Vacuum Pressure Basics

In simple terms, vacuum may be defined as:


A space or container from which the air has been completely or partially removed.

The first basic concept that the reader needs to understand is that of gas pressure. If you fill a balloon with gas, it is the pressure of the gas within the balloon that keeps it inflated. This pressure is a measure of the cumulative force of individual gas molecules colliding with each other and with the walls of their container (in this case the balloon). The force (pressure) that the gas exerts is a combination of the number of molecules present within the container and the velocity of their movement. The velocity of the molecules in the gas is given by a distribution that is dependent on the molecule's mass and temperatures, as shown in Figure 1.

The relative velocity distribution of various gases at 25¡C
Figure 1. The relative velocity distribution of various gases at 25°C.

The pressure on a container's surface (in this case, the inside of the balloon) is defined as the rate at which momentum, mass . volume, mv, is transferred to the surface. Since molecules hitting the surface do so at many different angles, the amount of momentum transferred in any given collision is also dependent on the angle of incidence of the collision. Without going into the details of the derivation, pressure can be expressed in molecular terms by the equation:

P = nkT

where P is the pressure (in Pascals), n is the number density of gas molecules (in m-3), k is a constant (known as the Boltzmann constant and having a value of 1.3806 x 10-23 joules/K) and T is temperature (K).

The key characteristic of vacuum for use in semiconductor processes is that a vacuum has so few atoms or molecules that they do not affect any process being carried out within the vacuum. Thus, one reason for vacuum processing in semiconductor manufacturing is the assurance of high purity in the finished product. The statement also implies other, more complex, advantages to the use of vacuum in semiconductor processing: e.g., ballistic transport of ions between a source and a substrate in ion implantation, or directional etching made possible by the lack of atom/ion scattering under vacuum conditions.

So, how many atoms or molecules is few? To understand this question, we first must understand how many atoms or molecules there are in a given volume of space at atmospheric pressure. Atmospheric pressure is the pressure around you on a normal day. We can get at this number (roughly) using the Ideal Gas law:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of substance in that volume, R is a constant known as the "Universal Gas Constant" and T is temperature. On a normal day, the pressure of the atmosphere around you is commonly designated as 1 atmosphere (1 atm), so P = 1 atm. (Note that pressure can be expressed in other units. These include pounds/sq. inch (14.7 psi = 1 atm) and Pascals (101.3 kPa = 1 atm)). The volume that we will consider is a cubic meter, so V= 1 m3, and the temperature is typically 25°C or 298K (K denotes degrees on the Kelvin temperature scale which starts at absolute zero or -273.15°C), so T = 298K. R, the Universal Gas Constant, has a value in these same units, of 8.205746 . 10.5 m3-atm/¡mole. This leaves only n, the number of moles of material present in the volume, to be determined. Re-arranging the Ideal Gas equation:

n = PV/RT = (1 atm x 1 litre)/( 8.205746 x 10-5 m3-atm/K-mole x 298K)

Doing the calculation and canceling the units yields the following answer for the number of moles of gas that is present in a cubic meter of volume at 1 atmosphere pressure and room temperature:

n = 40.8945 moles

This number, in turn allows us to determine how many molecules are present in the cubic meter of gas since a mole of any material contains Avogadro's number, NA, (6.022 x 1023) of molecules:

number of gas molecules in a m3 = n x NA = 40.8945 x 6.022 x 1023

= 2.4626849 x 1025 molecules in a cubic meter of gas at room temperature

= 6.9735479 x 1023 molecules in a cubic foot of gas at room temperature

Description  Pressure (Torr)   Pressure (Pa) Number of Molecules per m3 of Gas 
 Atmospheric Pressure  760  101.3 kPa  2.5 x 1025
 Low (Rough) Vacuum  25 to 760  3 kPa - 100 kPa  8.1 x.1023 - 2.5 x 1025
 Medium Vacuum  1 x 10-3 - 25  100 mPa - 3 kPa  3.2 x1019 - 8.1 x 1023
 High Vacuum  1 x 10-9 - 1 x 10-3  100 nPa - 100 mPa 3.2 x1013 - 3.2 x1019
 Ultra-High Vacuum (UHV) 1 x 10-12 - 1 x 10-9 100 pPa - 100 nPa 3.2 x 1010 - 3.2 x 1013
Extremely High Vacuum < 1x10-12 < 100 pPa < 3.2 x 1010
Outer Space <3 x 10-17 - 1 x 10-6 < 3 fPa - 100 µPa 970,000 - 3.2 x 1016

Table 1. Vacuum classifications and molecules/litre.

The term vacuum, in the formal sense, describes any pressure less than normal atmospheric pressure. In practical application, it is classified as one of three kinds of vacuum: either low (rough) vacuum, medium vacuum or high vacuum (Table 1). You can see from the values in the right-most column of Table 1 that even in the furthest reaches of outer space there are still nearly a million molecules of gas in a cubic meter. Most semiconductor processes are conducted under either medium or high vacuum conditions.

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