34ThermistorGauge Station 1.
—.— .——. -.. ——.-. ——Ns: GT340A ThermistorGauge 1,——36 84 724002 Tee. W
—.~
39: ~cuum purqz Akatel 1’—.. —....—. —.. .—-—-——— ——--—— -..—
+_.— ——. — ——-900 69 __,_4470~_IGW CJoss,8“ -l =* ________ 1’
901 — RF20 %wer .%p~, 13.56 M-&, 2000W, 15A 1
902——— —--.SA2080 li?athkitAntenna Tuner
—— 1:.—.-.—.—-—_—
903.———-. —-.— .— . -—. —,.-— — ..-—..--.. .. ——. -—. ....—.-.—W150 Leyboktlk)ots Blower 1. . . ,. .. . . . .. . . . ,_...-- .. . . . ___ . . . . .. .. ... . . . . . .. . . ~____ ___ .._. ..._..\
903 D30A hvbold Forewrro 1
118
B.2. Stainless-Steel Pianchettes
Twelve stainless steel type 304 substrate planchettes were machined for
holding the depleted uranyl nitrate solution and for conversion to U02. The
substrates were shaped in cylinders with an inner diameter of 1.007 cm, an
interior depth of O.t 46 cm, and a mass of 0.5370 g (Table B-3). The average
inner diameter was 1.007 cm and inner depth 0.146 cm.
Table B-3. Stainless Steel Type 304 Sample Substrates
Planchette Inner Mass (g) Height depth ThicknessNumber Diameter (mm) (mm) bottom
(mm) (mm)1 10.07 0.5389 1.82 1.54 0.282 10.08 0.5398 1.81 ‘i .43 0.383 10.05 .0.5348 1.82 1.47 0.354 10.07 0.5387 1.80 1.46 0.345 10.07 0.5401 1.82 1.46 0.366 10.03 0.5366 1.82 1.57 0.257 10.09 0.5334 1.80 1.56 0.248 10.03 0.5362 1.81 1.47 0.349 10.07 0.5365 1.81 1.51 0.3010 10.09 0.5387 1.82 1.41 0.4111 10.08 0.5347 1.82 1.35 0.4712 10.06 0.5388 1.81 1.32 0.49
Average 10.07 0.5373 1.81 1.46 0.35Average Deviation 0.02 0.0019 0.01 0.06 0.06
The average internal surface area of the pianchette is 0.796 * 0.003 cm2
is based on the average diameter, 1.007 Y 0.003 cm.
Following the many experiments, planchette number 1 was again
characterized to account for changes in its dimensions for the UOZ density
determination. Its empty weight had increased to 0.5867 g with an inner depth of
1.34 mm. Its inner diameter had not changed.
8.3. Pressure & Flow Characteristics
The plasma reactor is a cubic aluminum chamber whose volume is
approximately 0.125 m3. It has an inlet gas line, an outlet line to the recovery
119
system, and power-input leads. System pressure is affected by the gas flow rate
and power applied. The outlet conditions are fixed by the recovery system
pumping characteristics: This section presents details of the flow renditions
inside the reactor and recovery system, description of the mass continuity
equations, the calibration of the inlet flow rotameter, the recovery system pump
characteristics, the pressure in the reactor, and finally the reactor pressure and
effect of power on the pressure.
B.3. 1. Continuity Equation
Characterization of the plasma reactor and recovery system in terms of
pressure and flow of gaseous products is determined from the mole balance (or
mass balance) equation of continuity. Consider a chamber whose volume, V,
contains a gas at a pressure, p, with an inlet flow of FOmoles of gas per unit time
and an outlet flow of F moles per unit time. The applied RF power causes some
of the gas to dissociate and others to recombine for a net molar production rate,
G. The mole balance then becomes
(B-2)
The partial derivative is the accumulation of moles, q, in the chamber over
time, t. This section describes conditions for the gas inlet properties, the exhaust
properties, and the plasma reactor characteristics.
B.3.2. inlet Conditions (Rofameter Calibration)
The rotameter, Omega model S04-N082-03, was calibrated by bleeding
NFs gas into the plasma reactor at constant rotameter settings and inlet pressure
of 20 psig. All valves between the NFs gas supply and the vacuum chamber
were fully opened, except the rotameter valve which was adjusted as necessary
to maintain the desired flow, during these experiments. By measuring the
pressure increase with time in the reactor, the fiow parameters may be
determined. With the outlet valve to the pump closed, F = O in Equation (B-2),
and pressure builds up in the chamber as gas flows in. With no power, the temn
G is also zero and hence the mole balance equation becomes
120
(B-3)
~ Applying the ideal gas law (pV = qRT) and differentiating q leads 10
V dpFO= ——
RT dt(B-4)
Because the temperature rise in the reactor is near room temperature for
the conditions of this experiment, T is taken to be constant. R is the gas
constant (8.3144 J mol-l tC1). Since the number of moles is the ratio of mass, m,
of gas to its molecular weight, M, the mass flow rate becomes
dm W dp—=— — (B-5)dt RT dt
To determine the volumetric flow rate, consider a smali volume, Vf,
containing mass m of material and calculate how fast this volume passes a given
plane. Since the same gas is used, its density is p which is constant over time
and its mass is the density times Vf. Hence, from Equation (B-5),
dV1 .l?Mdp=Vdp—— —— (B-6)T pRT dt p dt
An industry standard is the SCCM, standard cubic centimeter per minute,
at one atmosphere. The mass flow rate must be the same at one atmosphere
and at the pressure p. Then from Equation (B-5), with subscripts O for the flow
rate at one atmosphere and no subscript for the reactor interior at pressure, p,
(Figure B-3)
Plasma Chamber
‘ro
1Jnlet
Figure B-3. Inlet and Reactor Conditions
121
dVf
)
Mp Wf = g- dvf . _P_ WfStaff=— —— — —
dt ~= poRT dt pO dt p. dt(B-7)
The time-pressure data at constant rotameter settings (measured in
centimeters) was determined experimentally and the pressure data differentiated
to yield the volumetric flow rate (cm3/s), mass flow rate (g/s), and SCCM. These
results were compared to the manufacturer’s correlation (Omega, 1995) in
Equation(B-8).
r(Sccwl = ~, T Po——Scciki ~ p“
in the above equation, ps is the
at standard conditions, T and p’ are the
(B-8)
specific gravity of NF3 relative to air (=1)
temperature and pressure at the outlet of
the flow meter, and the O subscript are conditions at standard conditions (298K
and 1 atm). As an approximation, the reactor pressure p and the flow outlet
pressure p’ were assumed equal.
Figure B-4 summarizes the experimental data and the manufacturer’s
correlation data. In (a), the mass flow rate is plotted against the reactor
pressure for rotameter settings of 20, 50, 100 and 150 cm. These results
indicate that the mass flow rate is independent of pressure in the range
examined and range from 0.08 to 2.2 mg/s. In (b), the data are transformed to a
flow rate at the reactor pressure. The flow rate existing in the reactor is found to
obey an exponential law, decreasing with increasing pressure. When this data is
converted to standard temperature and pressure (c), the SCCM are constant
with pressure and range from 1.7 to 44.2 SC(2M. The manufacturer’s SCCM
calibration correlation (equation (B-8)) is shown in (d) with
functions varying as the square root of the pressure.
From the above data, a plot of the mass flow rate
the data fitted with
and SCCM versus
rotameter setting can be generated to compare experimental data for the
calibrated flow and the manufacturer’s correlation (B-2). Below approximately 90
to 100 cm rotameter settings, both the manufacturer’s correlation and
122
experimental calibration data
rotameter settings, where the
pressure are equal, does the
are in fairly good agreement. Only at higher
assumption that the reactor and rotameter outlet
comparison sta~ to diverge. Since most of the
experimental data were taken at and below 100 cm, then either the
manufacturer’s correlation or the experimental data calibration may be used.
123
(a) Inlet Mass Flow Rate (NF3) lRotameter Model: S04-N082-031 (c) SCCM (NF3)
RF Power= OW100
1-10 100
Pressure (Pa)(b) inlet Volumetric Flow Rate(NF~)
105
\D o 20cm
1040 50cmv 1OOcm
&
● 150cm
103
dVldt = ae b)
I n2 b“ BOUIWJCnllbmlkm)ds“ibw.in-a~,“
1 10 100 1000
Pressure (Pa)tlmwcmdiionseqbmfg wpg
4419SCCM
18.09SCCM
ccm4n WI SC4JI-C4Calw’atim.lds“ilOwn.d1 10 100 1000 10000
Pressure (Pa)(d) Manufacturer’s Flow Meter Data (NF3)
i
10 20 30 40
Pressure (Pa)
Figure B-4. Experimental & Manufacturer’s Flow Calibration Data
124
.-
0.0025 “
0.0020 :~ ‘ :
0.0015 ‘ -Z ,()
0.0010
0.0005
“20
“ 10
OL u Jo 50 100 15:
Rotameter Flow Setting, F (cm)
Figure B-5. Rotameter Gas Flow Calibration
B.3.3. Recovery System Characteristics
The recovery system measures -7.1 Las determined by the expansion of
NF3 gas into the volume. It is constructed with 2.75” Conflat flanges and pipes
measuring approximately 1” internal diameter. The recovery system contains
liquid nitrogen and activated charcoal traps and an Alcatel forepump, model
201 2A. The purpose of this section is to characterize the pumping
characteristics of the recovery system.
The flow ranges from the intermediate to the viscous regime in the
recovery system with Knudsen numbers ranging from 0.016 at 10.8 Pa to 0.004
at 40 Pa for a 1” pipe. Thus, diffusion limited flow is expected for most of the
pressure range considered.
In determining the pumping characteristics, a volume of gas was fiowed
into the plasma reactor until an initial pressure (about 11 Torr) was achieved with
the outlet valve closed. At time t = O, the outlet valve was opened. Since the
125
inlet valve is closed, FO= O and with no RF applied, G = O. Hence, the mole
balance equation (B-2) becomes
4’“-F=% (B-9)
From the ideal gas law, equations (B-4), (B-5), and (B-6) apply for the
mole flow rate, the mass flow rate, and the volumetric flow rate, respectively, with
F replacing Fo.
The throughput, Q, is obtained from the expression
(B-1O)
Q is expressed in Pa-m3/s and for an isothermal system is a constant
throughout the system (Roth, 1982). With the plasma temperature of neutrals
and ions approximately constant near room temperature, the isothermal
approximation holds. Q is related to the conductance and pressure differential
between the plasma reactor (p) and the pump inlet (pI) by
Qc=— (B-n)@
4P= P-PI (B-12)
To obtain the outlet flow characteristics, two readily available gases, Nz
and NF3, were used. These gases, with molecular weights of 28 and 71 g/mole
respectively, provide a spread of values to assess the variation with molecular
weight. In this approach , the plasma reactor was flooded with the gas to a
pressure in excess of 11 Torr. At t = O, the outlet valve was opened and the
reactor pressure versus time measurements taken. The pressure measurement
errors are largest immediately after opening the valve, but as the flow stabilized,
accuracy was to within 1 mTorr.
The results of this experiment are shown in Figure B-6. In (a) the NF3
mass flow rate and volumetric flow rate (in SCCM) is shown over the range of
pressures measured. In the 10-50 Pa used for the majarity of the plasma
126
etching experiments, the mass flow rate ranges from 0.15 mg/s to 1.6 mgls (3 to
34 SCCM). In (b), the NF3 throughput Q ‘and the volumetric flow rate at the
reactor pressure are shown. The throughput ranges from 0.04 to 0.42 Pa m3 S-l
and the volumetric flow rate from 550 to 1400 cm3/s from 10 to 40 Pa. In (c) and
(d), the N2 parameters are shown. Mass flow rate in the range 10-40 Pa range
from 0.1 mg/s to 1 mg/s, flow rates range from 3.7 to 50 SCCM, throughput form
0.07 to 0.6 Pa m3 S-l, and volumetric flow rates from 575 to 1900 cm3/s.
The conductance calculation had to be approximated because it relies on
the pressure differential between the plasma reactor and the recovery system
pump inlet. The pump inlet gauge was no longer operational during these
experiments, so the data used was that obtained during plasma operation at the
time the gauge was operational. Consequently, the exiting gas is actually a
mixture of various species, more closely approximating NF3 molecular weight
based on CHEMKIN results. The data for the variation of pressure differential
versus plasma reactor pressure is shown in Figure B-7 (a) and the correlation is
fitted with a straight line through zero with a slope of 0.8036.
Applying the above pressure correlation to equation (B-11) with the Q
values calculated for NF3 and N2 yields a conductance that is only weakly
dependent on the species, as shown in Figure B-7 (b). The correlation listed
was for with NF3 data.
