Electron-hole recombination

An electron filling an electron hole removes both excitations relative to the filled-band background. Their electric charges cancel, consistent with charge conservation; the remaining electrons are still present. The released energy can leave through photon emission or other channels, including phonons. Formation of an exciton instead retains the excited electron and electron hole as a bound pair; recombination removes the pair. A valence band electron filling a nearby vacancy merely moves the electron hole and does not remove the total vacancy count.

In a weak-injection regime where the majority population is nearly fixed, a small excess minority charge carrier population often relaxes exponentially with time constant $\tau$. This lifetime describes carrier removal by recombination. It differs from the momentum relaxation time governing charge carrier mobility: many momentum-scattering events can occur before a carrier recombines. Traps and spatial transport can make a single exponential inadequate.

In a semiconductor, a conduction electron fills a vacant valence state and emits a photon. In a simple nondegenerate model the recombination rate is $Bnp$, while the equilibrium reverse generation rate is $B{n}_i^2$; their difference gives the displayed net pair-loss rate. This subtraction enforces detailed balance at thermal equilibrium. Photon momentum is small on the scale of a Brillouin zone, so a direct band gap permits a direct transition while an indirect band gap generally requires a phonon or another source of momentum.

In Auger recombination an electron-hole pair annihilates while transferring its energy to another electron or hole rather than to an emitted photon. The hot recipient subsequently loses energy, commonly to phonons. In a simple nondegenerate carrier-density model the rate is $R_A=C_n{n}^{2}p+C_{p}n{p}^2$, with electron and hole number densities $n,p$ and material-dependent coefficients. This makes the process especially important at high carrier injection. It is the reverse type of energy transfer to impact ionization, although detailed thresholds and matrix elements depend on the bands.