Assignment $8\mathrm{.}3$

A silicon pn junction photodiode has the following parameters at $T=300K$ :

$N_d=2{10}^{15}c{m}^{-3},N_a={10}^{16}c{m}^{-3}$

$D_p=10c\frac{m^2}{s},D_n=25c\frac{m^2}{s}$

${}_{p0}={10}^{-7}s,{}_{n0}=5{10}^{-7}s$

The cross$-$sectional area of the diode is $A={10}^{-3}c{m}^2.$ Assume that a reverse bias voltage of $5$ volts is applied and that light illumination induces a uniform generation rate for electron$-$hole pairs of $G_L={10}^{21}c{m}^{-3}{s}^{-1}$ throughout the entire photodiode. $($a$)$ Determine the prompt component of photocurrent. $($b$)$ Find the steady$-$state excess carrier concentrations in the p and n regions far from the junction. $($c$)$ Determine the total steady$-$state photocurrent.