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 carriers in a material with a non-crystalline structure such as amorphous semiconductors is considered to be non-Gaussian in nature. In this case, MSD is proportional to some power of time. Diffusion in this type of transport mechanism is classified as anomalous diffusion. The usual drift-diffusion equation (DDE) cannot adequately describe this process because it has non-Gaussian and dispersive transport mechanisms. Fractional calculus has been used to generalize the standard DDE 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 Riemann - Liouville time derivative of order α and the space variable. The effects of different physical factors such as light intensity, heat and applied electric field are discussed with the help of graphical illustrations.

有序半导体具有晶格，其中电荷载流子通过正态扩散的高斯过程四处移动。这些电荷载流子的均方位移（MSD）与时间成正比。相反，在诸如非晶半导体之类的具有非晶结构的材料中，载流子的移动本质上被认为是非高斯的。在这种情况下，MSD与时间的幂成正比。这种运输机制中的扩散被归类为异常扩散。常规的漂移扩散方程（DDE）由于具有非高斯和色散传输机制，因此无法充分描述此过程。小数演算已用于将标准DDE推广为时间小数方程，以便包括载流子传输的遗传效应。对于功率设备，热量的分布和传导是制造设备时要考虑的主要标准。因此，将热传导方程添加到模型中以包含可变温度。使用数值方案求解耦合系统，其中采用有限差分法离散阶数的黎曼-利维尔时间导数α和空间变量。通过图形说明讨论了不同物理因素（例如光强度，热量和施加的电场）的影响。