The conductance correlation was subsequently applied to the plasma etch
data to determine the mass and volumetric flow rates. From equations (B-6),
(B-1 O), and (B-12), the volumetric flow rate may be calculated from the
relationship
(B-13)
The experimental values of the mass flow rate and the volumetric flow
rate measured during plasma etching operations calculated using the mass flow
rate and conductance correlations and the appropriate flow equations. These
127
are plotted in Figure B-6(a) and (b) for the mass flow rate and the volumetric flow
rate. As can be seen, the data points fall on the NF3 measured flow rates.
128
(a) NF3Exhaust Flow Rate
ldrn/dt= +5.32E-71)2+1.92E-5$ -6.08E-5~!0015 .
0010 -
0 0+15- - 1(72
o0 xl m
Pressure(Pa)
(b) NF, Exhau?il Flow Rate
)
//
/
“o 50 100Preswm (Pa)
recOvery-flow-nf3- n2 .epg
Figure B-6. Recovery
1030
Imo
!Wo
,Wm
I
(c) N2 Exhaust Flcyi Role0.05
0,04-
g - 1500
[
4
0,01 - - w
o0 20Q 401 aoo me
Pressure (Po)
(d) N, Exhaust Flow Rete
❑
4- 0~.- ----- ---n -.---4W0
~-“ 30W‘E ~ .
#
E .;’Do
4 m
“a
o. moo
o~
2a2 400 m 404 10APmssum (Pa)
System Flow and Throughput Characteristics
Pressure Differential Between Chamber & Pump Inlet
40
y=ax max dev:3.96, ?=0.949a=O.8036
0/’ [email protected] I : I ! 10 10 20 30 40 50
Chamber Pressure (Pa)
5
1
f)
conductance Of Recovery System
C = -5.53E-5x2+0.0377x1+0.2.28
“o 50data.amductance-rt3-n2.epg
Figure B-7. Recovery System
100 150 200Pressure (Pa)
Pressure Differential & Conductance
130
B.3.4. Pressure In Reactor
During plasma processing, pressure and flow conditions within the plasma
eventually reach a steady state value. At steady state, the accumulation of
moles of gas in the chamber approaches zero. Thus, the mole balance equation
becomes
FO– F+G=O (B-14)
The net molar production rate, G, is made up of two sources: the bulk
volume species production and heterogeneous surface reactions that contribute
to the gas phase species.
G=~JrjdV+$Z*fijda (B-15)
J
The above function includes ~,the reaction rate of the ~ species; dV, the
elemental volume element i, the outward unit normal vector from the sutiace;
~,, the flux of species j from the sutiace; and da, the elemental surface
element. The volume integration (bulk volume term) is throughout the plasma
volume, the surface integration (heterogeneous term) is on all surfaces exposed
to the plasma, and the sum is over all species. When RF power is applied, NE
molecuies are dissociated into many species, including ions, radicals, and other
neutrals while sutiace losses will reduce the net formation of the plasma species.
Fluorination of solid U~ samples will release UFG into the gas phase according
to equation (B-16). For every mole of U@ reacted on the surface with 6 moles
of F atoms, one mole each of UF6 and 02 will desorb into the gas phase, for a
net loss in the gas phase of 4 moles for every mole of U~ reacted.
(B-16)
The total number of moles added in the gas phase after conditions in the
plasma have stabilized may be estimated from the ideal gas law as
(B-17)
131
Aq is the net change in the number of moles due to power increases, Ap
is the net change in pressure with RF power, V is ‘the reactor volume, and T the
temperature of the plasma (neutral gas temperature).I
In order to esfimate the bulk plasma contribution, the pressure increase
with power was measured without any uranium sample. Hence, only
contributions from the bulk plasma term are obtained, simplifyhg estimations of
contributions from UFG. The pressure rise with power for various NF flows
{rotameter settings) is shown in Figure B-8. In (a), the absolute reactor pressure
is plotted with absorbed power, showing the increase in pressure compared to
zero power. In (b) the number of moles generated in the bulk plasma is shown,
based on equation (B-17). The added contribution to the number of moles from
10.3 mg of UOp (typical sample mass) from the fluorination reactions (equation
(B-16)) can add up to 0.04 mmole of OZ and UFGto the gas phase and a loss of
0.24 mmole of F atoms, assuming a worse case that all UE and 02 remains in
the chamber.
132
u
3f
2(
1(
(
0.4
0.,m
‘o
x
Chamber Characteristics
~ Rotameter Modei S04-N082-031000 W Matching Network
v Vw uv v v v
-v
~~
-- -- ---50 100 150 ZIXJ
Absorbed Power (W)
Moles Gas Created DuringPlasma Operations
Source mtorr-pwrun.epgn
40 60 80 100pa-m01e2.epg
Rotameter Setting
Figure B-8. Effect of RF Power on Reactor Pressure
133
B.3.5. Residence Thne,r
The residence time is defined as
(B-18)
V is the chamber volume and the volumetric flow rate (d~/dt)~ is taken at
the entrance to the chamber. Note that the volumetric flow rate is NOT the
SCCM; it’s the flow rate at the given pressure obtained from equation (B-6).
From the ideal gas law equation of state (pV = qRT) with T, p, and R constant,
and differentiating this equation for the volumetric flow rate at the entrance gives
(wy (B-19)
The first form of the residence time uses equation (B-19). The second
form of residence time uses the entrance volumetric flow rate written in terms of
SCCM using equation (B-7) with POthe pressure at one atmosphere. The third
form uses the gas density p in the plasma and the inlet mass flow rate, tie.
pv vr— L–d’ ($-20)= FORT= (sCC~) PO me
B.3.6. Effect Of Power On Pressure
For a given rotameter flow setting with the recovery system rotary pump in
operation resulted in set pressures dependent on the operating power. These
results are shown in Figure B-9.
134
50
40
30
20
10
r)
❑ ✛ oe .1c1 14
v 24
●oA ‘; “1 AZ!?100
I
a-,.-
Es ..-
J
Rotameter Model: S04-N082-03
{
+ 168 Ae 21OWAbsorbed ~
-o 40 80 120
Rotometer Flow Head (cm)
Figure B-9. Rotameter Setting During Plasma Operation
13.3.7. Plasma Extinguishing Pressure
A plasma cannot be ignited at too low pressure (below about 0.7 Pa) nor
at high pressure. The extinguishing high-pressure plasma value was determined
by experiment, using as criteria a zero DC sheath voltage. The results are
summarized in Figure B-1 O. An initial charge of NF3 gas was introduced inside
the plasma chamber and then all inlet and outlet valves were closed. The lower
cufve in the figure shows this pressure level. Then, for each power, the pressure
increase that results with power application was determined (second curve).
Next, the NF3 gas inlet valve was opened until the extinguishing pressure was
found (top cume). The extinguishing pressures were found to vary from 105 Pa
at 38.5 W to 272 Pa at 168 W.
135
““1000 ~
100
10
Outlet valve to pumps is closedCriteriaFor Etitnguished Plasma is aSheath Voltage = 0.0 achieved byflowing NFqgas until plasma extinguished
7’
Extinguishing Pressure
Stabilized Pressure With RF, No Flow ❑n
c1
Startin~Base Pressure, No Power, No Flow
m%a am-50 100 150
Absorbed RF Power (W)
Figure B-1 O. Plasma Extinguishing Pressure
8.3.8. Knudsen Flow
In the range of pressure used, p = 10.8 to 40 Pa, the reactor chamber was
in the viscous flow regime with a Knudsen number, Kn, below 0.01 and transport
was therefore diffusive (Roth, 1982). The Knudsen number in these experiments
is related to the NF3 molecular diameter, d, the mean free path, k, the
temperature, T, and the pressure, p. Using a hard sphere approximation to
calculate d (Alberty, 1997) with the viscosity, v, equal to 0.0183 mPa-s (13raker
and Mossman, 1980) gives an NF3 molecular diameter of 4.61 xl 010 m. Applying
the ideal gas law to calculate 1 provides the relationships to calculate Kn. The
relationships are shown below.
d/[1
5 kTM 1’2——= 16v fl~ ‘
(B-21)
(B-22)‘=&’136
KJ2=A (B-23)d“
The Knudsen values for the experimental chamber Figure B-1 1) are.:
compared for different characteristic lengths to include the plasma reactor (0.5
m), a 1” diameter pipe, and the sheath thickness (-0.5 cm). For the pressure
(10.8 to 40 Pa) and temperature (-298K) range of the plasma, molecules
traversing the sheath are in the intermediate flow regime, that is, they will suffer
one or more collisions. Molecules traversing the reactor chamber are in the
viscous regime and will suffer many collisions. Molecules traversing a 1” pipe
will vary from the intermediate to the viscous regime.
10000
100
1
0.01
0.00010
t
Molecular Flow
L .—. — Li—-—.—-—- -—--
40 20 30 40
‘1Intermediate Flow
-—- -— --
v
Pressure (Pa)
Figure B-1 1. Type of Flow in Plasma Chamber.
137
APPENDIX C. DATA
C.1. Experimental Data
Table C-1 contains the depleted uranium oxide plasma processing data,
It contains only data during which the sample was continuously immersed in
plasma. Each sample contained 100 microliters of uranyl nitrate hexahydrate
solution pipetted into a 1.007 cm diameter stainless steel planchette which was
subsequently converted to UOZ by heating and flaming.
C.2. Table Abbreviations
The abbreviations and definitions used in the Table C-1 headings are as
follows:
ID
t (rein)
Flelative error, t
AbsorbedPower (W)
TransmittedPower (W)
Pressure (Pa)
NF3 Flow (cm)
Sheath (V)
Dilution Factor
Identification number
Plasma process time, in minutes, adjusted by 7 minutes toaccount for the delay in the plasma reaching operatingconditions.
The relative error in plasma immersion time.
Power absorbed by the plasma in watts.
Power transmitted (output of the RF-20 power supply) in watts.
Pressure in the plasma chamber during operation and aftersteady state has been reached, in Pascal.
The rotameter head indication in centimeters is indicative ofthe gas flow to the chamber.
Effective DC plasma sheath potential in volts. Because mostof the voltage is dropped in the powered electrode sheath, thisvoltage is effectively the voltage across the powered electrodesheath.
The ratio of either the total volume or mass of the sample tothe corresponding volume or weight of the aiiquot counted indeterrninina the activitv.
138
ID Identification number
Relative ErrorDilution
Alpha Detector(Ca) (cpm)
Alpha 2cJ (%)
C(t) (cpm)
Relative Errorc(t)
A(t) (dpm)
Relative errorA(t)
~ (dpm)
NR
Relative Error in
NR
Etch Rate
(ym/min)
The relative uncertainty in measuring the dilution of the washfor counting purposes. Significant changes during course ofthe experiments attributed to improved procedures.
The count rate (counts per minute) measured by the liquidscintillation. All reported values include curve fitting the alphapeak with a gaussian and first order polynomial, andintegration of the gaussian to determine this value.
The two sigma uncertainty determined by Poisson countingstatistics, expressed as a percent. This value is determined
r
~cazc where ~ is the counting time, generally 60as 200C=tc
minutes.
The count rate (counts per minute) corrected for alpha/betaparticle mislabeling.
The relative error in C(t).
The true activity remaining on the sample following plasmaimmersion, in disintegrations per minute.
The relative error of the activity.
The initial activity on a sample, prior to plasma immersion(disintegrations per minute). This value is not shown on thechart and is equal to 7764 dpm for the sampies used.
‘(t) it represents the amount of activityThe ratio 1– —.AO
removed from the sampie, normalized to the initiai activity.
The reiative uncertainty in k.
