Nonexponential relaxation dynamics of localized carrier densities in oxide crystals without structural or energetic disorder

A microscopic model for the nonexponential relaxation of localized-charge carrier densities in oxide crystals is derived by taking into account thermally activated diffusive hopping transport and the effect of trap saturation. Thereby it is shown that the relaxation, commonly described by a stretched-exponential function, can be successfully reconstructed without consideration of a structural or energetic disorder. Furthermore, the access to particular microscopic measures such as the lifetime of single hopping events and localized-carrier densities is enabled. The impact of the model approach valid for various complex relaxation processes is demonstrated with the nonexponential relaxation dynamics of optically generated small bound polaron densities experimentally determined in KNbO${}_3$ as an example.

Figure 1

Virgin-site probability ${\Delta }_n$ as a function of the number of steps taken. The right-hand plot shows the sum of ${\Delta }_i$ over $n$ according to Eq. (8). The dashed lines mark the asymptotic limits $1-R\approx 0.659463$ and $(1-R)n$, respectively.

Figure 2

(a) Temporal development of the walker density (open circles) for a walker and trap ratio of $\nu \left[0\right]/q\left[0\right]=0.99$. (b) Decay of the light-induced absorption in undoped KNbO${}_3$ at $\lambda =785\mathrm{nm}$ (gray line). The dashed and solid black lines are fits according to the KWW [Eq. (1)] and the TSE model [Eqs. (10) and (12)], respectively. The fit parameters are summarized in Table . In order to illustrate the fit quality, difference plots are given below the respective principal data plots. In the case of KNbO${}_3$, these plots have been smoothed to enhance the visibility.