= Solution
Generation increases the mobile <electron> or hole populations; interband excitation creates an <electron-hole pair>. Thermal excitation and absorbed photons are important sources, and <impact ionization> can multiply carriers in a strong field. Ordinary single-photon interband absorption needs enough photon <energy> to bridge the <band gap>, with the required momentum balance.
<Electron-hole recombination> removes a pair. <Radiative electron-hole recombination> emits a photon, with simple rate $Bnp$; <trap-assisted electron-hole recombination> uses localized defect levels and transfers <energy> to the lattice; <Auger recombination> transfers the <electron-hole recombination> <energy> to another carrier. The last process becomes especially important at high injection because its rate contains products such as $n^2p$ and $np^2$. The detailed band structure and available defects determine which channel dominates.
At thermal <thermodynamic equilibrium>, generation and <electron-hole recombination> continue at equal rates. For the simple radiative model the net <electron-hole recombination> rate is $B(np-n_i^2)$, enforcing the <semiconductor mass-action law>. Under weak excitation with the majority density nearly fixed, an excess minority density often decays as $\Delta n(t)=\Delta n(0)e^{-t/\tau}$, defining its <minority carrier lifetime>.
A short light pulse followed by time-resolved <electrical conductivity> or luminescence measures the relaxation. Spatial <diffusion>, trapping and instrumental response must be separated from <electron-hole recombination> before identifying a single fitted decay constant with the intrinsic lifetime. These processes control photodetector response and light-emitting-device efficiency.
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