Modeling Transient Currents in Time-of-Flight Experiments with Tempered Time-Fractional Diffusion Equations

In the present paper, we use tempered fractional advection-diffusion equations to model the dispersive transport in disordered materials. A numerical method, on a time graded mesh, is derived to approximate the solution of such differential models. We also prove that it is convergent and stable. Two numerical examples are presented: The first, with known analytical solution, is presented to illustrate the performance of the numerical scheme; the second is used to show that such models are appropriate to model time of flight transient currents for some disordered materials