Localization of Electronic States in Disordered Tight‐Binding Systems. I. Derivation and Study of the Model

Unger, H.-J.

doi:10.1002/pssb.2221200141

Cited by 6 publications

(2 citation statements)

References 22 publications

(10 reference statements)

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“…In the following a disordered system possessing compositional as well as positional disorder is described by a Hamiltonian which is represented in an "extended Hilbert space", defined as the direct sum of the single-site Hilbert spaces [20],…”

Section: Model Hamiltonian With Hybridized Atomic Orbitalsmentioning

confidence: 99%

“…Thus the problem of the convergence of the chains numerically generated in the recursion method by the tridiagonalization of the original Hamiltonian is irrelevant. If the existence of mobility edges in the system under consideration is experimentally verified and if their positions are numerically estimated in a preceding calculation as outlined above, then the termination procedures of the chains described in previous papers are always correct and all conclusions from them [20,21,23 to 251 are valid independently of the convergence of the chains for the given original system. Of course, if the system does not possess structural correlation, then an effective medium does not exist, and such a termination is impossible, i.e., all states are localized.…”

Section: (44)mentioning

confidence: 99%

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Covalent Bonds in Amorphous Semiconductors and Their Influence on the Structure of the Energy Spectrum

Unger¹

1990

Physica Status Solidi (b)

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The structure of the energy spectrum of amorphous semiconductors as determined by the formation of covalent bonds is analyzed. In contrast with other theoretical models all considerations are based on a realistic model of the atomic structure of a-Si and a-Ge. The mathematical method used throughout the paper is, within certain subspaces (cells) of the total Hilbert space, the partial diagonalization of the Hamiltonian represented in an "extended Hilbert space". Existing model Hamiltonians, e.g. the Weaire-Thorpe model, are generalized in such a way that real disordered solids can be described. The molecular model used in this paper yields the basic feature of the structure of the energy spectrum. For positionally disordered systems an Anderson-like Hamiltonian is obtained. The formation of extended and localized states in disordered solids is explained by taking into account the residual interactions. Conditions for the localization of electronic states and the existence of mobility edges depending on the local and global atomic structure of amorphous semiconductors are given. A generalization of the cell model in the spirit of the scaling theory of localization leads to a method for the determination of the position of the mobility edges. Structural correlation in amorphous semiconductors manifesting itself in short-range order and in the existence of voids, which is not taken into account e.g. in the Anderson model, is found to be the origin of the basic structural properties of the energy spectrum of disordered semiconductors. Conclusions from the theory proposed are in accordance with experimental findings and explain them.

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Section: Model Hamiltonian With Hybridized Atomic Orbitalsmentioning

confidence: 99%

Section: (44)mentioning

confidence: 99%

Covalent Bonds in Amorphous Semiconductors and Their Influence on the Structure of the Energy Spectrum

Unger¹

1990

Physica Status Solidi (b)

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Localization of Electronic States in Disordered Tight‐Binding Systems. II. Mobility Edges

Unger

1984

Physica Status Solidi (b)

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The model of a "partially disordered semi-infinite chain" for disordered real systems which was obtained from first principles in a foregoing paper is further investigated. The existence of mobilit,y edges in the spectrum is shown if t.hc recursion coefficients tend to constant limiting values. The convergence of t.hc sequence of recursion coefficients is discussed. Interesting relations to the theory of critical phenomena and to the percolation theory lire found. The physical picture behind converging rccursion coefficients, i.c. the existcncc of short-range order, is cleared up. A the0re.tical foundation for the Mott-CFO-niodel is givcn. Within t,he framewrrrk of the recursion method the dependence of the dcgrce of localization on the dimensionality is discussed.

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Study of the single-particle energy spectrum of disordered systems

Unger

1986

Z. Physik B - Condensed Matter

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Localization of Electronic States in Disordered Tight‐Binding Systems. I. Derivation and Study of the Model

Cited by 6 publications

References 22 publications

Covalent Bonds in Amorphous Semiconductors and Their Influence on the Structure of the Energy Spectrum

Covalent Bonds in Amorphous Semiconductors and Their Influence on the Structure of the Energy Spectrum

Localization of Electronic States in Disordered Tight‐Binding Systems. II. Mobility Edges

Study of the single-particle energy spectrum of disordered systems

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