EM Donors with CB Degeneracy

Under stress, a one-valley EM donor state follows the energy shift of the valley it belongs to. A study of the effect of a uniaxial stress on the donor spectra in a multi-valley semiconductor (silicon) has been undertaken by Tekippe et al. [140]. The treatment given below follows this presentation closely, with minor changes in the notations. Following the deformation potential analysis of [60], the shift in energy Aof valley j of the CB of silicon or germanium with respect to the zero-stress conditions is  

Let us consider the case of silicon. The multi-valley structure of the CB minimum of silicon is depicted in Fig. 8.1, with six constant energy surfaces along the 100 direction A of the BZ. A force F has also been included in this figure, whose direction is defined by polar angles 6 and 4 . 

When replacing in expression (8.2), the components ka 1 and k by the direction cosines /, m and n of the external stress, the shift of valley j becomes  

The shift of the centre of gravity (c.g.) of the six valleys deduced from (8.3) is  

The strain tensor is the product of the elastic compliance tensor of the crystal by the stress tensor with components oap. For cubic crystals, where the nonzero components of the elastic compliance tensor are Sn, S12 and S44, it can be expressed1 as  

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