Operator ordering and boundary conditions for valence-band modeling: Application to [110] heterostructures

Stavrinou, Paul N.; Dalen, R. van

doi:10.1103/physrevb.55.15456

Cited by 18 publications

(25 citation statements)

References 7 publications

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“…2, 3,8,9 As discussed by Foreman, 3 the ''adhoc'' symmetrization procedure includes the much larger interaction with s states, leading to an enhanced interband coupling. For a simple square well bound state problem, Foreman has shown that the symmetrization procedure gives unphysical solutions for the heavy-hole subbands with a quantum well effective mass quite sensitive to small changes in the Luttinger parameters at the well-barrier interface.…”

Section: Introductionmentioning

confidence: 99%

Tunneling properties of holes across abrupt heterostructures using Burt’s envelope function theory

Ekbote¹,

Cahay²,

Roenker³

1999

Journal of Applied Physics

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Articles you may be interested inTunneling field-effect transistor with Ge/In0.53Ga0.47As heterostructure as tunneling junction J. Appl. Phys. 113, 094502 (2013); 10.1063/1.4794010 Band offset determination of mixed As/Sb type-II staggered gap heterostructure for n-channel tunnel field effect transistor application J. Appl. Phys. 113, 024319 (2013); 10.1063/1.4775606 Size, composition, and doping effects on In(Ga)As nanowire/Si tunnel diodes probed by conductive atomic force microscopy Appl. Phys. Lett. 101, 233102 (2012); 10.1063/1.4768001Defect assistant band alignment transition from staggered to broken gap in mixed As/Sb tunnel field effect transistor heterostructureWe use the envelope function formalism ͓M. G. Burt, J. Phys. Condens. Matter 4, 6651 ͑1992͔͒ with the rigorous boundary conditions ͓B. A. Foreman, Phys. Rev. B 48, 4964 ͑1993͔͒ to analyze the tunneling properties of holes across an abrupt InP/In 0.53 Ga 0.47 As heterojunction. We compare our results to those derived with boundary conditions obtained from an ad hoc ''symmetrized'' form of Burt's Hamiltonian. Our analysis includes the coupling between heavy, light, and spin-orbit bands. The percentage difference between the tunneling coefficients of heavy and light holes calculated in the two approaches increases ͑up to a maximum value of 30%͒ with the magnitude of the hole wave vector component parallel to the heterointerface. In addition, the tunneling coefficients of holes are found to be quite sensitive to the orientation of the hole wave vector parallel to the heterointerface. This sensitivity is particularly noticeable for large values of the hole transverse wave vector.

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Section: Introductionmentioning

confidence: 99%

Tunneling properties of holes across abrupt heterostructures using Burt’s envelope function theory

Ekbote¹,

Cahay²,

Roenker³

1999

Journal of Applied Physics

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“…28 -33 A more rigorous set of boundary conditions was derived by Burt, 34 and implemented for the ͓001͔ hh, lh, and so valence bands by Forman 35 and for the ͓110͔ hh and lh valence bands by Stavrinou and van Dalen. 36 In Eq. ͑7͒, the 6ϫ6 matrices H 2 ␣ and H 1 ␣ are obtained by factoring the bulk Hamiltonian into powers of 28 and used to construct an eigenvector equation for the expansion coefficients, A N ␣ and the quantum-well…”

Section: Quantum-well Subband Calculationmentioning

confidence: 96%

Intersubband infrared absorption spectra ofSi/Si1−xGexquant

et al. 2002

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Matrix elements of the 6ϫ6 k"p Hamiltonian, H k"p , suitable for describing quantum wells grown in the ͓110͔ crystallographic orientation, are introduced. The k"p Hamiltonian is combined with a strain H st , and a spin-orbit H so Hamiltonian to yield a total Hamiltonian HϭH k"p ϩH st ϩH so that describes the bulk barrier and well regions of a single-quantum-well heterostructure. Eigenfunctions and eigenvalues of the total Hamiltonian are used together with the envelope-function approximation to calculate quantum-well dispersion relations and momentum matrix elements for B-doped Si/Si 1Ϫx Ge x quantum wells grown in the ͓110͔ direction. The momentum matrix elements are used together with a simple Lorentzian model for line broadening and an exchange energy correction to calculate the intersubband absorption spectrum. The results are in reasonable agreement with experimental observation, and confirm that quantum wells grown in the ͓110͔ direction exhibit strong normal incidence absorption.

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“…These terms derived by the exact envelope-function theory, 21 may have a real effect on the subband spectrum at very specific parameters of the QW. [22][23][24] …”

Section: B Effective Hamiltonianmentioning

confidence: 99%

Theory of bound-to-continuum infrared absorption inp-type quantum wells based on a mapping of the continuum spectrum

Shechter

Shvartsman

1998

Phys. Rev. B

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Theoretical treatment of the infrared absorption in p-type quantum wells ͑QW's͒ is important because of the possibility of selection rule breaking for the in-plane polarized light. Here, we present the theory of the bound-to-continuum (B→C) linear absorption in p-type QW's. The anisotropy of the hole spectra, fully incorporated in the calculations, is responsible for the in-plane optical anisotropy which varies with the layer orientation. In order to simplify the problem of B→C absorption it is accepted to put the QW in an artificial additional enclosure. In this way one can reduce the calculational problem to the bound-to-bound one, but the results depend on the artificial parameter, i.e., the size of this enclosure. This problem is known as the ''artificial quantization.'' The rate of optical excitations is calculated here after mapping the continuum states at the asymptotic limit of an infinitely wide external enclosure. An advantage of this approach is the avoidance of any artificial quantization. Also we eschew computational complexity associated with processes related to the fine energy mesh in a finite enclosure. These processes are replaced by a proper phase parametrization followed by a statistical averaging. As an example we present the polarization-dependent absorption spectra of GaAs/AlGaAs QW's for both the ͗001͘ and ͗011͘ orientations. ͓S0163-1829͑98͒00728-0͔

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Operator ordering and boundary conditions for valence-band modeling: Application to [110] heterostructures

Cited by 18 publications

References 7 publications

Tunneling properties of holes across abrupt heterostructures using Burt’s envelope function theory

Tunneling properties of holes across abrupt heterostructures using Burt’s envelope function theory

Intersubband infrared absorption spectra ofSi/Si1−xGexquant

Theory of bound-to-continuum infrared absorption inp-type quantum wells based on a mapping of the continuum spectrum

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