[UPSC CSE 2019] Semiconductors/Solar cell (Q179, 10M)

A silicon semiconductor sample at T=300\,\mathrm{K} having cross-sectional area of 0.5\,\mu\mathrm{m}^2 has a pentavalent donor doping profile given by C(x)=5\times10^{16}e^{-x/L_n}\,\mathrm{cm^{-3}}. Given, the mobility of the electrons in the sample is 1250\,\mathrm{cm^2\,V^{-1}\,s^{-1}} and the diffusion length of the electrons, L_n, is 4\,\mu\mathrm{m}. Calculate the diffusion current in the sample at distance x=2\,\mu\mathrm{m}.