Generalized effective mass approach for cubic semiconductor n-MOSFETs on arbitrarily oriented wafers

TL;DR

This paper develops a generalized effective mass approach for simulating cubic semiconductor n-MOSFETs on arbitrarily oriented wafers, accounting for quantum confinement and band structure anisotropy.

Contribution

It introduces a method to transform arbitrary wafer orientations into a simplified model for quantum transport analysis in n-MOSFETs.

Findings

Effective masses for silicon and germanium orientations calculated.

The approach simplifies the quantum transport problem under certain conditions.

Provides a framework for analyzing device behavior on various wafer orientations.

Abstract

The general theory for quantum simulation of cubic semiconductor n-MOSFETs is presented within the effective mass equation approach. The full three-dimensional transport problem is described in terms of coupled transverse subband modes which arise due to quantum confinement along the body thickness direction. Couplings among the subbands are generated for two reasons: due to spatial variations of the confinement potential along the transport direction, and due to non-alignment of the device coordinate system with the principal axes of the constant energy conduction band ellipsoids. The problem simplifies considerably if the electrostatic potential is separable along transport and confinement directions, and further if the potential variations along the transport direction are slow enough to prevent dipolar coupling (Zener tunneling) between subbands. In this limit, the transport problem can be solved by employing two unitary operators to transform an arbitrarily oriented constant energy ellipsoid into a regular ellipsoid with principal axes along the transport, width and confinement directions of the device. The effective masses for several technologically important wafer orientations for silicon and germanium are calculated in this paper.