Draft:Semiconductor equilibrium

In a semiconductor thermal equilibrium, all generation and recombination processes balance and no net current flows. In practice this means the generation rate G equals the recombination rate R, so carrier densities remain constant over time. Likewise, any diffusion current (from concentration gradients) is exactly canceled by drift current (from internal electric fields). Equivalently, the Fermi–Dirac distribution of carriers is fixed by a single, uniform Fermi level throughout the material. In short, ${\displaystyle G=S}$, ${\displaystyle I_{drift}+I_{diff}=0}$ at equilibrium. An important consequence is the law of mass action: at equilibrium^[1]:

${\displaystyle np=n_{i}^{2}}$

where n is the intrinsic carrier concentration. Physically, this means that for an undoped (intrinsic) semiconductor ${\displaystyle n=p=n_{i}}$, while doping sets one carrier type as majority and the other as the much smaller minority .

Characteristics

• Equilibrium condition: G = R and zero net current.
• Uniform Fermi level: The Fermi energy ${\displaystyle E_{F}}$ is flat (constant) throughout at equilibrium.
• Mass action low: ${\displaystyle np=n_{i}^{2}}$ (so in intrinsic ${\displaystyle n=p=n_{i}}$).

References

1. "Equilibrium Carrier Concentration | PVEducation". www.pveducation.org. Retrieved 2025-05-21.