Valley splitting and optical intersubband transitions at parallel and normal incidence in [001]-Ge/SiGe quantum wells

Abstract

We investigate intervalley splitting in the conduction band of strained [001]-Ge quantum well (QW) systems with finite SiGe alloy barriers by means of a sp3d5s∗ tight-binding Hamiltonian. We find that interaction between germanium bulk L minima splits each confined subband into a doublet. We first characterize this splitting as a function of the well width and of the strength of a uniform electric field superimposed along the growth direction. Varying the well width, an oscillating behavior of the splitting magnitude similar to that predicted for Si QW systems is observed and explained. Then we focus on the optical intersubband transitions occurring between states belonging to the fundamental and the first-excited doublets. Selection rules for intersubband transitions at normal and parallel incidence are discussed exploiting the parity character of the involved doublet states. Numerical results for infrared-absorption spectra, evaluated for both symmetric and biased Ge QWs, support our findings

Valley degeneracy in biaxially strained aluminum arsenide quantum wells

“…Theoretically, Rasolt proposed an understanding of the various continuous symmetries and symmetry-breaking in a multi-valley system in terms of an SU(N ) symmetry where N is the valley degeneracy number 20 , but did not explicitly derive the vanishing intervalley exchange integral which underlies this theory. Material specific calculations of quantum confinement and strain in highmobility Si and Ge structures are well studied for highsymmetry facets [29][30][31][32][33][34][35][36][37][38][39][40] and recently, such calculations have been been made in other quantum confined systems as well 41,42 . However, a combined treatment of quantum confinement, strain, and piezoelectric fields to determine valley degeneracy in QWs is lacking, especially for low symmetry facets.…”

Recent developments in tight-binding approaches for nanowires

“…The gauge-invariant Peierls-tight-binding approach has recently been used successfully to calculate optical matrix elements in quantum wells [19,20], valley splitting in Si quantum wells under a magnetic field [21], g-factor calculations [22] and in molecules [15,23]. Virgilio and Grosso [19,20] employ an sp 3 d 5 s * model for Ge/SiGe quantum wells and get good agreement with experimental optical absorption results. Kharche et al [21] employ the sp 3 d 5 s * model and calculate valley-splitting as a function of magnetic field in Si quantum wells, obtaining excellent agreement with experiment.…”

“…Interestingly, (3) can be shown to hold in the continuous position basis in ordinary (continuous) quantum mechanics, provided that one recognizes that the Hamiltonian matrix elements in this basis are generalized functions [18]. The gauge-invariant Peierls-tight-binding approach has recently been used successfully to calculate optical matrix elements in quantum wells [19,20], valley splitting in Si quantum wells under a magnetic field [21], g-factor calculations [22] and in molecules [15,23]. Virgilio and Grosso [19,20] employ an sp 3 d 5 s * model for Ge/SiGe quantum wells and get good agreement with experimental optical absorption results.…”

30-band k⋅p method for quantum semiconductor heterostructures

“…15 The resulting k · p / LCLK approach is an improvement over the conventional k · p method in EFA with low computational cost as compared to atomistic methods like the EPM associated to LCBB or 3,4 extendedbasis spds ‫ء‬ TB schemes. [5][6][7][8][9] We illustrate application of our k · p / LCLK model by considering the case of ͑GaAs͒ n / ͑AlAs͒ n SLs grown latticematched on a GaAs substrate. Such heterostructures provide a stringent test for evaluating the performance of ab initio and empirical approaches, 2,3,25 as the CBM occurs at a k-point different from ⌫ and depending on the SLs period n. In our calculations, the valence band offset has been chosen in accordance with experimental data: ⌬E v = 0.55 eV.…”

“…A precise band-structure description can also be obtained for heterostructures, with a unique submillielectron volt precision throughout the Brillouin zone ͑BZ͒, using a spds ‫ء‬ nearestneighbor tight-binding ͑TB͒ model including spin-orbit coupling. [5][6][7][8] In that case accurate parameters have been optimized for bulk materials to achieve improved agreement with experiment. 9 On the other hand, the need for simple and nonatomistic methods has led to the development of the k · p method and the envelope function approximation ͑EFA͒.…”