$(25$ points$)$ Recombination and Generation

The x$>0$ portion of an infinite semiconductor is illuminated with light. The light generates

GL$=1015$ electron$-$hole pairs$/$cm$3$s uniformly throughout the x$>0$ region of the bar. GL$=0$ for

x$<0,$ steady conditions prevail, the semiconductor is silicon, the entire bar is uniformly doped

with ND$=1018$ cm$-3,$ p$=10-6$sec and T$=300$K$.$

$($a$)$ What is the hole concentration at x$=-?$ Explain

$($b$)$ What is the hole concentration at x$=+?$ Explain

$($c$)$ Do low$-$level injection conditions prevail? Explain

$($d$)$ Determine $()$ for all x$.$

$($e$)$ Determine the electron concentration for all x$.$

$($f$)$ Determine the quasi$-$fermi level under illumination for all x$.$

Note: $(1)$ Separate $()$ expressions apply for x$>0$ and x$<0.$

$(2)$ Both $()$ and d$()/$dx must be continuous at x$=0.$

$3)(25$points$)$Ambipolar Transport

In a GaAs material at T $=300$ K$,$ the doping concentrations are Nd $=8$ x $1015$ cm$-3$ and Na $=2$

x $1015$ cm$-3.$ The thermal equilibrium recombination rate is Ro $=4$ x $104$ cm$-3$ s$-1.($a$)$ What is the

minority carrier lifetime? $($b$)$ A uniform generation rate for excess carriers results in an excess