3.4.2.2 Splitting of the L Valleys

For $[001]$ substrate the splitting becomes:

$$\Delta\epsilon^{(111)}=\Delta\epsilon^{(\overline{1}11)}=\Delta\epsilon^{(\overline{1}\overline{1}1)}=\Delta\epsilon^{(1\overline{1}1)}=0.$$ (3.61)

For $[110]$:

$$\Delta\epsilon^{(111)}=\Delta\epsilon^{(\overline{1}\overline{1}1)}=\frac{2}{3}\Xi_{u}^{L}\varepsilon_{12},$$ (3.62)

$$\Delta\epsilon^{(\overline{1}11)}=\Delta\epsilon^{(1\overline{1}1)}=-\frac{2}{3}\Xi_{u}^{L}\varepsilon_{12}.$$

For $[111]$:

$$\Delta\epsilon^{(111)}=2\Xi_{u}^{L}\varepsilon_{12},$$

$$\Delta\epsilon^{(\overline{1}11)}=\Delta\epsilon^{(\overline{1}\o... ...}1)}=\Delta\epsilon^{(1\overline{1}1)}=-\frac{2}{3}\Xi_{u}^{L}\varepsilon_{12}.$$ (3.63)

Expression (3.61) shows that the $L$ valleys are degenerate for the substrate orientation $[001]$. For $[110]$ and $[111]$ substrates they are split. This splitting is symmetric with respect to the mean energy for the substrate oriented along $[110]$ while it is asymmetric for the case of the substrate oriented along $[111]$. S. Smirnov: