On the origin of the second-order nonlinearity in strained Si–SiN structures

The development of efficient low-loss electro-optic and nonlinear components based on silicon or its related compounds, such as nitrides and oxides, is expected to dramatically enhance silicon photonics by eliminating the need for non-CMOS-compatible materials. While bulk Si is centrosymmetric and thus displays no second-order (χ(2)) effects, a body of experimental evidence accumulated in the last decade demonstrates that when a strain gradient is present, a significant χ(2) and Pockels coefficient can be observed. In this work we connect a strain-gradient-induced χ(2) with another strain-gradient-induced phenomenon, the flexoelectric effect. We show that even in the presence of an extremely strong strain gradient, the degree by which a nonpolar material like Si can be altered cannot possibly explain the order of magnitude of observed χ(2) phenomena. At the same time, in a polar material like SiN, each bond has a large nonlinear polarizability, so when the inversion symmetry is broken by a strain gradient, a small (few degrees) reorientation of bonds can engender χ(2) of the magnitude observed experimentally. It is our view therefore that the origin of the nonlinear and electro-optic effects in strained Si structures lies not in the Si itself but in the material providing the strain: the silicon nitride cladding.