Numerical Modeling of Two-Dimensional Device Structures Using Brandt’s Multilevel Acceleration Scheme: Application to Poisson’s Equation

In expanding numerical modeling for electronic and optoelectronic devices from a single dimension to mulitple dimensions, a large increase in machine storage space is required. Solution approaches based on relaxation techniques are typically used to minimize this increase, but they can be slow to converge. We present an adaption of Brandt’s multilevel acceleration scheme for control volume discretizations coupled with solvers based on either Stone’s strongly implicit method or the Gauss-Siedel (G-S) method to overcome this speed and storage space problem. We demonstrate this approach by solving Poisson’s equation in a two-dimensional amorphous silicon thin film transistor structure. The structure has a generalized density of states function whose occupancy is computed using nonzero degree Kelvin Fermi-Dirac statistics. We show that the use of the multilevel acceleration algorithm gives more than an order of magnitude increase in the asymptotic rate of convergence for the potential distribution in this thin film transistor. We also present the numerical results of the analysis.