Past exam of the physics A course of the University of Cambridge / 2011 / Paper 1 / Section D / D13

Joining p-type and n-type regions initially allows majority carriers to diffuse across and recombine. Exposed negative acceptor charge on the p side and positive donor charge on the n side form a depletion region. Its electric field points from n to p and balances diffusion at equilibrium. The Fermi level is then spatially constant, while the conduction and valence band edges bend across the built-in potential; this equilibrium barrier cannot supply continuous power to a load.

forward bias makes p positive relative to n, reducing the barrier from $q{V}_{bi}$ to $q(V_{bi}-V)$. electrons enter p material and holes enter n material, becoming minority carriers whose diffusion and recombination sustain the current. reverse bias enlarges the barrier and leaves a much smaller minority-carrier current until breakdown. The ideal diffusion model gives $I=I_0[e^{qV/k_{B}T}-1]$, the Shockley diode equation; depletion-region recombination, series resistance and breakdown limit this approximation. Minority-carrier injection on both sides is essential to the junction theory.^[ref]

forward bias injects electrons and holes into a common active region. Their electron-hole recombination can emit a photon as an electron falls from a conduction-band state into an empty valence-band state, with $h\nu$ approximately the band gap $E_g$ near the band edges. A direct band gap makes this radiative transition much more probable than an indirect gap requiring simultaneous phonon participation. Carrier confinement improves their overlap; nonradiative recombination and photon trapping reduce the external efficiency. This is spontaneous electroluminescence and does not require population inversion. The biased carriers have separate quasi-Fermi levels, rather than one global equilibrium Fermi level. The band-diagram downward arrow shows photon emission. As a concrete implementation, an InGaN/AlGaN double heterostructure was used for a bright blue junction LED.^[ref]

Absorption of photons with $h\nu \gtrsim E_g$ creates electron-hole pairs, the upward band-diagram arrow. In the depletion region the built-in field drives electrons towards n material and holes towards p material; diffusion also delivers carriers generated within a diffusion length outside that region. Selective contacts collect the two signs. Illumination maintains a nonequilibrium quasi-Fermi-level splitting, allowing a voltage and useful current through an external load; it is the light, rather than the equilibrium barrier, that supplies the energy.

Taking forward diode current as positive, an ideal illuminated junction haspower is delivered where $VI<0$ in this convention. Reflection, below-gap transmission, carrier thermalization, recombination and resistive losses limit real conversion; even an ideal single junction has radiative detailed-balance limits.^[ref]