A silicon sample has a non$-$uniform electron concentration given by

n$($x$)=51015$ cm$3+31014$ cm$4$x$.$ The sample is also subjected to an electric field of E$=50$ V$/$cm$.$

Assume n $=1350$ cm$2/$V and diffusion coefficient Dn$=35$cm$2/$s$.$

a$)$ Derive the total current density Jtotal $=$Jdrift $+$Jdiff

b$)$ Calculate Jdrift $,$ Jdiff $,$ and Jtotal $,$ at x$=10$ m$.$

c$)$ Discuss the relative contributions of drift and diffusion currents to the total current.