Engineered substrates, free-standing semiconductor microstructures, and related systems and methods

A free-standing microstructure comprising:

• a first silicon layer;
• a relaxed second silicon layer, the relaxed second silicon layer comprising a monocrystalline silicon film including a plurality of dislocations and substantially free of residual strain;
• and
• an intermediate layer between the first silicon layer and the relaxed second silicon layer comprising:
• a material having a different lattice constant than the first silicon layer or the second silicon layer, the material consisting essentially of silicon and germanium;
• and
• one or more voids wherein at least a portion of the material is absent between the first silicon layer and the relaxed second silicon layer.

A method of forming a free-standing microstructure comprising:

• forming an engineered substrate, wherein forming the engineered substrate includes:
• growing a monocrystalline silicon-germanium (Si1-xGex) material over a silicon substrate, the Si1-xGex material having a lattice constant different from a lattice constant of the silicon substrate;
• relaxing the monocrystalline Si1-xGex material by forming a plurality of dislocations and causing the monocrystalline Si1-xGex material to be substantially free of residual strain;
• growing a monocrystalline silicon film over the monocrystalline Si1-xGex material;
• relaxing the monocrystalline silicon film by forming a plurality of dislocations and causing the monocrystalline silicon film to be substantially free of residual strain;
• forming an opening through the monocrystalline silicon film;
• removing at least a portion of the monocrystalline Si1-xGex material from between the monocrystalline silicon film and the silicon substrate to form one or more voids.