Embed Size (px)
Citation preview
Energetic neutral fluxes towards surfaces in a magnetically enhanced reactive ion etch-like reactorWinfried Sabisch, Matthias Kratzer, and Ralf Peter Brinkmann Citation: Journal of Vacuum Science & Technology A 21, 1205 (2003); doi: 10.1116/1.1565153 View online: http://dx.doi.org/10.1116/1.1565153 View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/21/4?ver=pdfcov Published by the AVS: Science & Technology of Materials, Interfaces, and Processing Articles you may be interested in Numerical simulation of dual frequency etching reactors: Influence of the external process parameters on theplasma characteristics J. Appl. Phys. 98, 023308 (2005); 10.1063/1.1989439 Observation and evaluation of flaked particle behavior in magnetically enhanced reactive ion etching equipmentusing a dipole ring magnet J. Vac. Sci. Technol. B 22, 1688 (2004); 10.1116/1.1763592 Analytical model for ion angular distribution functions at rf biased surfaces with collisionless plasma sheaths J. Appl. Phys. 92, 7032 (2002); 10.1063/1.1524020 Modeling oxide etching in a magnetically enhanced reactive ion plasma using neural networks J. Vac. Sci. Technol. B 20, 2113 (2002); 10.1116/1.1511212 Magnetic field optimization in a dielectric magnetically enhanced reactive ion etch reactor to produce aninstantaneously uniform plasma J. Vac. Sci. Technol. A 16, 1600 (1998); 10.1116/1.581126
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Mon, 22 Dec 2014 08:16:17
Energetic neutral fluxes towards surfaces in a magnetically enhancedreactive ion etch-like reactor
Winfried Sabischa) and Matthias KratzerInfineon Technologies AG, MP TI CS SIM, Balanstrasse 73, D-81541 Munich, Germany
Ralf Peter BrinkmannDepartment of Electrical Engineering, Ruhr-University Bochum, D-47780 Bochum, Germany
~Received 2 October 2002; accepted 10 February 2003; published 1 July 2003!
In very large scale integrated microelectronics fabrication magnetically enhanced reactive ion etch~MERIE! reactors are established for many dry etch processes of conducting or dielectric materials.Angularly and energetically resolved distributions of the surfaces incident particles~ions andneutrals! as well as the fluxes of ions and neutrals play an essential role for feature scale profileevolution. The focus of this work is set on the calculation of the neutral to ion fluxes ratio. Thereforethe MERIE reactor’s boundary sheath is simulated by the technology-oriented computer aideddesign simulation tool hybrid plasma sheath model~HPSM!. HPSM consists of a self-consistentcoupling of a fluid dynamical part to a Monte Carlo part. The sheath and presheath regions aredescribed in one unified model. Energetic neutrals impinging the surface can be monitored inaddition to the positive ion species. Simulations with parameters in the range of about 100 mTorr,rf voltages of a few 100 V, magnetic fields of about 90 G, and plasma powers of about 1000 W arepresented. The simulations show that the flux of the energetic neutrals compared to the flux of theions is not neglectable and that the neutral flux makes an important contribution to the energy budgetof the surface impinging particles. ©2003 American Vacuum Society.@DOI: 10.1116/1.1565153#
I. INTRODUCTION
Magnetically enhanced reactive ion etch~MERIE! reac-tors are suited for many dry etch processes. Examples are theSi etch of high aspect ratio capacitor trenches1 or the etch ofSiO2 for the fabrication of very large scale integratedmultilayer structures. Butterbaughet al.2 showed that theetch yield for the selective SiO2 /Si etch is strongly influ-enced by the ratio of neutral to ion fluxes. Zhang andKushner3 investigated the surface reactions during C2F6
plasma etching of SiO2 with equipment and feature scalemodels. They demonstrated the dependency of etch featureprofile on the magnitude of the passivating neutral to ion fluxratio. Grayet al.4 discussed the dependence of ion-enhancedpoly-Si etching on the neutral-flux-limited etching regime.Whereby all of these works deal with thermal neutrals, Som-merer and Kushner5 showed for CF4 plasmas in a theoreticalstudy that the energetic~‘‘hot’’ ! F flux can be comparable tothe ion flux. Lieberman and Lichtenberg6 pointed at the re-duction of ion bombarding energy due to collisions in thesheath. They described the proportional increase of the totalenergetic particle flux but they did not quantify this flux. Theprevious studies elucidate the important influence of the neu-tral to ion flux on the plasma processes of SiO2 and Si etch-ing. The focus of this work is set on the calculation of theneutral to ion fluxes ratio for typical MERIE reactor processconditions.
