Strong Linear-kValence-Band Mixing at Semiconductor Heterojunctions

Abstract

This paper examines linear-k terms in the G 8 valence-band Hamiltonian for heterostructures of zincblende-type semiconductors. In bulk crystals such terms are known to be extremely small, due to their origin as relativistic perturbations from d and f orbitals. However, in heterostructures there is a nonvanishing contribution from p orbitals. This contribution is an order of magnitude larger than the corresponding bulk term, and it should give rise to an optical anisotropy comparable to (although smaller than) that seen in recent experiments on the quantum-well Pockels effect. DOI: 10.1103/PhysRevLett.86.2641 The discovery of the quantum-well Pockels effect by Kwok et al. [1] has attracted considerable interest in the semiconductor physics community over the past several years [2][3][4][5][6][7][8]. This effect involves a dramatic increase in optical anisotropy caused by the reduction in crystal symmetry (from T d to C 2y ) at a heterojunction between two zinc-blende-type semiconductors. It is now widely accepted that in type-I systems, the quantum-well Pockels effect is primarily a consequence of the mixing of light and heavy holes that arises from the rapid change in crystalline potential at an abrupt junction. Such microscopic interface effects can be described simply by adding a d-function potential to the standard valence-band envelope-function Hamiltonian [3,5,[9][10][11][12].It is, of course, well known that linear-k mixing of the G 8 valence states [13][14][15][16][17] must also contribute to the Pockels effect. However, apart from a few early studies [2,18] (which appeared before the significance of interfaceinduced mixing was known), linear-k mixing has been neglected in all theoretical models of the quantum-well Pockels effect. This is because there is universal agreement that such mixing is far too weak to account for the observed optical anisotropy in quantum wells. Indeed, the neglect of linear-k mixing is so common that it has become an automatic first step in almost all valence-band calculations.In this paper it is shown that, although the bulk mixing is indeed very small [19], linear-k valence-band mixing is greatly enhanced in the vicinity of a heterojunction. The G 8 linear-k mixing at an interface is an order of magnitude larger than in the bulk, and it should yield an optical anisotropy comparable to (but smaller than) that observed experimentally. (This conclusion is based on a comparison of the present Hamiltonian with similar Hamiltonians used in earlier studies; no optical spectra are calculated here.) Therefore, this source of mixing should be included in theoretical models of the quantum-well Pockels effect. It may or may not be significant in other situations, but the neglect of such mixing should no longer be considered automatic.The reason why interface linear-k mixing is so much larger than bulk mixing can be understood from simple symmetry arguments. Linear-k terms in the G 8 Hamiltonian arise to lowest order as second-order perturbations involving one matrix element of the spin-o...

Atomic scale images of acceptors in III-V semiconductors

“…Recent reports suggest that additional spin-orbit effects at the surface may be responsible for the enhanced anisotropy. For the interfaces of heterostruc-tures it was shown that interface induced asymmetry may lead to spin-orbit splitting effects that are one order of magnitude higher than what is expected for the bulk system [151].…”

Hole spin surfaces in A3B5semiconductors

“…The latter representation has been used in the construction of the linear part of the Hamiltonian (2) [12]. In the semiconductor physics in the analysis of the transport properties in high electric fields it is common to assume that the charge carrier state is characterized by a particular energy in the energy band.…”

“…Linear-k mixing within Γ 8 valence states (heavy-and light-mass bands) was considered by Kane [8,9] and its contribution was evaluated by k · p and LMTO (linear muffin-tin orbitals) methods by Cardona et al [10,11]. The linear-k Hamiltonian for both Γ 8 and Γ 7 (split-off) valence bands in bulk semiconductors and heterostructures was recently evaluated by Foreman [12], who demonstrated that its contribution in heterostructures is by an order …”

“…γ 1 , γ 2 , γ 3 , and ∆ values were taken from the recent review [15] on A 3 B 5 semiconductors and their alloys. The parameter c was taken from [11,12] (see also Table 1). To author's knowledge the magnitude of the parameter c ′ is not known as yet.…”

Semiconductor Spintronics: Role of the Valence-Band Holes

“…In the calculations, linear-k part of the Hamiltonian was taken from Ref. [15]. From the numerical calculations presented in [4,5] it follows that the inclusion of linear-k terms gives, in general, negligible effect on the shape of the spin surfaces in all A 3 B 5 semiconductors.…”