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 much smaller than the breakdown voltage, V_BR, the relationship between V_BR and N_D is given by

A. $${{\text{V}}_{{\text{BR}}}} \times \sqrt {{{\text{N}}_{\text{D}}}} = {\text{constant}}$$

B. $${{\text{N}}_{\text{D}}} \times \sqrt {{{\text{V}}_{{\text{BR}}}}} = {\text{constant}}$$

C. $${{\text{N}}_{\text{D}}} \times {{\text{V}}_{{\text{BR}}}} = {\text{constant}}$$

D. $$\frac{{\sqrt {{{\text{N}}_{\text{D}}}} }}{{{{\text{V}}_{{\text{BR}}}}}} = {\text{constant}}$$

Answer: Option C