Tight-Binding Theory of Phase-Change Materials
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1072-G01-03
Tight-Binding Theory of Phase-Change Materials Walter A. Harrison Applied Physics, Stanford University, GLAM/McCullough Bldg., Stanford, CA, 94305 ABSTRACT A simple theory of Ge, Sb, and Te crystals and glasses, based upon atomic valence orbitals with coupling given by universal parameters, is outlined. It is seen how dangling hybrids from Ge atoms can behave as negative U centers. In contrast, in Sb the nonbonding s orbitals play essentially no role, except to produce three-fold coordination and 90o bond angles. Te also has nonbonding s states, but also nonbonding p states causing two-fold coordination. These nonbonding p states form the top of the valence band, rather than the bond orbitals which formed the valence-band in Ge. We argue against lumping these totally different behaviors together as “lone pairs”. In the glass, bonds can form between all atom types, but bonds between different elements are energetically favored. Further, when Sb or Te atoms are involved, bonds can switch between neighbors with small energy change, in a manner suggested by Kastner, Adler and Fritsche. It is seen how to estimate the energy for these various different geometric configurations. INTRODUCTION Most computational studies of electronic structure are interpreted in terms of tight-binding concepts, but it is possible also to do the tight-binding analysis independently and all of the needed parameters are available [1]. Such calculations make approximations which are not necessary in the more complete LDA analyses, but are sometimes able, because of their simplicity, to treat the effects such as electron-electron interactions more realistically. When the geometry is uncertain, and not even restricted to the lowest-energy configuration as in phasechange material, the simplicity and qualitative reliability of tight-binding theory may be more important than numerical accuracy. At the same time, it does not sweep the central features under the carpet, as more qualitative discussions centering upon poorly defined concepts such as “lone pairs” are apt to do. Here we explore the way it can organize an understanding of phase-change materials, taking glasses of Ge, Sb, and Te as examples. Starting with the elemental materials, most concepts will be familiar, but it may be helpful to point out the central features explicitly before turning to the glasses. Elemental Structures Tight binding theory begins with the atomic valence states, and the atomic term values for these states are essentially the removal energy for that state from the atom and are meaningful also in the solid. They are shown for the three elements under discussion in Table 1. When the atoms are brought together to form a crystal, there is coupling between the atomic states on neighboring atoms which broadens the atomic levels into bands. There are simple forms for these couplings which do quite well for semiconductors. For s (l=0) and p (l=1) states given in terms of the internuclear distance d by1
Vll'm = ηll'm
h
2
md 2 .
(1)
For coupling between p (l
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