3.4.2.1 Splitting of the X Valleys

For $[001]$ and $[110]$ substrates the splitting is given as:

$$\Delta\epsilon^{(100)}=\Delta\epsilon^{(010)}=\frac{1}{3}\Xi_{u}^{X}(\varepsilon_{11}-\varepsilon_{33}),$$ (3.59)

$$\Delta\epsilon^{(001)}=\frac{2}{3}\Xi_{u}^{X}(\varepsilon_{33}-\varepsilon_{11}).$$

For $[111]$ substrate it becomes:

$$\Delta\epsilon^{(100)}=\Delta\epsilon^{(010)}=\Delta\epsilon^{(001)}=0.$$ (3.60)

Expression (3.60) means that for $[111]$ substrates the $X$ valleys remain degenerate. S. Smirnov: