Spectrum of an electron in a superlattice along a cylindrical quantum wire

Tkach, N. V.; Pronishin, I. V.; Maкhanets, О. М.

doi:10.1007/bf02766566

Cited by 11 publications

(11 citation statements)

References 7 publications

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“…The increase of quantum well size gives rise to new binding states and a particle monotonous energy reduction obtained both by the S-matrix scattering method (solid lines) and the effective-mass approximation (dashed lines). The derived results are in a good agreement with those in publication [13].…”

Section: Specific Calculations the Analysis Of The Obtained Resultssupporting

confidence: 88%

“…In many works the Bloch functions are replaced with the envelope ones and the effective mass approximation is used [5][6][7][8][9]. It is usual to assume that the envelope function and its derivatives need to be continuous across the interface [10][11][12][13]. In principle, these conditions would follow from a valid expression for the current operator in terms of the envelope functions.…”

Section: Introductionmentioning

confidence: 99%

“…In this way resonant diodes and quantum transistors used in novel nanoelectronic devices are made. Hence, in plenty of experimental as well as theoretical works, electron, hole,and exciton energy states are studied in composite quantum wires [10][11][12][13][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Specific Calculations the Analysis Of The Obtained Resultssupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…The theory of spectra and wave functions of quasiparticles (electrons, holes, excitons) in quantum dots embedded into the quantum wires is only at the start of development [12]. Such combined nanoheterosystems are rather complicated for mathematical description due to the complicated fitting conditions for the wave functions of quasiparticles.…”

Section: Cdsmentioning

confidence: 99%

“…Taking into account the cylindrical symmetry it is convenient to write the wave function Ψ (r) as in [12] Ψ nρm ( r) = −πρ…”

Section: The Theory Of Electron (Hole) Energy Spectrum In Cylindricalmentioning

confidence: 99%

Electron and hole spectra in quantum wire with two quantum dots in the electric field

Maкhanets¹,

Gryschyк²,

Dovganiuk³

2007

Condens. Matter Phys.

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The energy spectrum of electron and hole is investigated in a complicated nanoheterosystem consisting of two cylindrical semiconductor quantum dots placed into semiconductor quantum wire. Quantum dots are separated by barrier-layer, which is under the action of a constant electric field. The dependencies of electron and hole energies on geometric parameters of quantum dots and electric field intensity are analysed.

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