GAS TRANSPORT to the substrate

• It is important to know how fast the flow reaches the substrate and also the uniformity of the gas flow/velocities, which can determine the film uniformity
• The viscuous flow (λ << L) can be of two types:
  • Turbulent  - to be avoided in CVD, due to irreproducible film properties 
  • Laminar: when there is no turbulence, and the velocity of the viscuous flow is zero at walls (a laminar flow is shown in the picture below)

• The velocity for a laminar flow in a tube depends on the pressure gradient, gas viscosity (η) and the distance from the wall (r) (the velocity is 0 at walls and maximum in the center): , where r is the distance from the center of the tube
• The flow in the direction i can also be calculated by multiplying the concentration with the velocity:
• The boundary layer is the region close to the walls, where the molecules have lower velocity.
  • Some of the molecules from the boundary layer will be deposited on the walls.
  • The molecules have to diffuse through the boundary layer to reach the substrate. For high deposition rate, it is preffered that the boundary layer is thin.
  • The thickness of the boundary layer can be calculated: where N_Re is the Reynolds number, U₀ is the maximum speed, z is the distance from the entrance in the tube and p is the pressure.
  • It can be observed that the boumdary layer is thinner if the velocity in the center of the tube U₀ is higher, thus the deposition rate can be increased by increasing the velocity. Nevertheless for N_Re higher than 2300 (for hydorgen for example), the flow is not laminar anymore, becoming turbulent. This is not desired in CVD, due to the unpredictible results. Thus we cannot decrease too much the boundary layer thickness.
  • If the molecules in the boundary layer have very small velocities, the layer is called stagnant layer