Semiconductor Devices: Physics and Technology, 3rd Edition

Appendix K

Basic Kinetic Theory of Gases

The ideal gas law states that

where P is the pressure, V is the volume of one mole of gas, R is the gas constant (1.98 cal/mol-K, or 82 atm-cm³/mol-K), T is the absolute temperature in K, N_au is Avogadro's number (6.02 × 10²³ molecules/mole), and k is Boltzmann's constant (1.38 × 10⁻²³ J/K, or 1.37 × 10⁻²² atm-cm²/K). Since real gases behave more and more like the ideal gas as the pressure is lowered, Eq. l is valid for most vacuum processes. We can use Eq. l to calculate the molecular concentration n (the number of molecules per unit volume):

where P is in Pa. The density ρ_d of a gas is given by the product of its molecular weight and its concentration:

The gas molecules are in constant motion and their velocities are temperature dependent. The distribution of velocities is described by the Maxwell-Boltzmann distribution law, which states that for a given speed υ,

where m is the mass of a molecule. This equation states that if there are n