CHEMICAL VAPOR DEPOSITION OF THIN FILM MATERIALS FOR ...

In this equation, N, c (m/s), m (kg), kB (J/K), T (K) represent the number of molecules,
molecular speed, molecular mass, Boltzmann constant and absolute temperature respectively. By
using this equation, we assume that the gas phase temperature is in the range of an ordinary
thermal CVD process and thus the main mode of molecular excitation is translational instead of
the other three, i.e., rotational, vibrational and electronic. This equilibrium distribution is from
the continuous energy exchange due to random collisions between molecules or molecules with
the surfaces. An important parameter, mean molecular speed c under a fixed temperature, can be
derived from this equation, which is essential for the calculation of molecular impingement flux
and thus understanding of the thin film deposition rate. The well know Knudsen equation, which
employs this mean speed and the ideal gas law (true for all of the CVD processes where T is at or
above room temperature and P is at or below atmospheric pressure) for molecular impingement
flux calculation is listed below.
J i 2.63×10 20 p
MT (1.2)
The molecular impingement flux is in the unit of mc/cm 2 s (molecules per square centimeter per
second) and p, M, and T are in the units of Pa, g, and K respectively. It's noteworthy that this
molecular flux is quite different from the practical thin film deposition flux, which can be
calculated from the thin film growth rate and a thin film density. As will be mentioned later, this
is because a great fraction of the impingement flux would experience reflection from the
substrate surface or even desorption from an adsorbed state of low energy.
An important dimensionless value determining the gas phase flow is the so called
Knudsen number (Kn), which is defined as the ratio of the molecular mean free path to the
characteristic dimension of the process.[11] Basically, the value of the molecular mean free path
11