JVA061605 - Measurement of the Tangential Momentum Accommodation Coefficient of H2 on Stainless Steel Extreme Ultraviolet-resist and Polyimide

8/12/2019 JVA061605 - Measurement of the Tangential Momentum Accommodation Coefficient of H2 on Stainless Steel Extre

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Measurement of the tangential momentum accommodation coefficient ofH2 on stainless steel extreme ultraviolet-resist and polyimideJohannes F. M. Velthuisand Laurens van BokhovenCitation: J. Vac. Sci. Technol. A 31, 061605 (2013); doi: 10.1116/1.4816941View online: http://dx.doi.org/10.1116/1.4816941View Table of Contents: http://avspublications.org/resource/1/JVTAD6/v31/i6Published by theAVS: Science & Technology of Materials, Interfaces, and ProcessingRelated ArticlesPlasma etching: Yesterday, today, and tomorrowJ. Vac. Sci. Technol. A 31, 050825 (2013)Nucleation and growth of MgO atomic layer deposition: A real-time spectroscopic ellipsometry studyJ. Vac. Sci. Technol. A 31, 06F101 (2013)Enhanced response to molecular adsorption of structurally defective grapheneJ. Vac. Sci. Technol. B 31, 030602 (2013)Effects of Cs adsorption on the field emission characteristics of closed single-walled carbon nanotubesJ. Vac. Sci. Technol. B 31, 021802 (2013)Copper deposition on TiO2 from copper(II)hexafluoroacetylacetonateJ. Vac. Sci. Technol. A 31, 01A121 (2013)Additional information on J. Vac. Sci. Technol. AJournal Homepage: http://avspublications.org/jvstaJournal Information: http://avspublications.org/jvsta/about/about_the_journalTop downloads: http://avspublications.org/jvsta/top_20_most_downloadedInformation for Authors: http://avspublications.org/jvsta/authors/information_for_contributors

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Measurement of the tangential momentum accommodation coefficientof H2on stainless steel, extreme ultraviolet-resist, and polyimide

Johannes F. M. Velthuisa)

TNO Science and Industry, P. O. Box 155, 2600AD Delft, The Netherlands

Laurens van Bokhovenb)

ASML Netherlands B.V., De Run 6501, 5504 DR Veldhoven, The Netherlands

(Received 12 March 2013; accepted 12 July 2013; published 9 September 2013)

The tangential momentum accommodation coefficient (TMAC) of H2 on electropolished stainless

steel 304, extreme ultraviolet-resist, and polyimide was determined by measuring the mass flow

through a macroscopic rectangular channel (100 cm 10cm 1 cm) as a function of the pressure

drop in the Knudsen range Knave 00.6. The TMAC and Knudsen number determine the amount

of velocity slip taking place at the wall at rarefied conditions. By comparing the measurements

with an analytical expression for the mass flow through the channel, including the 1st order

slip flow contribution to continuum, the only remaining unknown, that is, the TMAC, was extracted.

VC 2013 American Vacuum Society.[http://dx.doi.org/10.1116/1.4816941]

I. INTRODUCTION

The value of the tangential momentum accommodation coef-ficient (TMAC), also referred to as r, and the thermal accom-

modation coefficient (TAC), also referred to as a, is important

as boundary conditions for the accurate simulation of flow and

thermal effects in extreme ultraviolet (EUV)-wafer scanners.

These scanners operate in a hydrogen environment in the

slip flow regime (0.01 < Kn< 0.1) and the early transitionalflow regime (Kn 0.4). Simulations models that are being

used are CFD (computational fluid dynamics) and DSMC

(direct simulation Monte Carlo) amongst others. Continuum

flow (Kn < 0.01) is modeled by applying zero velocity slipat the wall. At rarefied conditions (small pressures and/or

small channel dimensions), both velocity and temperature

slip take place at the wall. The velocity slip (1st order slipflow expansion of continuum) is a function of Knudsen num-

ber Kn and TMAC. The Knudsen number is a measure of

rarefaction and hence of the amount of velocity slip. For

channels, the Knudsen number computed at the channel av-

erage pressure (of the channel inlet and outlet) is representa-

tive, denoted Knave. The TMAC is a measure of the

momentum exchange between the gas and the surface, which

is a combined property of the gas and the surface involved.

