$(25$ points$)$ A p$-$n$-$p BJT has emitter $(N_E),$ base $(N_B),$ and collector $(N_C)$ doping of ${10}^{20}c{m}^{-3},{10}^{18}c{m}^{-3},$ and ${10}^{17}c{m}^{-3},$ respectively, and a base width $W_B$ of $0\mathrm{.}5$ micron. Given: $T=300K,n_i=1\mathrm{.}5{10}^{10}c{m}^{-3},lon=128\mathrm{.}85{10}^{-14}\frac{F}{c}m.$ Assume the emitter and collector regions are very long.

a$.(5$ points$)$ Calculate the peak electric field at the CB junction for the normal active mode of operation with a $V_{CB}=50V,$

b$.(5$ points$)$ and the CB depletion capacitance per unit area for the normal active mode of operation with a $V_{CB}=50V.$