3.4.2.2 Splitting of the L Valleys

For $ [001]$ substrate the splitting becomes:

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

For $ [110]$:
    $\displaystyle \Delta\epsilon^{(111)}=\Delta\epsilon^{(\overline{1}\overline{1}1)}=\frac{2}{3}\Xi_{u}^{L}\varepsilon_{12},$ (3.62)
    $\displaystyle \Delta\epsilon^{(\overline{1}11)}=\Delta\epsilon^{(1\overline{1}1)}=-\frac{2}{3}\Xi_{u}^{L}\varepsilon_{12}.$  

For $ [111]$:
    $\displaystyle \Delta\epsilon^{(111)}=2\Xi_{u}^{L}\varepsilon_{12},$  
    $\displaystyle \Delta\epsilon^{(\overline{1}11)}=\Delta\epsilon^{(\overline{1}\o...
...}1)}=\Delta\epsilon^{(1\overline{1}1)}=-\frac{2}{3}\Xi_{u}^{L}\varepsilon_{12}.$ (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: