Critical lateral dimension of nanopedestals for ultimate relief of strain from lattice mismatch in Ge on Si

Abstract

Nanopedestals (NPs) that can ultimately relieve the strain in the lattice-mismatched heterostructures grown on them are investigated. The strain relief is achieved by the local compliance associated with the elevation of a nucleation site from a given substrate by a square prism NP and the edge-induced relaxation along its boundary. These are highly effective at nm scale and characterized with their lateral dimension, ℓp, and height, hp. The conventional critical thickness defined on two-dimensional flat surfaces is not valid on three-dimensional (3D) NPs. Under the boundary conditions semi-analytically optimized for the structure and the axial/interfacial compliance ratio depending on the structure parameters, a Ge on Si NP aligned to [001] of which the misfit is 0.042 is explored with a 3D modeling that relies on the local compliance and the edge-induced relaxation. These relief mechanisms dramatically increase the critical thickness of Ge on Si NP by the joint relaxation that reduces the strain energy of the Si NP as well as the Ge epilayer. For ℓp comparable to or less than the critical lateral dimension, ℓp.c, the critical thickness diverges to infinity and the Ge/Si heterostructures are eventually free from the strain relaxation by misfit dislocations. From the model, ℓp,c correlated to given hp for the ultimate strain relief is extracted. The limitation of the model for its universal applications is addressed.