The U02 etch rate calculated from the experimentaiiydetermined density (4.8 g/cm3) as given in Appendix E from
the relationship[1
Mk2f4 NR
@N~ in(2) t
139
C.3. Depleted UOZ
Table C-1. Depleted UOZ Experimental Data
TransrnMed Press. NF3Flow(cm)
50505050505050505050505050505050505050505050505050505050
50
50
50
Sheath(v)
-45-46-46-46-44-44-45-45-45-45-45-45-126-128-127-127-130-130-136-136-134-134-134-134-140-140-140-444
-139
-36
-38
DilutionFactor
Rel.Error
dilution
AlphaDetectof
(cd(:q{)
369180191223196655362342735189165130?775036121155298345322310000
6415
2551
5444
5329
Alpha20 (70)
2.532.693.653.733.463.692.603.533.274.414,964.393.764.024.533.883.644.284.704,142.992.782.882.930.000.000.000.32
0.51
0.35
0.35
c(t)(cpm)
Rel. A(t) Ret. NR Rel. EtchRateError (dpm) Error Error (@rein)
ID
45910111213151618192026272629303132333435363736394045
49
80
81
(Jin)Rel, Absorb
error, t Powerw)
0011 49.60.011 49.60.006 49.60.008 49.60.005 49.60.005 49.60.003 49.60.002 49.60,002 49.60.001 49.60.001 49.60.001 49.60.004 49.60.004 49.60.033 49.60.033 49.60.001 49,60.001 49.60.002 49.60002 49.60.006 49.60.008 49.60.017 49.60.0’!7 49.60.000 49.60.000 49.60.000 49.60.011 49.6
0.003 49.6
0.002 0.1
0.002 0.1
Power(w)
120120120120120120120120120120120120120120120120120120120120120120120120120120120120
120
23.9
23.9
(Pa)c(t) A(t) NR
15.715.616.416.416.116.116.716.716,716.716.716.716.016.016.516.516,516.516.016,016.516.517.217.217.117.117.117.3
17.9
16.0
16.0
16.6019.0035.0035.0021.0021.0040.0040.0040.0040.0040.0040.0022.5723.2926.2916.0027.43240019.4316.0017.7115.1420.2921.2912.434.804.601.03
0.0510.0450.0280.0280.0410.0410.0260.0260.0260.0260.0260.02600300.0290.0270.0390.0260.0290.0340,0390.0360.0410.0330.0310<0490.0450.046
5.544E-05
5.272E-05
5,338E-05
4,632E-
41336417718821919f8351603225331851621271734833116150294340316307000
6334
0.0190,0200.0220.0210,0220.0230,0260,0350.0330.0470.0530.0450.0220.0230.0230.0250.0420.0560.0310,0290.0210.0210.0200.0190,0070.0070.0080.019
6855691062006590459440203311204523941284fool130141643776335027651304601225824055204514164526527
000
0.056
0.0520.036
0.0380.0490.0500.0400.0460,0440.0550.0610.0540.0400.0400.0380.0490.0520.08600480.0510.0440.0480.0410.0400.0520.0460.0490.025
0.1170.1100.2010,15104080.4820.5740.7370.6920.8350.8710.8320.4610.5140.5690.6440.8320.8970.7090.6900.3300.3380.1690.1591.0001.0001.0000.162
0.5590.5710.2440.3440.1000.0740.O460.02400290,0150.01f0.0150.0730.0590.0470.0380.0140.0090.0280.0320.1330,1340.3110.3290.0070.0070,0080.280
3.57E-013.35E-013.76E-012.84E-013.55E-014.20E-013.25E-012.85E-012.68G01,1.80E-011.86E411.80E-012.96E-013.29E-012.61E-012.98E-O?1.79E-011.93E-012.06E-012.03E-015.74E-015.68E-011.37E+o01.29E+O0
-.1.70E-021.70E-021.70E-024.93E-01
8813132826436363113113113383853531131138383141433
143314331433
8
53
84
1.167
1.11
2382 0.047 2779 0.050 0.642
0.240
0.039
0.177
2.95E-01
5320
5218
0.024 5903 0.028 6.95E-02
7.77E-021.09 0.023 5685 0.028 0.268 0.15284
140
ID
82
83
84
85
86
87
89
109
112
113
117
120
121
122
123
124
125
129
130
(iin)
53
53
23
23
68
68
38
113
83
83
53
53
53
53
36
38
38
8
8
Rel. Absorb TransmittedPress.error, t Power
(w)
0,003 0.1
0.003 0.1
0.006 0.1
0.006 0.1
0.002 0.1
0.002 0.1
0.004 0.1
0.001 49.6
0.022 49,6
0.022 49.6
0,003 49.6
0.033 212.6
0.033 212.6
0.033 212.6
0.044 212.6
0.044 212.6
0.044 212.6
0.133 212.6
0.133 212.6
Power (Pa)(w)
23.9
23.9
23.9
23.9
23.9
23.9
23.9
120
120
120
120
500
500
500
500
500
500
500
500
16.4
16.4
16.3
16.3
16.7
16.7
16.4
17.9
18.1
16.1
17.9
18.0
18.0
18.0
18.1
18.1
18.1
18.4
18.4
Table C-1. Depleted UOZ Experimental Data
NF3Flow
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
Sheath(v)
-21
-21
-30
-30
-20
-20
-31
-139
-133
-133
-136
-405
-405
420
-420
-398
-398
Dilution Rel. Alpha Alpha c(t) Rel. A(t) Ret. NR Rel. EtchRateFactor Error Detector 20 (%) (cPm) Error (dpm) Error Error (wrtlmin)
dilution
051.02 4.765E-
051.02 4,768E-
051.07 4.508E-
051.07 4.466E-
051.01 4.670E-
051.01 4.817E-
051.03 4.532E-
051.10 4.476E-
051.06 0.000E+
001.1,1 0.000E+
001.11 4.396E-
051.11 4,441E-
051,17 4.245E-
051.07 4.517E-
051.08 4.483E-
051.00 4.744E-
051.07 4.543E-
051.03 4.575E-
051.05 4.553E-
05
(cd(cpm)
6972
7100
6367
6665
6899
6361
6574
393
2709
2559
2869
116
60
81
120
407
190
3055
3281
c(t)
0.31 6878 0.020
0.31 7005 0.020
0.32 6241 0.023
0.32 6554 0,021
0.31 6791 0,021
0.32 6239 0.022
0.32 6469 0.021
1.30 195 0.529
0.50 2558 0,041
0.51 2411 0.043
0.48 2715 0.040
2.06 0 0.001
2.60 0 0.001
2.34 0 0.001
2.36 0 0!001
1.28 186 0,617
1.67 0 0.001
0.47 2834 0.051
0,45 3099 0!041
7044
7179
6670
7036
6868
6266
6651
215
2713
2682
3026
0
0
0
0
186
0
2913
3246
A(t) NR
0.025 0.093 0.530
0.025 0.075 0.664
0.027 0.141 0.337
0.026 0.094 0.529
0.026 0.115 0.418
0.027 0.190 0.235
0.026 0.143 0.326
0.529 0.972 0.015
0.044 0.651 0.035
0.045 0.655 0.035
0043 0.610 0.041
0.015 1.000 0.001
0.015 1.000 0.001
0.015 1.000 0.001
0.015 1.000 0.001
0.617 0.976 0.015
0.015 1.000 0.001
0.053 0.625 0.043
0.044 0.582 0.047
.
4,26E-02
3.46E-02
1.49E41
9.94E-02
4,14E412
6.62E-02
9.20E-02
2.1OE-O1
1.91E-01
1.92-E-01
2.61E-01
4.60E-01
4.60E-01
4.60E-01
6.41E-01
6.26E-01
6.41E-01
1.90E+O0
1.77E+O0
141
ID
131
140
141
442
143
144
147
148
149
152
153
154
155
156
157
158
159
160
161
162
(N/in)
6
53
53
53
53
53
53
53
53
53
53
53
53
53
53
53
53
53
53
23
Ret. AbsorbTransmittederror, t
0.133
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0,033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.067
(w)
212.6
42.8
42,8
41.4
39.4
39.4
41.4
41.4
40.3
39.2
39.2
44.6
44.6
39.6
39.6
44.7
44.7
40.3
40.3
23.7
Power
w)
500
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
72
Press.(Pa)
16.4
7.9
7.9
32.4
25.7
25.7
10.5
10.5
13.6
22.0
22.0
5.7
5.7
16.4
16.4
38.4
38.4
29.6
29.6
16.4
Table C-1. Depleted UOZ
NF3Flow(cm)
50
20
20
100
75
75
30
30
40
65
65
10
10
50
50
120
120
90
90
50
Sheath(v)
-398
-172
-172
-18
-66
-66
-153
-153
-135
-64
-84
-183
-183
-117
-117
-14
-14
-38
-38
-79
DilutionFactor
1.01
1.08
1.24
1,00
1.10
1.06
1.05
1.01
1.27
1.07
1.08
1.17
1,14
1.01
1.00
1.01
1.02
1.10
1,06
1.05
Rel.Error
dilution
4,630E-05
4.526E-05
4,285E-05
4,051E-05
4.352E-05
4.391E-05
4.558E-05
5.271E-05
4.264E-05
4,532E-05
4.525E-05
4.367E-05
4.432E-05
4.71$E-05
5.083E-05
4.927E-05
4.701E-05
4.494E-05
4.536E-05
4,590E-
Experimental Data
Alpha Alpha c(t)Detector 20 (%) (cPm)
(c.)(cc;)
6031
5069
4582
4793
5139
5857
6201
4369
5320
5001
6239
5860
5371
5752
5271
4436
4498
5689
0.44 3222
0.33 5940
0.36 4981
0.38 4411
0.37 4655
0.36 4999
0,34 5764
0.33 6106
0.39 4297
0.35 5176
0.37 4846
0.33 6166
0.32 6626
0.34 5738
0.35 5212
0.34 5564
0.36 5070
0.3677 4252
Rel.Errorc(t)
0.039
0.021
0.021
0.032
0.027
0.026
0.021
0.021
0.023
0.026
0,028
0.019
0.018
0,023
0.027
0.029
0.032
0.034
A(t)(dpm)
3262
6385
6179
4430
5119
5301
6036
6162
5453
5561
5242
7245
7556
5780
5238
5615
5151
4686
Ret.ErrorA(t)
0.042
0.025
0.026
0.035
0.031
0.030
0.026
0.025
0.028
0.030
0.032
0.024
0.024
0.028
0.031
0.033
0.035
0.037
NR
0.580
0.176
0.204
0.429
0.341
0.317
0.223
0.206
0.298
0.284
0.325
0.067
0,027
0.256
0.325
0.277
0.337
0.396
Rel. EtohRateError (pm/mIn)NR
0.046 1.77E+O0
0.252 8.17E-02
0.214 9.39E-02
0.079 1.97E-01
0.111 ‘- 1.57E-01
0.122 1.46E-01
0.191 1.02E-01
0,210 9.49E-02
0.131 1.37E-01
0.144 1.30E-01
0.120 1.49E-01
0.751 3.07E-02
1.951 1.23E-02
0.162 1.18E-01
0.119 1.50E-01
0.152 1.27E-01
0.118 1,55E-01
0.092 1.82E-01
0.385 4311 0.034 4557 0.037 0.413 0.086 1.90E-01
0,34 5566 0.022 5867 0.027 0.242 0.172 2.56E-01
142
Table C-1. Depleted U02 Experimental Data
ID
163
164
165
166
167
169
170
171
172
173
178
179
204
205
206
207
208
209
210
(N/in)
23
63
83
83
83
23
53
53
53
53
23
23
53
53
53
53
83
83
23
Ret. Absorb Transmittederror, t Power
(w)
0.067 23.7
0.022 102.4
0.022 102.4
0.022 23.7
0.022 23.7
0.067 102.4
0.033 23.7
0.033 23.7
0.033 102.4
0.033 102.4
0.006 49.6
0.006 49.6
0.033 96.1
0.033 96.1
0.033 103.4
0.033 103.4
0.022 26.5
0.022 26.5
0.067 26.5
(w)
72
240
240
72
72
240
72
72
240
240
120
120
240
240
240
240
72
72
72
Press(Pa)
16.4
17.1
17.1
16.3
16.3
17.2
16.1
16.1
17.5
17,5
16,7
16.7
10.9
10.9
30.3
30.3
10.9
10.9
11.1
NFsFlow(cm)
50
50
50
50
50
50
50
50
50
50
50
50
30
30
80
80
30
30
30
Sheath(v)
-79
-292
-292
-104
-104
-290
-103
-103
-266
-286
-170
-170
-273
-273
-185
-185
-116
-116
-115
Dilution Rel. Alpha Alpha c(t) Rel, A(t) Rel. NR Rel. Etch RateFactor Error Detector 2U (%) (cPm) Error (dpm) Error Error (umlmin)
dilution
051.06 4.502E-
051.03 4.724E-
051.03 4.762E-
051.03 4.567E-
051,02 4,617E-
1.07 4.4T3E.05
1,09 4.466E-05
1.10 4,473E-05
1.12 4.464E-05
1.06 4.491E-05
1.09 4.524E-05
1.08 4.504E-05
1.00 4.609E-05
1.01 4.500E-05
1.01 4.696E-05
1.02 4.486E-05
1.02 4.643E-05
1.04 4.566E-05
1.01 4.877E-05
(Ca)(cpm)
5771
1371
767
5365
4725
3403
5442
5556
650
1647
5665
