The temperature dependence of the luminescence intensity in nanocrystalline semiconductors, amorphous semiconductors, and chalcogenides has been reported to be of the Berthelot type $\exp {(T/T}_B),$ where $T_B$ is some characteristic temperature. A similar behavior has been reported for transport properties in certain semiconductors and in porous silicon. We propose a simple microscopic model for the origin of the Berthelot term. We assume that luminescence arises from a competition between radiative and hopping processes. The hopping process is modeled by assuming that the carrier tunnels through a static barrier. Optimizing this tunneling in a fashion similar to Mott’s treatment of variable range hopping leads to the Berthelot-type behavior. The class of barriers for which our result holds is large. We examine alternative proposals and find them wanting. Our model predicts that acceptable values of the barrier width (1 nm) yields Berthelot temperatures $T_B$ in the range 30–300 K. The experimentally reported $T_B$ in diverse systems ranging from nanocrystalline semiconductors to amorphous chalcogenides fall in our predicted range. Thus we demonstrate that the Berthelot temperature dependence has a definite and reasonable physical basis.

• Received 10 May 1999

DOI:https://doi.org/10.1103/PhysRevB.61.1941