Space-Charge Effects on Electron Tunneling

BenDaniel, David J.; Duke, C. B.

doi:10.1103/physrev.152.683

Cited by 851 publications

(449 citation statements)

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“…The Schrödinger equation with position-dependent mass has been studied in the contexts of supersymmetry, shapeinvariance, Lie algebra, point-canonical transformation, etc. It is well known that the kinetic energy operator in this case belongs to the two-parameter family [5] T However, the correct values of the parameters α, β, γ for a specific model is a long-standing debate [3,4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

A study of the bound states for square potential wells with position-dependent mass

et al. 2006

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Section: Introductionmentioning

confidence: 99%

A study of the bound states for square potential wells with position-dependent mass

et al. 2006

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“…Certain terms are larger than others, however. As shown by Leibler,16,17 to linear order only the BenDaniel-Duke operator 44 T BD = 1 2 pm −1 p and the Gora-Williams operator 22 …”

Section: Discussionmentioning

confidence: 83%

Valence-band mixing in first-principles envelope-function theory

Foreman

2007

Phys. Rev. B

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This paper presents a numerical implementation of a first-principles envelope-function theory derived recently by the author ͓B. A. Foreman, Phys. Rev. B 72, 165345 ͑2005͔͒. The examples studied deal with the valence subband structure of GaAs/ AlAs, GaAs/ Al 0.2 Ga 0.8 As, and In 0.53 Ga 0.47 As/ InP ͑001͒ superlattices calculated using the local-density approximation to density-functional theory and norm-conserving pseudopotentials without spin-orbit coupling. The heterostructure Hamiltonian is approximated using quadratic-response theory, with the heterostructure treated as a perturbation of a bulk reference crystal. The valence subband structure is reproduced accurately over a wide energy range by a multiband envelope-function Hamiltonian with linear renormalization of the momentum and mass parameters. Good results are also obtained over a more limited energy range from a single-band model with quadratic renormalization. The effective kinetic-energy operator ordering derived here is more complicated than in many previous studies, consisting in general of a linear combination of all possible operator orderings. In some cases, the valence-band Rashba coupling differs significantly from the bulk magnetic Luttinger parameter. The splitting of the quasidegenerate ground state of no-common-atom superlattices has non-negligible contributions from both short-range interface mixing and long-range dipole terms in the quadratic density response.

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“…To guarantee good behavior of the ECO's, these expressions must be matched across the two PPP-PDA heterojunctions present in the unit cell, enforcing the BenDaniel-Duke boundary conditions [3,13,14,17] that both ψ(x) and 1 m * (x) dψr dx be continuous at these points. Moreover, the periodicity condition [14] ψ(x + L) = ψ(x) exp(ikL).…”

Section: Computational Methodologymentioning

confidence: 99%

Mini‐bandstructure tailoring in π‐conjugated periodic block copolymers using the envelope crystalline‐orbital method

Mujica-Martinez

Arce

2010

Int J of Quantum Chemistry

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Abstract. A strategy for the systematic design of polymeric superlattices with tailor-made mini-bandgaps and carrier mini-effective masses is described and computationally implemented by means of an envelope crystalline-orbital method, which is a straightforward adaptation for molecules of the envelope-function approximation widely used in solid-state physics. Such strategy relies on the construction of π-conjugated periodic block copolymers from wellcharacterized parent polymers, in such a way that the above-mentioned electronic parameters can be predicted from the lengths of the blocks. Illustrative calculations for prototypical (PPPxPDAy)n superlattices demonstrate the plausibility of the strategy and the advantages of the computational implementation employed.To appear in International Journal of Quantum Chemistry 1. Introduction A solid-state superlattice is a periodic arrangement of many nanometric layers of two, or more, different semiconductor materials [1,2]. The ionization energies and electron affinities of these materials are such that the effective potential-energy profiles for electrons and holes along the direction of growth take the forms of periodic arrays of quantum wells. The barriers between the wells are thin enough so that their otherwise isolated single-particle levels become resonantly coupled by quantum tunneling. Such coupling mixes these levels, giving rise to so-called energy mini-bands, in an analogous fashion to the appearance of energy bands in a crystal. In this sense, a superlattice behaves as an artificial crystal with a much larger period (of the order of 10 nm) than any real crystal, and, consequently, with a much smaller (mini-)Brillouin zone in reciprocal space. The mini-bandwidths and, consequently, the carrier mini-effective masses are determined by the thickness of the barriers, whereas the mini-bandgaps are determined by the depths and widths of the wells. Therefore, the mini-band structure of a superlattice can be engineered by controlling these parameters [3].

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Space-Charge Effects on Electron Tunneling

Cited by 851 publications

References 28 publications

A study of the bound states for square potential wells with position-dependent mass

A study of the bound states for square potential wells with position-dependent mass

Valence-band mixing in first-principles envelope-function theory

Mini‐bandstructure tailoring in π‐conjugated periodic block copolymers using the envelope crystalline‐orbital method

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