GATE Electronics and Communications (EC) 2016 Shift 2 Solved Paper

Consider avalanche breakdown in a silicon ${\mathit{p}}^{+}\mathit{n}$ junction. The n-region is uniformly doped with a donor density ${\mathit{N}}_{\mathit{D}}$. Assume that breakdown occurs when the magnitude of the electric field at any point in the device becomes equal to the critical field ${\mathit{E}}_{\mathit{c}\mathit{r}\mathit{i}\mathit{t}}$. Assume ${\mathit{E}}_{\mathit{c}\mathit{r}\mathit{i}\mathit{t}}$ to be independent of ${\mathit{N}}_{\mathit{D}}$. If the built-in voltage of the ${\mathit{p}}^{+}\mathit{n}$ junction is much smaller than the breakdown voltage, ${\mathit{V}}_{\mathit{B}\mathit{R}}$, the relationship between ${\mathit{V}}_{\mathit{B}\mathit{R}}$ and ${\mathit{N}}_{\mathit{D}}$ is given by