INFRARED PHYSICS
& TECHNOLOGY
ELSEVIER Infrared Physics & Technology 37 (1996) 489-498
Parabolic quantum wells of A1GaAs: bandstructure calculations
N. Sekkal, B. Abbar, F. Tekia, N. Amrane, H. Aourag
Computational Materials Science Laboratory, D[partement de Physique, lnstitut de Scienees Exactes. Universit~ de Sidi Bel Abb~s, 22000,
Sidi Bel Abbbs, Algeria
Received 4 April 1995; revised manuscript received 12 July 1995
Abstract
In this paper, by using the envelope function method (EFM) coupled to the transfer matrix technique, we report the
calculations of both the conduction and the valence subbands of parabolic quantum wells (PQW) of A1GaAs. We note that
the conduction subbands are equidistant for all the values of k. We also observe that the valence subbands for PQW show a
lower mixing compared to the square quantum wells (SQW) and are less influenced by a longitudinal electric field.
1. Introduction
Fundamental research is actively interested in the parabolic quantum wells (PQW) [1-6] mainly for their
harmonic oscillator-like potential behaviour. Technologically speaking, the state of the art is such that one can
grow materials, monolayer after monolayer by using the molecular beam epitaxy (MBE), thus obtaining
ultrathin layers of 2.8 A for GaAs-A1As [7]. In the case of ternary semiconductors (A1GaAs, as it is the case
here) MBE allows the variation of the aluminium composition at each step which leads to the variation of the
potential shape. The studies have shown that in square quantum wells (SQW) [8-12], the mixing which occurs
between light holes (LH) and heavy holes (HH) when kll 4:0 (kll being the wave vector parallel to the interfaces
(krr = (k~ + k~)l/2)) is very important.
Many works concerned with PQW have considered only the contribution of the zone-center region, i.e.
kll = 0 [1-4,13]. This can be the source of non negligible errors since the other kll regions have been found to
influence seriously the electronic properties of quantum wells. For example, these regions are the source of the
observed forbidden transitions and the hole subbands mixing which affect seriously the electronic properties as
it is the case for the holes resonant tunneling effect [14-18].
In this paper, we want to study the bandstructure of PQW of AIGaAs without neglecting the whole-zone kll
regions. Our main concern is to show how the mixing of the valence subbands is modified compared to SQW
and to verify if the equidistance property holds for all values of kll too. We want also to study the longitudinal
Stark effect in PQW, without neglecting the variation of the effective masses as it was done previously in Ref.
[6]. Another improvement in this paper is the study of valence subbands under the longitudinal electric fields of
various intensities without neglecting the mixing. Our choice of A1GaAs will be very helpful due to its good
lattice matching. This will justify the neglect of the strain effects.
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