Origin of the anomalous temperature dependence of luminescence in semiconductor nanocrystallites

Abstract

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 nm͒ 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.

Optical Properties of Nanostructured Silicon

“…The quenching of the blue emission is not well described by the model given in Refs. [44,60]. Both peak positions are shifted to longer wavelengths as the temperature increases from 8 K to room temperature: the orange peak position shifts from 600 AE 2 to 630 AE 2 nm.…”

“…There exists some evidence [44] that the hopping term has an anomalous Berthelot type of temperature dependence,…”

“…This ionization process has been the subject of several recent theoretical studies because the photobleaching behavior is typically observed to follow a power law rather than a simple exponential decay in time [57][58][59]. An explanation of the temperature dependence of the luminescence of porous silicon based on a similar mechanism has also been provided; the steady-state intensity-temperature data can be fitted by an equation based on the competition between a phonon-mediated radiative decay that shows normal Arrhenius temperature dependence and ionization of the excited state through a tunneling process at finite temperature which has a Berthelot-type temperature dependence, [44,60]. This model was successfully fitted to experimental data for the temperature dependence of luminescence from porous silicon [61,62].…”

“…Kapoor et al [44] discussed temperature-dependent behavior of luminescence from semiconductor NCs by using the luminescence decay time , which can be expressed in terms of the competition between the radiative decay and nonradiative (or hopping) decay dynamics. Thus…”

“…Porous silicon is a disordered system and the time dependence of the PL intensity has been reported to be of the Kohlrausch type [44] with 0 < p < 1. Thus The time-integrated luminescence intensity is then given by…”