Explain the basic model for thermal oxidation of silicon?
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
F1 = h (C* – C0),
F2 = D (C0-Ci)/d ,
F3 = ks Ci
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
Ci: oxidizing species concentration in the oxide adjacent to the Si-SiO2 interface,
d: oxide thickness and
ks: reaction rate constant.
After solving at steady state, values of C0 and Ci can be obtained.
When D is very small, Ci →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, Ci=C0 (reaction controlled case). Oxidation rate depends on the reaction rate constant and Ci or
C0(Ci = C0 because D is high).
Basic model for thermal oxidation of silicon