Mathematical modeling of semiconductor-on-insulator (SOI) device operation

Numerical modeling of SOI devices is proposed through use of a bipolar carrier and time-dependent approach. Poisson's equation and the current continuity equations for electrons and holes are solved simultaneously. The former is solved over the whole area of the device in question, and the electrostatic potential at the silicon-insulator interface is determined so as to fulfill Gauss's theorem. To achieve accurate numerical calculations and to obtain a stable convergence in the numerical scheme, a variable transformation is employed in the current continuity equation. That is, quasi-Fermi potentials for electrons and holes rather than carrier densities are directly analyzed. An insulated layer is modeled in the current continuity equation using the zero intrinsic-carrier density and zero mobility to realize zero conductance in an insulator. Sample calculations demonstrate a quick and stable convergence in the numerical scheme, and clarify the operational mechanism of SOI devices. This modeling should become a helpful aid in SOI device design.