TMAC data of H2 on surfaces relevant for EUV-wafer

scanners could not be found in the literature; therefore, it

was decided to measure these parameters. The 1st order slip

flow expansion of continuum is also known to be valid in the

early transitional flow regime (Knave 0.4), the extent ofwhich is investigated by varying the Knudsen number over

the range Knave 00.6.

Several methods exist to measure TMAC, see, for exam-

ple, Agrawal and Prabhu.1 A popular method involves meas-

uring the flow rate over microchannels manufactured with

MEMS techniques usingthe rate of pressure rise (ROR) tech-

nique, see Arkilic et al.2 By comparing the measured mass

flow rate over the channel with the analytical expression for

the mass flow rate over the channel, including the 1st order

slip flow contribution to continuum, the remaining unknown,

that is, TMAC, can be determined.

We use a similar method but now applied to macroscopic

channels. Thus, the method is not limited to MEMS compati-

ble materials but can be applied to actual surfaces and condi-

tions, such as found in EUV-wafer scanners. Standard mass

flow sensors can be used, avoiding the difficulties associated

with the ROR technique. First, the TMAC of H2 in an elec-

tropolished stainless steel 304 (SS304) channel is measured.

Next, the channel is spray-coated to measure the TMAC on

EUV-resist (SPUR-V002). Finally, the channel is covered

with thin sheet material to measure the TMAC on polyimide

(Dupont Kapton type H-film).

II. THEORY

A. Channel mass flow rate

Figure1shows the channel with rectangular cross section.

Starting from the NavierStokes equations, a theoretical

expression for the laminar mass flow rate over the channel

can be derived, which includes a 1st order slip flow contribu-

tion to continuum as proposed by Maxwell in 1879.25 The

mass flow rate expression reads

_m

p2i p2o

A B 2

po pi

; (1)

where

A H3 W M

3

4 C1

24 l L R T ; (2)

B A C2

C1

2 r

r Kno po; (3)

C1 4

3 1

192

p5

H

W

X1

n1;3;5::

1

n5tanh

np

2

W

H

" #;

(4)a)

Electronic mail: [email protected])Electronic mail: [email protected]

061605-1 J. Vac. Sci. Technol. A 31(6), Nov/Dec 2013 0734-2101/2013/31(6)/061605/7/$30.00 VC 2013 American Vacuum Society 061605-1

http://dx.doi.org/10.1116/1.4816941http://dx.doi.org/10.1116/1.4816941http://dx.doi.org/10.1116/1.4816941http://dx.doi.org/10.1116/1.4816941http://dx.doi.org/10.1116/1.4816941http://dx.doi.org/10.1116/1.4816941mailto:[email protected]:[email protected]://crossmark.crossref.org/dialog/?doi=10.1116/1.4816941&domain=pdf&date_stamp=2013-09-09mailto:[email protected]:[email protected]://dx.doi.org/10.1116/1.4816941http://dx.doi.org/10.1116/1.4816941http://dx.doi.org/10.1116/1.4816941http://dx.doi.org/10.1116/1.4816941


3/8

C2 8 C1 256

p4 1

H

W

X1

n1;3;5::

1

n4tanh2

np

2

W

H

:

(5)

The mass flow rate _m (kg/s) is scaled with pi2po

2, where

p denotes pressure and subscript i and o refer to the

channel inlet and the channel outlet, respectively. The aver-

age pressure is defined as pave

(pi

po)/2. For an isother-mal channel of given dimension and given TMAC value r,

the terms A and B in Eq. (1) are constants, leading to a

linear relationship between the scaled mass flow rate and

inverse average pressure. The first term A represents the

scaled mass flow rate in the continuum limit, whose theoreti-

cal value is given by Eq. (2). The second term B accounts

for slip flow effects, whose theoretical value is given by

Eq.(3). Slip has the effect of enhancing the mass flow. The

slip term in Eq. (1) disappears when the absolute pressures

rises, despite B having a finite value. The Knudsen number

Kn is a measure for noncontinuum effects and is defined as

Kn k/H, where H is the channel height and k denotes

the mean free path of gas molecules between collisions

k l

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip M

2 R T

r : (6)

The density q of hydrogen is calculated with the ideal the

gas law, where R is the universal gas constant, T is the

temperature, and M is the molecular weight (2.016 g/mol).

