Ab initio Study of Nonlinear Optical Susceptibilities in Silicon Nanowires

Using Time Independent Density Functional Theory (TIDFT) it is shown that the 2nd order optical susceptibilities of narrow (1nm-2nm) Silicon Nanowires (SiNW) are enhanced due to surface termination. The value of $\chi^{(2)}$ is enhanced up to 200 pm/V which is promising a strong Second Harmonic Generation (SHG) in SiNWs. For [100], [110] and [111] SiNWs, yxx component of $\chi^{(2)}$ tensor is 81, 225 and 81 pm/V, respectively. These are in close agreement with $\chi^{(2)}$ values reported for strained silicon waveguides in experiments. The 3rd order susceptibility, $\chi^{(3)}$, is within the range of (0.1-12)x$10^{-18} \frac{m^{2}}{V^{2}}$ which is close to the experimental values of bulk silicon (0.1-0.2)x$10^{-18} \frac{m^{2}}{V^{2}}$ for [110] and [100] SiNWs and it is 100 times better for [111] SiNW. This study suggests possibilities of enhancing SHG in SiNWs through symmetry breaking via strain and surface termination/reconstruction as well as suitability of this DFT-based method in predicting nonlinear optical susceptibilities of nano structures.