A generalized model for time-resolved luminescence of localized carriers and applications: Dispersive thermodynamics of localized carriers

Abstract

Abstract For excited carriers or electron-hole coupling pairs (excitons) in disordered crystals, they may localize and broadly distribute within energy space first, and then experience radiative recombination and thermal transfer (i.e., non-radiative recombination via multi-phonon process) processes till they eventually return to their ground states. It has been known for a very long time that the time dynamics of these elementary excitations is energy dependent or dispersive. However, theoretical treatments to the problem are notoriously difficult. Here, we develop an analytical generalized model for temperature dependent time-resolved luminescence, which is capable of giving a quantitative description of dispersive carrier dynamics in a wide temperature range. The two effective luminescence and nonradiative recombination lifetimes of localized elementary excitations were mathematically derived as $${{\boldsymbol{\tau }}}_{{\boldsymbol{L}}}{\boldsymbol{=}}\frac{{{\boldsymbol{\tau }}}_{{\boldsymbol{r}}}}{{\bf{1}}{\boldsymbol{+}}\tfrac{{{\boldsymbol{\tau }}}_{{\boldsymbol{r}}}}{{{\boldsymbol{\tau }}}_{{\boldsymbol{t}}{\boldsymbol{r}}}}({\bf{1}}{\boldsymbol{-}}{{\boldsymbol{\gamma }}}_{{\boldsymbol{c}}}){{\boldsymbol{e}}}^{({\boldsymbol{E}}{\boldsymbol{-}}{{\boldsymbol{E}}}_{{\boldsymbol{a}}}){\boldsymbol{/}}{{\boldsymbol{k}}}_{{\boldsymbol{B}}}{\boldsymbol{T}}}}$$ τ L = τ r 1 + τ r τ t r ( 1 − γ c ) e ( E − E a ) / k B T and $${{\boldsymbol{\tau }}}_{{\boldsymbol{n}}{\boldsymbol{r}}}{\boldsymbol{=}}\frac{{{\boldsymbol{\tau }}}_{{\boldsymbol{t}}{\boldsymbol{r}}}}{({\bf{1}}{\boldsymbol{-}}{{\boldsymbol{\gamma }}}_{{\boldsymbol{c}}})}{{\boldsymbol{e}}}^{{\boldsymbol{-}}({\boldsymbol{E}}{\boldsymbol{-}}{{\boldsymbol{E}}}_{{\boldsymbol{a}}}){\boldsymbol{/}}{{\boldsymbol{k}}}_{{\boldsymbol{B}}}{\boldsymbol{T}}}$$ τ n r = τ t r ( 1 − γ c ) e − ( E − E a ) / k B T , respectively. The model is successfully applied to quantitatively interpret the time-resolved luminescence data of several material systems, showing its universality and accuracy.