GATE EC 2003 Set 1 Q39 — Electronic Devices

The electron concentration in a sample of uniformly doped $n$-type silicon at $300 \mathrm{~K}$ varies linearly from $10^{17} / \mathrm{cm}^{3}$ at $x=0$ to $6 \times 10^{16} / \mathrm{cm}^{3}$ at $x=2 \; \mu \mathrm{m}$. Assume a situation that electrons are supplied to keep this concentration gradient constant with time. If electronic charge is $1.6 \times 10^{-19}$ coulomb and the diffusion constant $D_{n}=35 \mathrm{~cm}^{2} / \mathrm{s}$, the current density in the silicon, if no electric field is present, is