Section II describes the hybrid plasma sheath model~HPSM! for the numerical simulation of the MERIE reac-tor’s boundary sheath. Special interest is focused on the
treatment of the energetic neutrals and the calculation of theangularly and energetically resolved distributions of them. InSec. III the process conditions for the simulations are sum-marized. The processes considered here are in an intermedi-ate pressure regime of about 100 mTorr. The main species inthe plasmas of interest is argon, therefore a calibrated argonmodel was used throughout all simulations. In Sec. IV thedistribution functions of neutrals and ions will be discussedas well as the flux ratios.
II. HYBRID PLASMA SHEATH MODEL „HPSM…
The detailed description of the hybrid plasma sheathmodel ~HPSM! used in this study has been givenelsewhere.7,8 HPSM is a one-dimensional plasma sheathmodel which covers the requirements of a technology-oriented computer aided design~TCAD!-suited simulator:~1! description of realistic process conditions like externalbias voltage, nonharmonic modulation of the periodic bound-ary sheath, multiple positive ion species, interaction with thebackground gas, etc., and~2! computational efficiency andnumerical stability of the model. The hybrid model consistsof a fluid-dynamic~FD! part for the computation of the time-modulated potential within the boundary sheath and a one-particle Monte Carlo~MC! part which treats the particle dy-namics of a sufficiently large number of energetic neutralsand positive ions subjected to the electrical field. Specialinterest has been directed to the consistency of both models.
The fluid-dynamical approximation takes into account thefirst two moments of the Boltzmann equations for electronsand ion species. In our model, we consider elastic scattering~ES! ~hard sphere and Langevin enhanced! and resonanta!Electronic mail: [email protected]
1205 1205J. Vac. Sci. Technol. A 21 „4…, Jul ÕAug 2003 0734-2101 Õ2003Õ21„4…Õ1205Õ5Õ$19.00 ©2003 American Vacuum Society
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Mon, 22 Dec 2014 08:16:17
charge exchange~CX! with the neutral background gas. Themodel solely treats the sheath and presheath region of theplasma, so ionization, attachment, and other chemical reac-tions are neglected. Coulomb interactions between chargedparticles are neglected as well because of the small ioniza-tion ratio of the plasmas under consideration here. The gov-erning fluid-dynamical equations for the electrons are
]ne
]t1
]
]x~neve!50, ~1!
]ve
]t1ve
]ve
]x52
e
meE2
Te
me
1
ne
]ne
]x2neve , ~2!
and for the ions
]na
]t1
]
]x~nava!50, ~3!
]va
]t1va
]va
]x5
qa
maE2
Ta
ma
1
na
]na
]x2nava , ~4!
with electron indexe, ion index a ranging from 1 toN,electron and ion velocitiesve and va , particle massesme
andma , electron temperatureTe , constant bulk temperatureof the ionsTa , electron and ion densityne andna , electricalfield E, electron and ion chargese andqa , and electron andion friction termsne andna . The friction terms are depen-dent on the hard sphere cross sectionsHS, the Langevinenhanced constantKL , and the charge exchange cross sec-tion sCX .
The set of fluid-dynamical equations is completed by thePoisson’s equation
«0
]E
]x5(
aqana2ene . ~5!
Equations~1!–~5! are solved using an asymptotic timeand length scale expansion and by assuming periodic exter-nal fields with frequencyv rf , an intermediate frequency re-gime vpi!v rf!vpe ~with plasma frequencies of ions andelectronsvpi and vpe), and a small Debye length with re-spect to the sheath thickness. Details of the mathematicalformulation will be presented in upcoming papers~e.g.,Ref. 9!.
In the Monte Carlo part the trajectories of a sufficientlarge number of particles are followed. The ions move in theelectric field as calculated by the FD module. Elastic andcharge exchange collisions with a spatial uniform back-ground gas are accounted for. Particle collisions are treatedby applying a null collision method.