5348
3010
2256
192
220
6272
6015
7238
c(t) A(t) NR
0.34 5678 0.021 6107 0.026 0.213 0.201
0.60 1177 0.095 1213 0.096 0.844 0.020
0,93 566 0.192 580 0.192 0.925 0.016
0.35 5243 0.024 5386 0,028 0,306 0.127
0.36 4589 0,027 4675 0.031 0.398 0.087
0.44 3234 0.038 3462 0.041 0.554 0.051
0.35 5303 0.026 5780 0.030 0.256 0.165
0.35 5420 0.025 5936 0.029 0.235 0.183
0.69 649 0.169 725 0,170 0,907 0.018
0.64 1452 0.079 1574 0.061 0.797 0.024
0.3424 5552 0.024 6036 0.029 0.223 0.196
0,3531 5183 0.028 5585 0.032 0.261 0.148
0,47 2795 0.050 2804 0.053 0.639 0.040
0.54 2017 0.071 2037 0.073 0.738 0.031
1.86 0 0.001 0 0.015 1.000 0.001
1.74 0 0.001 0 0.015 1.000 0.001
0.326 6158 0.022 6250 0.027 0.195 0.227
0.3329 5896 0.023 6133 0,027 0.210 0.206
0.3035 7139 0.020 7186 0.025 0,074 0.674
2.26E-01
2.48E-01
2.72E-01
9.00E-02
1.17E-01
5.67E-01
1.18E-01
1,08E-01
4.17E-01
3.67E-01
2.36E-01
2.97E-01
2.94E-01
3.39E-01
4.60E-01
4.60E-01
5.73E-02
8.17E-02
7.89E-02
143
ID
211
212
213
214
215
216
217
218
219
222
223
224
225
226
227
228
229
230
231
232
(M’in)
23
53
53
83
83
53
53
23
23
53
53
23
23
83
83
53
53
’23
23
63
Rel. Absorb Transmittederror, t
0.067
0.033
0.033
0.022
0.022
0.033
0.033
0.067
0.067
0033
0.033
0.067
0.067
0.022
0.022
0.033
0.033
0,067
0.067
0.022
Power(w)
26.5
26.5
26.5
27.3
27.3
27,3
27.3
27.3
27.3
50.6
50.6
50.6
50.6
50.2
50.2
50.2
50,2
50.2
50.2
96.1
Power
(w)
72
72
72
72
72
72
72
72
72
120
120
t 20
120
120
120
120
120
120
120
240
Press(Pa)
11.1
10.9
10,9
32.4
32.1
31.6
31.6
31.7
31.7
11.1
11,1
11.2
11.2
35.2
35.2
35.1
35.1
35.7
35.7
10.8
Table C-1. Depleted U02
NF3Flow(cm)
30
30
30
100
100
100
100
100
100
30
30
30
30
100
100
100
100
100
100
30
Sheath(v)
-115
-111
-111
-9
-9
-8
-6
-8
-8
-179
-179
-177
-177
-18
-18
-20
-20
-36
-36
-325
DilutionFactor
Rel.Error
1.02
1.00
1.01
1.01
1.01
1.03
1.01
1.07
1.03
1.00
1,00
1.00
1,00
1.01
1.00
1.01
1.01
1,00
1.00
1.00
4.621E-05
4,660E-05
4,547E-05
4.710E-05
4.612E-05
4.563E-05
4.628E-05
4.503E-05
4.597E-05
4.670E-05
4.568E-05
5.021E-05
4.515E-05
4.586E-05
4.599E-05
4.362E-05
4.625E-05
4.818E-
4.;7E-05
4.455E-
144
Experimental Data
Alpha Alpha c(t) Ret.Detector 2CI (%) (cpm) Error
(ccl) c(t)(cpm)7062 0.3068 6978 0.020
6510 0.32 6363 0.024
6303 0.3252 6164 0.024
7108 0.3063 6995 0.021
6326 0.3246 6163 0.024
6722 0.3149 6604 0.022
6880 0.3113 6748 0.022
6705 0.3153 6591 0,021
7313 0.3019 7207 0.020
4954 0.3668 4807 0.028
6074 0.3313 5932 0.024
6608 0.3176 6488 0.022
5537 0.347 5365 0.028
1172 0.7542 946 0.133
1456 0.6767 1239 0.100
3155 0.4596 2987 0.040
2721 0.495 2550 0,045
3710 0.4239 3538 0.036
3147 0.4602 2964 0.043
1193 0.7474 994 0.113
A(t)
7115
6386
6196
7033
6251
6809
6812
7042
7405
4827
5957
6518
5382
951
1243
3009
2566
3546
2976
999
ReLErrorA(t)
0.025
0.028
0,028
0.026
0.028
0.026
0.027
0.026
0.025
0.031
0.029
0.027
0.032
0.134
0.101
0.043
0.048
0!039
0.045
0.114
NR
0.084
0.177
0.202
0.094
0.195
0.123
0.123
0.093
0.046
0.378
0.233
0.161
0.307
0.878
0.840
0.612
0.669
0.543
0.617
0.671
Rel. Etch RateError (prn/min)
NR
0.596 8.86E-02
0.259 8.1 5E-02
0.221 9.28E-02
0.525 2.77E-02
0.231 5.72E-02
0.391 5.88E-02
0.395 5.84E-02
0.535 9.85E-02
1.120 4.90E-02
0.095 1.74E-01
0.185 1.07E-01
0.288 1.70E-01
0.131 3.25E-01
0,020 2.58E-01
0.021 2.47E-01
0.041 2.82E-01
0.034 3.08E-4M
0.052 5.75E-01
0.041 6.53E-01
0.018 2,58E.01
Table C-1. Depleted U02 Experimental Data
ID
234
235
236
237
238
239
240
241
242
243
248
249
250
251
252
253
259
260
261
(Mtin)
83
63
23
23
23
23
53
53
53
53
53
53
53
53
113
113
293
293
83
Rel Absorb Transmittederror, t Power
(w)
0.022 98.5
0.022 98.5
0.067 96.1
0.067 96.1
0.067 98.5
0.067 98.5
0.033 49.6
0.033 49.6
0,033 104.1
0.033 104.1
0.033 147.7
0.033 147.7
0.O33 179.8
0.033 179.8
0.017 102,4
0,017 102.4
0.001 49.6
0.001 49.6
0.022 102.6
Power(w)
240
240
240
240
240
240
120
120
240
240
400
400
400
400
240
240
120
120
240
Press.(Pa)
40.1
40.1
11.3
11.3
39.6
39.6
30.4
30.4
24.1
24.1
11.2
11.2
31.2
31,2
16.9
16.9
16.7
16.7
32.0
NF3Flow(cm)
100
100
30
30
100
100
85
85
65
65
30
30
80
80
50
50
50
50
85
Sheath(v)
-150
-150
-317
-317
-179
.179
-94
-94
-250
-250
460
460
-335
-335
-236
-236
.135
-135
-150
tXlution Rel. Alpha AlphaFactor Error Detector 20 (Y.). .
dilution
051,01 4.615E-
051.00 4.442E-
051.00 4.712E-
051.00 5.077E-
051.01 4.566E-
051.01 4,842E-
051.00 4.698E-
051.00 4.796E-
051.01 4.499E-
051.00 4.494E-
051.01 4.788E-
051.00 4.791E-
051,01 4.517E-
051.01 4.644E-
051.00 4.579E-
051.00 4.676E-
051,00 0.000E+
001.00 0.000E+
001.00 0.000E+
(c.)(cpm)
155
240
4274
3014
391
316
3067
2489
416
355
2061
1653
133
139
570
471
603
759
112
2.0708
1.6664
0.395
0.4703
1.3065
1.4533
0.47
0.52
1.27
1.37
0.57
0.60
2.24
2,19
1.08
1.19
1.05
0.94
2.44
c(t) Rel. A(t) Rel. NR ReL EtchRate(cpm) Error (dpm) Error Error (prnlmin)
c(t) A(t) NR
o 0.001 0 0.015 1.000 0.001 2.94E-01
24 4.559 24 4.559 0.997 0.014 2.93E-01
4113 0.032 4128 0.035 0.468 0.066 4.96E-01
2821 0.046 2833 0,049 0.635 0.039 6.73E-01
171 0.664 172 0.664 0.978 0.015 1.04E+O0
113 0,928 113 0.928 0.985 0.014 1,04E+O0
2857 0.049 2868 0.051 0.631 0.041 2.90E-01
2253
177
115
1833
1603
0
0
309
211
345
511
0
0.064
0.700
1.078
0.074
0090
0.001
0.001
0.443
0s40
0.391
0.258
0.000
2261
178
115
1845
1611
0
0
310
212
345
511
0
0.066 0.709 0.034
0.700 0.977 0.016
1.078 0.985 0.016
0.076 0.762 0.028
0.091 0.793 0.027
0.015 1.000 0.001
0.015 1.000 0.001
0.443 0.960 0.019
0.641 0.973 0.018
0.391 0.956 0.018
0.259 0.934 0.019
0.015 1.000 0.000
3.26E-01
4.49E-01
4,53E-01
3.51E-01
3.64E-01
4.60E-01
4.60E-01
2.07E-01
2.IOE-01
7.95E-02
7.77E-02
2.94E-0100
145
Table C-1. Depleted U02 Experimental Data
ID
262
263
264
265
266
269
271
272
273
274
275
276
277
279
260
281
262
285
286
287
(Mtin)
83
23
23
53
53
83
53
53
23
23
113
113
113
113
113
203
203
113
113
203
Rel. Absorb Transmitted Presserror, t
0.022
0.067
0.067
0.033
0.033
0.022
0.033
0.033
0.067
0.067
0.017
0.017
0.017
0.017
0.017
0.010
0.010
0.017
0.0!7
0.010
Power(w)
102,6
102.6
102.6
50.6
50.6
51,7
51.7
51.7
51.7
51.7
51.7
51.7
96.1
50.6
50.6
50,4
50.4
50.4
50.4
49.6
Power (Pa)(w)
240
240
240
120
120
120
120
120
120
120
120
120
240
120
120
120
120
120
120
120
32.0
31.7
31.7
10.9
10.9
40.1
39,9
39.9
40.3
40.3
40.4
40.4
11.2
11.3
11.3
34.9
34.9
34.9
34.9
17.5
NF3Flow
85
65
65
30
30
120
120
120
120
120
120
120
30
30
30
103
103
102
102
51
Sheath(v)
-150
-154
-154
-230
-230
-9
-9
-9
-9
-9
-9
-9
-272
-146
-148
-13.5
-13.5
-15
-15
-135
Dilution Rel. AlphaFactor Error Detector
dilution (Ca)(;p#
1.00 0.000E+00
1.00 0.000E+ 212100
1.00 0.000E+ 149500
1.00 0.000E+ 527100
1,00 0.000E+ 581600
1.00 0.000E+ 485300
1.00 0.000E+ 642000
1.00 0.000E+ 676400
1.00 0.000E+ 673100
1.00 0.000E+ 682700
1.00 0.000E+ 450400
1.00 0.000E+ 453200
1.00 0.000E+ 83100
1.00 0.000E+ 419800
1,00 0.000E+ 502200
1.00 0.000E+ 100700
1.00 0,000E+ 118700
1.00 0.000E+ 152700
1.00 0.000E+ 106600
1.00 0,000E+ 340
Alpha2U (%)
2.39
0.56
0.67
0.36
0.34
0.37
0.32
0.31
0.31
0.31
0.38
0.38
0.90
0.40
0.36
0.81
0.75
0.66
0.79
4,40
c(t)(cpm)
o
1892
1251
5043
5615
4689
6275
6625
6586
6691
4318
4346
571
3966
4843
622
993
1336
670
130
Ret.Errorc(t)
0.000
0.073
0.110
0,035
0.030
0.030
0.024
0.023
0.023
0.023
0,034
0.033
0.242
0.041
0.031
0.125
0.110
0.084
0.125
0.631
A(t)
o
1892
1251
5043
5615
4689
6275
6625
6586
6691
4318
4348
571
3966
4843
822
993
1336
870
130
Rel.ErrorA(t)
0.015
0.074
0.111
0.038
0.034
0,033
0.028
0.027
0.028
0027
0.037
0.036
0.243
0.044
0.034
0.126
0.111
0.085
0.126
0.631
NR
1.000
0.756
0.839
0.350
0.277
0.396
0.192
0.147
0.152
0.136
0.444
0.440
0.926
0.489
0.376
0.694
0.872
0.826
0.688
0.963
Rel,ErrorNR
0+000
0.029
0,023
0.113
0.153
0.089
0.235
0.323
0.311
0.345
0.076
0.077
0.020
0.068
0.098
0.016
0.018
0.020
0.017
0.014
EtchRate(Vm/min)
2.94E-01
8.OIE-01
8.89E-01
1.61E-01
1.27E-01
1.16E-01
8.82E-02
6.74E-02
1.61E-01
1.47E-Of
9.57E-02
9.49E-02
2.00E-01
1.06E-01
8.’12E-O2
1.07E-01
1.05E-01
t ,79E-01
1.92E-01
1.18E.01
146
ID(IJin)
288 203
289 203
290 203
291 209
292 209
293 204
294 204
295 53
296 53
297 293
298 293
301 145
302 145
303 248
304 248
307 248
308 248
309 248
310 248
Rel. Absorb Transmitted Press.error, t Power
0.010
0.010
0.010
0.009
0.009
0.009
0.009
0.033
0.033
0.007
0.007
0.013
0.013
0.008
0.008
0.008
0.008
0.008
0.008
(w)
49.6
101.9
101.9
50.6
50.6
23.5
23.5
98.2
98.2
50.3
50.3
50.5
50.5
49.6
49.8
50.4
50.4
23,5
23.5
Power(w)
120
240
240
120
120
72
72
240
240
120
120
120
120
120
120
120
120
72
72
(Pa)
17.5
17.5
17.5
10.9
10.9
17.3
17.3
40.3
40.3
34.9
34.9
34.9
34.9
17.3
17.3
35.2
35.2
17.3
17.3
Table C-1. Depleted U02 Experimental Data
NF3Flow(cm)
51
40
48
31
31
52
52
101
101
101
101
104
io4
51
51
102
102
52
52
Sheath(w
-135
-240
-240
-186
-186
-85
-85
-113
-113
-20
-20
-20
-20
-135
-135
-19
-19
-82
-82
Dilution Rel. Alpha AlphaFactor Error Detector 20 (Y.)
