Self-assembled Ge islands were grown on stripe-patterned Si(001) substrates by solid source molecular beam epitaxy. The surface morphology obtained by atomic force microscopy and cross-sectional transmission electron microscopy images shows that the Ge islands are preferentially grown at the sidewalls of pure Si stripes along the [−110] direction at 650 °C or along the trenches, whereas most of the Ge islands are formed on the top terrace when the patterned stripes are covered by a strained GeSi buffer layer. Reducing the growth temperature to 600 °C results in a nucleation of Ge islands both on the top terrace and at the sidewall of pure Si stripes. A qualitative analysis, based on the growth kinetics, demonstrates that the step structure of the stripes, the external strain field, and the local critical wetting layer thickness for the islands formation contribute to the preferential positioning of Ge islands on the stripes.

Magnetotransport properties are investigated in a high-mobility two-dimensional electron system in the strained Si quantum well of a (100) ${\mathrm{S}\mathrm{i}}_{0.75}{\mathrm{G}\mathrm{e}}_{0.25}{/\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}}_{0.75}{\mathrm{G}\mathrm{e}}_{0.25}$ heterostructure, at temperatures down to 30 mK and in magnetic fields up to 45 T. We observe around $\nu =1/2$ the two-flux composite fermion (CF) series of the fractional quantum Hall effect (FQHE) at $\nu =2/3,3/5,4/7$, and at $\nu =4/9,2/5,1/3$. Among these FQHE states, the $\nu =1/3,4/7$, and $4/9$ states are seen for the first time in the $\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}\mathrm{G}\mathrm{e}$ system. Interestingly, of the CF series, the $3/5$ state is weaker than the nearby $4/7$ state and the $3/7$ state is conspicuously missing, resembling the observation in the IQHE regime that the $\nu =3$ is weaker than the nearby $\nu =4$ state. Our results can be quantitatively understood in the picture of CF's with the valley degree of freedom.

Self-assembled Ge islands were grown by solid-source molecular-beam epitaxy on the submicron stripe-patterned Si(001) substrates at $\text{650\hspace{0.05em}°}\mathrm{C}.$ Atomic-force microscopy shows that the Ge islands grow preferentially at the sidewall of the Si stripes, oriented along the $\text{[−110]}$ direction. The migration of the Ge adatoms from the top terrace down to the sidewall accounts for the island formation at the sidewall of the stripes. However, most of the Ge islands are formed on the top terraces when the patterned stripes are covered by a strained GeSi multilayer buffer prior to Ge island growth. Apparently, the strained buffer layer acts as a stressor and contributes to the preferential growth of islands on the top terrace.

The apparent metal-insulator transition is observed in a high-quality two-dimensional electron system (2DES) in the strained Si quantum well of a $\mathrm{Si}∕{\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ heterostructure with mobility $\mu =1.9\times {10}^5{\mathrm{cm}}^2∕\mathrm{V}\mathrm{s}$ at density $n=1.45\times {10}^{11}{\mathrm{cm}}^{-2}$. The critical density, at which the thermal coefficient of low $T$ resistivity changes sign, is $\sim 0.32\times {10}^{11}{\mathrm{cm}}^{-2}$, a very low value obtained in Si-based 2D systems. The in-plane magnetoresistivity $\rho \left(B_{ip}\right)$ was measured in the density range, $0.35\times {10}^{11}<n<1.45\times {10}^{11}{\mathrm{cm}}^{-2}$, where the 2DES shows the metalliclike behavior. It first increases and then saturates to a finite value $\rho \left(B_c\right)$ for $B_{ip}>B_c$, with $B_c$ the full spin-polarization field. Surprisingly, $\rho \left(B_c\right)∕\rho \left(0\right)\sim 1.8$ for all the densities, even down to $n=0.35\times {10}^{11}{\mathrm{cm}}^{-2}$, only 10% higher than $n_c$. This is different from that in clean Si metal-oxide-semiconductor field-effect transistors, where the enhancement is strongly density dependent and $\rho \left(B_c\right)∕\rho \left(0\right)$ appears to diverge as $n\to n_c$. Finally, we show that in the fully spin-polarized regime, dependent on the 2DES density, the temperature dependence of $\rho \left(B_{ip}\right)$ can be either metalliclike or insulating.