Energetic neutrals are generated by scattering processes ofions with the background gas. Above a user-specified energythreshold the energetic neutrals will be tracked in addition tothe ions. The energetic neutral’s flux towards surfaces is cal-culated with respect to the ion flux.
Particles hitting the surface contribute to the calculationof the angularly and energetically resolved distributions of
ions and energetic neutrals. An energy discrimination in theangular distribution of the neutrals separates thermalized par-ticles from energetic particles.
III. PROCESS CONDITIONS
Table I summarizes the process conditions consideredhere. The conditions are typical for a MERIE reactor in aSiO2 etch regime. Reactor characteristics like geometry,magnetic field, and plasma density are used to determine theboundary condition between the presheath/sheath and plasmabulk region by a ‘‘simplified,’’ algebraic plasma bulk model.Due to uncertainties in the exact plasma density, calculationswere also performed for 109 cm23 and 1011 cm23.
In Table II the collisional parameters for argon are listed.Three scattering processes are concerned. The collision pa-rameters are calibrated with experimental data.8 All simula-tions trace 100 000 ions in the Monte Carlo part. The ionsstart at a distance of 3 cm from the surface in the middle ofthe reactor with a kinetic energy of several meV correspond-ing to the assumed gas temperature and with uniformly dis-tributed phase between 0 and 2p. The mean free path lengthl0 is much smaller than this distance; therefore the initialdistribution of the particles has no influence on the angularlyand energetically resolved distributions of ions and neutrals.
IV. SIMULATION RESULTS AND DISCUSSION
A. Distributions of ions
Figures 1 and 2 show energetically and angularly resolveddistributions. The pressure varies from 50 to 120 mTorr andthe sheath voltage according to Table I. All distributions areplotted normalized to unity.
The typical bimodal structure~with peaks at minimumand maximum sheath voltage! for rf sheaths in the low pres-sure regime is not obtained under the process conditions wewere interested in this study. Instead, the whole distributionfunction is shifted towards lower energies. At 50 mTorr allions have an energy less than 250 eV although the sheath
TABLE I. Process conditions for three different pressure-voltage pairs.
rf frequency 13.56 MHzrf voltage 2530/2470/2430 VPressure 50/80/120 mTorrGas temperature 500 KElectron temperature 2.5 eVMagnetic field 90 GPlasma density 1010 cm23
Reactor height 6 cmReactor radius 11 cmPositive ion species Ar1
TABLE II. Heavy particle collision parameters~argon discharge!.
Ar11Ar→Ar11Ar sCX54.0310219 m2
sHS52.5310219 m2
KL51.2310215 m3 s21
Ar1Ar→Ar1Ar sHS57.0310220 m2
1206 Sabisch, Kratzer, and Brinkmann: Energetic neutral fluxes towards surfaces 1206
J. Vac. Sci. Technol. A, Vol. 21, No. 4, Jul ÕAug 2003
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Mon, 22 Dec 2014 08:16:17
potential drop is 530 V. This behavior can be explained by alarge number of collisions of the ions in the sheath regionleading to broadening of the distribution function. These col-lisions cause an energy transfer to the neutrals.
The small peaks in the distribution function are character-istic for capacitively coupled rf discharges of argon~e.g.,Ref. 10!. Wild and Koidl11 explained the structure by theinteraction of ions produced by charge exchange reactions inthe sheath with the rf modulation of the sheath potential.Position and intensity depend on process parameters such aspressure and bias voltage. For higher pressure the distribu-tion functions of the ions are shifted even more to lowerenergy levels.
For the angular distibution rotational invariance is as-sumed. The angle of incidencex is defined as the anglebetween the direction of the incoming particle and the sur-face normal. The total fluxGa of speciesa is given by
Ga52pE0
p/2
Ca~x!sinx dx, ~6!
whereCa(x)sinx denotes the angular distribution function.The ions hit the surface mainly under angles between 0°
and 4°. The maximum of the angular distribution is shiftedtowards higher angles by an increased pressure.
