A quantum mechanical semiconductor device simulator

Semiconductor device simulators have generally been based on either classical or semi-classical approaches. In these approaches, the Poisson's equation is solved with either the current continuity equation or the Boltzmann transport equation. Methods based on quantum mechanics have been generally very computer intensive, and thus until recently not much favored. However, with the availability of faster and more powerful computers this picture is changing. As the physical dimensions of the semiconductor devices are reduced, the assumptions made in the classical and the semi-classical approaches become invalid and the simulation results become inaccurate. For such cases, quantum mechanical concepts must be introduced to provide accurate simulation results. This dissertation presents the proof of concept of a semiconductor device simulator based on the quantum mechanical principals. The simulation technique is based on the self consistent solution of the Poisson's and time independent Schrodinger wave equation for a 1-D finite differenced grid. The applicability of the technique to a 2-D finite differenced grid is also presented. The simulation is performed by first solving for the Fermi energy distribution inside the simulation domain. The initial estimates about the carrier concentrations are developed from the Fermi energy distribution. Based on the carrier concentrations, the potential distribution inside the device is updated using the Poisson's equation. The updated potential distribution is then used in the time independent Schrodinger's equation and the carrier wave vectors are thus determined. The carrier wave vectors, along with appropriate density of state function and distribution function are used to update the carrier concentrations. For the 1-D case, the density of state function is based on a single dimension of a three dimensional volume with the assumption that the density of states is the same for all the three dimensions. The distribution function used is the Fermi-Dirac distribution function. The new carrier concentrations thus computed are then substituted back into the Poisson's equation, and self consistency is obtained when minimum error criteria has been met. The device simulator has the capability of simulating heterojunctions semiconductor devices fabricated from elemental semiconductors such as Si and Ge, as well as binary and tertiary compound semiconductors.