Feature Article - Semiconductor Superlattices with Small Band Offsets

Abstract

Optical transitions in small band offset superlattices are studied within the framework of the nearly free electron approximation, in which the weak superlattice potential is treated as a perturbation. Interband selection rules are derived for transitions involving conduction and valence band states at the superlattice Brillouin zone center and the zone edge. It is found that a number of new transitions can occur in such small-offset superlattices due to wave function mixing of different subband states. The effect of the effective mass on the optical transitions is also discussed. The theory is used to explain the results observed in magneto-optical absorption experiment in ZnSe/Zn1-xMnxSe small-offset superlattices. Furthermore, the nearly free electron formulation is fouud to be in excellent agreement with rigorous multi-band numerical calculation on superlattices involving small band offsets.

Optical transitions in semiconductor superlattices with small band offset in one band and large in the other

“…where R is the ratio of the well thickness to the SL period, R = L w /L. On the other hand, the band offset in the conduction band is very small, and the conduction subbands can be satisfactorily described by the nearly-free-electron model [3]. In this approximation, it is assumed that the offset V (z) is small in comparison with the kinetic energy h2 k 2 /2m * , where k is the electron momentum.…”

“…Thus minigaps will appear at k = ±nπ/L, with the magnitude of 2|V n |. The wave functions associated with the upper and lower energy states at the nth minigap are [3]…”

“…Recently, there have been both experimental and theoretical investigations of the electronic band structure of SLs with very small offsets both in the conduction and in the valence bands [2][3][4]. It was found that a large number of new optical transitions emerge because of the wave function mixing of different subband states when the band offsets are small and that transitions which occur at § Present address: Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK.…”

“…the Brillouin zone centre and at the zone edges can be readily distinguished in this regime [2,3]. In this paper we focus on another subset among wide-gap semiconductor multilayers: SLs whose band offsets are small in one band and large in the other.…”

“…Such subbands are localized not by the confining potentials but by interference of Bragg-reflected electron waves. To describe the optical properties in such LSO-SLs, we develop a formalism in which the electronic wave functions of the states in the small-offset band are obtained from the nearlyfree-electron model [3] and the wave functions of the states localized in the wells with large offset are approximated by the wave functions in infinitely deep potential wells. Wave functions overlaps between various conduction and valence subband states can in this case be obtained analytically.…”