GATE EC 2016 Set 2 Q36 — Electronic Devices

Consider avalanche breakdown in a silicon $p^{+}n$ junction. The $n$-region is uniformly doped with a donor density $N_{D}.$ Assume that breakdown occurs when the magnitude of the electric field at any point in the device becomes equal to the critical field $E_{crit}.$ Assume $E_{crit}$ to be independent of $N_{D}$. If the built-in voltage of the $p^{+}n$ junction is smaller than the breakdown voltage, $V_{BR}$, the relationship between $V_{BR}$ and $N_{D}$ is given by