Generalized Fit for Asymptotic Predictions of Heavy-Tail Experimental Transients

Abstract

Transient responses in disordered systems typically show a heavy-tail relaxation behavior: the decay time constant increases as time increases, revealing a spectral distribution of time constants. The asymptotic value of such transients is notoriously difficult to experimentally measure due to the increasing decay time-scale. However, if the heavy-tail transient is plotted versus log-time, a reduced set of data around the inflection point of such a plot is sufficient for an accurate fit. From a derivative plot in log-time, the peak height, position, line width, and, most importantly, skewness are all that is needed to accurately predict the asymptotic value of various heavy-tail decay models to within less than a percent. This curve fitting strategy reduces by orders of magnitude the amount of experimental data required, and clearly identifies a threshold below which the amount of data is insufficient to distinguish various models. The skew normal spectral fit and dispersive diffusion transient fit are proposed as four-parameter fits, with the latter including the stretched exponential as a limiting case. The line fit and asymptotic prediction are demonstrated using experimental transient responses in previously published amorphous silicon and amorphous InGaZnO data.