  Photo-excited carriers, distributed among the localized states of
self-assembled quantum dots, often show very anomalous temperature dependent
photoluminescence characteristics. The temperature dependence of the peak
emission energy may be non-monotonic and the emission linewidth can get
narrower with increasing temperature. This paper describes a
quasi-thermodynamic model that naturally explains these observations.
Specifically, we introduce a temperature dependent function to parameterize the
degree of thermalization of carriers. This function allows us to continuously
interpolate between the well-defined low and high temperature limits of the
carrier distribution function and describe the observed anomalies in the
photoluminescence spectra with just two fitting parameters. We show that the
description is equivalent to assuming that the partially thermalized carriers
continue to be described by equilibrium statistics, but with a higher effective
temperature. Our treatment of the problem is computationally simpler than the
usually employed rate equations based analyses [e.g. Sanguinetti, et al. Phys.
Rev. B 60, 8276 (1999)], which typically also have many more under-determined
fitting parameters. The model is extended to quantum dots with a bimodal size
distribution.
