Non-Bloch Nature of Alloy States in a Conventional Semiconductor Alloy:GaxIn1−xPas an Example

Abstract

Contrary to the conventional wisdom, electronic states in a "well behaved" semiconductor alloy such as Ga x In 1-x P may drastically deviate from a Bloch state, which can be true even for band edge states if they are derived from degenerate critical points.For Ga x In 1-x P in the entire composition range, k-space spectral analyses are performed for the important critical points, revealing the significance of the (near) resonant inter-and intra-valley scatterings of the fluctuation potential in the alloy. The non-trivial impications of such scatterings on the transport and strain effect are discussed. * yong_zhang@nrel.gov 1 An electronic state in a conventional semiconductor alloy A x B 1-x is often described in the same way as in a pure semiconductor, i.e., using a well defined k vector in the reduced Brillouin zone (BZ) within the framework of the "virtual crystal approximation (VCA)". [1,2] The conventional wisdom seems to suggest that the effect of disorder can be viewed as an energy shift from the VCA value plus a spectral broadening (at least for states near the band edge). [3,4] Indeed, it has been verified theoretically that a fundamental band edge state (either the conduction band minimum, CBM, or valence band maximum, VBM) does contain more than 90% of one particular k component of the BZ. [5] Therefore, it appears reasonable to classify the alloy state according to the Bloch state symmetry ("majority representation"), [5] with the understanding that the deviation from the VCA does make an alloy somewhat different from a pure semiconductor in certain important aspects. Among them, are the zerophonon emission and absorption at an indirect band gap, [6], a reduction in carrier mobility, [7] and various statistical effects such as the linewidth broadening in an optical transition.[8] However, it is not clear to what extent quantitatively the VCA picture remains useful for the global electronic structure of an alloy, i.e., including electronic states beyond the band edge (e.g., high lying critical points), and it has not been realized that there are subtle but important effects for the degenerate band edge states although at the first glance they seem to obey the "majority representation". [5] We now find that in a conventional alloy a large number of alloy states are surprisingly "non-Bloch" or it is not always appropriate to associate an alloy state with a well defined k point, and there are strong inter-valley scatterings among the degenerate critical points of the VCA. These 2 findings should have significant impacts on the understanding of optical and transport properties of the alloy in general.We have choosen the alloy system Ga x In 1-x P for this study. This system has been shown to exhibit zero-phonon absorption and emission even in the indirect band-gap region with small amount of In (< 10%). [9,10] It is also well known to exhibit spontaneous ordering when grown by MOCVD.[11] Besides being widely used in HBT's for telecommunications, the alloy with x ~ 0.5 is a key component in a latti...

Pathway to oxide photovoltaics via band-structure engineering of SnO

“…35,36 Strong perturbations can effectively destroy the E(k) relationship. The substitution of Sn 2+ by the divalent cations Mg, Ca, Sr, and Sn is obviously a rather strong perturbation, as these ions do not possess the stereoactive lone pair and usually exhibit a very different coordination environment.…”

Systematic approach for simultaneously correcting the band-gap andp−dseparation errors of common cation III-V or II-VI binaries in density functional theory calculations within a local density approximation

“…This approach is expected to be as accurate as GW, sometimes even better, for many practical applications but without the demand for large computational resources. [50] b Reference [51] c Reference [52] d Reference [53] e Reference [54] f Reference [4] [55] b Reference [56] c Reference [57] d Reference [58] e Reference [59] f Reference [60] g Reference [61] h Reference [62] i Reference [63] j Reference [64] k Reference [65] l Reference [66] m Reference [67] n Reference [68] p Reference [69] q Reference [70] r Reference [71] …”

Global electronic structure of semiconductor alloys through direct large-scale computations for III-V alloys GaxIn1−xP

“…(1), the calculation will be extremely expensive. In that case, one is either limited to analyze only a few special k points (Γ, X, L) while using a large supercell (e.g, ~30,000 atoms) [10,15] or forced to use smaller supercells (e.g., ~4,000 atoms or below) in order to get the full dispersion curves. [11] For instance, in our previous effort studying the band structure of Ga x In 1-x P with x = 0.8 using a 27648-atom supercell, even though the Γ-like state located at merely ~ 0.1 eV above the band edge, A(Γ,E) spreads over a large spectrum range, thus, we had to calculated 200 states over a 230 meV spectral range for this large supercell.…”

“…An empirical pseudopotential method (EPM), [13] which has been successfully applied to the study of the electronic structure of Ga x In 1-x P alloys, [6,10] is used in this work. The (reciprocal-space) empirical pseudopotential takes the form of…”

“…[9] We have recently found that, by a direct calculation using the 27648-atom supercell, for Ga x In 1-x P with x = 0.8 in the indirect bandgap region the A(Γ,E) spectrum shows barely a peak to allow for the identification of the Γ-like state in the alloy. [10] However, for x = 0.5 in the direct bandgap region, the 27648-atom supercell is far from adequate to reveal the intrinsic A(Γ,E) spectrum, because the alloy scattering to the Γ state is very weak.…”