Basic model for thermal oxidation of silicon

 

Explain the basic model for thermal oxidation of silicon?

 

Solution:

 

Model assumptions:
This model is valid for a temperature range of 700-1300C, 0.2 – 1 atm pressure, and oxide thickness of 300 – 20,000 Angstrom.

The oxidizing species-

1. are transported from the bulk gas phase to gas-oxide interface with flux F₁ (Flux means a number of species crossing a unit area per unit time).

2. are transported across the existing oxide towards the silicon with flux F₂.

3. react at the Si-SiO2 interface with the silicon with flux F₃. And

4. at steady-state F₁=F₂=F₃

Here

F₁ = h (C* - C₀),

F₂ = D (C₀-C_i)/d ,

F₃ = k_s C_i

Where
C₀: equilibrium concentration in the oxide at the outer surface,
C*: equilibrium bulk concentration in the oxide,
h: gas-phase mass transfer coefficient,

D: diffusion coefficient
C_i: oxidizing species concentration in the oxide adjacent to the Si-SiO2 interface,
d: oxide thickness and
k_s: reaction rate constant.
After solving at steady state, values of C₀ and C_i can be obtained.

 

Limiting cases:
When D is very small, C_i →0 and C₀→ C* (diffusion-controlled case) Oxidation rate depends on the supply of oxidant to the interface through the oxide layer.

When D is large, C_i=C₀ (reaction controlled case). Oxidation rate depends on the reaction rate constant and C_i or
C₀(C_i = C₀ because D is high).

Basic model for thermal oxidation of silicon