Interface electronic states and boundary conditions for envelope functions

Tokatly, I. V.; Tsibizov, Alexander; Горбацевич, А. А.

doi:10.1103/physrevb.65.165328

Cited by 40 publications

(43 citation statements)

References 42 publications

(78 reference statements)

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“…20 As this theory was originally developed for strained zinc-blende crystals, the equations must be augmented for heterostructures by boundary conditions, which describe how the envelope functions are to be joined at the boundaries of adjacent regions. [31][32][33][34][35][36][37] For QDs, the operator of Eq. ͑13͒ is converted into a differential operator via the replacement…”

Section: Calculation Of Energy Levelsmentioning

confidence: 99%

Eight-band k⋅p calculations of the composition contrast effect on the linear polarization properties of columnar quantum dots

Andrzejewski

Sęk

O’Reilly

et al. 2010

Journal of Applied Physics

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Access to the full text of the published version may require a subscription. We present eight-band k · p calculations of the electronic and polarization properties of columnar In z Ga 1−z As quantum dots ͑CQD͒ with high aspect ratio embedded in an In x Ga 1−x As/ GaAs quantum well. Our model accounts for the linear strain effects, linear piezoelectricity, and spin-orbit interaction. We calculate the relative intensities of transverse-magnetic ͑TM͒ and transverse-electric ͑TE͒ linear polarized light emitted from the edge of the semiconductor wafer as a function of the two main factors affecting the heavy hole-light hole valence band mixing and hence, the polarization dependent selection rules for the optical transitions, namely, ͑i͒ the composition contrast z / x between the dot material and the surrounding well and ͑ii͒ the dot aspect ratio. The numerical results show that the former is the main driving parameter for tuning the polarization properties. This is explained by analyzing the biaxial strain in the CQD, based on which it is possible to predict the TM to TE intensity ratio. The conclusions are supported by analytical considerations of the strain in the dots. Finally, we present the compositional and geometrical conditions to achieve polarization independent emission from InGaAs/GaAs CQDs. Rights

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Section: Calculation Of Energy Levelsmentioning

confidence: 99%

Eight-band k⋅p calculations of the composition contrast effect on the linear polarization properties of columnar quantum dots

Andrzejewski

Sęk

O’Reilly

et al. 2010

Journal of Applied Physics

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“…When applied to semiconductor quantum structures, it is implicitly assumed that the EFA equations are also valid across an atomically abrupt material interface. The original derivation by Luttinger and Kohn [52] is, however, not strictly applicable to this case and a lot of work has been done to derive a consistent EFA theory [66][67][68][69][70][71][72], with position-dependent material parameters. Burt [73,74] and Foreman [75,76] have developed an alternative formulation of the envelope function theory for semiconductor heterostructures, starting from the single-particle Schrödinger equation.…”

Section: The Envelope Wave Function Theory Of Burt and Foremanmentioning

confidence: 99%

Theory of the electronic structure and carrier dynamics of strain-induced (Ga, In)As quantum dots

Boxberg

Tulkki

2007

Rep. Prog. Phys.

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Strain-induced quantum dots (SIQD) confine electrons and holes to a lateral potential minimum within a near-surface quantum well (QW). The potential minimum is located in the QW below a nanometre-sized stressor crystal grown on top of the QW. SIQD exhibit well-resolved and prominently atomic-like optical spectra, making them ideal for experimental and theoretical studies of mesoscopic phenomena in semiconductor nanocrystals.In this report we review the theory of strain-induced confinement, electronic structure, photonics and carrier relaxation dynamics in SIQD. The theoretical results are compared with available experimental data. Electronic structure calculations are mainly performed using the multiband envelope function approach. Many-body effects are discussed using a direct diagonalization method, albeit, for the sake of computational feasibility, within a two-band model.The QD carrier dynamics are discussed in terms of a master equation model, which accounts for the details of the electronic structure as well as the leading photon, phonon and Coulomb interaction processes. We also discuss the quantum confined Stark effect, the Zeeman splitting and the formation of Landau levels in external fields. Finally, we review a recent theory of the cooling of radiative QD excitons by THz radiation. In particular we discuss the resonance charge transfer of holes between piezoelectric trap states and the deformation potential minima. The agreement between the theory and experiment is fair throughout, but calls for further investigations.

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“…There are many studies [2,3,7,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] (see references therein) aimed at choosing matching conditions for the envelope wave functions at the interface and constructing a simplified system of equations valid for the whole heterostructure. However, in this paper, we do not intend to analyze and discuss the results of the studies.…”

Section: Introductionmentioning

confidence: 99%

The models of electron scattering at the GaAs/AlAs(001) interface

Karavaev¹,

Grinyaev²

2007

Russ Phys J

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593.293.011Simplified models for description of conduction-band electron scattering at the GaAs/AlAs(001) interface are discussed. The models correspond to two approximations taking into account abrupt and smooth changes in the potential at the interface. They are constructed on the basis of calculations by the pseudopotential method [1]. The first model using an abrupt-interface approximation is similar to the three-valley Ando model on the basis of calculations by the strong coupling method [2,3]. The second model describes the potential in the proximity of the interface using a fragment of the (GaAs) 2 ,(AlAs) 2 , superlattice equal to a half of the superlattice period. It is shown that the developed models adequately describe the results of the corresponding exact calculations. It is found that the difference between the smooth-and abrupt interface models becomes more prominent for the case of heterostructures with thin layers and for the states with detectable localization of electron density in the vicinity of interface.

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Interface electronic states and boundary conditions for envelope functions

Cited by 40 publications

References 42 publications

Eight-band k⋅p calculations of the composition contrast effect on the linear polarization properties of columnar quantum dots

Eight-band k⋅p calculations of the composition contrast effect on the linear polarization properties of columnar quantum dots

Theory of the electronic structure and carrier dynamics of strain-induced (Ga, In)As quantum dots

The models of electron scattering at the GaAs/AlAs(001) interface

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