Deal-Grove Model

An initial thickness $X_i$ is typically assumed to be 25nm regardless of it being bare silicon

As we can observe, there are two primary regimes:

• Kinetically Controlled $\propto t$ at $\frac{4B}{A^2}t\ll 1$
  • $x(t)=\frac{B}{A}t=\frac{N_{0}k}{n}t$
• Diffusion Limited $\propto \sqrt{t}$ at $\frac{4B}{A^2}t\gg 1$
  • $x(t)=\sqrt{Bt}=\sqrt{\frac{2N_{0}D}{n}}\sqrt{t}$

Where $A\equiv \frac{2D}{n};B\equiv \frac{2D{N}_0}{n}$