A free-standing microstructure may be formed from an engineered substrate including a first silicon layer, a second silicon layer, and an intermediate layer. The second silicon layer may include a monocrystalline silicon film. The intermediate layer may be between the first silicon layer and the second silicon layer. The intermediate layer may include a silicon- or germanium-based material having a different lattice constant than the first silicon layer or the second silicon layer. The intermediate layer of the free-standing microstructure may further include one or more voids wherein at least a portion of the silicon- or germanium-based material is absent between the first silicon layer and the second silicon layer.