Strain-designed strategy to induce and enhance second-harmonic generation in centrosymmetric and noncentrosymmetric materials

Second-harmonic generation is described by the second-order nonlinear susceptibility ${\chi }^{\left(2\right)}$ which, in the electric-dipole approximation, requires a noncentrosymmetric medium. It is very challenging and of high technological interest to search whether it is possible to find a way to break inversion symmetry in centrosymmetric crystals in order to induce second-order nonlinearities. A new intriguing way to observe second-order nonlinear phenomena is strain. Here, we present a detailed analysis of the correlation between the strain and the ${\chi }^{\left(2\right)}$ in both centrosymmetric and noncentrosymmetric materials. We considered Si and SiC as test materials and we studied different types of strain (tensile/compressive), in different directions (uniaxial/biaxial) and for different light-polarization directions. We found which is the type of strain necessary in order to induce, tune, and enhance second-harmonic generation in different energy regions for centrosymmetric and noncentrosymmetric materials.

Figure 1

Panel (a) Unstrained eight atom unit cell in 3D panel. Panel (b) Unstrained eight atom unit cell projected in the $YZ$ plane (red circle) and on the $XY$ plane (red circle and black cross). Panel (c) Uniaxially strained eight atom unit cell. Panel (d) Biaxially strained eight atom unit cell.

Figure 2

Representation of the 24 uniaxial strained structures studied on a C-T plane. The points on this plane are defined by the couple (C,T) and are correlated to the percentage of compression and elongation applied. For each structure the value of HP is reported. The bisector $\text{T}=\text{C}$ (dashed-dotted red line) and $\text{T}=-\text{C}$ (dashed-dotted cyan line) are also represented.

Figure 3

${\chi }_{zzz}^{\left(2\right)}\left(\omega \right)$ spectra for uniaxial C1.8_X strained Si [panel (a)], uniaxial C0.7_X strained Si [panel (b)], uniaxial T1.8_X strained Si [panel (c)] and uniaxial T0.7_X strained Si [panel (d)]. The insets show a magnification of the low-energy regions.

Figure 4

${\chi }_{xyz}^{\left(2\right)}$ and ${\chi }_{zzz}^{\left(2\right)}$ spectra for unstrained bulk SiC and for C1.8_X and T1.8_X strained SiC.

Figure 5

The ${\chi }_{zzz}^{\left(2\right)}$ and ${\chi }_{YYY}^{\left(2\right)}$ spectra for the C1.8_X, C1.8_X_Y, T1.8_X, and T1.8_X_Y systems. Panel (a) is for Si and panel (b) is for SiC.

Figure 6

Representation of the magnitude of peak I on a C-T plane for the 24 uniaxial strained structures.

Figure 7

Representation of the magnitude of peak II on a C-T plane for the 24 uniaxial strained structures.

Figure 8

Representation of the magnitude of peak III on a C-T plane for the 24 uniaxial strained structures.