(a) Determine the built-in potential barrier \(V_{b i}\) in a silicon pn junction for (i) \(N_{d}=N_{a}=5 \times 10^{15} \mathrm{~cm}^{-3}\); (ii) \(N_{d}=5 \times 10^{17} \mathrm{~cm}^{-3}\) and \(N_{a}=10^{15} \mathrm{~cm}^{-3}\); (iii) \(N_{a}=N_{d}=10^{18} \mathrm{~cm}^{-3}\).

(b) Repeat part (a) for GaAs.