Comparison of А$^{\mathrm{III}}$В$^{\mathrm{V}}$ heterostructures grown on Ge/Si, Ge/SOI, and GaAs

А$^{\mathrm{III}}$В$^{\mathrm{V}}$/Ge/Si (001), А$^{\mathrm{III}}$В$^{\mathrm{V}}$/Ge/SOI (001), and А$^{\mathrm{III}}$В$^{\mathrm{V}}$/GaAs (001) heterostructures were formed and investigated. The Ge buffer layer was produced by the “hot wire” technique on a Si substrate (001) for the А$^{\mathrm{III}}$В$^{\mathrm{V}}$/Ge/Si structure. In the case of the А$^{\mathrm{III}}$В$^{\mathrm{V}}$/Ge/SOI, the Ge buffer layer was grown on the SOI (001) substrate by molecular beam epitaxy via two-stage growth. The growth of А$^{\mathrm{III}}$В$^{\mathrm{V}}$ layers were performed by metalorganic chemical vapor deposition. It is shown that the Ge/SOI formed via two-stage growth allows the growth of А$^{\mathrm{III}}$В$^{\mathrm{V}}$ layers that are not inferior in structural and optical quality to those formed on the Ge/Si.