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. 01350-4495/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 1350-4495(95)00083-6