An abrupt silicon (n_i = 10¹⁰ cm^-3) p-n junction consists of a p-type region containing 10¹⁶ cm^-3 acceptors and an n-type region containing 5 x 10¹⁶ cm^-3 donors.

a). Show the energy diagram of a pn junction at thermal equilibrium.

b). Determine the built-in potential of this p-n junction.

c). Determine the total width of the depletion region if the applied voltage, V, equals 0, 0.5 and -2.5 V.

d). Derive an expression for the maximum electric field, in terms of the depletion zone width, built in potential and applied voltage using full
depletion approximation, and then determine the maximum electric field in the depletion region at zero bias.