Correctly Weighting Tetrahedron Method for k‐Space Integration of F.C.C. Structures

Hanke, M.; Kühn, W.; Strehlow, Roger A.

doi:10.1002/pssb.2221230150

Cited by 8 publications

(2 citation statements)

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“…They also use three separate U s-U ss , U sp and U pp . The method is extended to defects (Hanke et al 1986and Kühn et al 1987 by calculating the electrostatic interactions exactly for a small cluster around the defect (generally the four nearest neighbours) and embedding it in the Madelung field for the crystal. Reasonable agreement with such experimental and ab initio results as are available is obtained.…”

Section: Self-consistent Tight-bindingmentioning

confidence: 99%

Tight-binding modelling of materials

1997

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The tight-binding method of modelling materials lies between the very accurate, very expensive, ab initio methods and the fast but limited empirical methods. When compared with ab initio methods, tight-binding is typically two to three orders of magnitude faster, but suffers from a reduction in transferability due to the approximations made; when compared with empirical methods, tight-binding is two to three orders of magnitude slower, but the quantum mechanical nature of bonding is retained, ensuring that the angular nature of bonding is correctly described far from equilibrium structures. Tight-binding is therefore useful for the large number of situations in which quantum mechanical effects are significant, but the system size makes ab initio calculations impractical.In this paper we review the theoretical basis of the tight-binding method, and the range of approaches used to exactly or approximately solve the tight-binding equations. We then consider a representative selection of the huge number of systems which have been studied using tight-binding, identifying the physical characteristics that favour a particular tightbinding method, with examples drawn from metallic, semiconducting and ionic systems. Looking beyond standard tight-binding methods we then review the work which has been done to improve the accuracy and transferability of tight-binding, and moving in the opposite direction we consider the relationship between tight-binding and empirical models.

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Section: Self-consistent Tight-bindingmentioning

confidence: 99%

Tight-binding modelling of materials

1997

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“…The only symmetry used is inversion. For both calculations the tetrahedron method [15] was used in order to perform the k point integration in the BZ. The very good agreement between the two curves demonstrates the usefulness of our approach.…”

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confidence: 99%

Efficientk⋅pmethod for the calculation of total energy and electronic density of states

Iannuzzi

Parrinello

2001

Phys. Rev. B

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Charge Self‐Consistent Tight‐Binding Parameters. Application to III‐V Compound Semiconductors

Strehlow¹,

Hanke

Kühn³

1985

Physica Status Solidi (b)

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on the occasion of his 80th birthdayThe description of defects (impurities, surfaces, etc.) in the framework of empirical tight-binding method (ETBN) suffers from the drawback that already the 'IIB parameters of the unperturbed crystal are not uniquely defined when obtained from pure fitting to existing band structures. Such an uncertainty enters the defect model via both, the unperturbed problem itself and the defect potential. It is suggested to overcome these difficulties by determining the diagonal TB parameters and orbital populations always self-consistently. I n the present paper and as the first step a method is developed to construct such charge self-consistent TB parameter sets for the pure crystal within the framework of a special fitting procedure including up to second-nearest neiglibour interactions. With this additional self-consistency requirement band structures are obtained being even better than those calculated from other parameter sets. The method is applied to the 111-V compound semiconductors Gap, GaAs, GaSb, InP, InAs, and InSb. Chemical trends are discussed.Bei der Beschreibung von Defekten (Storstellen, Oberflachen, UJW.) im Rahmen der ETBM erweist sich als nachteilig, daB bereits die TB-Parameter des ungestorten Kristalles nicht eindeutig definiert sind, wenn sie allein durch Anpassung an gegebene Bandstrukturen bestimmt werden. Eine solche Unbestimmtheit ubertragt sich auf die Defekteigenschaften sowohl durch das ungestorte Problem als auch durch das Defektpotential. Es wird vorgeschlagen, diese Schwierigkeiten dadurch zu uberwinden, da8 diagonale TB-Parameter und orbitale Populationen stets selbstkonsistent bestimmt werden. In dieser Arbeit wird als erster Schritt dazu eine Methode zur Konstruktion solcher ladungsselbstkonsistenter TB-Parametersatze fur den reinen Rristall im Rahmen einer speziellen Anpassungsprozedur entwiclrelt, die Wechselwirkungen bis zu zweitnachsten Xachbarn einschlieat. Mit dieser zusltzlichen Selbstkonsistenzforderung werden Bandstrukturen erhalten, die sogar besser sind als die, die mit anderen Parametrisierungen erhalten werden. Die Methode wird auf die 111-V-Verbindungshalbleiter Gap, GaAs, GaSb, InP, Inks und InSb angewendet . Chemische Trends werden diskutiert.

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Correctly Weighting Tetrahedron Method for k‐Space Integration of F.C.C. Structures

Cited by 8 publications

References 5 publications

Tight-binding modelling of materials

Tight-binding modelling of materials

Efficientk⋅pmethod for the calculation of total energy and electronic density of states

Charge Self‐Consistent Tight‐Binding Parameters. Application to III‐V Compound Semiconductors

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