The Quasi‐Molecular Large Unit Cell Model in the Theory of Deep Levels in Imperfect Crystals: Point Defects in Graphitic Boron Nitride

Dobrotvorskii, A. M.; Evaeestov, E. A.

doi:10.1002/pssb.2220660108

Cited by 66 publications

(14 citation statements)

References 23 publications

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“…(Strictly speaking, such a relation may be only done for infinite clusters.) Supplying the boundary conditions to the cluster with LUC, one gets naturally crystalline states corresponding to the chosen LUC [23]. (Fig.…”

Section: Calculations For Oxidesmentioning

confidence: 99%

Molecular cluster approach to magnesium and calcium oxide crystals. I. Perfect crystals

Ermoshkin

Kotomin

Ėvarestov

1975

Physica Status Solidi (b)

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The model of the molecular cluster (MC) is used t o determine the properties of the perfect crystals MgO and CaO (the widths of the valence bands and forbidden gap, the effective charges of ions). The effective charges in the perfect crystal are shown to be h1.6 in MgO and k1.8 in CaO, which indicates high degree of covalency effects of the chemical bonding in these crystals. The obtained band widths are in reasonable agreement with the results of the other band structure calculations. The best results are obtained when the MC simulating the perfect crystal is chosen in the form of the LUC, that means t'hat even the indirect consideration. of the translational symmetry turns to be more important than that of the point symmetry. Das Model1 des Molekiilclusters (MC) wird zur Bestimmung der Eigenschaften der ungestorten Kristalle von MgO und CaO benutzt (Breite der Valenzbiinder und der verbotenenZone, effektive Ionenladungen). Es wird gezeigt, daS die effektiven Ladungen in den ungestorten Kristallen &1,6 fur MgO und f l , 8 fur CaO betragen, was auf einen hohen Anteil von Kovalenzeffekten der chemischen Bindung in diesen Kristallen hinweist. Die erhaltenen Bandbreiten befinden sich in vernunftiger ubereinstimmung mit den Ergebnissen anderer Bandstrukturberechnungen. Die besten Ergebnisse werden erhalten, wenn der MC, der den ungestorten Kristall simuliert, in Form der LUC gewiihlt wird, was bedeutet, daS sogar die indirekte Beriicksichtigung der Translationssymmetrie wesentlicher ist als die Beriicksichtigung der Punktsymmetrie.

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Section: Calculations For Oxidesmentioning

confidence: 99%

Molecular cluster approach to magnesium and calcium oxide crystals. I. Perfect crystals

Ermoshkin

Kotomin

Ėvarestov

1975

Physica Status Solidi (b)

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“…[12][13][14][15][16][17][18][19][20] is connected with the slab-supercell approach, but there is a difference due to the different introduction of cyclic boundary conditions (CBC). In the latter approach, these conditions are, in fact, introduced for a very large system, e. g., the main region of the 2D periodic plane, so that the band theory methods are used in slab calculations.…”

Section: Infinite Models Of Surfacesmentioning

confidence: 99%

Connection between slab and cluster models for crystalline surfaces

2001

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Different models for the theoretical description of bare crystalline surfaces are compared and discussed in terms of stoichiometry and conservation of the point symmetry. While infinite models such as the semi-infinite model or the slab model in general preserve the symmetry of the perfect crystal surface, special care has to be taken when finite cluster models are considered. The connection between molecular cluster choice and surface unit cell of the slab model is demonstrated for metal oxides such as MgO, TiO 2 , V 2 O 5 , and Al 2 O 3 , analyzing how atoms of the primitive unit cell of the parent three-dimensional crystal are distributed in different planes of slab and cluster models. General rules for the construction of finite cluster models based on stoichiometry and symmetry considerations are given and illustrated with calculations on water adsorption at rutile (110).Crystalline surfaces are of high importance in many chemical and physical processes [1,2]. They are therefore subject of an increasing number of studies, both experimental and theoretical [3]. In the last decades, quantum-chemical calculations have become an important tool for investigations of structural, electronic and catalytic properties of surfaces. Methodological developments and the rapid improvement of computer hardware enabled theorists to treat systems of increasing complexity. Thereby it was possible not only to reproduce experimental findings with increasing accuracy, but also to aid in the interpretation of experimental results.For simulations of the electronic structure of surfaces of crystalline solids three basic approaches are used: cluster, slab, and semi-infinite crystal models [4]. The latter is the most appropriate, because it takes into account an infinite number of atoms of the crystal below the surface [5]. Slab and cluster models are nevertheless by far more popular, since they are more feasible from the computational point of view. The cyclic cluster model [4] is intermediate between slab and molecular cluster models. It takes into account the translational symmetry of the surface but considers only a finite number of interatomic interactions within a strictly defined region.The choice of the cluster model (both molecular and cyclic) for a surface allow to employ all those quantum chemical techniques that have been developed for molecular systems. It is also possible to study defects or adsorption reactions in the limit of low coverage. Care has to be taken in the selection of cluster size and shape due to the unavoidable presence of boundary effects. Different schemes have been developed to reduce boundary effects in the cluster model, either by embedding procedures or by the introduction of cyclic boundary conditions. Slab models eliminate twodimensional boundary effects and are widely used for the study of periodic surface structures.In the present work, the connection between slab and cluster models based on a symmetry analysis of the crystalline surface is considered. As far as we know, this connection has not...

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“…The approach mentioned appears to be fruitful also in the theory of deep levels in imperfect crystals [2]: the LUC model of the imperfect solid is capable to describe the origin of the defect levels necessary for understanding the defect nature.…”

Section: Introductionmentioning

confidence: 98%