Design a pn junction to meet maximum electric field and voltage specifications.
Consider a silicon pn junction at T=300 \mathrm{~K} with a p-type doping concentration of N_{a}=2 \times 10^{17} \mathrm{~cm}^{-3}. Determine the \mathrm{n}-type doping concentration such that the maximum electric field is \left|\mathrm{E}_{\max }\right|=2.5 \times 10^{5} \mathrm{~V} / \mathrm{cm} at a reverse-biased voltage of V_{R}=25 \mathrm{~V}.