Theory of semiconductor superlattice electronic structure

Smith, D. L.; Mailhiot, C.

doi:10.1103/revmodphys.62.173

Cited by 559 publications

(219 citation statements)

References 195 publications

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“…Specifically, we measure the lattice rotations and strain fields associated with a single misfit dislocation in a freestanding GaAs/In 0.2 Ga 0.8 As/GaAs membrane. This material has intrinsic scientific importance as a key ingredient in integrated circuits, light-emitting diodes and solar cells 30,31 . A thin membrane sample is chosen in order to allow a direct comparison with TEM.…”

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confidence: 99%

X-ray micro-beam characterization of lattice rotations and distortions due to an individual dislocation

et al. 2013

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Understanding and controlling the behaviour of dislocations is crucial for a wide range of applications, from nano-electronics and solar cells to structural engineering alloys. Quantitative X-ray diffraction measurements of the strain fields due to individual dislocations, particularly in the bulk, however, have thus far remained elusive. Here we report the first characterization of a single dislocation in a freestanding GaAs/In 0.2 Ga 0.8 As/GaAs membrane by synchrotron X-ray micro-beam Laue diffraction. Our experimental X-ray data agrees closely with textbook anisotropic elasticity solutions for dislocations, providing one of few experimental validations of this fundamental theory. On the basis of the experimental uncertainty in our measurements, we predict the X-ray beam size required for threedimensional measurements of lattice strains and rotations due to individual dislocations in the material bulk. These findings have important implications for the in situ study of dislocation structure formation, self-organization and evolution in the bulk.

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confidence: 99%

X-ray micro-beam characterization of lattice rotations and distortions due to an individual dislocation

et al. 2013

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“…Such structures are of particular interest for device applications in non-linear optics, for example to design optical switches. Piezoelectric field in strained heterostructures has been theoretically predicted by Smith and Mailhiot [1,2] and then experimentally proved [3,4,5]. Fields in excess of 105 V/cm are experimentally observed in HI-V and 11-V1 [6,7] heterostructures strained by about 1%.…”

Section: Introductionmentioning

confidence: 92%

Non-linear piezoelectric effect in CdTe and CdZnTe

André

Bodin

Cibert

et al. 1993

Le Journal de Physique IV

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Strained quantum wells (QWs) grown along the polar axis (1 11) in a zincblende semiconductor exhibit a piezoelectric field. This field strongly modifies the energy of excitons confined in QWs. We have extracted, from optical measurements of excitonic transitions, the piezoelectric field value in a large set of QWs: CdTdCdZnTe, CdTeICdMnTe, CdZnTeICdMnTe. By suitably choosing the composition of alloys, we have obtained different values of strains (compressive or extensive) due to the lattice mismatch between QWs and barriers. The non-linear piezoelectric effect appears clearly when plotting the piezoelectric tensor component e 4 versus lattice mismatch. For example el4 increases from 0.07 C/m2 to 0.15 C/m2 wien the lattice mismatch varies from -0.3% to -1.7%.

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“…p theory [14,24,[30][31][32]. Like the present work, they sharply reduce the computational cost of realistic band-structure calculations.…”

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confidence: 99%

“…The Bloch functions of GaAs and AlAs are very similar, so their differences can be treated accurately in perturbation theory [24]. Since Bloch functions cannot be identical unless the bulk potentials (5) are identical (to within a constant offset DV S 0 ), the actual perturbation is the difference between the heterostructure potential V ͑r͒ and the reference ͑Al 0.5 Ga 0.5 As͒ potential.…”

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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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Theory of semiconductor superlattice electronic structure

Cited by 559 publications

References 195 publications

X-ray micro-beam characterization of lattice rotations and distortions due to an individual dislocation

X-ray micro-beam characterization of lattice rotations and distortions due to an individual dislocation

Non-linear piezoelectric effect in CdTe and CdZnTe

Analytical Envelope-Function Theory of Interface Band Mixing

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