DEAL - GROVE MODEL

• Shows how the oxide thickness varies in time as a function of oxidation conditions (pressure, temperature)
• The flows of the oxidant gas is written as a function of concentrations in the three ambients (gas, oxide, silicon), in order to find out the oxide thickness. Notations: J₁ is the flow of molecules in air arriving at the film surface, J₂ is the flow of particles diffusing inside the oxide, J₃ is the flow which reacts at the interface, C_g is the concentration of particles in the air, C_o is the oxygen concentration in the oxide, C_s is the oxidant concentration at the surface and C_i is the concentration of molecules incorporated in the film. The reaction rate (R) is calculated from the equations written below.

• Two special cases can be written:
  • For thin oxides, the growth rate is linear (t_ox is small, thus t_ox2 << t_ox and t_ox2 can be neglected)
    • t_ox = B/A(t + τ)
    • B/A - linear rate coefficient
  • For thick oxides, the growth rate is parabolic (t_ox is large, thus t_ox2 >> t_ox, t_ox can be neglected)
    • t_ox2 = B(t + τ)
    • B - parabolic rate coefficient

• The model is not suited for very thin oxides (< 10 nm), it does not fit the experiment. Initially a very fast oxidation rate (t_ox ~ tα, α >1) is observed.