Electron-hole pair generation and recombination

Electron–hole pair generation is the process by which thermal energy (or light) promotes a bound valence electron into the conduction band, freeing a mobile electron and simultaneously leaving behind a mobile hole. Recombination is the reverse: a free electron drops back into a vacant bond, annihilating one electron and one hole together. Carriers are always created and destroyed in pairs.

Generation

A valence electron is locked in a covalent bond. If it picks up at least a bandgap’s worth of energy, $E_g$ (about $1.1\text{eV}$ for silicon), it can escape the bond into the conduction band and become a free carrier. The most common energy source is simply heat — at any temperature above absolute zero, lattice vibrations occasionally deliver enough energy to a bond to break it. The instant the electron leaves, the broken bond is a hole. So a single generation event always produces one free electron and one hole at the same time: an electron–hole pair.

Electron–hole pair generation in intrinsic silicon; in thermal equilibrium the generation and recombination rates are equal.

Recombination

The opposite also happens continuously. A free conduction-band electron wandering through the crystal can fall into a vacant bond — a hole — releasing roughly $E_g$ of energy as heat or light. That event removes one free electron and one hole simultaneously. Recombination is more likely when there are more carriers around, so its rate rises with the carrier concentrations.

Thermal equilibrium: rates balance

At a fixed temperature, generation runs at a steady rate set by how often thermal energy breaks a bond, while recombination runs at a rate that grows with how many carriers are present. The carrier populations adjust until the two rates are exactly equal — the generation rate equals the recombination rate. This is thermal equilibrium. It is not a static situation: pairs are constantly being created and destroyed, but the concentrations hold steady because creation and destruction balance.

In pure (intrinsic) silicon, equilibrium fixes the electron concentration $n$ and hole concentration $p$ at the common value

$n=p=n_i$

the Intrinsic carrier concentration. More generally, even after Doping shifts $n$ and $p$ apart by orders of magnitude, equilibrium pins their product through the Mass-action law $np=n_i^2$ — a direct consequence of the generation/recombination balance, since the same thermal generation rate must be matched by a recombination rate proportional to $np$.

Why it matters

This pair-wise generation and recombination is the microscopic engine behind everything in the semiconductor chapter. It determines the intrinsic carrier count, makes the mass-action law hold, and supplies the few minority carriers that carry the Reverse saturation current in a reverse-biased PN junction. Devices like photodiodes and solar cells work by deliberately using light to drive generation; LEDs work by driving recombination to emit light.