Quantum well to quantum wire crossover in AlAs/GaAs/AlAs heterostructures induced by interface roughness increase

Abstract

Adopting a real-space tight-binding supercell approach, we i n vestigate interface roughness e ects in semiconductor heterostructures. AlAs GaAs AlAs 001 QWs of average width W are considered, in which one of the interfaces is planar and the other has a shape de ned by periodic steps with amplitude A and wavelength . The oscillator strength f of the fundamental transition in the well describes the optical nature of the heterostructures. By investigating the wavefunctions as a function of the interface parameter A, w e conclude that the f behavior with A is an optical signature of the quantum well to quantum wire crossover in the heterostructures. Recently, photoluminescence experiments showed that hydrostatic pressure produces an increase in the optical e ciency of heterostructures in which the interfaces present a high degree of roughness. In order to investigate this optical behavior, we discuss hydrostatic pressure e ects on rough-interface heterostructures. I IntroductionThe recent progress in crystal fabrication techniques allows the growth of heterostructures with semiconductor materials of di erent atomic compositions. The interface roughness e ects in AlAs GaAs heterostructures have been intensively studied in the last years 1 -2 . In spite of optical experiments suggesting that completely at interfaces can be generated from particular growth conditions, the advent of highly sensitive microscopy techniques, as STM and TEM, indicates that some interfaces exhibit roughness over a few monolayers 3 . The optical and electronic properties of the heterostructures are very sensitive to uctuations in interface width. A very interesting problem in this context is the investigation of interface roughness e ects on the electronic properties of semiconductor heterostructures.In this work we i n vestigate the quantum well to quantum wire crossover in AlAs GaAs heterostructures induced by i n terface roughness. The optical properties of such structures were obtained within a realspace tight-binding supercell approach 4 , with periodic boundary conditions p.b.c. , using the sp 3 s parametrization proposed by V ogl et al 5 .The optical behavior of the heterostructures is described by the oscillator strength f of the transition be- where m is the free electron mass and E = E e 1 , E h 1 is the energy di erence between je 1 i and jh 1 i, which also gives the well's energy gap. Results for at interfaces quantum wells QWs 6 show that narrow wells display indirect-gap behavior, i.e., f = 0, and an abrupt transition into direct bandgap f nite occurs for W = 10 ML monolayers; 1 ML = a 2 , where a is the conventional cubic cell parameter . For the value of W considered here 16 ML and in the absence of interfaces roughness, the rst optical transition in the well is dipole-allowed.Recent photoluminescence experiments 7 show that hydrostatic pressure produces an increase in the

An extended Hückel study of the electronic properties of III–V compounds and their alloys

“…10. For the Al and Ga atoms in an alloy, the values of their on-site energies were set equal to the same average, which implies that the atoms partially lost their individuality and become a pseudo atom with orbital energies between the former values, in a similar fashion to the Virtual Crystal Approximation (VCA) [11]. However, only the on-site energies were varied: the zetas and the expansion coefficients were kept at their original values given in the Table I. Random alloys, as were considered in this article, lack formal translational symmetry and thus k is not a good quantum number, leading an inadequacy of the language of bandstructure dispersion E(k) to describe the energy states of the alloys.…”

“…However, only the on-site energies were varied: the zetas and the expansion coefficients were kept at their original values given in the Table I. Random alloys, as were considered in this article, lack formal translational symmetry and thus k is not a good quantum number, leading an inadequacy of the language of bandstructure dispersion E(k) to describe the energy states of the alloys. Nevertheless, several theoretical approaches have been proposed in the literature [11][12][13][14][15][16], intending to restore the relation between the energy and k. The Virtual Crystal Approximation [11] (VCA) was one of the first approximation employed in the theoretical study of A x B 1−x C semiconductor alloys into the TB frame, where the A and B atoms are replaced by a fictitious atom, whose TB parameters are calculated as weighted averages of the AC and BC binary parameter values. More realistic approaches, where the atom identity is preserved, are based on the spectral decomposition of the alloys eigenstates [13,14] or the unfolding of the supercell Brillouin zone [12,15,16]: the former approach employing plane waves as basis set and the second localized orbitals.…”