:: IPCI ::

DEPOSITION RATE

Two main processes can limit the deposition process, thus the deposition rate:

Diffusion to the substrate
Reaction at the substrate

Diffusion to the wafer takes place due to the gradient in concentration
- It can be observed that at the surface the gas concentration is lower due to the fact that it was consumed in the surface reactions
- Diffusion coefficient: D ~ T3/2 (weak dependence on temperature, compared to the reaction rate which has Arrhenius dependence on temperature)
The flux to the substrate can be written as a function of reactants concentration or partial pressures in the gas-phase and at the substrate: , where δ is the thickness of the boundary layer
- For low pressure, the flux is higher due to a higher diffusion coefficient
The flux which arrives at the substrate is equal to the one that reacts for steady-state situations: , where the two fluxes can be written as: and:
From the above equations we extract the concentration of gas at the surface:
Deposition rate is equal with the reaction flux divided by the number of particles incorporated in the film:
Deposition can be:
- Mass-transport limited: h_g << k_r
  - limited by the supply of reactants (h_g = D/δ)
  - happens at high temperature, when chemical reactions are very fast (reaction rate is more dependent on temperature : , than the diffusion constant: D ~ T3/2)
  - deposition rate in this case is:
  - it is very important to insure an uniform flow towards the substrate (constant boundary layer thickness)
- Reaction-rate limited: k_r << h_g
  - limited by the speed with which molecules react (k_r)
  - happens for low temperature, when chemical reactions are slow
  - deposition rate in this case is:
  - it is very important to insure uniform heating of the substrate in order to obtain uniform film
In the graph it can be noticed that at high temperature, deposition rate is not so much influenced by temperature, while at low temperature it has an Arrhenius behavior. The two regimes can be easily observed.