| Abstract: |
| An ordered semiconductor has a crystalline lattice in which charge carriers move around by the Gaussian process of normal diffusion. The mean square displacement (MSD) of these charge carriers is proportional to time. On the contrary, the movement of charge carriers in a disordered material such as amorphous semiconductors is assumed to be non-Gaussian in nature and their MSD is proportional to some power $\alpha$ of time, where $\alpha$ is a dispersive parameter ($ 0 < \alpha < 1 $) depending on the disordered energy and temperature of the medium. Such a transport mechanism is classified as anomalous diffusion. This kind of transport cannot be sufficiently described by the usual drift-diffusion equation because it has non-Gaussian and dispersive transport mechanisms Fractional calculus approach has been used to generalize the standard drift-diffusion equation to a time fractional equation in order to include the hereditary effects of the carrier transport. For power devices, the distribution and conduction of heat is the primary criteria considered when making a device. Therefore, an equation for heat conduction is added to the model for inclusion of variable temperature. The coupled system is solved using a Numerical scheme wherein Finite Difference method has been employed to discretize the Caputo time derivative of order $\alpha$ and Finite element method has been used to discretize the space variable. The scheme is validated by computing error estimates and the effects of different physical parameters such as intrinsic currents and applied electric field are discussed with the help of graphical illustrations. |
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