  A perfectly compliant substrate would allow the monolithic integration of
high-quality semiconductor materials such as Ge and III-V on Silicon (Si)
substrate, enabling novel functionalities on the well-established low-cost Si
technology platform. Here, we demonstrate a compliant Si substrate allowing
defect-free epitaxial growth of lattice mismatched materials. The method is
based on the deep patterning of the Si substrate to form micrometer-scale
pillars and subsequent electrochemical porosification. The investigation of the
epitaxial Ge crystalline quality by X-ray diffraction, transmission electron
microscopy and etch-pits counting demonstrates the full elastic relaxation of
defect-free microcrystals. The achievement of dislocation free heteroepitaxy
relies on the interplay between elastic deformation of the porous micropillars,
set under stress by the lattice mismatch between Ge and Si, and on the
diffusion of Ge into the mesoporous patterned substrate attenuating the
mismatch strain at the Ge/Si interface.
