Cycle-Free Approximations to Amorphous Semiconductors
- 15 March 1972
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 5 (6), 2233-2241
- https://doi.org/10.1103/physrevb.5.2233
Abstract
The Hall-Weaire tight-binding semiconductor Hamiltonian is solved when the geometric structure has no closed cycles and is homogeneous, using a method developed by Onsager for ionic energies in ice. The solution yields two bands and two δ functions in the density of states in agreement with the general theorem of Weaire. This solution is proposed to be a reasonable first approximation for the band structures of amorphous semiconductors. The Hamiltonian is also solved when the underlying structure is the inhomogeneous Cayley tree for which surface states predominate. In this case the bands have the property of being nowhere continuous. Instead of just two δ functions outside the bands, there are sequences of bound-state δ functions which bridge the energy gap between bands when the model parameters fall in a finite interval.Keywords
This publication has 10 references indexed in Scilit:
- Electronic Density of States of Amorphous Si and GePhysical Review Letters, 1971
- Hopping Conductivity in Disordered SystemsPhysical Review B, 1971
- Electronic Properties of an Amorphous Solid. I. A Simple Tight-Binding TheoryPhysical Review B, 1971
- Existence of a Gap in the Electronic Density of States of a Tetrahedrally Bonded Solid of Arbitrary StructurePhysical Review Letters, 1971
- Theory of amorphous semiconductorsPhysics Today, 1971
- Review of the theory of amorphous semiconductorsJournal of Non-Crystalline Solids, 1970
- Conduction in non-crystalline materialsPhilosophical Magazine, 1969
- Phase Transition of a Bethe Lattice Gas of Hard MoleculesJournal of Mathematical Physics, 1967
- On the theory of cooperative phenomena in crystalsAdvances in Physics, 1960
- Toeplitz Forms and Their ApplicationsPhysics Today, 1958