$$q$$-Fractional multiple trapping model for charge carrier transport in amorphous semiconductors

In this work, we present a thorough theoretical model, the $$q$$ -Fractional Multiple Trapping Model, which refines the description of anomalous transit-time dispersion in disordered semiconductors. Unifying stochastic multiple trapping theory, fractional calculus and nonextensive statistical mechanics (Tsallis statistics), the model accounts for structural inhomogeneity, long-range correlations and memory effects. Analytical and numerical results derived using the inverse Laplace transform and the Padé approximation demonstrate that the transient current profile is collectively governed by three parameters: the fractional parameter $$\alpha$$ , the nonextensive parameter $$q$$ , and a structural homogeneity parameter $$\theta$$ . Key findings reveal that the nonextensive parameter $$q$$ interpolates between classical and anomalous transport, while the structural parameter $$\theta$$ dictates the emergence and sharpness of the characteristic transit time $$t_{\rm{tr}}$$ . Specifically, a small value of $$\theta$$ indicates strong disorder and broad power-law decay, whereas a large value of $$\theta$$ yields a sharp $$t_{\rm{tr}}$$ consistent with experimental observations. The model successfully reproduces experimental time-of-flight transients in amorphous selenium (a-Se) across a wide temperature range. This emphasizes the necessity of incorporating both nonextensive dynamics and structural disorder in order to accurately characterize anomalous transport phenomena in such media.