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B7. Error Function

The lateral doping profile of a diffusion step starting from a constant surface concentration can be calculated by


\begin{displaymath}
c(x,t) = c_0 \cdot \mathop{\rm erfc}\nolimits \left ( \frac{x}{2 \sqrt{D \cdot t}} \right )
\end{displaymath} (B17)

with

\begin{displaymath}
\mathop{\rm erfc}\nolimits (z) = 1 - \frac{2}{\sqrt{\pi}} \i...
...a \cdot \delta} \ d\delta =
1 - \mathop{\rm erf}\nolimits (z)
\end{displaymath} (B18)

where $\mathop{\rm erfc}\nolimits $ is the complementary error function $\mathop{\rm erf}\nolimits $ [12].




R. Plasun