  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.
