Hoffman D.M., Singh B., Thomas J.H. (Eds). Handbook of Vacuum Science and Technology

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492 Chapter 4.7: Outgassing of Materials

balance results in the equation

PnSn + Pn^fnenm^m = ^^nm^m " V(dpjdt) (6)

where

p„

is the partial pressure of the nth gas in torr,

S„

is the net pumping speed

for this gas in liters/sec, A,„ is the exposed area in cm^ of the mth material,

K,,,,^

the "free" or intrinsic outgassing rate in torr • liter

s~^cm"^

of this material for

the nth gas, defined as the outgassing rate when readsorption is negligible, t is the

time in seconds, V is the chamber volume in liters,

e„,n

is a sticking or sorption

coefficient for the nth gas on the mth material, and

f, = {RoT/27rM,y^'lO-' (7)

is the "effusion law" factor in units of liters

s ~^

cm~^ at the absolute temperature

T for the nth gas of molecular weight M„ and

is the molar gas constant

(RQ

8.31 X lO'^ergsdeg-^Kmol"^).

The total pressure p in the vacuum chamber at the pumping time t in seconds is

given by [2]

K„,„A,„

- Vidpjdt)

P = lPn = I.^ (8)

where it is assumed that the partial pressure, p„, of each gas species is known by

measurement with a mass spectrometer or residual gas analyzer

(RGA).

Since out-

gassing rate measurements on individual materials are often made with total pres-

sure gauges, such as an ionization gauge, using the air or nitrogen calibration fac-

tor, in practice the preceding equation can be simplified to

K„Am

- V(dp/dt)

P = '^ W

where p is the total pressure as measured with the air calibration factor, ^„, is

the air- (or nitrogen-) equivalent free outgassing rate at the time t, ^,„ is the air-

equivalent sorption coefficient,/a is the value of/„ when the molecular weight M„

is taken as 29 (or 28), and S is the net pumping speed for air. When the chamber

is empty of material to be processed and the outgassing from elastomer gaskets

can be neglected, this equation simplifies further to

p = -^S^ "^—^ (10)

^ /aO-A + S ha A + S dt

4.7.1 Relationships Among Pressure, Speed, and Outgassing Rate 493

where a is the effective air-equivalent sorption coefficient for the wall material

(of geometric surface area A), which may be somewhat larger than the ordinary

sticking coefficient because of the porosity of the oxide layer and will depend on

the fraction of adsorption sites that are occupied at time r; A is the chamber wall

area; and

Kn,

= Kn/(t/3600r (U)

where Kfi is the free outgassing rate of the wall material after one hour of pump-

ing and / is in seconds. This equation contains the hidden factor (one hour)" = 1,

which allows for values of a other than 1.

RELATIONSHIP BETWEEN REQUIRED SPEED

AND CHAMBER DIMENSIONS

The volume V in liters of a cylindrical vacuum chamber of length L (cm) and ra-

dius R (cm) with dished heads can be estimated from

V= 10-3 7r/?2(L +0.4/?) (12)

where L is usually about 3R corresponding to V = R^/lOO, The area (in cm^) of

the walls of such a chamber can be estimated from

A = lirRiL +

1.1/?)

(13)

and for L = 3/? the area

A = 26/?2 (14)

For typical industrial vacuum systems filled with material to be processed (such

as vacuum coating) the net air speed, S^, (in liters/sec) of the high-vacuum pump

(diffusion pump or turbomolecular pump) should be about 2.5 times the volume V

of the empty chamber, or

5d = 2.5V=/?V40 (15)

and the roughing pump or backing pump speed, 5r, is usually about 5d/100 or

S, = W40 = /?V4000 (16)

For typical industrial vacuum systems with chambers filled with material to be

processed,

5d/A = /?/1000 (17)

where A is the wall area of the empty chamber.

494 Chapter 4.7: Outgassing

Materials

4.7.2

INITIAL PUMPDOWN FROM ATMOSPHERIC PRESSURE

During the initial pumpdown from atmosphere of the empty chamber with a me-

chanical pump (roughing pump) of net speed

S^,

the outgassing and sorption terms

can be neglected until the pressure produced by the roughing pump alone falls be-

low a value given by the semiempirical formula

= 300 K^A/V (18)

where ^i is the net outgassing rate (including readsorption) at one hour and the

numerical coefficient has the dimensions of time. This pressure p^ is typically

in the range from 10"^ to

""^

torr when the ultimate pressure of the roughing

pump is less than 10"^ torr. In the region from atmospheric pressure, po, (about

750 torr) to Pv integration of Equation (10), neglecting the outgassing and sorp-

tion terms, with a roughing pump of maximum speed

Sj.

and ultimate pressure/7ru,

gives

P=Pru+Poexp(-5rf/V) (19)

and the time (in s) to reach the pressure p will be

t, = 2.3 (W5r)logio[(Po -

PruViP

Pru)]

(20)

Then the time to reach the pressure p^ will be approximately

r, = 12 V/S, (21)

For L = 3/? the ratio A/Vin Equation (18) equals 2600/R so that

Pv = 7.8 X 10^ K^/R (22)

Since Ky is often of the order of 10"^ torr • liter

s'^cm"-^,

then for R of about

30 cm (1 foot) Pv is about 3 X 10"^ torr. Since oil diffusion pumps can operate

when the forepressure is less than a few tenths of

torr, there is no need to wait

until the pressure falls to py to switch the high-vacuum pump into operation by

opening the high-vacuum valve. From Equation (20) and Equation (16), the

roughing time, or time to reach the switchover pressure, p^, for diffusion-pumped

systems of about 0.2 torr will typically be

fv = 8 V/Sr = 320s = 5.3 minutes (23)

For cryopumped systems, the safe switchover pressure depends on the volume of

the chamber, and the recommendations of the manufacturer should be followed.

4.7.3

Pressure

Vs.

Time

During Outgassing 495

4J.3

PRESSURE

VS.

TIME DURING OUTGASSING

4.7.3.1 Pumpdown with Outgassing

After switching to operation with a high-vacuum pump of constant speed

S^^

100 ^r, the time to reduce the pressure from p^ to p^ = lO'^p^ (neglecting out-

gassing) will be

r,d = 4.6 V/S^ (24)

or, since these systems typically have a time constant r =

V/S^^

= 0.4 s, the pres-

sure will drop from p^ = 0.2 ton* to p^ = 2 X

10 ""^

torr in about 2 s. When the

pressure reaches

p^^S^/S^^

= 3 X 10~^ torr, the pressure then decreases more

slowly as outgassing, and inleakage become the limiting processes. The term

~[yKfa^^ + S)](dp/dt) can usually be neglected when the pressure decreases

by another factor of

or typically when the pressure with the high-vacuum pump

operating is less than 1 X 10~^ torr. The pressure is then given by

P = K,^A/if,aA + 5d) + /7, = {Kn/h-

)/(f,a

+ S,/A) + p, (25)

where

is the "ultimate pressure" (lower pressure limit) due to leaks and perme-

ation from the atmosphere, fh is the pumping time in hours, and a is the sticking

probability based on the geometric surface area A. At room temperature (298 K)

the value of/a (for air) is 11.7 liters

s~^cm~^.

For empty chambers with metal

walls that have not been baked, the gas at pressures below

"^ torr is about 90%

water vapor. The effusion law factor,/^v, for water vapor at 298 K is 14.8 liters

s~^cm~^.

For stainless steel, as shown below, it can be assumed that a is about 6 X 10"^

after one hour of pumping, so that for chambers with S^/A < I

(or

R < 1000 cm)

the readsorption iermf^a = 0.089 for water vapor cannot be neglected in com-

parison to SJA.

The preceding relationships are illustrated by Figure 1 for the pumpdown

curve of a typical vacuum system with V = 2000 liters, S, = 50 liters/sec, A =

80,000 cm2, 5a = 5000 liters/sec,

K^^

= I X 10"^ torr • liter

s'^cm'^

po =

750 torr,/7s = 0.2 torr,/?^ = 10"-^ torr, and ultimate pressure/7u = 1 X 10~^ torr

with the diffusion pump operating as shown by the dashed line.

4.7.3.2 Rate of Rise of Pressure in Closed Chamber

If the high-vacuum valve is closed after the time to (in seconds), then 5 = 0 and,

using Equation (11), the differential equation. Equation (10), for the pressure

496

Chapter 4.7: Outgassing of Materials

Fig.l.