The dynamic viscosity l of hydrogen is taken according to

TableI. For comparison, at isothermal conditions, the mean

free path of hydrogen is inversely proportional to pressure

and reads k 12 mm at 1 Pa and 293.5 K. We differentiate

between the outlet Knudsen number Kno (evaluated at the

channel outlet pressure po) and the average Knudsen num-ber Knave (evaluated at the average channel pressure pave).

As in our measurements, we always enforce p i to be greater

than or equal to two times po; this in practice means that

Knave is always less than 2/3Kno. Note that for isothermal

conditions, the product (Knp), for example, appearing in

Eq. (3), is constant. The coefficients C1 [Eq. (4)] and

C2 [Eq. (5)] account for the channel aspect ratio (H/W).

For a plan-parallel channel with infinitely small aspect ratio

(H/W 0), the coefficients read C1 4/3 and C2/C1 6.

For a channel with finite aspect ratio (H/W 0.1), as applies

for our experimental setup, the channel sides reduce the con-

tinuum mass flow rate by approximately 7%, when com-

pared to a channel with zero aspect ratio.

By linear curve-fitting the measured data for the scaled

mass flow rate versus inverse average pressure according to

Eq.(1), an experimental value is obtained for the line inter-

cept A and slope B. From these and the previous given theo-

retical expression for the slope [Eq. (3)], the unknown

TMAC valuer is extracted, according to

r 2

1B

A

1

Kno Po

C1

C2

: (7)

In this paper, we will determine the TMAC value, orr, in

the Knudsen range Kno 01.2, equivalent to Knave 00.6.

B. Assumptions

In the derivation of the scaled mass flow rate expression

[Eq.(1)], a number of simplifying assumptions are used. The

experimental conditions must meet these simplifying

assumptions (see Sec. IV), otherwise the extracted TMAC

values become ill-defined. The simplifying conditions are as

follows:

(1) Laminar flow. For this, the hydraulic Reynolds numbers

should stay below the laminar-turbulent flow transition,Re2H 2300.

(2) Negligible inertial effects. For this, the product of Mach

number at the channel inlet Mi, Mach number at the

channel outlet Mo, and heat capacity ratio c should be

smaller than unity (cMoMi 1), see Karniadakis and

Beskok.3

(3) Isothermal channel. For isothermal conditions, the varia-

tion in channel temperature in time and in place must be

limited, i.e., less than 3 K, which corresponds to 1% rela-

tive error in absolute ambient temperature.

(4) Slip flow (Knave< 0.1). Notwithstanding this condition, itis generally known that Eq. (1) with associated TMAC

(derived for the 1st order slip flow regime) also reprodu-

ces the mass flow rate in the early transitional flow regime

(Knave 0.4) quite well. When lumping higher order

Knudsen effects to Eq. (1) by simply modifying the

TMAC value, this per definition will result in a Knudsen

dependency of the TMAC. Plotting these lumped TMAC

values is of limited practical significance, other than as an

indicator for higher order Knudsen effects. As in our

experiments Knave does not exceed the value 0.6, we

expect that this Knudsen dependency is still limited.

(5) Developed flow. To say negligible entrance and exiteffects

on the channel pressure drop. Duan and Muzychka7 give

FIG. 1. Channel with rectangular cross section (L 100cm, W 10 cm,

H 1 cm).

TABLE I. Dynamic viscosity of H2[(reported (Ref.6) accuracy 60.5%].

T (K) l(lPas)

290 8.766

300 8.969

310 9.170

061605-2 J. F. M. Velthuis and L. van Bokhoven: Measurement of the TMAC 061605-2

J. Vac. Sci. Technol. A, Vol. 31, No. 6, Nov/Dec 2013



4/8

an expression for the apparent friction factor for flow in a

plane parallel channel including slip flow and entry

effects. Using this expression, it can be shown that the rel-

ative error in the scaled mass flow rate due to entry/exit

effects, relative to that of a channel with developed flow,

stays below 0.1% for Reynolds numbers Re2H< 25,where it is assumed that the exit effect is of the same

order of magnitude as the entrance effect.

III. EXPERIMENT

A. Vacuum system

The vacuum system consists of two vacuum vessels,

referred to as inlet vessel and outlet vessel, see Fig. 2.

Each vessel has a volume of1.4 m3. A stainless steel 304

channel connects the two vessels (see Sec.III Bfor details).

The inlet vessel is not pumped and the respective pump-

openings are closed. The outlet vessel is pumped by option-

ally four Turbo Molecular Pumps (TMP), type Shimadzu

TMP-H3153LMC. The pumps are water-cooled with achiller to lab temperature level (293 K). The individual

pump speed is 2600 l/s H2 at 24 000 rpm (100%) for abso-

lute pressures in the normal operating range (


5/8

C. Surface preparation

1. Stainless steel

The cleaning procedure of the electropolished stainless

steel 304 channel parts consisted of degreasing, rinsing in

demineralized water, alkaline cleaning, and repeated rinsing

in demineralized water of increasing purity, followed by dry-

ing in air. After mounting in the test setup, the channel

resided in vacuum (1 Pa) for a few days and was allowed

to outgas before the experiments started. This outgassing

procedure was followed for all materials studied.

2. EUV-resist

For the TMAC measurement on EUV-resist, the internal

wetted surface of the stainless steel channel was spray-

coated with several layers of EUV-resist (SPUR-V002, seeTableIV), with drying in between. The resist itself is almost

colorless in appearance. After applying a few layers, the

coating showed colorization, indicating a layer thickness of

typically 0.25 lm (1=4 wavelength of visible light). Between5 and 10 layers were applied in total until the colorization

disappeared. Subsequently, the resist was baked at 105 C,

using a lint heater wrapped around the channel.

3. Polyimide (Kapton)

For the TMAC measurement on polyimide, the internal

wetted surface of the stainless steel channel was coated with

a 25 lm thin polyimide sheet (Dupont Kapton type H film),

with negligible effects on channel height and the variation in

channel height.

D. Measurement procedure

A typical measurement series consists of tuning the outlet

channel pressure po to a constant value (within 1%) and

varying the inlet pressure to approximately multiples of the

outlet pressure (pi npo, n 2). Next, the scaled mass flow

rate is plotted versus inverse average pressure according to

Eq. (1), including error bars in both coordinate directions

due to sensor accuracies or resolution, whichever is larger.The error bars are determined using linear error propagation

techniques and assuming square-root weighted averaging of

the individual error contributions, assuming independent

measurement quantities. All uncertainties mentioned in this

paper are based on a 99.8% confidence level (3stdev/

mean). Next a linear curve fit of the plotted data is made

using the total least squares (TLS) technique.8 The TLS tech-

nique takes into account the errors bars present in the data,

in both coordinate directions. The curve fit procedure results

in a value for the line intercept A (scaled mass flow in the

continuum limit) and for the slope B (slip effect), together

with their associated uncertainties DA and DB. Next,

the TMAC value r is calculated according to Eq. (7). Theuncertainty Dr is determined again using linear error propa-

gation techniques, now with linear addition of the individual

error contributions. Thus, a certain measurement series

can be associated with a specific (constant) channel outlet

pressure po, a corresponding Knudsen number Kno, and a

TMAC value. By measuring multiple data series at varying

discrete channel outlet pressures, the TMAC values can be

plotted as function Kno. As already stated in Sec. II B, the

relevance of plotting TMAC beyond the early transition

range (Knave 0.4) is limited, other than as an indicator for

higher order Knudsen effects. Typical discrete outlet pres-

sures selected are in the range po 201 Pa. The highest

occurring channel outlet Knudsen numbers is Kno 1.2,

which is equivalent to a measurement series in which the

average Knudsen number is varied between Knave 0 and

0.6. Measurements at even higher Knudsen numbers (lower

pressures) were not conducted, as these where limited by the

resolution of the pressure sensors and accuracy of the mass

flow controllers.

To determine the TMAC valid for the slip flow regime

(and early transitional flow regime), all measurement series

were collected in one plot (scaled mass flow rate versus

inverse average pressure) and fitted to Eq. (1) in the range

Knave 0.4. The resulting scaled mass flow in the continuum

FIG. 3. (Color online) Stainless steel channel consisting of bottom part and lid.

TABLE III. Channel dimensions.

Item Descriptiona

Height H 10.16 6 0.17mm

Width W 100.0 6 0.1mm

Length L 1000.8 6 0.5mm

C1 1.248b

C2 7.588b

a99.8% confidence level (3stdev/mean).bAt nominal dimensions.

TABLE IV. EUV-resist (SPUR-V002). Source material safety data sheet.

Item Description

Product SPUR-V002

Supplier Shin-Etsu Chemical Co Ltd., Japan

Composition 50% cyclohexanone,


6/8

limit (intercept A) is compared with the theoretical value

Eq.(2), by inserting in this equation the channel dimensions,

temperature, and corresponding H2 dynamic viscosity. The

uncertainty in the theoretical value is determined based on

square-root weighted averaging of the individual error

contributions.

IV. RESULTS

Over the course of the electropolished stainless steel

experiments, the channel temperatures stayed within

293.8 6 1.5 K, indicating that the channel can be considered

isothermal during the experiments (Sec. II B). As already

mentioned in Sec. III D, uncertainties given in this paper

refer to a 99.8% confidence level (3stdev/mean). The tem-perature of the channel during all the EUV-resist experi-

ments stayed within 293.5 6 0.5 K. The temperature of the

channel during all the polyimide experiments stayed within

293.2 6 0.3K.

The Reynolds numbers (not shown) during all flow

experiments stayed below 10, well below the previously

determined criterion for the laminar to turbulent flow

transition of Re 2300 (Sec. II B). Entrance and exit

effects on the channel pressure drop can therefore be safely

neglected, and the flow can be considered developed

throughout the channel. Inertia effects are also considerednegligible, as the product of inlet Mach number, outlet

Mach number, and heat capacity ratio c during all experi-

ments stayed below 0.05, far less than the previously deter-

mined criterion of unity (Sec.II B).

Figure 4 shows a typical measured data series in which

the channel outlet pressure po is kept constant during

the experiments and the channel inlet pressure pi is varied.

For this particular example, po 10 Pa (equivalent to

Kno 0.12). The outlet pressure pi is varied between 20

and 100 Pa, which is equivalent to 1/pave 0.020.07 or

Knave 0.020.08. The mass flow rate is scaled with the the-

oretical continuum mass flow rate, which is equal to a con-

stant times (pi2po2). The inverse average pressure 1/pave isgiven along the x-axis. To convert the x-axis to Knave, a lin-

ear scaling factor of 1.2 must be used. The error bars in the

scaled mass flow rate become larger toward the right side of

the graph (lower pressure range), as the associated mass flow

rates fall into the lower, less accurate flow range of the

MFCs. The error bars in the x-direction are not visible on

this scale. As expected, the measured data fall on a straight

line conform Maxwells model. The associated TMAC for

this data series with Kno 0.12 is given in Fig. 5, together

FIG. 4. (Color online) Scaled mass flow rate vs inverse average pressure. To

convert to Knavemultiply the x-axis with 1.2. Shown is a typical data series

in which po is kept constant and pi is varied. Straight lines are Maxwells

model [Eq.(1)] with TMAC as fit parameter.

FIG. 5. (Color online) TMAC as function of Knoobtained by fitting a meas-

ured series of mass flow data to Maxwells model [Eq. (1)]. A specific value

of Knocorresponds to a data series in which pois kept constant and piis var-

ied (Knavevaries between roughly 0 and 2/3Kno).

FIG. 6. (Color online) Scaled mass flow rate vs inverse average pressure for

SS304. All data series collected. To convert to Knave multiply the x-axis

with 1.2. The straight line is Maxwells model [Eq. (1)] with the TMAC fit-

ted in the range Knave 0.4.

FIG. 7. (Color online) Similar as Fig.6but now for EUV-resist.


JVST A - Vacuum, Surfaces, and Films



7/8

with the results of the other data series. The highest outlet

Knudsen number reads Kno 1.2, which corresponds to a

data series in which the average Knudsen number varies

between Knave 0 and 0.6. As remarked in Sec. II B4 plot-

ting TMAC values as a function of Kno based on measure-

ment data lying outside the early transition flow regime

(Knave 0.4) is of limited practical significance, other than

as an indicator of higher order Knudsen effects. The

Knudsen dependency of the TMAC shows a similar trend as

that observed in Refs. 2 and 3 for nitrogen and argon gas in

contact with a silicon microchannel in the range Kno< 0.4,namely, a small decrease in lumped TMAC value up to a

Kno 0.2, after which the TMAC becomes more or less

constant. This seems consistent with the finding that the 1st

order slip flow model still holds in the early transitional flow

regime (Knave 0.4) as the measurements stay close to this

range. The TMAC of SS304 at Kno 1.2 shows a deviation

and larger uncertainty than the EUV-resist and polyimide

results. This is most probably due to the limited variation ofthe channel inlet pressure used in the SS304 experiments. As

the SS304 channel at that time was already coated with

resist, this particular SS304 experiment could not be repaired.

This was rectified in later experiments for EUV-resist and pol-

yimide, by adding more pressure data points.

Figures 68 show all measured data series collected in

one graph per surface material. The mass flow rate is scaled

with the theoretical continuum mass flow rate, which is

equal to a constant time (pi2po

2). To convert the inverse

average pressure along the x-axis to Knave, a linear scaling

factor of 1.2 must be used. The straight lines are Maxwells 1st

order slip flow model [Eq.(1)], where the associated TMAC is

fitted on that subset of the data for which Knave 0.4, that

is, lying in the early transitional flow regime. These TMAC

values are summarized in Table V. This table also compares

the intercept of the fitted line with the theoretical value as

given by Eq.(2). These values are equal to each other within

the measurement uncertainty. The slope of the curve connect-

ing the measurement points increases only very gradually,

indicating the onset of higher order rarefaction effects at higher

Knudsen numbers. The data support the general finding that

the 1st order slip flow model can be used throughout the early

transitional flow regime (Knave 0.4).

Another way of representing the data is plotting the mass

flow rate versus the average Knudsen number, similar as in

given Ref.3 (Fig. 5.14). The mass flow rate is scaled with the

theoretical free molecular mass flow rate which is equal to aconstant times the pressure difference (pipo) over the channel.

The resulting graph is shown in Fig. 9, ignoring the exact value

of the constant. Maxwells model [Eq. (1)] with TMAC 0.83

is given as comparison. As the measurement range does not

exceed Knave 0.6, it is still too early to see a local minimum

in the scaled mass flow rate which in general is observed

around Knave 1, the so-called Knudsen minimum.3

TACs on the same prepared surfaces were separately

measured by Philips,9 using the heated parallel disk method

and by fitting the results with the ShermanLees10 relation-

ship for heat transfer between parallel gaps in the continuum

FIG. 8. (Color online) Similar as Fig.6but now for polyimide.

TABLE V. TMAC and TAC (Refs. 9and10) of H2on SS304, EUV-resists, and polyimide (Knave< 0.4). Confidence level 99.8% (3stdev/mean).

Surface

Theoretical

scaled mass

flow [Eq.(2)]

Measured scaled

mass flow in the

continuum limit [Eq.(1)]

Measured slope

[Eq.(1)]

Momentum accommodation

coefficient TMAC

Thermal accommodation

coefficient TAC (Refs.9and10)

Atheory Ameas Bmeas r a

[kg/(s Pa2

)] [kg/(s Pa2

)] [kg/(s Pa)] [] []

SS304 3.8 6 0.2 1010 3.64 6 0.02 1010 3.71 6 0.02 109 0.83 6 0.01 0.32 6 0.04

EUV-resist 3.8 6 0.2 1010 3.65 6 0.02 1010 3.70 6 0.02 109 0.84 6 0.01 0.39 6 0.04

Polyim ide 3.8 6 0.2 1010 3.67 6 0.02 10

10 3.78 6 0.02 109 0.83 6 0.01 0.35 6 0.04

FIG. 9. (Color online) Mass flow rate channel vs Knave. The mass flow rate is

scaled with the theoretical free molecular mass flow rate, which is propor-

tional to (pipo). The line is Maxwells model [Eq.(1)] with TMAC0.83

(fitted in the range Knave 0.4).


J. Vac. Sci. Technol. A, Vol. 31, No. 6, Nov/Dec 2013



8/8

to transitional flow regime (Kn 01.2). These TAC values

can be found in TableV.

V. SUMMARY AND CONCLUSIONS

The tangential momentum accommodation coefficient

(TMAC) of H2on various surfaces was determined, by meas-

uring the mass flow through a macroscopic rectangular chan-

nel (100 cm 10cm 1 cm) as a function of pressure drop inthe Knudsen range Knave< 0.6. This works main advantage isthe possibility of using macroscopic channels (as compared to

frequently used MEMS microchannels and MEMS materials).

Therefore, this method can be easily applied to a number of

actual surfaces, for example, relevant for EUV-wafer scanners.

The results support the general finding that the 1st order slip

flow expansion can be used throughout the early transitional

flow regime (Knave 0.4). The TMAC value for H2 on stain-

less steel 304 and polyimide (r 0.83 6 0.01) was found to

be almost identical to that on EUV-resist (r 0.84 6 0.01).

ACKNOWLEDGMENT

This project is funded by ASML Netherlands B.V.

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(2001).3G. E. Karniadakis and A. Beskok, Micro Flows(Springer, New York, 2002).4J. Jang and S. T. Wereley, J. Micromech. Microeng. 16, 493 (2006).5F. M. White,Viscous Fluid Flow(McGraw-Hill, New York, 2006).6

M. J. Assaei, S. Mixafendi, and W. A. Wakeham, J. Phys. Chem. Ref.

Data 15, 1315 (1986).7

Z. Duan and Y. S. Muzychka,J. Fluids Eng. 132, 011201(2010).8W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,

Numerical Recipes in Fortran (Cambridge University Press, Cambridge,

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coefficient for ASML, Philips Research, Report Ref: ATP591-11-0405/

01, 2011.10D. J. Rader, W. M. Trott, J. R. Torczynski, J. N. Casta~neda, and T. W.

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Report SAND2005-6084, 2005.


JVST A - Vacuum, Surfaces, and Films
http://dx.doi.org/10.1116/1.2943641http://dx.doi.org/10.1017/S0022112001004128http://dx.doi.org/10.1088/0960-1317/16/3/004http://dx.doi.org/10.1063/1.555764http://dx.doi.org/10.1063/1.555764http://dx.doi.org/10.1115/1.4000692http://dx.doi.org/10.1115/1.4000692http://dx.doi.org/10.1063/1.555764http://dx.doi.org/10.1063/1.555764http://dx.doi.org/10.1088/0960-1317/16/3/004http://dx.doi.org/10.1017/S0022112001004128http://dx.doi.org/10.1116/1.2943641

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JVA061605 - Measurement of the Tangential Momentum Accommodation Coefficient of H2 on Stainless Steel Extreme Ultraviolet-resist and Polyimide