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

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.