Origin of the anomalous temperature dependence of luminescence in semiconductor nanocrystallites

The temperature dependence of the luminescence intensity in nanocryststllin e semiconductors, amorphous semiconductors, and chalcogenides has been repo rted to be of the Berthelot type exp(T/T-B), where T-B is some characterist ic temperature. A similar behavior has been reported for transport properti es in certain semiconductors and in porous silicon. We propose a simple mic roscopic model for the origin of the Berthelot term. We assume that lumines cence arises from a competition between radiative and hopping processes. Th e hopping process is modeled by assuming that the carrier tunnels through a static barrier. Optimizing this tunneling in a fashion similar to Mott's t reatment of variable range hopping leads to the Berthelot-type behavior. Th e class of barriers for which our result holds is large. We examine alterna tive proposals and find them wanting. Our model predicts that acceptable va lues of the barrier width (1 nm) yields Berthelot temperatures T-B in the r ange 30-300 K. The experimentally reported T-B in diverse systems ranging f rom nanocrystalline semiconductors to amorphous chalcogenides fall in our p redicted range. Thus we demonstrate that the Berthelot temperature dependen ce has a definite and reasonable physical basis.