Effective-mass Hamiltonian and boundary conditions for the valence bands of semiconductor microstructures

Foreman, Bradley A.

doi:10.1103/physrevb.48.4964

Cited by 248 publications

(195 citation statements)

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“…A first popular k ជ · p ជ multiband calculation scheme for bulk materials is due to Luttinger and Kohn 12,13 which later on was extended to heterostructures by an ad hoc symmetrization procedure. 14 In order to overcome this ad hoc procedure, Burt formulated the socalled exact envelope-function method 15,16 and soon after Foreman 17 used this method to derive a six-band model for the valence bands of zinc-blende heterostuctures. Pokatilov et al 18 have provided an eight-band model for the conduction and the valence bands.…”

Section: Introductionmentioning

confidence: 99%

Optical properties and optimization of electromagnetically induced transparency in strained InAs/GaAs quantum dot structures

et al. 2009

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Section: Introductionmentioning

confidence: 99%

Optical properties and optimization of electromagnetically induced transparency in strained InAs/GaAs quantum dot structures

et al. 2009

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confidence: 99%

“…Less well known is Burt's theory of the envelope-function representation [4,5], which is an exact representation of the Schrödinger equation, fully capable of describing any effect found in pseudopotential theory. Thus far, the main applications of this theory have been a one-dimensional proof [5] that in long-period superlattices, interface-induced mixing is a small perturbation on the EFA, and the resolution of an ambiguity in the EFA ordering of differential operators [6,7].Unfortunately, the former work [5] is often misconstrued as implying that Burt's theory is no different from the EFA [8][9][10][11]. This interpretation is not warranted, because even small perturbations can have a dramatic impact when they introduce couplings of a qualitatively different nature.…”

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confidence: 99%

Analytical Envelope-Function Theory of Interface Band Mixing

Foreman

1998

Phys. Rev. Lett.

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An analytical theory of intervalley mixing at semiconductor heterojunctions is presented. Burt's envelope-function representation is used to analyze a pseudopotential Hamiltonian, yielding a simple d-function mixing between G and X electrons and light and heavy holes. This coupling exists even for media differing only by a constant band offset (i.e., with no difference in Bloch functions).[S0031-9007(98)06534-X] PACS numbers: 73.20. Dx, 71.15.Th, 73.61.Ey It is well known in semiconductor physics that bulk effective-mass theory [1] is not valid at an abrupt heterojunction, since the rapid change in potential at the interface causes a mixing of wave functions in different energy bands, and the neglect of such mixing is a key approximation in the development of this theory. It is consequently almost universally believed that a realistic description of the interface can only be achieved numerically, by performing a microscopic supercell calculation. The purpose of this paper is to demonstrate that a careful application of modern envelope-function theory yields a fully analytical description of interface band mixing.The most widely used form of envelope-function theory is Bastard's "envelope-function approximation" (EFA) [2], which openly ignores any interband mixing not found in bulk k ? p theory [3]. Less well known is Burt's theory of the envelope-function representation [4,5], which is an exact representation of the Schrödinger equation, fully capable of describing any effect found in pseudopotential theory. Thus far, the main applications of this theory have been a one-dimensional proof [5] that in long-period superlattices, interface-induced mixing is a small perturbation on the EFA, and the resolution of an ambiguity in the EFA ordering of differential operators [6,7].Unfortunately, the former work [5] is often misconstrued as implying that Burt's theory is no different from the EFA [8][9][10][11]. This interpretation is not warranted, because even small perturbations can have a dramatic impact when they introduce couplings of a qualitatively different nature. In this paper the envelope-function representation is used to analyze an empirical pseudopotential model [12] of the GaAs͞AlAs (001) heterojunction. The result is a simple analytical theory of the interface-induced mixing between G and X electrons [13][14][15][16] and light and heavy holes [17][18][19], in which the coupling takes the form of a finite-width d function whose strength is given directly in terms of pseudopotential form factors. The most striking outcome is that there is no limit in which the EFA is valid for abrupt heterojunctions, since the coupling exists even for identical Bloch functions.I begin by presenting a paraphrased (nonrigorous) version of Burt's theory. Let the microscopic Hamiltonian be H p 2 ͞2m 1 V ͑r͒, and choose as basis functions the complete orthonormal Luttinger-Kohn functions [1] x n ͑r͒ U n ͑r͒e ik?r , where U n ͑r͒ is a periodic Bloch function from some bulk reference crystal (e.g., the virtual crystal Al 0.5 Ga ...

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“…III, it is also common practice to estimate the Rashba coupling K ·␣· by the approximation 39 K ·␣· Ӎ K ␣ , which amounts to an extension of the BenDanielDuke hypothesis to the antisymmetric terms in the Luttinger Hamiltonian. 29 Table III Table IV is not discussed here beyond a brief comment that although BenDaniel-Duke operator ordering is not a very good approximation in any case, it is typically better for light holes than for heavy holes, and better for cation perturbations than for anion perturbations.…”

Section: Effective-mass Parametersmentioning

confidence: 99%

Valence-band mixing in first-principles envelope-function theory

Foreman

2007

Phys. Rev. B

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This paper presents a numerical implementation of a first-principles envelope-function theory derived recently by the author ͓B. A. Foreman, Phys. Rev. B 72, 165345 ͑2005͔͒. The examples studied deal with the valence subband structure of GaAs/ AlAs, GaAs/ Al 0.2 Ga 0.8 As, and In 0.53 Ga 0.47 As/ InP ͑001͒ superlattices calculated using the local-density approximation to density-functional theory and norm-conserving pseudopotentials without spin-orbit coupling. The heterostructure Hamiltonian is approximated using quadratic-response theory, with the heterostructure treated as a perturbation of a bulk reference crystal. The valence subband structure is reproduced accurately over a wide energy range by a multiband envelope-function Hamiltonian with linear renormalization of the momentum and mass parameters. Good results are also obtained over a more limited energy range from a single-band model with quadratic renormalization. The effective kinetic-energy operator ordering derived here is more complicated than in many previous studies, consisting in general of a linear combination of all possible operator orderings. In some cases, the valence-band Rashba coupling differs significantly from the bulk magnetic Luttinger parameter. The splitting of the quasidegenerate ground state of no-common-atom superlattices has non-negligible contributions from both short-range interface mixing and long-range dipole terms in the quadratic density response.

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Effective-mass Hamiltonian and boundary conditions for the valence bands of semiconductor microstructures

Cited by 248 publications

References 8 publications

Optical properties and optimization of electromagnetically induced transparency in strained InAs/GaAs quantum dot structures

Optical properties and optimization of electromagnetically induced transparency in strained InAs/GaAs quantum dot structures

Analytical Envelope-Function Theory of Interface Band Mixing

Valence-band mixing in first-principles envelope-function theory

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