Two-level systems: a possible structure and its role in amorphisa tion

We show that a particular interstitial structure in c-Si has both ring structures characteristic of a-Si and low-energy excitations of a tunnelling type and a bond-switch (soliton) type. These excitations exist for reasons of symmetry. not because of anomalous bond angles or lengths. We suggest these defects may act as nuclei for amorphisation under irradiation and offer a possible explanation of the observed relation between tunnelling level systems and the extent of amorphisation in quartz. It is well known that the thermal properties of amorphous solids deviate from the predictions of the Debye model at very low temperatures (for a survey, see Elliott 1984). The specific heat and thermal conductivity are affected, and the changes are customarily described in terms of tunnelling systems or two-level systems. Phenomenologically, this is successful. However, when one seeks atomic models, there are surprisingly few on offer: site switching involving bridging atoms such as oxygen, rotations of tetrahedra, or possibly impurities such as hydrogen. There are, of course, extensive discussions of continuous random networks (see especially Rivier 1987) and of possible ways that these might be constructed systematically from corresponding crystalline networks (e.g. Weaire and Wooten 1985, Wooten and Weaire 1985). In most discussions the tunnelling systems are unplanned side effects of the randomisation, identified only by deforming the final amorphous structure. Moreover, such tunnelling systems are normally taken to be one-atom tunnelling states (e.g. Smith 1979). In our present paper we draw attention to a distinct and general class of possible tunnelling centres, and one which has particular promise for such systems produced during radiation amorphisation. Since we are concerned primarily with the initiation of the amorphous structure, it is possible to illustrate this class of two-atom tunnelling states by a specific crystal defect. The particular example we discuss is the so-called Jackson interstitial (Kimerling 1979) in silicon, though other examples will certainly be possible. The Jackson interstitial has a very complicated structure of low symmetry, though it can be understood quite simply by imagining its creation in a (fictitious) two-step process. First, remove four adjacent Si atoms, namely an equilateral triangle of three atoms, A , B and C, and their common neighbour, D . The result at this intermediate stage has two key features. The system