Connection of envelope functions at semiconductor heterointerfaces. I. Interface matrix calculated in simplest models

Ando, Tsuneya; Wakahara, S.; Akera, Hiroshi

doi:10.1103/physrevb.40.11609

Cited by 96 publications

(52 citation statements)

References 77 publications

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“…Let us write the effective-mass equation (3) in the dimensionless form analogous to (5) From here on we will denote by w (for convenience) the reciprocal of the effective mass (m -1 ).…”

Section: Application Of Matrix Methods To Effective-mass Equationmentioning

confidence: 99%

“…The connection rules for z/i and dψ/dz are discussed, e.g., in [4][5][6]8] -here we consider their simplest form [1]: This is so-called direct matching procedure. It is the transfer matrix method foundation.…”

Section: The Effective -Mass Equationmentioning

confidence: 99%

“…quantum wells, quantum wires, and superlattices) are commonly interpreted theoretically within the effective-mass theory [1][2][3][4][5][6][7][8][9][10][11]. In this context the main task is aimed towards an accurate solution of one-dimensional effective-mass equation (1DEME) for envelope function (Eq.…”

Section: Introductionmentioning

confidence: 99%

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New Numerical Matrix Methods of Solving the Quasi-One-Dimensional Effective-Mass Equation

et al. 1999

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New efficient numerical methods of computing eigenvalues and eigenvectors of quasi-one-dimensional effective-mass Hamiltonian with arbitrary coordinate dependence of charge carrier mass are presented. Within the proposed approach the effective-mass equation is replaced by a nonsymmetric or symmetric matrix eigenproblem which can be analysed numerically with the help of existing computer routines. The presented methods are verified in special semiconductor heterostructure cases that are solvable within other approaches. A generalization of the presented methods for nonparabolic materials is also discussed.

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“…Let us write the effective-mass equation (3) in the dimensionless form analogous to (5) From here on we will denote by w (for convenience) the reciprocal of the effective mass (m -1 ).…”

Section: Application Of Matrix Methods To Effective-mass Equationmentioning

confidence: 99%

Section: The Effective -Mass Equationmentioning

confidence: 99%

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New Numerical Matrix Methods of Solving the Quasi-One-Dimensional Effective-Mass Equation

et al. 1999

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“…It is well known 17,20 that the element T 21 can be interpreted as an interface δ-function potential. Indeed, a nonzero T 21 introduces a jump of the first derivative which is proportional to the value of the wave function, exactly as an interface δ-potential does.…”

Section: B Interface States In the 4-band Kane Modelmentioning

confidence: 99%

Interface electronic states and boundary conditions for envelope functions

2002

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The envelope-function method with generalized boundary conditions is applied to the description of localized and resonant interface states. A complete set of phenomenological conditions which restrict the form of connection rules for envelope functions is derived using the Hermiticity and symmetry requirements. Empirical coefficients in the connection rules play role of material parameters which characterize an internal structure of every particular heterointerface. As an illustration we present the derivation of the most general connection rules for the one-band effective mass and 4-band Kane models. The conditions for the existence of Tamm-like localized interface states are established. It is shown that a nontrivial form of the connection rules can also result in the formation of resonant states. The most transparent manifestation of such states is the resonant tunneling through a single-barrier heterostructure.

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“…The best one can do there is to connect the bulk envelopes across the interface using connection rules obtained from microscopic models [6][7][8][9][10][11][12][13][14][15]. Such rules indicate that the envelopes are discontinuous in general, so it seems clear that the use of differential equations is not justified near an abrupt junction (although it may be a reasonable approximation in a few special cases).…”

mentioning

confidence: 99%

Connection Rules versus Differential Equations for Envelope Functions in Abrupt Heterostructures

Foreman

1998

Phys. Rev. Lett.

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The controversial question of whether envelope functions are continuous or discontinuous at an abrupt heterojunction is addressed by developing a systematic procedure for obtaining interface connection rules from differential equations. The results show that even though modern envelope-function theories are smooth and continuous, their associated connection rules are discontinuous, in agreement with traditional concepts. This resolves the dispute in favor of both sides, by showing that the two views are physically equivalent. [S0031-9007(98)

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Connection of envelope functions at semiconductor heterointerfaces. I. Interface matrix calculated in simplest models

Cited by 96 publications

References 77 publications

New Numerical Matrix Methods of Solving the Quasi-One-Dimensional Effective-Mass Equation

New Numerical Matrix Methods of Solving the Quasi-One-Dimensional Effective-Mass Equation

Interface electronic states and boundary conditions for envelope functions

Connection Rules versus Differential Equations for Envelope Functions in Abrupt Heterostructures

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