Kinetic and Strain-Induced Self-Organization of SiGe ...

12 CHAPTER 1. SILICON-GERMANIUM MATERIAL SYSTEM
Figure 1.9: Lattice parameters of Si1−xGex alloys and deviation from Vegard’s
rule [51].
� Source: SiGe Vegards-rule.jpg
1.4 Silicon Germanium Alloys (Si1−xGex)
Silicon and germanium form a continuous series of solid solutions Si1−xGex providing a grad-
ual change in some parameters (e.g. lattice parameter a) with x ranging from 0 to 1 [3].
The lattice parameter aSiGe of Si1−xGex alloys shows a small deviation from Vegard’s rule,
i.e. from the linearity between the lattice constants of pure Si and Ge. According to ex-
periments by Dismukes et al. [51] (see Fig. 1.9) and theoretical Monte Carlo simulations of
Si1−xGex alloys the lattice constant for Si1−xGex alloys aSiGe lies below Vegard’s rule [5].
1.4.1 Bandstructure of SiGe-Heterostructures
The lattice mismatch (4.2%) strain between Si and Ge enables band engineering for SiGe-
heterostructures. Due to the different symmetries in Si- and Ge-band structure the SiGe-
alloy bandstructure shows a cross-over in the lowest conduction band edge from Si-like [100]-
symmetry to Ge-like [111]-symmetry at x ∼ 0.85 [3]. Fig. 1.10 [6, 52] shows the compositional
dependence of the indirect energy gap for unstrained Si1−xGex alloys with the change from
the conduction band (CB) minimum at the ”∆”-point (Si-like) to the L-point (Ge-like) (upper
curve in Fig. 1.10). The two lower curves show the vast influence of strain for pseudomorphic
SiGe-layers on a Si-substrate. The in-plane compressively strained SiGe-layers show a signif-
icantly lowered bandgap with a splitting of the valence band (VB) maximum in heavy-hole
(HH) and light-hole (LH) band. [6, 52]