Abstract
A further study is made of the properties of the simple tight-binding Hamiltonian for which Weaire has recently shown that a band gap exists in a tetrahedrally bonded solid regardless of its structure. An exact transformation of the density of states is found which relates it to that generated by a much simpler Hamiltonian, providing, at once, an alternative proof of Weaire's result and a powerful tool for future study of this Hamiltonian. Various generalizations and extensions of the model are discussed. These include the definition of a Hamiltonian appropriate to a compound semiconductor and the generalization of the proof of the existence of a gap to cover this case. The resulting structure-independent formula for the gap, in terms of its homopolar and heteropolar parts, bears a close resemblance to that used in Phillips's semiempirical theory of tetrahedrally bonded semiconductors.
Original language | English (US) |
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Pages (from-to) | 3518-3527 |
Number of pages | 10 |
Journal | Physical Review B |
Volume | 4 |
Issue number | 10 |
DOIs | |
State | Published - 1971 |
ASJC Scopus subject areas
- Condensed Matter Physics