In Figs. 3 and 4 the energetic and angular distributions ofthe ions are plotted for different plasma densities and a fixedpressure of 85 mTorr. The simulated sheath thicknessesdsh
range between 2.2 and 5.0 mm with the smallestdsh for theplasma density case of 1011 cm3. As the number of collisionsin the sheath scales with its length, the ion energy distribu-tion function is shifted towards lower energies when theplasma density is decreased. Due to the longer sheath thick-ness, the angular distribution broadens for a decreasedplasma density.
B. Distributions of energetic neutrals
The energetic neutrals are generated by collision pro-cesses of the accelerated ions in the sheath region. Figure 5shows the energy distribution of these neutrals. The thresholdfor the energetic neutrals is 10 eV; a neutral with an energy
FIG. 1. Ion energy distributions~IED! for different pressures. Process con-ditions as in Table I.
FIG. 2. Ion angular distributions~IAD ! for different pressures. Process con-ditions as in Table I.
FIG. 3. Ion energy distributions~IED! for varying plasma densities. Pres-sure: 85 mTorr; other process conditions as in Table I.
FIG. 4. Ion angular distributions~IAD ! for varying plasma densities. Pres-sure: 85 mTorr; other process conditions as in Table I.
1207 Sabisch, Kratzer, and Brinkmann: Energetic neutral fluxes towards surfaces 1207
JVST A - Vacuum, Surfaces, and Films
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Mon, 22 Dec 2014 08:16:17
gain above 10 eV will be tracked in the MC simulation oth-erwise not. Overall, the energy distribution ranges from 0 to100 eV. By increasing the pressure the number of collisionsincreases. Therefore the steepest distribution function appliesfor the highest pressure of 120 mTorr. In semiconductor fab-rication, damage by high energetic particles~ions or neutrals!must be avoided; hence a process regime with higher pres-sure seems favorable.
The angularly resolved distribution functions of the ener-getic neutrals are plotted in Fig. 6. Again, the maximum ofthe distribution function is slightly shifted towards higherangles by increasing the pressure~quite similar to the ionangular distributions!. There is a second maximum at about20° which shifts in the same direction for increasing thepressure. The broad angular distribution reflects that the en-ergetic neutrals are not directed by the electrical field andundergo several collisions.
C. Fluxes of ions and energetic neutrals
The ion flux towards the waferG ion is computed from the‘‘simplified,’’ algebraic plasma bulk model which is used forthe computation of boundary conditions for the sheathmodel. The ion fluxG ion scales linearly with the plasma den-sity as noted in Table III and reduces with increasing pres-sure due to an increased collision frequency in the diffusionconstant.
The energetic neutral fluxGneutral listed in Table III iscomputed directly from HPSM. In addition, the ratios of en-ergetic neutral to ion fluxr 5Gneutral/G ion is also given. Theenergetic neutral flux as well as the flux ratior always in-crease with higher pressures. For an intermediate plasmadensity of 1010 cm23 flux ratios r can be reached up to 9.3;an increase in plasma density will further decreaser . r goesthrough a maximum by varying plasma density because ofthe delicate dependence of the energetic neutral fluxGneutral
on the ion fluxG ion and the sheath thickness. By increasingthe plasma densityG ion will be increased but the sheaththickness~zone of production of energetic neutrals! will bereduced. These competing effects let the flux ratior decreasefor higher plasma densities. The smallest plasma density of109 cm23 gives an energetic neutral flux which is more sen-sitive to pressure changes than in high plasma density re-gimes ~e.g., for 109 cm23: r (85 mTorr)/r (50 mTorr)52.2,for 1010 cm23: r (85 mTorr)/r (50 mTorr)52.1, and for1011 cm23: r (85 mTorr)/r (50 mTorr)51.8). This illustratesthe trade-off for a semiconductor fabrication process be-tween achieving either high flux ratiosr or achieving sensi-tive or stable pressure dependencies ofr .
Another enlightening flux ratioGY can be postulatedwhich takes into account the yield functionY(E,E0) (E0
denotes the activation energy threshold! of the surface acti-vation process
GY5*E0
` Cneutral~E!Y~E,E0!dE
*E0
` C ion~E!Y~E,E0!dE. ~7!
Assuming a common activation process scale ofY(E,E0)}AE2AE0 we get for the intermediate plasma density of1010 cm23 the activation energy threshold dependence ofGY
as shown in Fig. 7. For high activation energy thresholds
FIG. 5. Energetic neutral energy distributions~NED! for different pressures.Process conditions as in Table I.
