The p-n Junction

An abrupt p-n junction in the depletion approximation. Where the p and n regions meet, mobile carriers diffuse away and leave a charged depletion layer; its built-in field bends the bands by $qV_{bi}=kT\ln(N_AN_D/n_i^2)$. The depletion width follows $W=\sqrt{2\varepsilon(V_{bi}-V)/q\,(1/N_A+1/N_D)}$, so reverse bias widens it and forward bias narrows it, while the diode passes the ideal current $I=I_0(e^{qV/kT}-1)$: nothing at zero bias, an exponential turn-on, a tiny reverse saturation. The space charge is exactly balanced, $N_Ax_p=N_Dx_n$, the field is triangular, and $1/C^2$ is linear in $V$ (Mott-Schottky).