Assignment $8\mathrm{.}2$

A silicon pn junction solar cell with an area of $2c{m}^2$ has the following parameters:

$N_d={10}^{19}c{m}^{-3},N_a=3{10}^{16}c{m}^{-3}$

$D_p=6c\frac{m^2}{s},D_n=18c\frac{m^2}{s}$

${}_{p0}=5{10}^{-7}s,{}_{n0}=5{10}^{-6}s$

Assume that the excess carries are uniformly generated in the solar cell and that $J_L=25m\frac{A}{c}{m}^2.$ Let $T=300K.($a$)$ Plot the I$-$V characteristics of the diode, $($b$)$ calculate the open circuit voltage $V_{oc},($c$)$ determine the maximum power output $P_{\text{m}\text{a}\text{x}}$ of the solar cell, $($d$)$ calculate the fill factor, and $($e$)$ calculate the external load resistance $R_L$ that will produce the maximum power.