10^

-1

e-10

2 -2

-- 10

-3

(o -4

s 10

Q. -5

10'

--8

-_..V=-20QQ.li ^=JBQQQQ.cml

\ I

Ps___\[__

^_Sr_=ML/S

:y'

KEZi:::::

i__Pru_.

Sd = 5000 L/s

0.001

TIME (h)

Curves of pressure vs. time during pumpdown in presence of outgassing.

becomes

where

dpidt + cp = hl(t + t^Y

(26)

c=/aCrA/V (27)

b = {3600r K^^A/V (28)

and t is the time in seconds after closing the valve. Assuming a independent of

pressure and time, this equation can be integrated to give

P=Poe

be'

Jo {f + t^r

"^^

(29)

where the integral must be evaluated numerically and

Po = (/i:fiA/rho")/(5+/acrA) (30)

in which

t^Q

is the total pumping time in hours at which the valve was closed.

When the pressure rise time in seconds t « t^,

p=Poe-'' + {b/cton(l-e-'') (31)

4.7.4

The

Outgassing Rate

Elastomers and Plastics

497

where

blc

{?>6mrKnlho-

(32)

From Equation (31) the rate-of-rise equation

dpidt

[(b/ton

cpo]e-''

(33)

and

the

initial

{t = 0)

rate-of-rise times

the

chamber volume

divided

by the

chamber wall area A

(V/A) dpIdt

(Kn/tuon/(l ^hcrAIS)

(34)

which

just

the net

(measured) outgassing rate (including readsorption)

at the

pumping time

(in h)

when

the

valve

was

closed. When SI A

» f^a, one ob-

tains

the

free outgassing rate

rno- This

is one

method

measuring

the

out-

gassing rate. The equations are based

the assumption that the time exponent

is constant over the times involved

the measurements, which

usually approx-

imately true for typical values of a and times up to f

defined in Section 4.7.1.2

(p.

485)

and

Section 4.7.4.1

(p.

500).

course, when

the

system contains layers

of oil or solids with volatile plasticizers, the evolution of vapors from these sources

will not follow Equation (31).

47.4

THE OUTGASSING RATE OF ELASTOMERS AND PLASTICS

4.7.4.1 Outgassing

Diffusion

Absorbed

Gas

to Exposed Surface

has

been found experimentally

[2]

that

the

outgassing rate

elastomers

and

plastics, once the volatile organic matter (plasticizer) has been removed,

deter-

mined mainly

the diffusion

absorbed gas and water molecules from the bulk

of the material

to the

exposed surface, where

the

molecules

can

escape directly

from open pores

move

surface diffusion

adsorption sites

on the

exposed

surface from which they soon evaporate. Nitrogen and oxygen molecules initially

adsorbed

on the

directly exposed (geometric) surface

are

desorbed

less than

second

room temperature because

the

energy

adsorption

elastomers

and

plastics

less than

kcal/mol. Similarly, water molecules

on the

exposed sur-

face

are

desorbed quickly from most elastomers

and

plastics

(but not

from sili-

cone elastomers). However,

air and

water molecules that have dissolved

in the

bulk material

diffusion through capillary pores before evacuation

are

only

re-

moved slowly

room temperature because

the small diameter

the capillar-

498 Chapter 4.7: Outgassing of Materials

ies and the "random walk process," which is the nature of diffusion along a capil-

lary pore.

The diffusion of gas into or out of a solid is controlled by Pick's law [8]

d ( dC\ d ( dC\ d ( dC\ dC

dx\ ' dxj dy\ ^ dyj dz\ dzj dt

where C is the concentration (in molecules cm~^) of gas in the solid at the loca-

tion (x, y, z), Di, D2, and D3 are diffusion coefficients (in cm^s"^), which may

vary with the location

(jc,

y, z) and the direction of the concentration gradient, and

t is the time (in s). For material in sheet form of sufficient thickness, w,„, that it

can be treated as a semiinfinite solid with a uniform concentration

at time zero

and a constant diffusion coefficient

D„„j

for the nth gas, when the exposed surface

is suddenly exposed to a very low pressure by fast pumping of the vacuum cham-

ber containing the material, the concentration distribution along the jc axis per-

pendicular to the surface at the time / will be given by

C(x, t) = Co erf[;c/2(A„„0^^^] (36)

where erf refers to the error function, which is tabulated in various mathematical

handbooks [9].

