Hot-Carrier Model for an Anomalous Exponent of Photoconduction

Experiments often show that the photoconductance $\sigma$ of a semiconductor system and the light intensity $I$ are related by $\sigma \sim I^{\gamma }$. Conventional theories give a satisfactory explanation for $\gamma =1$ or $\gamma =1\mathrm{/}2$, but anamalous exponents close to $\gamma =3\mathrm{/}4$ are often observed. This paper argues that there is a universal anomalous regime for which $\gamma =3\mathrm{/}4$ (or $\gamma =2\mathrm{/}3$ in two-dimensional samples), resulting from the kinetics of electron-hole recombination being controlled by Coulombic attraction. Because the local electric fields are extremely high, the theory appeals to the ‘hot-carrier’ model for transport in semiconductors.