Interface States in a Linear Model of Heterojunctions

Kandilarov, B. D.; Detcheva, V.; Petrova, P.

doi:10.1002/pssb.2220700238

Cited by 11 publications

(4 citation statements)

References 7 publications

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“…The results of Pig. 3 show that the energies of the interface states riso when the bulk potentials in crystal I become stronger than those in crystal 11. This applies to either of the three treatments.…”

Section: Kumerical Analysismentioning

confidence: 94%

A Study of Relativistic Interface States

Roy

1984

Physica Status Solidi (b)

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A relativistic study is made of the interface states in a solid which is reduced to a one-dimensional system. The electronic states of such a model are governed by a two-component Dirac equation. The interface connects two semi-infinite solids represented by two semi-infinite chains of &function potential wells with a certain strength for either solid. In solving the Dirac equation for this model one is led to the energy-momentum relation of the system, that is to the band structure associated with non-localised states and t o isolated energy eigenvalues referring t o interface states with certain complex momentum wave vectors. To eliminate isolated energy eigenvalues associated with states which increase exponentially towards the bulk on either side of the interface, existence conditions are derived which guarantee that only eigenvalnes referring to interface states are selected. The influence of relativistic effects on the spectrum of interface states is demonstrated by choosing various sets of values for the parameters characterising the two solids. For the same purpose these interface state energies are recalculated for a,n approximately relat.ivistic case using an approach by Steslicka and Davison, and for the strictly non-relativistic case. E s wird eine relativistische Bet,rachtung der GrenzflachenzustLnde eines Festkorpers durchgefiihrt, der zu einem eindimensionalen System rediiziert wird. Die Elektronenzustande eines derartigen Modells werden durch die zweikomponentige Dirac-Gleichung bestimmt. Die Grenzflache verbinden zwei halbunendliche Fest.korper, die durch zwei halbunendliche Ketten von 6-Funktions-Potentialtpfen mit einer bestimmten Stkrke fiir jeden Festkorper dargestellt werden. Rei der Losung der Dirac-Gleichung fiir dieses Model1 wird man zur Energie-Impuls-Beziehung des Systems gefiihrt, d. h. zur Bandstmktnr, verkniipft mit nichtlokalisierten Zustanden und zu isolierten Energieeigenwerten, die sich auf Grenzflachenzustiinde mit b,estimmten komplexen Wellenvektoren beziehen. Zur Eliminierung der isolierten Energieeigenwerte, die mit Zusthden rerkniipft sind, die exponentiell zum Volumen zu beiden Seiten der Grenzflache anwachsen, werden Existcnzbedingungen abgeleitet, die garantieren, daR nur Eigenwerte ausgewahlt werden, die sich auf die Grerzflache beziehen. Der EinfluB der relativistischen Effekte auf das Spektrum der Grenzflachenzustiinde wird durch die Wahl verschiedener Satze fiir die Parameter, die die beiden Festkorper charakterisieren, demonstriert. Zum gleichen Zweck werden diese Grenzflachenzustandsenergien fur einen genilherten relativistischen Fall mit einem Verfahren von Steslicka und Davison, sowie fur den strikten nichtrelativistischen, Fall berechnet.

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Section: Kumerical Analysismentioning

confidence: 94%

A Study of Relativistic Interface States

Roy

1984

Physica Status Solidi (b)

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“…The sign of F may be determined by using the well-known fact that 5 must be positive for localized states, and taking into account that [ 141 eZaC tanh 2a5 < -sin 2ak it appears that the sign of F' may be determined again by using (12), (13a), and (13b) with k and 5 satisfying now the existence condition for interface atates in this case. Then the comparison with the ideal heterojunction proceeds in the same way and by using the same arguments as in the asymmetrical case already discussed.…”

Section: N = {mentioning

confidence: 97%

“…This approach is based on a model already developed in [12] for a discussion of the role of interface induced perturbations in the potential of the end atoms at the boundary. Of course, a shrinkage of the lattice immediately a t the interface may be analogically treated as a lattice with an int.erstitia1 impurity.…”

Section: Deformations At the Interfacementioning

confidence: 99%

Influence of the position of the interface boundary on the existence of interface states

Kandilarov

Tashkova

Petrova

et al. 1978

Physica Status Solidi (b)

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(a), M. G. TASHKOVA (a), P. C. PETROVA (a), and V. DETCHEVA (b) Necessary and sufficient conditions for the existence of interface states localized at the interface in two one-dimensional models of deformedheterojunctions are derived in terms of a scattering theoretical method. The existence conditions thus obtained are compared with the corresponding expression for an ideal undeformed heterojunction. The impact of both symmetrical and asymmetrical deformations on the existence of interface states is discussed.Die Existenzbedingungen fur diskrete Interface-Niveaus, die an der Grenze zweier deformierter Kristalle lokalisiert sind, werden mit Hilfe einer streuungstheoretischen Methode abgeleitet. Der EinfluD der Deformation auf die Existenzbedingungen von Interface-Niveaus bei symmetrisch bzw. asymmetrisch deformierten Heteroubergiingen wird diskutiert und mit dem entsprechenden Ausdruck fur einen idealen nichtdeformierten Heteroubergang verglichen.

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“…The particular energy-band profile for a given heterojunction can be determined from equation (1). It should be noted that figure 2 explains, for example, the existence of a lower bound on the magnitude of the interface potential step, below which interface states cannot exist (Kandilarov et al 1975, Kandilarov andDetcheva 1978); this implies that we are no longer considering the region where a common energy gap may exist. Because of the computational procedure used to determine which of the various heterojunctions has an interface state with a given energy, we have to restrict ourselves just to those heterojunctions for which this level occurs in the relevant common energy gap.…”

mentioning

confidence: 99%

α,β-Unsaturated Heteroatomic Compounds in 1,3-Dipolar Addition Reactions

Galishev¹,

Chistokletov²,

Петров³

1980

Russ. Chem. Rev.

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The simultaneous appearance of both band-edge discontinuities and interface states in the energy-band profile of a semiconductor heterojunction is discussed on the basis of a model that is as simple as possible, consistent with it remaining useful. An attempt is thus made to bridge the gap in the treatment of the two most important features that characterise the energy-band structure of a heterojunction.

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Interface States in a Linear Model of Heterojunctions

Cited by 11 publications

References 7 publications

A Study of Relativistic Interface States

A Study of Relativistic Interface States

Influence of the position of the interface boundary on the existence of interface states

α,β-Unsaturated Heteroatomic Compounds in 1,3-Dipolar Addition Reactions

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