Unbound states in quantum heterostructures

Ferreira, Robson; Bastard, G.

doi:10.1007/s11671-006-9000-1

Cited by 24 publications

(12 citation statements)

References 83 publications

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“…8 Additionally, in nuclear physics the Breit-Wigner resonances 1 and in atomic physics the Fano effect 2 deal with interactions of a bound state with the continuum. The existence of bound states above the continuum threshold in epitaxial self-assembled QDs has been debated recently, calling 7 for further studies and a quantitative assessment of their importance, especially in connection with the QD-based infrared photodetectors. [9][10][11] Indeed, unlike the flat interfaces characterizing quantum wells, QDs have curved shapes, leading to the strain-induced formation of local potential barriers ͑"wings"͒ around the QD.…”

Section: Strain-induced Localized States Within the Matrix Continuum mentioning

confidence: 99%

Strain-induced localized states within the matrix continuum of self-assembled quantum dots

Popescu

Bester

Zunger

2009

Applied Physics Letters

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Quantum dot-based infrared detectors often involve transitions from confined states of the dot to states above the minimum of the conduction band continuum of the matrix. We discuss the existence of two types of resonant states within this continuum in self-assembled dots: (i) virtual bound states, which characterize square wells even without strain and (ii) strain-induced localized states. The latter emerge due to the appearance of “potential wings” near the dot, related to the curvature of the dots. While states (i) do couple to the continuum, states (ii) are sheltered by the wings, giving rise to sharp absorption peaks.

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Section: Strain-induced Localized States Within the Matrix Continuum mentioning

confidence: 99%

Strain-induced localized states within the matrix continuum of self-assembled quantum dots

Popescu

Bester

Zunger

2009

Applied Physics Letters

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“…2.2. These states have been considered by several researchers [19,20], and sometimes are interpreted as resonances between plane waves; often they are called virtual bound states (VBSs). Their interpretation in the effective mass Hamiltonian equation is straightforward.…”

Section: Three-dimensional Solutionsmentioning

confidence: 99%

Single Band Effective Mass Equation and Envolvent Functions

Ĺuque

Mellor

2015

Photon Absorption Models in Nanostructured Semiconductor Solar Cells and Devices

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The single-band effective mass Schrödinger equation to calculate the envelope functions is described and its grounds are shown. These envelope functions are used to multiply periodic part of the Bloch functions to obtain approximate eigenfunctions of the Hamiltonian of a nanostructured semiconductor. The Bloch functions, which are the product of a periodic function and a plane wave, constitute the exact solution of a homogeneous semiconductor; they are taken as a basis to represent the nanostructured Hamiltonian. The conditions that make possible the use of this single band effective mass Schrödinger equation are explained. The method is applied to the calculation of the energy spectrum of quantum dots for wavefunctions belonging to the conduction band. A box-shaped model of the quantum dots is adopted for this task. The results show the existence of energy levels detached from this band as well as eigenfunctions bound totally or partially around the quantum dot. The absorption coefficients of photons in the nanostructured semiconductor, which is our ultimate goal, are calculated. The case of spherical quantum dots is also considered.Keywords Solar cells Á Quantum calculations Á Quantum dots Á Energy spectrum Á Absorption coefficientsThe easiest way to approach to the behavior of electrons in semiconductors is the use of effective mass equations. This is presented in this chapter for the specific cases of nanostructured semiconductors. The approximate treatment presented here applies to the case that the nanostructure has a mesoscopic size, much larger than the size of the semiconductor microscopic structure, that is, where the individual atoms are located.We shall see that the effective mass equation is only of application when we are dealing with electrons in a single semiconductor band, namely the conduction band. Therefore, the bipolar behavior, crucial for the understanding of most semiconductor devices, in which both electrons and holes enter into the game-or in other words, when electrons in the CB and in the VB are to be considered-cannot be explained with the resources of the simple effective mass treatment studied in this chapter. They will be properly studied in the following chapter. Nevertheless, the

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“…For the unbound motion, when Ͼ0, the constructive interference inside the slab leads to the appearance of VBS, which occur at discrete energies, similar to the confined bound states, but, unlike those, are characterized by a finite lifetime. Whereas analytical models for the potential allow one to evaluate the VBS eigenvalues, their broadening, and lifetime, 10,45 our numerical determination is inherently sensitive to the size of both supercell and the basis set used in the calculations. We obtain a dense ladder of states describing the barrier continuum with an average spacing of Ӎ1 meV.…”

Section: A Prototype States and Their Wave Functionsmentioning

confidence: 99%

“…This coexistence has a number of interesting consequences, 10 including lasing action of far infrared response, 11,12 nonlinear upconversion, 13 or dephasing of excited carriers. 14 Quasibound states in the continuum, socalled virtual bound states ͑VBSs͒, have long been known to occur in sharply varying ͑e.g., square well͒ potentials.…”

Section: Introductionmentioning

confidence: 99%

Coexistence and coupling of zero-dimensional, two-dimensional, and continuum resonances in nanostructures

2009

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Quantum dots ͑QDs͒ embedded in a matrix exhibit a coexistence of "zero-dimensional" ͑0D͒ bound electron and hole states on the dot with "three-dimensional" ͑3D͒ continuum states of the surrounding matrix. In epitaxial QDs one encounters also "two-dimensional" ͑2D͒ states of a quantum well-like supporting structure ͑wetting layer͒. This coexistence of 0D, 2D, and 3D states leads to interesting electronic consequences explored here using multiband atomistic pseudopotential calculations. We distinguish strained dots ͑InAs in GaAs͒ and strain-free dots ͑InAs in GaSb͒ finding crucial differences: in the former case "potential wings" appear in the electron confining potential in the vicinity of the dot. This results in the appearance of localized electronic states that lie above the threshold of the 3D continuum. Such resonances are "strain-induced localized states" ͑SILSs͒ appearing in strained systems, whereas in strain-free systems the dot resonances in the continuum are the usual "virtual bound states" ͑VBSs͒. The SILSs were found to occur regardless of the thickness of the wetting layer and even in interdiffused dots, provided that the interdiffusion length is small compared to the QD size. Thus, the SILSs are well isolated from the environment by the protective potential wings, whereas the VBSs are strongly interacting. These features are seen in our calculated intraband as well as interband absorption spectra. Furthermore, we show that the local barrier created around the dot by these potential wings suppresses the 0D-2D ͑dot-wetting layer͒ hybridization of the electron states. Consequently, in contrast to findings of simple model calculations of envelope function, 0D-to-2D "crossed transitions" ͑bound hole-to-wetting layer electron͒ are practically absent because of their spatially indirect character. On the other hand, since no such barrier exists in the hole confining potential, a strong 0D-2D hybridization is present for the hole states. We show this to be the source for the strong 2D-to-0D crossed transitions determined experimentally.

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Unbound states in quantum heterostructures

Cited by 24 publications

References 83 publications

Strain-induced localized states within the matrix continuum of self-assembled quantum dots

Strain-induced localized states within the matrix continuum of self-assembled quantum dots

Single Band Effective Mass Equation and Envolvent Functions

Coexistence and coupling of zero-dimensional, two-dimensional, and continuum resonances in nanostructures

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