Pergamon Solid State Communications, Vol. 106, No. 9, pp. 559-562, 1998 @ 1998 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1098I98 $19.00 + .OO PII: s0038-1098(98)00151-3 ENERGY LEVEL SPLITTING IN DOPED NONABRUPT GaAs/Al,Gal_,As DOUBLE QUANTUM WELL J.A.K. Freire, G.A. Farias * and VN. Freire Departamento de Fisica, Universidade Federal do CearB, Centro de Ciencias Exatas, Campus do Pici, Caixa Postal 6030, 60455-760 Fortaleza, CearB, Brazil zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON (Received 3 February 199:3; accepted 16 March 1998 by G Bastard) The electron energy levels oj‘doped nonabrupt GaAs/Al,Gal_,As dou- ble quantum wells are calculated. It is shown that their characteris- tic splitting is reduced considerably when interface widths of only two GaAs lattice units are considered. The nonabrupt interfaces shift the energy levels toward high energies. The energy level shift and splitting are sensitive to the level of doping. @ 1998 Elsevier Science Ltd. All rights reserved 1. INTRODUCTION Multiple quantum well semiconductor tures are important candidates for technologic,sl ap- plications [I]. Resonant interband tunnel diodes based on double quantum wells-triple barriers have a bet- ter performance than those based on single quantum wells-double barriers [2]. Multiple doped quantum wells are also important since they are the basis for several electronic devices as, for example, infrared multiple quantum well phototransistors [3]. BasIcally, the technological applications of multiple quantum well semiconductor systems depend on their optical and transport properties that are determined by the wells and barriers widths, as well as on the quality of their interfaces. GaAs/Al,Gal_,As double symmetric quantum wells are modified when the existence of graded interfaces heterostruc- is taken into account. The interface description used here is based in the scheme proposed early by Freire, Auto and Farias [7]. It is briefly described in the Sec- tion 2, where is also presented the model for the doped nonabrupt GaAs/Al,Gal_,As double quantum wells used in this work. The results of the numerical calcula- tions are presented in Section 3, while the concluding remarks are in Section 4. Interface regions with width of two and three unit cells were observed in multilayers GaAs/Al,Gal _,As highly doped with Be (2 1018cm-3) [4]. Freire et al. [5] showed that interface and accumulation layers effects on the energy levels and carrier tranumis- sion in GaAs/Al,Gal_,As heterojunctions are im- portant for high doping levels and large interfaces. The existence of interfaces was also shown to be re- sponsible for changes in the energy levels of doped GaAs/Al,Gal _,As single quantum wells [6]. The purpose of this work is to perform an investi- gation on how the energy levels of electrons in doped * Corresponding author: E-mail: gil@fisica.ufc.br 2. THE MODEL By assuming that the aluminium molar fraction is a linear function of the coordinate z in the growth di- rection, it is easy to show that the interface potential is a parabolic function of z, while the interfacial elec- tron effective mass is a linear function of z [7]. To de- scribe the doping, we considered a homogeneous dis- tribution of the free carriers within the quantum wells. In this case, the maximum band bending at the center of the wells and barriers is proportional to the carrier concentration, and a parabolic shape is a quite good representation of the electron potential associated to the doping in GaAslAl,Gal _,As quantum wells [8,9]. According these assumptions, the potential V(z) and the electron effective mass m(z) in one of the wells of doped nonabrupt GaAs/Al,Gal_,As double sym- metric quantum wells (DSQW) are described by the 559