FIG. 6. Energetic neutral angular distributions~NAD! for different pressures.Process conditions as in Table I.
TABLE III. Fluxes of ions and energetic neutrals toward surfaces.r is theratio of energetic neutral to ion fluxGneutral/G ion .
Pressure@mTorr#
nplasma
@cm23#G ion
@1018 cm22 s21#Gneutral
@1018 cm22 s21# r
50 109 0.811 0.38 0.585 109 0.552 0.64 1.1120 109 0.418 0.80 1.950 1010 8.11 26.4 3.385 1010 5.52 37.5 6.8120 1010 4.18 39.8 9.350 1011 81.1 164.0 2.085 1011 55.2 196.0 3.6120 1011 41.8 209.0 5.0
1208 Sabisch, Kratzer, and Brinkmann: Energetic neutral fluxes towards surfaces 1208
J. Vac. Sci. Technol. A, Vol. 21, No. 4, Jul ÕAug 2003
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Mon, 22 Dec 2014 08:16:17
the ion flux dominatesGY at all pressures. Nonetheless, forSiO2 etching the threshold will be less than about 40 eV; theflux ratiosGY show the same dependencies as discussed forthe flux ratiosr .
V. SUMMARY AND CONCLUSION
In this article we have presented sheath simulations fortypical plasma process conditions for SiO2 or Si etch. Pro-cess conditions were in an intermediate pressure regime ofabout 100 mTorr with magnetic fields of about 90 G, plasmapowers of about 1000 W, and rf sheath voltages of a few100 V.
The simulation tool used for these studies was HPSM, theTCAD simulation tool hybrid plasma sheath model. Ener-
getically and angularly resolved distribution functions forions and energetic neutrals have been obtained. The ion andenergetic neutral fluxes towards surfaces have been moni-tored.
Due to a multitude of ion-neutral collisions in the bound-ary sheath, the energy distribution of the ions tends to lowerenergy levels; a bimodal structure—as known from low pres-sure plasma regimes—is not obtained. Pressure dependenciesare discussed as well as dependencies of the energy distribu-tion on the plasma density. The dependency of the angulardistributions on pressure or plasma density is mostly thesame as for the energy distributions.
Neutrals with energies up to 100 eV are generated in theboundary sheath. The ratio of the energetic neutral to the ionfluxes was found to extend up to 9.3. Sensitivity of the fab-rication process on energetic neutral flux is favored by a lowplasma density (;109 cm23); high fluxes of energetic neu-trals can be obtained for medium plasma densities of about1010 cm23.
1J. Bondur, R. Bucknall, F. Redeker, and J. Su, Proc. SPIE1803, 45~1992!.
2J. W. Butterbaugh, D. C. Gray, and H. H. Sawin, J. Vac. Sci. Technol. B9, 1461~1991!.
3D. Zhang and M. J. Kushner, J. Vac. Sci. Technol. A19, 524 ~2001!.4D. C. Gray, H. H. Sawin, and J. W. Butterbaugh, J. Vac. Sci. Technol. A9, 779 ~1991!.
5T. J. Sommerer and M. J. Kushner, J. Appl. Phys.70, 1240~1991!.6M. A. Lieberman and A. J. Lichtenberg,Principles of Plasma Dischargesand Materials Processing~Wiley, New Orleans, 1994!, p. 350ff.
7M. Kratzer and R. P. Brinkmann,The IEEE International Conference onPlasma Science~IEEE, New York, 2000!, 3D03.
8M. Kratzer, R. P. Brinkmann, W. Sabisch, and H. Schmidt, J. Appl. Phys.90, 2169~2001!.
9R. P. Brinkmann, J. Appl. Phys.~submitted!.10J. Janes and C. Huth, J. Vac. Sci. Technol. A10, 3522~1992!.11C. Wild and P. Koidl, J. Appl. Phys.69, 2909~1991!.
FIG. 7. Energetic neutral flux ratioGY for different pressures. Process con-ditions as in Table I.
1209 Sabisch, Kratzer, and Brinkmann: Energetic neutral fluxes towards surfaces 1209
JVST A - Vacuum, Surfaces, and Films
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.21.35.191 On: Mon, 22 Dec 2014 08:16:17
