Page 91 - Semiconductor Manufacturing Handbook

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VACUUM TECHNOLOGY

7.12 SEMICONDUCTOR FUNDAMENTALS AND BASIC MATERIALS

To calculate the outgassing load for a given material one must know the outgassing rate (at the
temperature it will experience inside the vacuum vessel) and the amount of surface area of the mate-
rial inside the vacuum vessel.
Q = q × A
x x x
where Q = outgassing load for material x, torr⋅1/s
x
q = outgassing rate for material x, torr⋅1/s⋅cm 2
x
A = area of material x exposed to the interior of the vacuum vessel, cm 2
Note: Many reference books provide values for outgassing rates (q) in W/m . To convert from W/m 2
2
2
to torr⋅l/s ⋅cm divide by 1333.2.
The total outgassing load for all materials inside the vacuum vessel is given by
y
Q outgas = ∑ Q
tot y
1
where Q outgas = total outgassing load, torr ⋅1/s
tot
Q = outgassing load for material y
y
It should be noted that for a vacuum system at equilibrium, the relationship between pressure,
volume temperature, and amount of gaseous material inside the vacuum vessel is given by the Ideal
Gas law.
PV = nRT
where P = total pressure, atm
V = volume, 1
n = amount of material, mol
R = Ideal Gas law constant, atm ⋅1/k ⋅mol
T = temperature, K

The numeric value of the ideal gas law constant R is 0.08206 l⋅atm/K⋅mole. One mole of materi-
23
al contains approximately 6.023 × 10 molecules of the material and weighs 1 g atomic weight. For
example, 1 mol diatomic nitrogen gas weighs approximately 28 g and 1 mol of helium gas weighs 4 g.
Permeation. Permeation is the transport of a fluid (in this case gas) through a contiguous solid.
In order for gases to permeate through a solid material, gas molecules must land on the outer sur-
face of a solid material, become adsorbed, diffuse through the bulk of the solid and, desorb from
the inner surface. The driving force for permeation of gases through materials is the pressure dif-
ferential for each gas species. Tables of permeation rates (K ) for a wide variety of materials used
p
in vacuum are available in the books listed in the references. To calculate the permeation gas
load, one must specify the gas permeating through a solid, know the area the gas is permeating
through, and the thickness of the permeable solid. The equation for calculating permeation rate
is
K ∆ P
q = px x
x
d
where q = permeation rate for a specified gas through a specified solid, W/m 2
x
2
K = permeation coefficient for a specified gas through a specified solid, m /s
px
∆P = pressure differential across solid interface for the specified gas, Pa
x
d = distance the gas must permeate through, m
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