In  processes such as deposition (CVD or PVD) or thermal growth, gases are introduced in the reactors. Thus a few notions of gas kinetics are necessary for a better understanding. More about gas flow dynamics can be found in the module "Principle of CVD". Futhermore, most of the processes, including diffusion and implantation take place in vacuum or low pressure. Therefore also some notions about vacuum technology are given in this module.

GAS KINETICS

In the processes with gases, the velocity of the gas particles is an important factor. However, the particles have not a constant speed, and it is impossible to find out the velocity of each particle in a gas. (There are around 1019 particles in a cm3 of gas). Maxwell-Boltzmann distribution (shown in the picture below) can be used to find average velocities. The probabilty of having a certain velocity can be defined as in the  expression below, depending on the mass of the gas molecule (m) and temperature (T). The probabilty has a maximum for average velocities, and goes to zero for higher or lower velocities.

• Maxwell-Boltzmann speed distribution:

                              

• The average velocity can be extracted from Maxwell-Boltzmann speed distribution:
  • average velocity:
  • average velocity in direction x:

• The flux of atoms impinging on a surface per unit time can be calculated by integrating the concentration of molecules that hit the surface in the specified time:  

           If we calculate how may atoms reach the substrate in a second, at a very low pressure of 10-6 Torr, by writing the concentration as a function of pressure, we obtain that one monolayer is deposited.

• The pressure exerted by gas on a surface can be calculated by multiplying the flux with the impulse of the particles:

• The mean free path  (λ) is a very important parameter in CVD, besides the pressure. It indicates how long is the molecule path in average until it collides with other molecule. If you divide the total length of the reactor L, with the mean free path, you can find out how often does the particle collides in the reactor in average. The mean free path depends on the gas concentration (n) and the molecule diameter (d). With increasing the gas concentration, more collisions take place in the reactor, thus the mean free path decreases. Also the probability of collision is higher when the molecules are larger, for the same reactor volume. By writing the gas concentration as a function of pressure, we can calculate what is the mean free path for various pressures (10 cm for 1 mTorr, and 10-5 cm for 1 atm). Thus the lower the pressure in the reactor, the higher the mean free path.