Numerical simulation in the field of semiconductor device development advanced to a valuable, cost-effective and flexible facility. The most widely used simulators are based on classical models as they need to satisfy time and memory constraints. To improve the performance of field effect transistors such as MOSFETs and HEMTs these devices are continuously scaled down in their dimensions. Consequently the characteristics of such devices are getting more and more determined by quantum mechanical effects arising from strong transversal fields in the channel.
In this work an approach based on a two-dimensional electron gas is used to describe the confinement of the carriers. Quantization is considered in one direction only. For the derivation of a one-dimensional Schrödinger equation in the effective mass framework a non-parabolic correction for the energy dispersion due to Kane is included. For each subband a non-parabolic dispersion relation characterized by subband masses and subband non-parabolicity coefficients is introduced and the parameters are calculated via perturbation theory.
The method described in this work has been implemented in a software tool that performs a self consistent solution of Schrödinger- and Poisson-equation for a one dimensional cut through a MOS structure or heterostructure. The calculation of the carrier densities is performed assuming Fermi-Dirac statistics. In the case of a MOS structure a metal or a polysilicon gate is considered and an arbitrary gate bulk voltage can be applied. This allows to investigate quantum mechanical effects in capacity calculations, to compare the simulated data with measured CV curves and to evaluate the results obtained with a quantum mechanical correction for the classical electron density. The behavior of the defined subband parameters is compared to the value of the mass and the non-parabolicity coefficient from the model due to Kane.
Finally the presented characterization of the subbands is applied to the carrier transport simulation in a single particle Monte Carlo program. The input parameters for the developed Monte Carlo program are supplied by the self consistent Schrödinger Poisson solver in form of subband parameters and overlap integrals, specified as effective widths for the wavefunctions.