Carrier Generation and Recombination

Carrier generation is the process by which electron-hole pairs (EHPs) are created within the semiconductor. In direct-bandgap semiconductors, such as gallium arsenide (GaAs), this occurs efficiently when energy absorption prompts valence electrons to leap into the conduction band, leaving behind holes.

This process is given by the generation rate G and is efficient due to the conservation of momentum between the valence band maximum and conduction band minimum.

Indirect generation involves an intermediate step and is typical in indirect-bandgap semiconductors like silicon (Si). Indirect-bandgap semiconductors require additional momentum from phonons, making carrier generation less efficient. Auger generation and impact ionization produce multiple EHPs in high-energy environments, such as strong electric fields.

Recombination is the process that reduces the number of free-charge carriers. Direct band-to-band recombination occurs in semiconductors like Gallium Arsenide, where electrons and holes recombine directly without intermediary states.

The recombination rate for an n-type semiconductor, where electrons are the majority carriers, is given by:

Where B is the recombination coefficient, and n and p, are the concentrations of electrons and holes, respectively. Indirect recombination involves traps: localized energy states within the bandgap. Carriers are temporarily captured by these states and then recombine, releasing energy as heat, a non-radiative process.

The equilibrium between generation and recombination is described by:

In non-equilibrium conditions, excess carriers cause a net recombination rate U, which tends towards restoring equilibrium. At low-level injection, where the minority carrier concentration (Δp) is significantly lower than the majority carrier concentration, the rate is:

Carrier generation and recombination rates are balanced at thermal equilibrium. However, when external forces such as light or electrical fields disturb this equilibrium, the semiconductor enters a non-equilibrium state. The dynamics of returning to equilibrium involve complex interactions between these generation and recombination mechanisms.