Piezospectroscopic tensor

If it is assumed that the TDDs are oriented preferentially along a <110> axis, with a C2V site symmetry, the piezospectroscopic results can be explained satisfactorily on the basis of the stress-induced line shifts and polarizations calculated by Kaplyanskii [73], which are discussed in the next section. This led to propose the C2V site symmetry for the TDDs in silicon [137]. In expression (8.15), the non-zero components of the piezospectroscopic tensor for C2v centres, labelled as orthorhombic (or rhombic) I, are Axx (A2), Ayy (A2), Azz Wi) and Axy = Ayx (A3). These orthorhombic I centres have a C2 symmetry axis in the <100> direction and the 1 s —> 2po transitions have their transition dipole moment oriented along this axis for a Is state constructed from a pair of valleys along this axis, while the Is —> 2p transitions have their transition dipole moment oriented in a plane perpendicular to this axis. In a cubic crystal, a C2V centre has a sixfold orientational degeneracy represented by the six diagonals of a cube (see Fig. 8.16a). 

In cubic crystals, one can distinguish six kinds of centres whose symmetries are those of the polyhedra shown in Fig. 8.27. In this figure are also indicated the components Ay of the piezospectroscopic tensor defined in (8.15). 

The centres with trigonal and rhombic I crystallographic symmetries are considered in detail. A trigonal centre has a C3 symmetry axis along a <111> direction and the piezospectroscopic tensor At,ng has two independent components A and A. A rhombic I centre has one C2 axis along a <110> direction and the piezospectroscopic tensor Arhomb has three independent components A, A l and A3, (see Fig. 8.27). 

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