Dynamics of an electron with space-dependent mass and the effective-mass method for semiconductor heterostructures

Takhtamirov, E. E.

doi:10.1070/pu1997v040n10abeh001575

Cited by 11 publications

(19 citation statements)

References 15 publications

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“…The present approach, based on quadratic response theory, 124 fits well with the k · p perturbation formalism of Leibler,47,48,[65][66][67][68][69] in which the heterostructure perturbation is treated as small in comparison to the energy separating the bands of interest from other remote bands. Leibler's theory is used here to develop a multi-band effective-mass theory that includes all terms of the same order as the position dependence of the effective mass.…”

Section: B Basic Assumptions and Limitationsmentioning

confidence: 99%

“…Takhtamirov and Volkov [65][66][67][68][69] have recently demonstrated ͑using an instructive analogy to the leading relativistic corrections to the Schrödinger equation͒ that most derivations of heterostructure effective-mass equations in the literature ͑in-cluding those of the present author͒ do not consistently include all perturbative corrections of the same order. This section presents a review and discussion of their results, with the objective of establishing which terms are to be retained in subsequent perturbative approximations.…”

Section: Order Of Terms Includedmentioning

confidence: 99%

“…65,66,68 The differences are primarily due to the use of atomic pseudopotentials ͑rather than a model based on periodic bulk potentials͒, the inclusion of long-range Coulomb potentials, and the use of linear response theory to simplify the interface Hamiltonian, as discussed in Sec. IX.…”

Section: ͑1͒mentioning

confidence: 99%

“…II with a discussion of which terms are to be retained in k · p perturbation theory, based upon a review of important recent work by Takhtamirov and Volkov. [65][66][67][68][69] The main results of the quadratic response theory developed in the preceding paper 124 are presented ͑in modified form͒ in Sec. III.…”

Section: Outline Of the Papermentioning

confidence: 99%

“…II, higher-order terms cannot consistently be described in terms of local differential equations. [65][66][67][68][69] …”

Section: B Basic Assumptions and Limitationsmentioning

confidence: 99%

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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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