1.00
1.00
1.00
1.00
1.00
1.00
1,00
1.00
1.00
1,00
1.00
1.00
t .00
1.00
1.00
1.00
1,00
1.00
1.00
dilution
000.000E+
000.000E+
000.000E+
000.000E+
000.000E+
O.O::E+00
0.000E+00
0.000E+
O.O::E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
147
(c.)(cpm)
722
168
218
2725
2755
4174
4053
469
314
250
249
1074
775
775
535
525
778
3675
.,
0.96
1.99
f.75
0.49
0.49
0.40
0.41
1.19
1.46
163
1.64
0.79
0.93
0.93
1.12
1.13
0.93
0.43
0.43
c(t) Rel. A(t) Rel. NR Ret,(cpm) Error (dpm) Error Error
c(t) A(t) NR
520
0
2
2543
2572
4014
3887
256
97
0.209 520
0.001 0
72.830 2
0.048 2543
0.048 2572
0.032 4014
0.033 3887
0.436 256
1.156 97
0.209
0.015
72.830
0.050
0.050
0.035
0.037
0.436
1.156
0.933
1.000
1,000
0.672
0.669
0.483
0.499
0.967
0.988
0.015
0,001
0.014
0.034
0.034
0.064
0.081
0.015
0,015
Etch Rate(pmlmin)
1.12E-01
1.20E-01
1:20E-01
7,84E-02
7.80E-02
5.77E-02
5.97E-02
4.45E-01
-4k4E-ol
o 0.000 0 0.015 1.000 0!000 8.32E-02
o 0.000 0 0015 1.000 0.000 8.32E-02
815 0.172 815 0.173 0.895 0.021 1.50E-01
520 0.260 520 0.260 0.933 0.019 1.57E-01
568 0.196 568 0.197 0.927 0.016 9.11 E-02
317 0.381 317 0.361 0.959 0.018 9.43E-02
309 0.368 309 0.368 0.960 0.015 9.44E-02
559 0.210 559 0.211 0.928 0.017 9.12E-02
3493 0.037 3493 0.040 0.550 0.051 5.41E-02
3497 0.037 3497 0.040 0.550 0,051 5.40E-02
Table C-1. Depleted U02 Experimental Data
ID
311
312
313
314
315
316
317
318
319
320
321
322
323
324
327
328
329
330
331
332
(din)
23
23
158
158
158
158
23
23
303
303
203
203
8
8
83
83
23
23
53
53
Rel. Absorb Transmitted Presserror, t Power
w)
0.067 49.7
0,067 49.7
0.012 49.6
0.012 49.6
0,012 23.6
0.012 23.6
0.067 169.5
0.067 169.5
0.006 23.6
0,006 23.6
0.010 96.1
0.010 96.1
0.133 167.5
0.133 167.5
0.022 148.8
0.022 148.8
0.067 150.0
0.067 150.0
0.033 167.5
0.033 167.5
Power
w)
120
120
120
120
72
72
400
400
72
72
240
240
400
400
400
400
400
400
400
400
(Pa)
30.9
30.9
17.1
17,1
16.9
16,9
17.2
17.2
17.2
17.2
10.8
10.8
17.1
17,1
10.5
10.5
10.4
10.4
17,3
17.3
NF3Flow(cm)
68
88
50
50
51
51
54
54
51
51
30
30
51
51
31
31
32
32
51
51
Sheath(v)
-70
-70
-133
-133
-77
-77
-340
-340
-89
-89
-268
.268
-334
-334
-378
-378
-375
-375
-340
-340
Dilution Rel. Alpha Alpha c(t) Rel, A(t) Rel. NR Ret. EtchRateFactor Error Detector20(%) (cPm) Error (dpm) Error Error (pm/mIn)
1.00
1.00
1.00
1.00
1.00
1,00
1.00
1.00
1.00
1.00
1,00
1.00
1,00
1,00
1.00
1,00
1.00
1.00
1.00
1.00
dilution
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0,000E+00
0.000E+00
0.000E+00
0.000E+00
0,000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+
O.O::E+00
0.000E+00
0.000E+00
0.000E+
O.O::E+
148
(c.)(cc&)
4679
667
540
3608
3849
1290
1919
4254
3732
163
334
4155
4580
741
923
4107
4198
539
531
c(t)
0.35 5243 0.027
0.38 4493 0.033
1.00 439 0.277
1.11 301 0.415
0.43 3422 0.039
0.42 3663 0.037
0.72 1070 0.115
0.59 1721 0.070
0.40 4077 0.034
0.42 3539 0.039
2.02 0 0.000
1,41 78 1.693
0.40 3961 0.037
0.38 4390 0.034
0.95 478 0.291
0.85 658 0.216
0.40 3912 0.037
0<40 40!3 0.035
1.11 282 0.474
1.12 270 0.503
5243
4493
439
301
3422
3863
1070
1721
4077
3539
0
78
3961
4390
478
658
3912
4013
282
270
A(t) NR
0.031 0.325 0.119
0,036 0.421 0.083
0.277 0.944 0.017
0.416 0.961 0.017
0.042 0.559 0.050
0.040 0.528 0.056
0.116 0.862 0.020
0.071 0,778 0.024
0.037 0.475 0.067
0.042 0.544 0.054
0.015 1.000 0.000’
1.693 0990 0.017
0.040 0.490 0.065
0.037 0.435 0.079
0.291 0.938 0,019
0216 0.915 0.021
0.040 0.496 0.063
0,038 0.483 0.066
0.474 0.964 0.018
0.503 0.965 0.018
3.44E-01
4.46E-01
1.46E-01
1.48E-01
8.63E-02
8.15E-02
9<14E-01
8.25E-01
3,82E-02
4.38E42
1,20E-01
I,19E-01
1.49E+O0
1.32E+O0
2.76E-01
2,69E-01
5.26E-01
5.12E-01
4.43E-01
4.44E-01
ID
333
334
335
336
337
336
339
340
341
342
343
344
345
346
(M’in)
8
8
8
8
23
23
83
63
113
113
83
83
113
113
Rel. Absorb Transmitted Press.error, t Power
w)
0.133 179.8
0.133 179.8
0.133 160.0
0.133 180.0
0.087 179.9
0.067 179.9
0.022 96.1
0.022 96.1
0.017 96.1
0.017 96.1
0.022 166,7
0.022 166.7
0.017 148.8
0.017 148.8
Power (Pa)(w)
400
400
400
400
400
400
240
240
240
240
400
400
400
400
35.5
35.5
31.2
31.2
31.1
31.1
10.8
10.8
10.8
10.8
17.1
17.1
10.5
10.5
Table C-1. Depleted UOZ Experimental Data
NF3Flow(cm)
92
92
82
82
81
81
30
30
30
30
50
50
31
31
Sheath(v)
-255
-255
-272
-272
-272
-272
-280
-280
-277
-277
-347
-347
-385
-385
Dilution Rel, Alpha Alpha c(t) Rel.Factor Error Detector 20 (%) (cpm) Error
dilution (c.) c(t)(cpm)
001.00 0.000E+ 648 1.01 416 0.295
001.00 0.000E+ 986 0.62 782 0.143
001.00 0.000E+ 1144 0.76 925 0.131
001.00 0,000E+ 1757 0.62 1550 0.079
001.00 0.000E+ 247 1.64 17 6.813
001.00 0.000E+ 424 1.25 188 0.651
001.00 0.000E+ 1101 0.78 916 0.114
001,00 0,000E+ 1878 0.60 1664 0,070
001.00 0.000E+ 1204 0.74 973 0,132
001.00 0,000E+ 834 0.89 604 0.204
001.00 0.000E+ 406 1.28 154 0.849
001,00 0.000E+ 670 1.00 415 0.324
001.00 0.000E+ 1006,22 0,814 753 0.162
001.00 0.000E+ 1207.11 0.7432 962 0.141
A(t)
416
782
925
1550
17
168
916
1684
973
604
154
415
753
962
Rel. NR Ret. Etch RateError Error Qunlmin)A(t) NR
0.298 0.946
0.144 0.899
0.132 0.881
0,080 0.800
8.813 0.996
0.651 0.976
0.115 0.882
0.071 0.783
0.133 0.875
0.205 0.922
0.650 0.980
0.017
0.017
0.019
0,023
0.015
0.016
0.017
0.024
0.020
0.018
0.017
2.86E+O0
2.74E+O0
2.68E+O0
2.44E+O0
1.06E+O0
1.03E+O0
2.59E-01
2.30E-01
1.89E-01
1.99E-01
2.88E-01
(.324 0.947 0.019 2.78E-01
0.182 0.903 0.020 1.95E-01
0.142 0.876 0.021 1,89E-0100
149
..-—
APPENDIX D. CHEMKIN
This appendix includes details of the Chemkin validation not
the main text.
D.1. Thermodynamic Data
The following thermodynamic data includes all CHEMKIN gas
required to run CHEMKIN, and is
code, which is a polynomial fit for
constant pressure as a function of
with the FITDAT utility. The data
based on the NASA Chemical
the enthalpy, entropy, and spe
temperature. These fits may b{
shown below are the coetlicier
equations, and details are available in the CHEMKIN Ill (Kee et. al.
SURFACE CHEMKIN Ill (Coltrin et. al, 1996) documentation.
D. 1.1. Thermodynamic Data for CHEMtUN Ill:THERMO
300.000 1000.000 5000.000E 120186E 1 G 0300.00 5000.00 1000.000.02500000E+02 O.OOOOOOOOE+OO 0.0000OOOOE+OO 0.0000OOOOE+OO O.OOOOOOOOE+OO
-0.07453749E+04-0.01173403 E+03 0.02500000E+02 O.OOOOOOOOE+OO 0.0000OOOOF,+OO0.0000OOOOE+OO 0.00000000E+00-0.07453750E+04-0.01173403E+03
F 121286F 1 G 0300.00 5000.00 1000.00O.O2687459E+O2-O.O2O1O358E-O2 0.08597957E-06-0.01644974E-09 0.01166160E-130.08722883E+05 0.03882212E+02 0.02913905E+02-0.07336339E-02 O.O5571O15E-O5
-0.02666871E-OB 0.08643255E-12 0.08651201E+05 0.02677115E+02F2 121286F 2 G 0300.00 5000.00 1000.000.04018308E+02 0.06221479E-02-0.02420845E-05 0.04742076E-09-O.03418141E-13
-0.01300713E+05 0.01126327E+02 0.02940287E+02 0.03491492E-01-O-02458208E-040.01837073E-08 O.O285O917E-1I-O.O1O1O43OE+O5 0.06694194E+02
N2F2 42489F 2N 2 G 0300.00 3000.00 1000.000.07255211E+02 O.O227441OE-O1-O.O2793346E-O5-O.02203844E-08 0.05359234E-120.06360353E+C5-0 .O1O94248E+O3 0.03127143E+02 O.O1O57134E+OO-O.O9746112E-O5
-0.07208357E-07 O.O3567978E-10 0.07615831E+05 O.O11O7465E+O3N 12018614 1 G 0300.00 5000.00 1000.000.02450268E+02 O.O1O66146E-O2-O.O7465337E-O6 O.O1879652E-O9-O.O1O25984E-130.05611604E+06 0.04448758E+02 0.02503071E+02-O.02180018E-03 0.05420529S-06
-0.05647560E-09 0.02099904E-12 0.05609890E+06 0.04167566E+02N2 121286N 2 G 0300.00 5000.00 1000.000.02926640E+02 0.01487977E-01-O.05684761E-05 O.O1OO97O4E-O8-O.O6753351E-13
-0.09227977E+04 0.05980528E+02 0.03298677E+02 0.01408240E-01-O.03963222E-04O.O5641515E-C7-O.O2444855E-1O-O.O1O2O9OOE+O5 0.03950372E+02
N3 121286N 3 G 0300.00 5000.00 1000.000.05208505E+G2 O.O24445O7E-O1-O.O1O38941E-O4 0.019774:7E-08-O.01395644E-120.04796i78E+06-O.03612756E+02 0.02882219E+02 0.08930338E-01-O.08539038E-04O.O5O45585E-O7-O.OI521248E-1O 0.04863468E+06 0.08481757E+02
NF 121286N lF 1 G 0300.OG 5000.00 1000.000.03862177E+02 0.07551806E-02-O.03044943E-05 0.05874447E-09-O.04187479E-130.02867243E+06 0.03457233E+02 0.02871947E+02 0.03312153E-Oi-O.02691159E-040.01121951E-O?-C.02475131E-11 C.02896257E+06 0.08640247E+02
NF3 62394N lF 3 0 OG 300.000 4000.000 1000.000.82191658E+01 0.12927436E-02-O.16520647E-06-O.68563703E-10 0.14209565E-13
-0.17080596E+G5-C.17275919E+02 0.29812291E+01 O.116O531OE-O1-O.974O7462E-O6-0.84367731E-08 0.41166593E-11-O.15457758E+05 O.1O762127E+O2NF2 62394N lF 2 0 OG 300.000 4000.000 1000.000.59553924.E+O1 O.75965584E–O3-O.1O16646OE-O6-O.3781O439E-1O 0.80034466E-140.18727911E+04-O.49131246E+01 0.31983922E+01 0.59982142E-02-O.45932120E-06
-O.4O1O1686E-O8 0.18564607E-11 0.27531292E+04 0.99338350E+01
150
N2F4 L12/86N 2F 4 0 OG 298.150 5000.000 1000.001.29150660E+01 3.50813620E-03-1.55468900E-06 3.O456218OE-10-2.1952354OE-14
-7.2OO8189OE+O3-3.771O8998E+O1 9.87812940E-01 5.00295240E-02-7.36767080E-055.2523455OE-O8-1.4712961OE-11-4 .6101O86OE+O3 2.04857192E+01-2.64600820E+03
F+ J 6182F lE -1 0 OG 298.150 6000.000 1000.002.68834861E+O0-1.76182961E-04 6.06940639E-08-8.91530067E-12 5.47552167E-162.11744095E+05 4.27480838E+O0 3.O8421O84E+OO-9.OOO62139E-O4-1.64599174E-O?1.10121336E-O9-5.5627O92OE-I3 2.11619101E+O5 2.14597653E+O0 2.12499113E+05
F- J 6/82F lE 1 0 OG 298.150 6000.000 1000.002.50000000E+O0 0.0000OOOOE+OO 0.0000OOOOE+OO 0.0000OOOOE+OO 0.0000OOOOE+OO-3.14241522E+04 3.26488285E+O0 2.50000000E+O0 0.0000OOOOE+OO 0.0000OOOOE+OO0.0000OOOOE+OO 0.0000OOOOE+OO-3-14241522E+04 3.26488285E+OO-3.06787772E+04
N+ L 7/88N lZ -1 0 OG 298.150 6000.000 1000.002.51112967E+O0 3.46441751E-06-1.59426938E-08 7.24865663E-12-6.44501426E-162.25624340E+05 4.92767661E+O0 2.80269445E+O0-1.44758911E-03 2.77118380E-06
-2.40187352E-09 7.80839931E-13 2.25575244E+05 3.57877835E+O0 2.26366632E+05N- L 7/88N lE 1 0 OG 298.150 6000.000 1000.002.50897099E+O0-9.58412751E-06 3.8521OO62E-O9-5.68935998E-13 4.20991172E-175.62083017E+04 4.94953202E+O0 2.62723403E+OO-5.93445018E-04 1.12028916E-06
-9.62585603E-1O 3.11119557E-13 5.61880871E+04 4.40111176E+O0 5.69531625E+04N2+ TPIS89N 2E -1 0 OG 298.150 6000.000 1000.003.58661363E+O0 2.53071949E-04 1.84778214E-07-4.55257223E-11 3.26818029E-151.80390994E+05 3.09584150E+O0 3.77540711E+00-2 .06459157E-03 4.75752301E-06
-3.15664228E-09 6.70509973E-13 1.80481115E+05 2.69322186E+O0 1.8I551099E+O5N2- J 9/77N 2E 1 0 OG 298.150 5000.000 1000.003.11567530E+O0 1.45886880E-03-6.01731480E-07 1.I348423OE-10-7.9658518OE-151.68590580E+04 6.38985600E+O0 3.88268480E+OO-3.19244460E-03 8.52278380E-06
-7.34037460E-09 2.20568150E-12 1.67969350E+04 3.11180520E+O0 1.?8744680E+04Z2+ 90994N OF 2E -1 OG 300.000 4000.000 1400.000.40871696E+01 0.28773994E-03-O.42124171E-07-O. 10744347E-10 0.24084770E-140.38982081E+06 0.19017669E+01 0.30832281E+01 0.20225300E-02-O.37376336E-06
-0.72879480E-09 0.31362716E-12 0.39018441E+06 0.74287305E+01NF3+ 90994N lF’ 3E -1 OG 300.000 4000.000 1400-000.82772875E+01 0.12120609E-02-0. 14293019E-06-O.65834289E-10 0.13135263E-130.28434403E+06-0.17602449E+02 0.35353677E+01 O.1OO82626E-O1-O.19761912E-O5
-0.41118668E-08 0.18401435E-11 0.28588697E+06 0.80730133E+01NF2+ 90994N lF 2E -1 OG 300.000 4000.000 1400.000.60226760E+01 0.68474363.E-03-0.858O5958E-O7-O.34O53354E-1O 0.69562801E-140.27545450E+06-0.53112230E+01 0.34224713E+01 O-54404330E-02-O.i0449339E-05
-0.21526023E-08 0.95328823.E-12 0.27632822E+06 0.88361416E+01NF+ 41895N lF lE -1 G 0300.00 5000.00 1000.000.03862177E+02 0.07551806E-02-O.03044943E-05 0.05874447E-09-O.04187479E-131.69734638E+05 0.03457233E+02 0.02871947E+02 0.03312193E.-O1-O.O2691159E-O40.01121951E-07-O.02475131E-11 1.70024780E+05 0.08640247E+02
END
D.1.2. Thermodynamic DataforSURFACE CHEMKINIII:
MATERIAL CHM4BERSITE/WALL/ SDEN/4.05E-9/ !SDEN based on Al 2.702 g/cm3, 4.04A crystal,AL(S) ALF(S) ALF2(S) ALF3(S)END
1234123412341234123412341234
01234
91234
012341234
26.9815g/mol
SITE/SILICON/ SDEN/5.63E-10/ !SDEN based on Si crystal, 5.43A, cubic SDEN= l/a”2*NaS1(S) SIF(S) SIF2 {s) SIF3(S)END
BULK SI(B) /2.33/THZFU40300 500 1000AL(S) 62987AL 1 G 0300.00 5000.00 0600.00O.O2559589E+O2-O.1O632239E-O3 O.O72O2828E-O6-O.O212I1O5E-O9 0.02289429E-130.03890214E+06 0.05234522E+02 0.02736825E+02-0 .05512374E-02-O.04033937E-050.02322343E-07-O.01705599E-iO 0.03886794E+06 0.04363879E+02! Thermodynamic values for ALF, ALF2, ALF3 need to be redone.ALF(S) 32989AL IF 1 G 0300.00 4000.00 1000.000.02775845E+02-0.06213257E-02 0.04843696E-05-O.12756146E-09 0.i1344813E-130.05339790E+06 0.04543298E+02 0.03113515E+02-O.02330991E-01 0.03518530E-04
-0.02417573E-07 0.06391902E-11 0.05335061E+06 0.03009718E+02ALF2 (S) 32989AL iF 2 G 0300.00 4000.00 1000.000.02775845E+02-O.06213257E-02 0.04843696E-05-O.12756146E-09 0.11344818E-130.05339790E+06 0.04543298E+02 0.03113515E+02-O.02330991E-01 0.03518530E-04
-0.02417573E-07 0.06391902E-ii 0.05335061E+06 0.03C09718E+02ALF3 (s) 32989AL lF 3 G 0300.00 4000.OC 1000.000.02775845E+02-O.06213257E-02 0.04843696E-05-O.12756146E-09 0.i1344818E-i30.05339790E+06 0.04543298Z+C2 0.03113515E+02-O.02330991E-01 0.03518530E-04
151
1234
12341234123
-0.02417573E-07 0.06391902E-11 0.05335061E+06 0.03009718E+02 4S1(S) J 3/67S1 100 0000 0000 00G 300.000 5000.000 1
0.26506014F, 01-O.35763852E-03 O.29592293E-O6-O.728O4829E-1O o.57963329E-14 20.53437054E 05 0.52204057E 01 0.31793537E 01-O.27646992E-02 0.44784038E-05 3
-0.32833177E-08 0.91213631E-12 0.53339032E 05 0.27273204E 01SIF(S)
0.00000000 441S89S1 lF 1 0 OG 300.000 3000.000 1000.00 0 1
0.41200666)2+010.35488207E-03-0.72002223E-07-0.21904345E-10 0.67645906E-14 2-0.75613784E+04 0.27842460E+01 0.31449478E+01 0.2S885573E-02-O.57959124E-06 3-0.18072788E-08 O.1O411718E-11-O.7294439OE+O4 0.78767738E+01 4SIF2 (S) 41889S1 lF 2 0 OG 300.000 3000-000 1000.00 0 10.61424704E+01 0.78079745E-03-O.13393120E-06-O.62648393E-10 0.17251383E-13 2
-0.77440422E+05-O.47123275E+01 0.38453453E+01 0.60384651E-02-O.11677322E-05 3-0.45795536E-08 0.26074143E-11-O.76816336E+05 0.72729836E+01SIF3(S) 41889S1 lF 3 0 OG 300.000 3000.000 1000.00 0 :0.85247898E+OI O.13237924E-O2-O.21O42787E-O6-O.11495040E-09 0.30553014E-13 2
-0.12235223E+06-O.15502343E+02 0.46628685E+01 O.1OO87878E-O1-O.18O55442E-O5 3-0.77692990E-08 0.43778518E-11-O.12129652E+06 0.46729660E+01 4S1 (B) J 3/67S1 100 000 000 OS 300.000 1685.000 1O.24753989E 01 0.88112187E-03-O.20939481E-06 0.42757187E-11 0.16006564E-13 2
-0.81255620E 03-O.12188747E 02 0.84197538E 00 O.8371O416E-O2-O.13O77O3OE-O4 30.97593603E-08-O.27279380E-11-O.52486288E 03-O.45272678’E01 4
END
D.2. Pressure and Mole Fraction Estimates in Perrin et. al. (1990)Experiment
At RF power other than 200 W, the total system pressure in the
experimental setup of Perrin et.al., 1990 cannot redetermined. Butthepar&ial
pressures ofall species except HF are known at all pressures, and thus theHF
pressure can reestimated bya ratio method as shown in Figure D-1. The
results for total pressure and the experimental mole fractions obtained from
Perrin’sfigure8 are shown in Table D-1.
Comparison of Chemkin with these experimental valuesare shown in
Figure D-2. At200 W, Chemkin and experiment compare to within ~ 5.3 ‘A
relative error. The error increases at lower power with CHEMKIN predicting
lower NF~dissociation than experiment, less SiFd formed, and less N2 formed.
Although the relative error becomes large, the overall comparison is reasonable,
given the complexity ofthe reactions.
Table D-l. Experimental Mole Fractions&Pressure
Power (W) 300 200 150 100 50NF3 0.144 0.253 0.329 0.466 0.664N2 0.353 0.315 0.294 0.24 0.154SiFg 0.455 0.408 0.37 0.308 0.199Other (N2F4, HF) 0.292 0.224 0.’t8O 0.121 0.062TOTAL 1.244 1.200 1.173 1.135 1.079Pressure (Pa) 12.4 12.0 11.7 11.3 10.8
152
A summaty of all the CHEMKIN predicted species mole fractions, )$, from
Pernn et. al. (1990) experiment from 50 to 300 W is included in Table D-2.
12.5 r 1 I J 1
12.0
11.5
11.0
10.51~1y=8. 12e-8x3-5.92e-5x2+cx+10 max dev2.48E-8,?=1.00C=O.0186
urve with knownpj forced at 200W
by allowing linear termo
orIly to varyO pj Of NF3, N2i SiF4, and N2F4
\y=ax3+bx2+cx+lOmaxdevO.0896,r2=0.990a=8.12E-8,b=-5.92E-5,c=O.0168
,00 ~
o 100 200 300
RF Power (W)
Figure D-1. Determining the HF Partial Pressure
0.8
0.6
0.4
0.2
1 1 1
\
+Solid-Experimental
Q\Dashed–CHEMKl N
7
l\\\\
o~ I i I I
100 200 300
Power (W)
Figure D-2. Comparison of Chemkin and Experiment
153
Table D-2. CHEMKIN Predictions, ~, for Perrin’s Experiment
Power (W)300 200 150” 100 50
Electrons 9.03E-06 1.88E-06 8.32E-07 3.21 E-O? 7.89E-08N 12.38E-02 4.04E-03 1.75E-03 7.15E-04 1.93E-04N2 “0.288 0.248 0.204 0.140 1 0.058Ns 2.06E-26 3.49E-26 3.44E-26 2.79E-26 1.52E-26N+ 1.60E-06 3.35E-08 4.69E-09 5.91E-10 4.09E-11N2+ 4.17E-06 9.09E-07 3.17E-07 8.56E-08 1.15E-08
fNFa 0.079 0.218 0.342 0.521 0.760
NF* 2.43E-03 9.OIE-03 1.41 E-02 1.93E-02 12.23E-02NF ]2.65E-03 \4.17E-03 4.01 E-03 [3.25E-03 1.95E-03N*F* 11.82E-04 12.83E-03 6.58E-0311 .16E-02 1.44E-02
NZF4 13.64E-11 4.92E-10 1.17E-09 12.14E-09 2.71 E-09
F2 0.003 0.019 0.021 0.015 0.006F i 0.202 0.162 I 0.129 I 0.089 / o.04flF+ 1.79E-07 6.84E-08 3.16E-08~1.llE-08 2.08E-09F2+ 2.47E-08 3.36E-08 1.57E-08 4.42E-09 5.34E-10NF+ 2.98E-06 1.56E-06 1.24E-06 1.06E-06 9.03E-07NF2+ 3. 19E-05 4.67E-05 4.82E-05 4.38E-05 3.03E-05NF3+ 1. 17E-04 7.12E-05 4.79E-05 2.75E-05 1.12E-05
F- 1.49E-04 1.1 9E-04 19.69E-05 7.22E-05 4.23E-05
S}Fq 0.399 0.333 0.277 0.199 0.096
0.3. Predictions of Mole Fractions for U02 Etching Experiment
Mole fraction predictions forthe UOzetching expefimentat 17 are shown
below. The parameters set in CHEMKIN are summarized in Table D-3. The NFs
flow rate varied from 5.34 to 5.71 SCCM. The conditions for a well mixed reactor
applies best at 17 Pa since the glow fills the entire chamber.
Table D-3. CHEMKIN Parameters for U02 Etching Experiment
item Value
Volume {ms) 0.125Area (m2j 1.604Power (W) 25 to 250Pressure, piasma (Pa) 17Flow (SCCM) 5.34 to 5.71Ambient Temperature (K) 298H (W m-2 s-’) 1486
154
Predicted species mole fractions at 17 Pa are tabulated in Table D-4 as a function of power absorbed in the
plasma.
Table D-4. CHEMKIN Predicted Mole Fractions at 17 Pa for UOZ Etching Experiments.
Power(W)Species 25 50 75 100 125 150 175 200 225 250E 4.77E-10 1.75E-09 3.76E-09 6.66E-09 1.06E-08 1.57E-08 2.24E-08 3.09E-08 4.19E-08 5.66E-08N 1.57E-07 3.30E-07 5.44E-07 8.16E-07 1.16E-06 1.57E-06 2.06E-06 2.64E-06 3.34E-06 4.21 E-06N2 1.22E-02 2.74E-02 4.25E-02 5.62E-02 6.77E-02 7.74E-02 8.56E-02 9.30E-02 9.97E-02 1.06E-01N3 3.63E-57 5.20E-57 6.18E-57 7. IOE-57 8.19E-57 9.52E-57 1.11 E-56 1.30E-56 1.52E-56 I’.78E-56N+ 1.44E-16 7.94E-16 2.61E-15 7.OIE-15 1.66E-14 3.59E-14 7.27E-14 1.42E-13 2.73E-13 5,30E-13N2+ 1.07 E-I 1 5.71 E-11 1.66E-10 3.74E-10 7.22E-10 1.26E-09 2.06E-09 3.26E-09 5.06E-09 7.86E-09NF3 0.89993 0.7994 6.99E-01 6.05E-01 5.24E-01 4.55E-01 3.94E-01 3.40E-01 2.90E-01 2,44E-01NF2 8.91 E-03 1.03E-02 1.09E-02 1.14E-02 1.19E-02 1.24E-02 1.28E-02 1.32E-02 1.34E-02 1.35E-02NF 1.87E-12 2.33E-12 2.65E-12 2.99E-12 3.42E-12 3.94E-12 4.56E-12 5.28E-12 6. IOE-12 7,04E-12N2F2 3.13E-09 1.58E-09 9.84E-10 7.OIE-10 5.55E-10 4.70E-10 4.14E-10 3.72E-10 3.36E-10 3.OIE-10NzF4 4.48E-04 2. 15E-04 1.25E-04 8.25E-05 5.96E-05 4.56E-05 3.60E-05 2.87E-05 2.28E-05 1.78E-05F2 4.57E-03 1.24E-02 1.85E-02 2.17E-02 2.22E-02 2.12E-02 1.94E-02 1.73E-02 1.51 E-02 1.29E-02F 7.39E-02 0.15032 2.29E-01 3.05E-01 3.74E-01 4.34E-01 4.88E-01 5.36E-01 5.81 E-01 6.24E-01F+ 1,72 E-1 1 7.49 E-I 1 1.96E-10 4.11 E-10 7.44E-10 1.22E-09 1.88E-09 2.76E-09 3.94E-09 5.55E-09F2+ 1.89E-12 1.23 E-I 1 3.52 E-I 1 7.21 E-I 1 1.22E-10 1.82E-10 2.53E-10 3.37E-10 4.38E-10 5.62E-10NF+ 1.49E-08 1.75E-08 1.97E-08 2.11 E-08 2.16E-08 2.15E-08 2.09E-08 2.01 E-08 1.89E-08 1.75E-08NF2+ 2.70E-06 4.62E-06 6.05E-06 7.15E-06 8.00E-06 8.64E-06 9.11 E-06 9.40E-06 9.54E-06 9.51E-06NF3+ 8.74E-07 1.92E-06 3.02E-06 4.19E-06 5.41 E-06 6.66E-06 7.94E-06 9.24E-06 1.06E-05 1.20E-05F- 3.59E-06 6.55E-06 9.09E-06 1.14E-05 1.34E-05 1.53E-05 1.70E-05 1.86E-05 2.01 E-05 2,15E-05
155
D.4. Reveree Rate Coefficient Calculation
The reverse rate coefficient, k,, can be obtained from Gibbs free energy of
formation of the species in a given reaction and the forward rate constant, kf
(Alberty and Silbey, 1997). The forward rate constant, kf is given by equation
(D-1 ). C/R””has units of K; R is the gas constant, B is dimensionless, T is the
temperature (K), v, is the stoichiometric coefficient of the reaction (positive for
products, negative for reactants), j is the species type, and k. is the rate
rconstants with units of (cm3nzolecule ‘]S-l, where n is the order of reaction,
Equations (D-2) through(D-5) show the development needed to obtain the
reverse rate coefficient from the equilibrium rate coefficient for a reaction. Co
and PO are the concentration and pressure of an ideal gas in the standard state
(1 mol/L, 1 bar). Although Gf values are pressure and temperature dependent,
the corrections are less than 0.075 kJ/mole (Appendix E) and can be neglected
for the operating conditions of the plasma.
kf = kOT8e-& (D-1 )
G, =~vjGy {D-2)
Gr = hThKP (D-3)
-x”,Kc = (CORT/ p“) ‘ Kp (D-4)
(D-5)
D.5. Sticking Coefficient
The sticking coefficient, y, a dimensionless quantity defined as the
reaction rate divided by the incoming flux of species, is the probability of a
surface reaction. Conversion from sticking coefficient to rate constant is
accomplished as described in the CHEMKIN documentation (Coltrin et. al., 1996)
and summarized by Equation (D-6). In this equation, R is the gas constant, T the
temperature, M the molecular weight, r the surface site concentration, and VI the
156
stoichiometric coefficient (positive for products
surface site concentration may be calculated
(assumed cubic) and Avogadro’s number.
1?57
and negative for reactants). The
from the crystal dimensions, a,
(D-6)
(D-7)
APPENDIX
El. Etch Rate Conversion
E. ANALYSIS
The etch rate of the UOZ, J(t), is obtained from the following relationships
with ~R a dimensionless variable representing” the fraction of UC)2activity etched
from the stainless steel planchette, t the plasma immersion time, and r the
characteristic etch time.
NR = N,,= (1 -e- ‘i’). (E-1)
[1dN~ N~,=J(t) = — e< = JOe<.
dt=r(E-2)
To convert J from inverse minutes to micrometers per minute, the
relationships shown below are applied. in these expressions, ~R are the moies
of UOP etched, mR is the mass of U02 etched, M is the molecular weight of U02,
N are the number of molecules etched, NA is Avogadro’s number, f is the activity
ratio of 2%U, tln is the half-life of 238U,AO is the initial activity of the sample, A is
the final activity of the sample, S is the surface area of the sample, p is the
density of the UQ2 sample, NR is given by equation (E-1), and J is given by
equation (E-2). The error in assuming that the number .of molecules, N, is equal
to the number of 238Umolecules is less than 0.05Y0. The assumptions inherent
in this derivation are that the sample is uniform, that etching is along the axis of
the cylindrical stainless steel planchette, and the surface area, S, remains
constant.
(E-3)
(E-4)
dqR = 1 dm~ _ Sp dh fll,zAo dN~.— _—— (E-5)dt M dt M dt = N. in(2) dt ‘
$=E?2LI-’”)158
(E-6)
Ave($) =[1Mt112fAo NR (E-7)@NA in(2) Y
dm [1~=/+=:;:, J(t). (E-8)
A
Table E-1 contains the parameters needed in the calculation of the el
rate, equations (E-6) and (E-8). The value in brackets in Equation (E-7) is 27.
pm and in equation (E-8) it’s 10.56 mg. The mass etch rate is better express
as a mass flux in which case the factor in equation (E-8) normalized to the crc
sectional area of the sample, S, becomes 13.3 mg/cm2.
Table E-1. Parameters for Etch Rate Calculation
Symbol Description VaiueM UOZ Molecular Weight (g/mole) 270.05f Activity Ratio, 238Uto U - 0.895tl/2 Half-life, 238U(years) 4.47X109
Ao Initial Activity of Sample (Bq) 129.4Density of UOZ Sample (g/cm3) 4.8
: Surface area of U02 Sample (cm2) 0.796
E.2. Ion-Molecular Collision Cross Section
The ion-neutral collision cross sections (Lieberman
p. 78) of a number of elements are known, but the cross
NF3 were not found in the literature. By comparing the
cross
cross
cross
cross
& Lichtenberg, 19$
sections for NFz a
geometrical and tr
sections, it was desired to determine if the ion-molecular coliision (tn
sections of NF, NlF2 and NF3 could be estimated from the geometri
sections and the cross sections of the known atoms. The geometri~
section was determined based on the radius of the appropriate elemel
(Aiberty and Siibey, 1997, p. 364).
The NF molecuiar dimensions are given in Lide (1993), and the fiuori
and nitrogen diameters by Aiberty and Siibey (1997), and shown in Figure E
The geometrical cross section of the two moiecules, NF2 and NF3, w{
159
determined based on the NF dimensions and bond angles, using a drawing
program.
A compilation of physical data for species of interest are shown in Table
E-2 and the cross sections are piotted in Figure E-2. The estimated (Est.) true
cross sections in Tabie E-2 are based on the comeiation shown in Figure E-2 for
the true cross section. Based on these resuits, calculations of the cross section
for NF2 or NF3 based on the Ar moiecuie differ by a factor of 1.5 and 2.7,
respectively.
Atomic & Molecular Dimensions/
\
N-F: 135.28pmAngle F-N-F: 103,18dF = 79.2 pmdN = 104,2 pm
F292.82
N~b F
~135.30~
NF2 uF NF3
Figure E-1. NFz and NFs Geometrical Cross Sections
Tabie E-2. Physicai Data on Seiect Species
Species Z M 2radius (m) ~geo (cm ) ~t~e (cm2) O,we
o geo
He 2 4.0026 2.91 E-11 2.66E-17 2.00E-15 75.18F 9 18.9984 3.96E-11 4.93E-17 Est: 2.46E-15 49.96
Ne 10 20.1797 3.54E-11 3.94E-17 2.55E-15 64.77Ar 18 39.948 6.59E-11 1.36E-16 5.27E-15 38.63
NF2 25 52.0035 1.46E-10 6.73E-16 Est:8.03E-15 11.93NF? 34 74.0019 1.57E-10 7.72E-16 Est: 1.41 E-14 18.25
160
n,01
ECJ
True Cross Section
10-’4 : Ar
He
v c = +2.88E-18M2 -3.57E-17M1 +2. 10E-15
-17He
10! I I
o 20 40 60
Molecular Weight, M (amu)
Figure E-2. Cross Section Correlation
E.3. Ion Energy in Traversing the Plasma Sheath.
ions traversing the plasma sheath undergo acceleration in traversing the
sheath. If there were no collisions, the total energy gained would equal the
effective RF sheath voltage, in electron volts. But because of collisions between
ions and neutral particles in the sheath, the actual energy gained will be less
than the equivalent DC sheath potential. The purpose of this analysis is to
calculate the energy gained by an ion in traversing the sheath based on plasma
theory (Lieberman and Lichtenberg, 1994).
An ion of mass, m, and molecular weight, M, traversing a sheath with an
effective plasma potential,
temperature in eV given
temperature given by TG
V., in volts, in a plasma with pressure, p, electron
by $, ion density given by Xi, and neutral gas
will experience one or more collisions unless the
pressure is less
the permittivity
than 0.4 Pa (Lieberman & Lichtenberg,
of free space (8.854x10-12 F/m), e
161
1994, p. 350). Let ~ be
the charge on an ion
(1.601 x10-’9 C), and m the ion-atom collision cross-section. The following
equations in Table E-3 apply to this development, where the referenced
paragraphs are to Lieberman and Lichtenberg, 1994.
Table E-3. Plasma Sheath Thickness and Ion Energy.
Noxipni =
RT~
Napn~. —RT~
Relationship Description Reference NumberEquationi
e~q=~
Eiectron Temperature (K)(E-9)
p,=Xip Ion Pressure(E-IO)
(E-1 1)Ion number density
II&o@A= —eni
/li=~nG 0,
Plasma density
Debye Length 2.4.22
Ion mean free path in 3.5.7sheath
Bohm Velocity at 6.2.4plasma/sheath interface
Modified Bohm velocity at 11.2.53plasma/sheath interface
IIe~UB. —
mi
u, =
{r)
Al+7r—
2A,
s=p.,; ] ]
0.5 0.4 sheath thickness~,1.5~0.5
2e , from Child’s Law with0;
r eniu, collisions
AVe Ion net kinetic energyE, = 0.62-
5 after traversing the sheath
t 1.2.54
11.2.57
(E-12)
(E-13)
(E-14)
(E-15)
(E-16)
(E-1?)
(E-1 8)
1Equations numbers are those given in Liebermanand Lichtenberg, 1994.162
,,The CHEMKIN predictions of the ion mole fraction, electron energy, and
neutral gas temperature are summarized in Table E4, along with the
experimentally measured sheath voltage. A MathCad calculation of the
parameters is summarized in Table E-5 at 50 W. For a plasma immersion time
of 30 minutes, with ions impinging the electrode from both sides, the power
deposited is 0.378 W for a total energy deposition of 680 J.
Table E-4. Calculated Mole Fractions of Plasma Species at 17 Pa.
Species 50 VV IoowIon,XI 6.6E-06 1.1 E-05Sheath Voltage (V) -142 -261Electron Energy (eV) 5.21 4.87Neutral Temperature (K) 298.2 298.3Sheath Thickness (cm) 0.13 0.16Ion Energy (eV/molecule) 11.3 17.9Ion Energ y (kJ/mol) 1087 1731
The ion energy is not too sensitive above a cross section of 1xl 0-18m2 for
the NF3 ion as shown in Figure E-3.
t i
-o
j
NF~ Ion
Sheath Voltage”-261 V
o
-\o
\
O\o~o
~o (I I
o 1 2 3
Cross Section x 10-’8 (m2)
Figure E-3. ion Energy Dependence on Cross Section.
163
Ob..0*V0: ~stimato ttao _?t-rgy of -n NF=* ion tr~rsin~ the pIa*ma sho~h andimp_ Cting ● curface. Inc$udo Collisions in th- shosth +- tho Chitd ~. Obtain theplasm= nhwuth thickness. Obtain the enarey dapasite+d an m Z- diarnater stainlessat-d planch~te at a specifted plasm= processing time. l%e equations specK96d arefound in Liabarrnan & Uctnenberg. 1994.
Input- :=1.dol.lo--a Electron Ch=rgo
k :- I,sl .lCI-=.J.K-l 1301tzman Constant
P :* SO.W -l=s?na XSorbad F’_r
p := 17 .p. Plasm- pmssum
na :.71 .- Molecular -ight of ion50~u):=s.21-v Electron Temperature in eV
x ~ :=6s5.10-6 10n Mole Fraction
-r * :.298 .17-K Gas temperature
=i := 1.41 .lQ-1=.*2 ion collision Cross Section
v ● := 142-V Sheath Voltage
t ~ :.m - PIasma Pr0c9ssing Time
Int errnediate Results-I- e-e* :._
k~i:=x
MA
Fi:=xi”P
~.:= pi”NA. R.T ~
p-NAXxe :--—
R.TO
-- ----
T= =6.O4.1O* K
Xui = 1.17P .10-2S k=
pa= I .113-10-* P-
Xla =2.705-101= L*3
A = 1 .032-10-4 m
. . -- .=-. — ---- . . .
A i = 1 .717.10-+ m
u~ =2.66-103?s
~i.l.pos.los=s
Ui:= F=A2.A~
Results
.:=[,.=..o.[~y=.v~:=~:”~ s =o.124-cltl Sheath Thickness
Ji:=ni-ui 3 i = 5.16.10’” ~ Ian Flux to Surfacean= -s
A i.v ● ..3Ei :=0.62. E= = 1.S06.10-xe J Ion Energy
m
Eev :=? Eev=ll.279V
E -1. := Ei.N * = mol. = 1 .0s7 .105-2mol
Q ,=2.J1.A.~. x Q =0.378 W Heat Generatwdfrom 2 sides of planchette
E_Total := Q.tp E_T o%ed = 679 .87S J Total Enary Deposited
R :=S.3144-Jamal- 1 .K- 1
Vel :=0.125-=
L :=0.0365 .cat
d :=2.*
A ,=7?4=T
A = 2.027 .10-3 ma
Electron Temperature
Mass ion
Pressure ion
Ion number density
Gas number Dansity
Debye L=ngth
---- ---- ---- ---- -—--- ----- .
Jon m-an frsa path
EIohm Velocity
Ion Velocity
E_~ux := ~ E_fiux = 1S6 .334 -~ Energy Flux~a
164
E.4. Energy Deposited From Exothermic Reactions of U02 and F
A Mathcad calculation for the maximum energy deposited as heat from
samples of U02 and F atom radicals is included in Table E-6. The maximum
energy deposited as heat from a sample is 62 J. By comparison, the energy
deposited by ion bombardment is 680 J (Table E-5).
165
Table E-6. Energy From U02 Reactions with
Energy Deposition From Exothermic Reactl
- Objective: Estimate the energy deposited on the SS planch~due to reaction of the UQ and F atoms at 50 W RF Power. Assure-energy is converted to heat. Base the estimate on 100 ~ of uranylsample converted to a uniform layer of LQ. Assume that all the U(
* UFe within 30 minutes (actual time follows exponential and takes -
Reaction
CcmstantsN := 236.1o19
kw
Ss := 16”—m-K
d := 1.00?.cm
L := 0.0365.cm
NA := 6.022-1#.mole-1
AH r := - lS38.4@-!-mole
t p := 30”min
U(32+ 6F --> W* +02
Molecules of UOZpersamF
Thermal Conductivity of Sta
Diameter of planchette
Thickness of planchette
Avogadro’s Number
Reaction Enthalpy [exother
Plasma Processing Time
titermediate Resulti
~ , n-c?.=— S = 7964”10-5 m24
Crosssectional
NT := —
NA-r) = 3.919 .10-5 lnol Moles of U02
-AH r-qQ ,= Q = 0.033W Maximum heat I
‘P
E_tota{ := Q-t ~ E_total = 62.249 J
E.5. Vapor Pressure Correlation
Vapor pressure correlations and the related te
described in Table E-7. References to the cc
166
Table E-7. Vapor Pressure Correlation.
Species Vapor Pressure Temperature (K)
UF6,.
UF5
UF4
UF3
UF2
UF
u
U02
U02F
U02F2
Correlation (Pa)Low High
~,521-~133.2x1O T 273 342
,3,994-W133.2x1O T 125 420
~2,6-16i400
133.2x1O 7 ‘3”02”r’Og’07 298 1309~~45_~
133.2x1O T 1543 1673
Reference
Lange and Forker (1967), p.1450,
Katz et. al. (1986) Vol. 1,p308
Jacob et. al. (1980), p. 27,
Jacob et. al, (1980), p 6I
No data Bond dissociation energy suggests p- PUF4
(Hildenbrand and Lau, 1992)
No data~71-25230
1.01X105X10 T 1480 2420 Katz e. al. (1986), Vol 1, p. 228
28.65-34:0—-5.64 *LwIOI’
106X10 3120 5000 Ohse et. al. (1979)
No data~68-15106
1.01X105X10 r 956 1000 Lauet. al (1985)- (1/g. s)*Puo2F2 at
UOF4 1000K - “ Lau et. al. (1985)
167
E.6. Gibbs Energy Correction For Pressure And Temperature
The Gibbs free energy of formation has a pressure ~ependence (Alberty
and Silby, 1997) that depends on ‘whether the material is in the solid (or liquid)
phase, or in the gas phase. In the solid phase, the volume, V, of the material is
independent of pressure. The Gibbs energy of formation, G, is given by
G= GO+ V(p-pO) (E-19)
GO is the Gibbs energy at standard temperature (T = 298K) and pressure,
PO= 1 bar).
Taking one mole of the amorphous U02 (density - 6.8 g/cm3), the
equivalent mass is equal to the molecular weight, 270 g/mole. Using the density
and mass, V -56.25 cm3 per mole of UOZ. The chamber pressure at the lower
operating limit is 10.8 Pa, which gives the greatest error in the above equation.
The correction, in kJ/mole units repofied for Gibbs, gives
G = Go – 5.6x10-3 (kl/mole) (E-20)
to the
to the
Therefore, for solid materials, the correction is extremely small compared
typical values found for the reaction sets and can be neglected compared
standard state values. Since the reactions are with absorbed F atoms on
the surface, corrections to the Gibbs energies for
corrections either. The Gibbs free energy of F atoms
fluorine will not require
in the gas phase will be
used as an approximation.
The UF6 desorbs into the gas phase, and
applied to this gas. The correction in this case for
given by
[)G= GO+qRTln ~
P
so the ideal gas law can be
the Gibbs heat of formation is
(E-21)
Using the same values as before leads to the following correction
G = Go – 0.075(ti / mole) (E-22)
168
Again, this comection is small for the reactions of interest and will be
neglected.
The
Therefore,
apply.
plasma gas temperature is -298K for the operating pressures used.
standard state temperature values of Gibbs energies of formation
E.7. Thermodynamic Analysis of Reactions
Thermodynamic analysis from Gibbs free energy of reaction, GR, is
determined from the Gibbs free energy of formation, Gj, of species j and the
stoichiometric coefficient, ~j, of reactants and products. ~ The stoichiometric
coefficient is positive for products and negative for reactants. Simiiariy, the
enthalpy of reaction, HR, is detemlined from the enthaipy of formation, Hj, of
each species, determines whether the reaction is exothermic (negative HR) or
endothermic (positive HR). The reaction vaiues are given as:
GR= ~vjGj (E-23)
H,=~v,Hj (E-24)J
When GR is positive, the reaction cannot proceed spontaneously but
requires energy to proceed. When GR is negative, the reaction is favorabie. The
reaction possibilities of one or two absorbed F atoms with U02 based on
combinations of U-O-F combinations (Chapter 6) is detaiied in Figure E-4. if GR
is positive (dashed iine), the reaction sequence is terminated. When GR is
negative (soiid iine), the reaction sequence is continued to the end product,
which is UF6. The uranium metai reaction with F atoms are quite different. The
initiai reaction is with a singie absorption site as shown in Figure E-5. Since no
oxygen atoms are in the reaction, oniy uranium fluorides form and there are no
unfavorable reactions.
169
XF+ IJ02
Reactions and Gibbs Free Energy (kJ mot-f)Note: dashedIiinfavorabla raatitonO or 02 raac%onprcductsnotshown
* iJF+898 , .
/ IL/~ -,/ “+664 > ~~f~
\
----
\\ 427
\\ UOZFa\
;,$;::.V&lj~~
\ -650
\Y
-112
<,4
➤ UF(3\ -223\ I\ UOF3 -f33
+282\ ,’+248, ‘%275 I
1U02F2 0 -164 U4F4
\ ‘//
‘+ ‘ ‘, -387\ -162
+@;_:~e, t~ \+29
J -368 I+ ‘;355,J&---.. uF~ > ‘“
:.-:.... .. .
Figure E-4. Reaction Sequence of F Atoms and UOZ.
Reactions and Gibbs Free Energy (kJ mb)
-1627
-2X2
/-449 UF4
/-670
UF3 > -162
UF2
/
UF5~
-661
UF~
‘m-396
49 UF ~
\ -162UF5 ~
UF6
UF6
UF6
UF6
UF6
Figure E-5. Reaction Sequence of F Atoms and U MetaL
170
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