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**:
$$x_0^2 + Ax_0 = B(t + \tau)$$
- $B$: 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.