Second Harmonic Generation in Silicon Based Heterostructures: The Role of Strain and Symmetry

Silicon is today the electronic material par excellence. Nevertheless the increasing demand for new, innovative and more efficient devices has driven scientists to explore new functionalities in Si-based materials. In silicon photonics the introduction of second-order nonlinearity by proper material engineering would be highly desirable. However a bulk second-order dipolar nonlinear optical susceptibility in Si is forbidden due to the bulk crystal centrosymmetry. Different approaches have been used to break this inversion symmetry: interfacing Si with different materials and/or introducing strain. In this paper we theoretically investigate second-harmonic generation, described by the second-order nonlinear susceptibility χ ⁽²⁾ in Si/Ge heterostructures. The role of symmetry and strain will be carefully analyzed also through a comparison with the computed results for unstrained and strained bulk Si and SiC systems, the first system being initially centrosymmetric, the second from the start non centrosymmetric. Thus we are able to elucidate the type of strain and symmetry breaking necessary to induce, tune and enhance second-harmonic generations in different energy regions for Si-based systems.