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VACUUM TECHNOLOGY

7.10 SEMICONDUCTOR FUNDAMENTALS AND BASIC MATERIALS

the gas molecules is provided by the conductance element(s). At near atmospheric pressure, the flow
of gases is well described by viscous flow. Viscous flow may be further broken down into turbulent
and laminar flows. In turbulent flow, the motion of gas molecules is characterized by disorganized
eddies and currents not unlike a raging river rapid. Once pressure is further reduced, the gas flow
shifts to laminar, which is like that seen in wind tunnels—an orderly flow of gases in sheets. Further
reduction in pressure results in a transition between the viscous and molecular flows. Once the mean
free path of molecules is approximately the same length as the inside diameter of the conductance
element, the trajectory of molecules is more strongly influenced by the inner walls of the vacuum
vessel than by other gas molecules. The mean free path is the average length a gas molecule travels
between collisions with other gas molecules. For air, the mean free path is a function of pressure and
is given by
×
l = 510 −3
P
where l = mean free path, cm
P = pressure, torr
In molecular flow, gas molecules travel in straight lines between collisions and their motion tends
not to be influenced by pressure differentials.

7.6.2 Conductance of Gases Through Tubes and Orifices
In the viscous flow regime, conductance of gases is a function of the length and diameter of the con-
ductance element as well as the average pressure of the gas in the element.

C = 3000 PD 4
L
where C = conductance, 1/s
P = average pressure, torr
D = inside diameter of conductance element, in
L = length of conductance element, in
In the transition flow regime the conductance of gases is given by
4
C = 3000 PD + 80 D 3
L

and in the molecular flow regime the conductance of a straight tube is given by

C = 80 D 3
L
Often conductance elements of different diameters are connected in series. The total conductance
of a series connection of conductance elements is given by

tot ∑
C = n 1
1 C n
where C = total conductance, 1/s
tot
C = conductance of element n, 1/s
n
n = number of conductance elements

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