On the Origin of the Second-Order Nonlinearity in Strained Si-SiN Structures

TL;DR

This paper investigates the origin of second-order nonlinearity in strained silicon-silicon nitride structures, proposing that the nonlinear effects mainly originate from the silicon nitride layer rather than silicon itself, through a connection with the flexoelectric effect.

Contribution

It introduces a new understanding that the observed second-order nonlinearity in strained Si structures is primarily due to the silicon nitride cladding, not silicon, linking strain-gradient effects to flexoelectricity.

Findings

Strain gradients induce significant  effects in silicon nitride.

The nonlinear response in silicon is mainly due to the silicon nitride layer.

Bond re-orientation in SiN explains the observed  magnitudes.

Abstract

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 (\c{hi}(2)) effects, a body of experimental evidence accumulated in the last decade demonstrates that when a strain gradient is present, a significant \c{hi}(2) and Pockels coefficient can be observed. In this work we connect a strain-gradient-induced \c{hi}(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 chi^(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) re-orientation of bonds can engender chi^(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 in not in the Si itself, but in the material providing the strain: the silicon nitride cladding.