6.1 Bandstructure Calculations

**Table 6.1:** Bandstructure parameters extracted from numerical band structure calculations.
parameter	EPM value	Units
$\Xi_u^\Delta$	9.29	eV
$\Xi _{u'}$	7.0	eV
$\Delta$	0.53	eV
	0.914	$\ensuremath{\mathrm{m}}_0$
	0.196	$\ensuremath{\mathrm{m}}_0$
$\kappa$	52.83	1
$\eta$	-0.809	1

**Figure 6.1:** Calculated band edge energies of the $\Delta$ -valleys and -valleys of (a) strained Si and (b) strained Ge on Si $_{1-y}$ Ge buffer with respect to valence band edge. Calculations (lines) are compared to results obtained by Rieger [Rieger93] (symbols).
[a] $\includegraphics[width=8.cm]{xcrv-scipts/epmCompVogl1_bw.eps}$ [b] $\includegraphics[width=8.cm]{xcrv-scipts/epmCompVogl2_bw.eps}$

The parameters relevant for the modeling of strain effects on the conduction bands of Si were extracted from EPM calculations and are given in Table 6.1. The value for the uniaxial deformation potential $\Xi_u^\Delta$ coincides with the value extracted by Rieger [Rieger93]. The value for the shear deformation potential $\Xi_{u'}=7.0$ eV compares well with the values extracted from experimental data: a value of $5.7 \pm$ 1 eV [Hensel65] has been predicted from cyclotron resonance experiments. From more recent measurements of the indirect exciton spectrum of Si the value $7.5 \pm$ 2 eV has been obtained [Laude71]. By calculations based on a self-consistent perturbation theory [Goroff63] the value 7.8 eV was obtained for the shear deformation potential. The effective masses and the band separation $\Delta=0.53$ eV between the two lowest conduction bands at the conduction band minimum are in good agreement to experimental values [Hensel65]. Finally, the two parameters defined in (3.89), $\kappa=4\Xi_{u'}/\Delta=52.83$ and $\eta=-0.809$ were extracted from EPM calculations. These two parameters are used in the analytical expressions for the effective mass change (3.94), (3.98), and (3.99), and the valley shift (3.100) induced by shear strain.


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