For gas molecules that are adsorbed on the walls of capillary pores in a solid

with adsorption lifetime, r^, and that diffuse along the capillary by desorption fol-

lowed by collision with the wall and readsorption, the diffusion coefficient is

given approximately by [2]

D„„, = (A2/4)/[(A/M„„) + rj (37)

where

is the mean distance (in cm) in the

direction traveled by a molecule

bewteen collisions with the capillary wall and

M,„„

is the average molecular veloc-

ity at the temperature

T,„

of the solid.

The free outgassing rate in molecules

s ~ ^

"^^

is then given by

N(t) = D„„,[dC(x,t)/dxh^o (38)

where the concentration gradient is evaluated at

= 0 corresponding to the ex-

posed surface and t > 7rA^/16D,„„. Substituting Equation (36) in Equation (38)

gives

Nit) = Co{D„j7rty^^ (39)

and the free outgassing rate in ton*

•

liter

s"^cm"^

is then

K^ = (RJ/60N,)Co(D,J^t^y^^ (40)

where R^ = 62.36 torr

•

liter K"

the molar gas constant in vacuum engineer-

ing units, T is the absolute temperature of the gas in the vacuum chamber,

A^a

6.02 X 10^^ is Avogadro's number (the number of gas molecules in one mole).

4.7.4 The Outgassing Rate

Elastomers and Plastics

499

Table 5

Diffusion Coefficients (in cm^/s) for Gases Through NonmetalHc Materials

Material

Neoprene

Perbunan

Pyrex

Rubber (vulcanized)

Gas

C02

Temp.

°C

D„„

1.8 X 10"^

1.9 X 10"^

4.1 X 10-6

2.5 X 10"^

4.5 X lO-'i

8.5 X 10-6

1.5 X 10-6

2.1 X 10-6

1.1 X 10-6

Ref.

No.

[1]

[2]

[1]

References

R. M. Barrer,

Diffusion

in and

Through

Solids (Cambridge University Press, London, 1941).

G. J. van Amerongen, 7.

Appl.

Phys., 17 (1946) 972.

and ^h is the pumping time in hours but cannot be less than (7rA^/16Z)„,„)/3600.

Thus,

for elastomers and plastics where the outgassing rate is controlled by diffu-

sion of a single molecular species with constant adsorption lifetime r^, the value

of a in Equation (2) is about y and the free outgassing rate at one hour depends on

the initial molecular concentration

according to

Kn = {R,T/60N,){D^/7r)

'^^

Q (41)

where the diffusion coefficient varies with the absolute temperature, 7,,,, of the

solid according to

Dnm

d„„,

Qxp(-H,JjRTJ (42)

Values of the diffusion coefficient,

D,„„,

for gases through nonmetallic materials

are given in Table 5 and values of the constants

d,,„,

and //„,„ are listed in Table 3.

The solubility coefficient (in cm^(STP)/cm^ per torr) for the nth gas in the mth

material at the temperature r,„ is given by

s„,,

= OA(a„Jd„jQxp[-(E„„, - H„J/jRTJ (43)

because it can be shown that

U„„

= 10^„,„A„„ (44)

The initial gas concentration

(in molecules/cm"^) in Equation (41) will be a

sum of the concentrations due to the solution in the material of gases in the at-

mosphere during exposure. If the exposure time is long so that equilibrium is

500

Chapter 4.7: Outgassing of Materials

reached at the prevailing temperature, the concentration of the nth gas will be

Qo = (760/273) X lO~\NJR,)s„oP„o'^^ (45)

where

5„o

is the value of the solubility coefficient

s^^^

for the nth gas at the initial

pressure P„o and temperature r,„ =

TQ.

Of course, in addition to the atmospheric

gases dissolved in the solid elastomer or plastic there will usually be some resid-

ual plasticizer, but the vapor pressure of the plasticizer may be so low that the out-

gassing rate is determined mainly by the dissolved gas content. Table 6 lists val-

ues of the solubility coefficients for common gases in typical solids.

