Oxidation Kinetics
Silicon Oxidation Kinetics describes the rate at which silicon oxide grows during thermal oxidation — governed by the Deal-Grove model, which predicts oxide thickness as a function of temperature, time, and ambient (O2 or H2O).
Deal-Grove Model (1965)
Three transport steps in series:
1. Gas-phase transport: Oxidant from bulk gas to surface.
2. Diffusion through oxide: Oxidant diffuses through already-grown SiO2.
3. Interface reaction: Oxidant reacts with Si at SiO2/Si interface.
Resulting Rate Equation:
- $B$: Parabolic rate constant (diffusion limited).
- $B/A$: Linear rate constant (reaction limited).
- $\tau$: Time offset for initial oxide thickness.
Two Regimes
- Linear (thin oxide, $x_0 << A/2$): $x_0 \approx \frac{B}{A} t$ — reaction at interface limits rate.
- Parabolic (thick oxide, $x_0 >> A/2$): $x_0 \approx \sqrt{Bt}$ — diffusion through oxide limits rate.
Temperature Dependence
| Temp | Dry O2 Rate | Wet O2 Rate |
|---|---|---|
| 900°C | ~10 nm/hr | ~50 nm/hr |
| 1000°C | ~30 nm/hr | ~200 nm/hr |
| 1100°C | ~100 nm/hr | ~800 nm/hr |
Wet vs. Dry Oxidation
- Dry O2: Slow, dense, high-quality — used for gate oxide (1–5 nm).
- Wet (H2O): Fast, less dense — used for thick field oxide (100–500 nm).
- H2O diffuses faster through SiO2 (higher B coefficient) → faster growth.
Limitations of Deal-Grove
- Under-predicts thin oxide (<5 nm) growth — enhanced initial oxidation not captured.
- Doesn't account for stress effects, crystal orientation, or pressure.
- Extended models (Massoud) add empirical correction terms for thin oxides.
Understanding oxidation kinetics is essential for gate dielectric process control — achieving sub-0.5 nm gate oxide thickness uniformity across 300mm wafers requires precise temperature and time control guided by the Deal-Grove model.