2.4.2.3 Analytical Band Structures of Si and Ge

For Si the lowest extrema of the conduction band are located along the $\Delta$ axes near the $X$ points of the first Brillouin zone and are called $X$ valleys. In the case of Ge they are located exactly at the $L$ points of the first Brillouin zone and called $L$ valleys. Thus the surface of constant energy^2.24 for Si, equation (2.76), represents six full ellipsoids while for Ge it represents eight half-ellipsoids. This is also shown in Fig. 2.6.

Figure 2.6: The surfaces of constant energy for Si and Ge.

Two of the three effective masses are equal to each other and called transverse effective masses. The third mass is called the longitudinal effective mass. They are denoted by $m_{t}$ and $m_{l}$, respectively^2.25. The numerical values [20] for the parameters of the analytical expression for the conduction band of Si and Ge are given in Table 2.1.

Table 2.1: Analytical conduction band structure parameters for Si and Ge.

	$m_{t}^{X}$	$m_{l}^{X}$	$m_{t}^{L}$	$m_{l}^{L}$	$\alpha_{X}$	$\alpha_{L}$
Silicon	0.191	0.903	0.126	1.634	0.5 $eV^{-1}$	0.3 $eV^{-1}$
Germanium	0.204	1.791	0.101	1.387	0.5 $eV^{-1}$	0.3 $eV^{-1}$

S. Smirnov: