Article,
Quantum confinement in nonadditive space with a spatially dependent effective mass for Si and Ge quantum wells
PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES, (2014)
DOI: 10.1016/j.physe.2014.05.005
Abstract
We calculate the effect of a spatially dependent effective mass (SPDEM)
adapted from Costa Filho et al. (2011) on an electron and a hole
confined in a quantum well (QW). In the work of Costa Filho et al., the
translation operator is modified to include an inverse character length
scale, gamma, which defines the SPDEM. The introduction gamma means that
translations are no longer additive. In nonadditive space, we choose a
`skewed' Gaussian confinement potential defined by the replacement x
->gamma In-1(1+gamma x) in the usual Gaussian potential. Within the
parabolic approximation gamma is inversely related to the QW thickness
and we obtain analytic solutions to our confinement Hamiltonian. Our
calculation yields a reduced dispersion relation for the gap energy
(E-G) as a function of QW thickness, D : E-G D-1, compared to the
effective mass approximation: E-G similar to D-2. Additionally,
nonadditive space contracts the position space metric thus increasing
the occupied momentum space and reducing the effective mass, in
agreement with the relation: m(0)(*-1) proportional to upsilon
E-2/upsilon k(2). The change in the effective mass is shown to be a
function of the confinement potential via a point canonical
transformation. Our calculation agrees with experimental measurements of
E-G for Si and Ge QWs. (c) 2014 Elsevier B.V. All rights reserved.
Tags
- dependent
- effective
- germanium;
- interface}
- mass;
- nonadditive
- silicon;
- space;
- spatially
- {nanostructure;
