Bond orbital description of the strain-induced second-order optical susceptibility in silicon

We develop a theoretical model, relying on the well established sp3 bond-orbital theory, to describe the strain-induced ${\ensuremath{\chi}}⁽²⁾$ in tetrahedrally coordinated centrosymmetric covalent crystals, like silicon. With this approach we are able to describe every component of the ${\ensuremath{\chi}}⁽²⁾$ tensor in terms of a linear combination of strain gradients and only two parameters $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ which can be theoretically estimated. The resulting formula can be applied to the simulation of the strain distribution of a practical strained silicon device, providing an extraordinary tool for optimization of its optical nonlinear effects. The application of the first order theory to the photoelastic effect in C, Si, and Ge showed very good phenomenological and numerical agreement, up to 3% in Si. The model was then used to the second-order nonlinear susceptibility, and we were able not only to confirm the main valid claims known about ${\ensuremath{\chi}}⁽²⁾$ in strained silicon, but also estimate the order of magnitude of the ${\ensuremath{\chi}}⁽²⁾$ generated in that device.