Review of Numerical Solutions of Differential Equations Applied to Semiconductor Materials

Many differential equations can't be solved analytically, and for many applications, such as in electronic engineering – numerical solution is often more sufficient. Schrodinger equation, Poisson equation and Continuity equations are the most popular differential equations used in semiconductor materials. In this paper, the numerical solution of these equations is reviewed while focusing on some specific methods which are compared and evaluated. Schrodinger equation is solved using both Numerov method and Finite Difference method. Poisson equation is solved using Finite Difference method at various types of boundary conditions. Continuity equation is solved using Scharfetter-Gummel method. Numerical solutions are compared with the exact results and the dependence of error on the mesh size is shown.