Since experiments have shown [2] that the sorption probability, £,„„, for the

common gases colliding with the exposed surface of an elastomer and diffusing

some distance into the bulk through the entrance to an open capillary pore, is

less than 1 X 10"^ so that/„g„,„A„, is negligible compared to 5„ when

S,JA,„

1 X

10 ~'^,

then ^fi is approximately equal to the net outgassing rate from elasto-

mers in most systems.

Equation (39) should be valid until t^ >

^hm*

where

^hm = [7r(w,/20)2/16D,„J/7200 (46)

in which

w^^

is the thickness (in mm) of a sheet of elastomer exposed to the vac-

uum on both sides [2]. When f h >

^hm»

the outgassing rate should begin to decay

more or less exponentially with pumping time as the gas content of the elastomer

becomes more than half depleted.

Table

Solubility Coefficients for Common Gases in Typical Materials (in units of

cm^(STP)/cm^

per torr)

Material

Iron (a)

Neoprene G

Neoprene

Perbunan

Pyrex

Rubber (natural)

Gas

Temp.

°C

300

500

s„^

2.9 X 10-^

3.8 X 10-5

4.7 X 10-5

9.9 X 10-5

2.0 X 10-^

3.7 X 10-5

4.6 X 10-5

1.0 X lO""*

1.1 X 10-5

6.8 X 10-5

1.3 X 10-^

Ref.

No.

[3]

[2]

[1]

[2]

[1]

[2]

References

R. M. Barrer,

Diffusion

in and

Through

Solids (Cambridge University Press, London, 1941).

G. J. van Amerongen,

AppL

Phys., 17 (1946) 972.

C. J. Smithells (ed.), "Metals Reference Book," 5th ed. (Butterworths, London, 1976).

4.7.5 The Outgassing Rate of Metals and Ceramics 501

4.7.4.2 Experimental Data on Outgassing

of Elastomers and Plastics

Measured values of the outgassing rate

K„ji

and the exponent a

after one hour of

pumping are listed in Table 2 for common elastomers and plastics. Also listed are

the area A,„ (in cm^) of the outgassing material and the net pumping speed, 5a, for

air at 25 °C in the chamber containing the outgassing material. Although the ratio

SJA,n was smaller than 0.01 in some experiments, the values of

K,„i

can be con-

sidered to be the free outgassing rate because the sorption coefficient for solution

of gas in the bulk is sufficiently low, as noted earlier.

Data are also available on the percentage of different gases evolved obtained by

mass spectrometer measurement for some materials [10,11], but in general the

main constituent is water vapor, together with some nitrogen, oxygen, and carbon

dioxide, when the material has been exposed for some time to the atmosphere and

not baked under

vacuum.

Carbon monoxide sometimes shows up in the mass spec-

trometer, but this may be due to interaction of H2O with carbon-contaminated hot

filaments in the gauges [12].

4.7.5

THE OUTGASSING RATE OF METALS AND CERAMICS

4.7.5.1 Experimental Data on Outgassing

of Metals and Ceramics

Measured values of the outgassing rate

K^^i

and the exponent a

after one hour of

pumping are listed in Table 7 for conunon metals and ceramics. Also listed is the

area

A,„

(in cm^) of the outgassing material and the net pumping speed, 5a, for air

at 25 °C (usually limited by an orifice) in the test chamber containing the out-

gassing material. Since the outgassing of unbaked metals is mainly due to evolu-

tion of water vapor from the oxide layer on the surface, and the sorption probabil-

ity for water vapor in the oxide layer in general varies from about

10 ""^

to 10"^

depending on the fraction of adsorption sites occupied and surface heterogeneity,

the listed values of

K^ni

cannot be considered as free outgassing rate constants but

may depend on the ratio A,„/5w, where 5^ is the net pumping speed for water va-

por at 25°C, as well as the partial pressure,

p^.,

of water vapor in the atmosphere

and the time of exposure, fg, before pumpdown.

Table 1 gives reported outgassing rates at one hour, K,n\, for aluminum alloy

and stainless steel for various values of A JS^, p^ and t^ as well as the free out-

gassing rate (where readsorption would be zero) calculated from the semiempiri-