Semi-analytical model for charge control in SiGe quantum well MOS structures

Abstract

This paper discusses a semi-analytical model to calculate charge distribution in a silicon Metal-Oxide-Semiconductor (MOS) structure with a buried, strained Si 1−xGe x quantum well. This charge distribution model is applicable to a device structure that consists of the following layer sequence: n-type substrate; p + doping spike; Si spacer layer; SiGe quantum well; Si cap layer; insulator and gate. The sheet density of mobile charge in the SiGe well is calculated using a quantum mechanical potential well description with the addition of a first-order perturbation analysis to accommodate the application of a gate bias. The carrier density in the inversion layer at the oxide/Si interface is found in a similar manner using the triangular well approximation. These expressions are coupled with an explicit algorithm to compute the electrostatic potential and depletion charge for various gate biases. Case studies are presented for quantum well MOS structures reported in the literature, and the carrier distributions found utilizing the semi-analytical model are in reasonable agreement with those calculated numerically via self-consistent solution of Schroedinger's and Poisson's equations. This semi-analytical framework allows a means to relate the effects of changing device physical parameters on circuit oriented characteristics. With an appropriate carrier transport description, this one-dimensional treatment can be expanded to quantum well MOS-Field Effect Transistors (MOSFETs) to quantify their static and dynamic characteristics.