Consider an n$-$type semiconductor with ND$=1015$cm$3$ND$=1015$cm$3.$ There is a uniform applied electric field, E$=105$V$/$cmE$=105$V$/$cm$,$ throughout the semiconductor. At t$=0$t$=0,$ the semiconductor was illuminated by a sharply focused pulse of laser to create an excess hole concentration of $$p$($t$=0)=1012$cm$3$p$($t$=0)=1012$cm$3$ at x$=0$x$=0.$

Find the expression for the excess hole concentration, $$p$($x$,$t$)$p$($x$,$t$),$ as a function of xx and tt for t$>0$t$>0,$ i$.$e$.$ after the laser pulse is gone. Write your expression in terms of applied electric field EE$,$ generation rate GG$,$ minority carrier lifetime $($tau$),$ diffusion coefficient DD and mobility $($mu$).$ Your equation does not have to contain all of these variables.