Electronic state mixing in X x and X y valleys in AlAs/GaAs (001)

Karavaev, G. F.; Chernyshov, V. N.

doi:10.1134/1.1385717

Cited by 4 publications

(6 citation statements)

References 10 publications

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“…The solutions to Eqs. (14) and (15) for the energies between -0.4 and + 0.7 eV adequately reproduce the CBS in GaAs and AlAs. For these energies, the general solution to the Schrödinger equation can be written in the following form (γ denotes either GaAs or AlAs):…”

Section: Construction Of An Approximate Descriptionmentioning

confidence: 67%

“…Let us briefly consider the approach we used in numerical calculations to solution of a problem of description of charge-carrier behavior in nanostructures [1,5,[13][14][15][16][17][18][19][20][21][22]. We consider a heterostructure consisting of several layers along the z axis.…”

Section: Construction Of An Approximate Descriptionmentioning

confidence: 99%

“…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%

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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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Section: Construction Of An Approximate Descriptionmentioning

confidence: 67%

Section: Construction Of An Approximate Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Karavaev¹,

Grinyaev²

2007

Russ Phys J

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“…T(z 1 ) is the matching matrix for the envelope functions at the interface z = z 1 . It is shown in [4,5] that if certain conditions are fulfilled, the matching matrix for the envelope functions T(z 1 ) is related with I(z 1 ) by the following equation:…”

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confidence: 99%

An analysis of boundary conditions in heterostructures

Chernyshov

2008

Russ Phys J

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General relations satisfied by scattering matrices, matching matrices for coefficients, transfer matrices, and matching matrices for envelope functions are derived for systems with heteroboundaries. It is shown that the relations found for these matrices are fulfilled to good accuracy within the models proposed for the GaAs/AlAs(001) heterostructure.At present, the scattering matrix method has gained acceptance for solving various quantum-mechanical problems for systems with heteroboundaries. To calculate matrix elements of the scattering matrix S(N), where N is the number of heteroboundaries, various approximations are used. To verify these approximations, we should have exact relations the matrix must satisfy. Note that the well-known unitarity conditions for the scattering matrix proper are insufficient for verification, because in this case, the relations are obtained only for a small number of matrix elements composing the complete scattering matrix. Recall that a matrix formed from the matrix elements of the complete scattering matrix S(N) corresponding to the propagating (non-decaying at infinity) states is referred to as the scattering matrix proper [1].Various problems for systems with heteroboundaries can be solved using the transfer matrix method. For finding both the transfer t(n) and scattering S(N) matrices, use is made of the matching matrices for coefficients I(n) calculated using different models and approximations. Therefore, to verify these approximations, the relations satisfied by the t(n) and I(n) matrices should be known. We note that the I(n) matrices can also be used for constructing various simplified models, for example, the envelope function model. Thus, given general relations for I(n), the relations for the envelope-function matching matrix can be found and used to verify the validity of a simplified model for the exact problem.This work is aimed at deriving general relations satisfied by the scattering matrices, matching matrices for coefficients, transfer matrices, and matching matrices for envelope functions in systems with heteroboundaries. The relations are used for verification of applied approximations by the example of the GaAs/AlAs (001) heterostructure. Recall the fundamental relations of the abrupt interface potential model [1, 2]. Let us consider a system with N heteroboundaries passing over the ( 1, 2,..., ) n z z n N = = planes. A medium n is in the 1 n n z z z − ≤ ≤ region. Some of the N+1 materials (subsystems) forming the system can be identical. To the left of the z 1 interface, there is a semi-infinite medium 1. To the right of z N+1 , there is a semi-infinite medium N+1. Within this model, a general solution to the Schrödinger equation for an arbitrary component of the heterostructure can be represented at fixed || k and energy E as ( ) ( ) ( ) , , ,

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“…A number of works is devoted to the heterostructures with interface planes GaAs/AlAs in which the layers of AlAs are placed in crystals GaAs or vice versa [1][2][3][4]. Electronic properties of such heterostructures are associated with electrons of the Γ-valley of the band spectrum.…”

Section: Introductionmentioning

confidence: 99%

Properties of a charge in the nanoheterosystems with quantum wells and barriers

Boichuk¹,

Bilynskyi²,

Shakleina³

et al. 2010

Condens. Matter Phys.

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In the paper a quasi-one-dimensional three-layer nanowire (NW) with an intermediate layer at the separation boundaries is described by the Kronig-Penney model with δ-function potentials. The distance between the last or supreme atoms of the intermediate layer is a parameter of the problem and ranges from zero to two lattice parameters of crystals. A precise solution is obtained for the quantum-mechanical reflection coefficient R which makes it possible to determine the dependence of the factor on a wave vector, widths of an intermediate layer and a monolayer of the nanoheterostructure. The specific calculations are performed for the GaAs/AlAs/GaAs and AlAs/GaAs/AlAS nanowires. The comparison of the reflection coefficients in the envelope-function approximation and in the effective mass method is performed at small values of a wave vector. It is shown that similar results can be received using the refined procedure, originally proposed by Harrison, with appropriately taken parameters. For the cosinusoidal dependence of the energy on a wave vector which arises in the Kronig-Penney model within the framework of the S-matrix scattering method, we determined the binding states energy for a AlAs/GaAs/AlAs quantum well wire.

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Electronic state mixing in X x and X y valleys in AlAs/GaAs (001)

Cited by 4 publications

References 10 publications

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

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

An analysis of boundary conditions in heterostructures

Properties of a charge in the nanoheterosystems with quantum wells and barriers

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