= Solution
A <p-n junction> joins p-type and n-type semiconductors. Initial carrier diffusion exposes ionized acceptors and donors, creating a <depletion region> and an internal electric field. At equilibrium the <Fermi level> is uniform and drift balances diffusion, so the built-in potential produces no net terminal current. For nondegenerate abrupt doping, its magnitude is $V_{\rm bi}=(k_BT/e)\ln(N_AN_D/n_i^2)$.
Forward bias lowers the barrier and injects minority carriers across the junction. In the ideal low-injection diffusion model, the <Shockley diode equation> is $I=I_s[e^{eV/(k_BT)}-1]$. Reverse bias broadens the depletion region and leaves a small leakage current until breakdown mechanisms become important.
The asymmetric current-voltage curve enables rectification. Illumination produces electron-hole pairs that the junction field can separate, giving a <photodiode> or <solar cell>. Forward injection and radiative recombination in a suitable direct-gap material give a <light-emitting diode>. Measuring dark and illuminated current-voltage curves distinguishes electrical injection from photogenerated current; an ideal junction need not have zero reverse leakage or identical behavior in every material.
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