3.2.4.2 Shift of the Mean Energy

The shift of the mean energy of the conduction band extrema of type $k$ is expressed as:

$$\Delta\epsilon_{c,av}^{(k)}=\biggl(\Xi_{d}^{k}+\frac{1}{3}\Xi_{u}^{k}\biggr)Tr(\hat{\boldsymbol{\varepsilon}}).$$ (3.31)

This shift can become important when more than one type of valley is taken into account as in general the deformation potentials $\Xi_{d}$ and $\Xi_{u}$ have different values for different valley types. The relative shift of the mean energy for valleys of different type can cause a repopulation between these valleys as schematically shown in Fig. 3.7 for the case of $X$ and $L$ valleys. Expression (3.31) is

Figure 3.7: Repopulation effect between $X$ and $L$ valleys in strained material.

derived as an average of particular shifts given by (3.30). Thus some valleys of a given type can still significantly move which will cause a repopulation between particular extrema of different type while the transitions between other extrema will be reduced. S. Smirnov: