<i>Γ</i>-<i>X</i>mixing in the miniband structure of a GaAs/AlAs superlattice

Pulsford, N. J.; Nicholas, R.J.; Dawson, Philip E.; Moore, K. J.; Duggan, G.; Foxon, C.T.

doi:10.1103/physrevlett.63.2284

Cited by 63 publications

(17 citation statements)

References 15 publications

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“…1,2 However, recent studies have increasingly emphasized interface-related effects lying outside the scope of conventional envelope-function theory, such as optical [3][4][5] and electrical [6][7][8] anisotropy, intervalley mixing, [9][10][11][12][13][14][15] and spin polarization phenomena. [16][17][18][19][20][21][22][23][24][25][26][27] These effects are generated ͑wholly or in part͒ by interface band-mixing terms in the heterostructure Hamiltonian, such as valence-band mixing of light and heavy holes, [28][29][30] ⌫-X coupling, 10,11 and the conduction or valence band Rashba coupling.…”

Section: A Background and Motivationmentioning

confidence: 99%

First-principles envelope-function theory for lattice-matched semiconductor heterostructures

Foreman

2005

Phys. Rev. B

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In this paper a multiband envelope-function Hamiltonian for lattice-matched semiconductor heterostructures is derived from first-principles self-consistent norm-conserving pseudopotentials. The theory is applicable to isovalent or heterovalent heterostructures with macroscopically neutral interfaces and no spontaneous bulk polarization. The key assumption-proved in earlier numerical studies-is that the heterostructure can be treated as a weak perturbation with respect to some periodic reference crystal, with the nonlinear response small in comparison to the linear response. Quadratic response theory is then used in conjunction with k · p perturbation theory to develop a multiband effective-mass Hamiltonian ͑for slowly varying envelope functions͒ in which all interface band-mixing effects are determined by the linear response. To within terms of the same order as the position dependence of the effective mass, the quadratic response contributes only a bulk band offset term and an interface dipole term, both of which are diagonal in the effective-mass Hamiltonian. The interface band mixing is therefore described by a set of bulklike parameters modulated by a structure factor that determines the distribution of atoms in the heterostructure. The same linear parameters determine the interface band-mixing Hamiltonian for slowly varying and ͑sufficiently large͒ abrupt heterostructures of arbitrary shape and orientation. Long-range multipole Coulomb fields arise in quantum wires or dots, but have no qualitative effect in two-dimensional systems beyond a dipole contribution to the band offsets. The method of invariants is used to determine the explicit form of the Hamiltonian for ⌫ 6 and ⌫ 8 states in semiconductors with the zinc-blende structure, and for intervalley mixing of ⌫ and X electrons in ͑001͒ GaAs/ AlAs heterostructures.

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Section: A Background and Motivationmentioning

confidence: 99%

First-principles envelope-function theory for lattice-matched semiconductor heterostructures

Foreman

2005

Phys. Rev. B

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“…The mixing of bands is introduced according to the scheme proposed by Pulsford et al [5], in the same spirit of Ref. [8].…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…[8]. The boundary conditions at the interfaces are introduced via an unitary matrix that involves an adjustable phenomenological parameter γ [5] .…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…By the application of a magnetic field, Pulsford et al [5], have demonstrated the anticrossing behavior between Γ and X in strongly coupled GaAs/AlAs superlattice. Their theoretical model was developed to deal with Γ-X mixing at the interfaces within the envelope-function approach.…”

Section: Introductionmentioning

confidence: 97%

“…The effective-mass approximation (EMA) can be extended to take into account mixing between Γ and X conduction-band valleys at heterointerfaces by including boundary conditions expressed in terms of an interface matrix providing a set of linear relations between the envelope functions and their derivatives at the interface [1,5,8]. Several works in the EMA have been reported taking into account the elastic Γ-X intervalley transfer by introducing an additional δ -function scattering potential at each well/barrier heterointerface of GaAs/AlAs/GaAs low dimensional heterostructures [2,3,7].…”

Section: Introductionmentioning

confidence: 99%

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Hydrostatic pressure effects on the Γ–X conduction band mixing and the binding energy of a donor impurity in GaAs–Ga_1–xAl_xAs quantum wells

Duque¹,

López

2007

Physica Status Solidi (b)

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PACS 71.55. Eq, 73.21.Fg, 78.67.De Mixing between Γ and X valleys of the conduction band in GaAs -Ga 1-x Al x As quantum wells is investigated taken into account the effect of applied hydrostatic pressure. This effect is introduced via the pressure-dependent values of the corresponding energy gaps and the main band parameters. The mixing is considered along the lines of a phenomenological model. Variation of the confined ground state in the well as a function of the pressure is reported. The dependencies of the variationally calculated binding energy of a donor impurity with the hydrostatic pressure and well width are also presented. It is shown that the inclusion of the Γ -X mixing explains the non-linear behavior in the photoluminescence peak of confined exciton states that has been observed for pressures above 20 kbar.

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On the Farsightedness (hyperopia) of the Standard k � p Model

Zunger

2002

phys. stat. sol. (a)

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The use of a small number of bands in conventional k Á p treatment of nanostructures leads to "farsightedness" (hyperopia), whereby the correct, detailed atomistic symmetry is not seen by the model, but only the global landscape symmetry is noted. Consequently, the real symmetry is confused with a higher symmetry. As a result, a number of important symmetry-mandated physical couplings are unwittingly set to zero in the k Á p approach. These are often introduced, after-thefact, "by hand", via an ansatz. Sometimes physical effects (e.g., piezoelectricity) are invoked to fix the otherwise incorrect symmetry. Thus, whereas in atomistic theories of nanostructures (tightbinding, pseudopotentials) the physically correct symmetry is naturally forced upon us by the structure itself, in the standard k Á p model it is accommodated ex post facto once it is known from sources outside the model itself.

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Γ-Xmixing in the miniband structure of a GaAs/AlAs superlattice

Cited by 63 publications

References 15 publications

First-principles envelope-function theory for lattice-matched semiconductor heterostructures

First-principles envelope-function theory for lattice-matched semiconductor heterostructures

Hydrostatic pressure effects on the Γ–X conduction band mixing and the binding energy of a donor impurity in GaAs–Ga_1–xAl_xAs quantum wells

On the Farsightedness (hyperopia) of the Standard k � p Model

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Γ-Xmixing in the miniband structure of a GaAs/AlAs superlattice

Cited by 63 publications

References 15 publications

First-principles envelope-function theory for lattice-matched semiconductor heterostructures

First-principles envelope-function theory for lattice-matched semiconductor heterostructures

Hydrostatic pressure effects on the Γ–X conduction band mixing and the binding energy of a donor impurity in GaAs–Ga1–xAlxAs quantum wells

On the Farsightedness (hyperopia) of the Standard k � p Model

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Hydrostatic pressure effects on the Γ–X conduction band mixing and the binding energy of a donor impurity in GaAs–Ga_1–xAl_xAs quantum wells