Surface Second-Harmonic Generation (SHG) Lab

In materials with bulk spatial inversion symmetry (such as crystalline silicon, germanium, diamond, metals, and liquid electrolytes), second-order electric dipole nonlinear susceptibility \(\chi^{(2)}\) is strictly zero in the bulk because reversing spatial coordinates (\(\mathbf{r} \to -\mathbf{r}\)) requires \(\chi^{(2)} = -\chi^{(2)} \equiv 0\). However, at a surface, buried interface, or 2D monolayer boundary, the crystal terminates and spatial inversion symmetry is inherently broken. Consequently, electric dipole second-harmonic generation (SHG) radiates exclusively from the atomic monolayer boundary without any background signal from the bulk substrate, making it an extraordinary non-destructive probe of buried interfaces.

When a static electric field \(E_{\text{DC}}\) exists across an interface (due to trapped oxide charges, space-charge band bending, or an applied gate bias), it couples with the fundamental laser field via the third-order nonlinear susceptibility \(\chi^{(3)}\). This generates an effective second-order polarization \(\mathbf{P}^{(2\omega)} = \epsilon_0 (\chi^{(2)}_{\text{surface}} + \chi^{(3)} E_{\text{DC}}) \mathbf{E}^{(\omega)} \mathbf{E}^{(\omega)}\). Because the total SHG intensity is proportional to the square of this effective susceptibility, \(I(2\omega)\) traces a parabola as a function of applied bias. The minimum of the parabola directly determines the flatband voltage \(V_{\text{fb}}\), while the shape and hysteresis quantify the interface trap density \(D_{it}\) and fixed oxide charge \(Q_{\text{ox}}\) without fabricating electrical contacts.

Monolayer transition metal dichalcogenides (TMDs such as MoS2 and WS2) possess non-centrosymmetric \(D_{3h}\) crystal symmetry. When the sample is rotated azimuthally by angle \(\phi\) relative to the laser polarization, the parallel polarized second-harmonic intensity follows \(I_{pp}(\phi) \propto \cos^2(3\phi)\). This produces a sharp 6-petal cloverleaf polar pattern whose intensity maxima correspond exactly to the armchair crystallographic directions. This provides an instantaneous, non-contact optical determination of grain boundaries, crystal lattice misorientations, and interlayer twist angles in moiré heterostructures.

In lithium metal and solid-state battery cells, the solid-electrolyte interphase (SEI) forms at the electrode-electrolyte boundary under extreme local electric fields (> 10 MV/cm). Because the electrolyte and metal anode bulks are centrosymmetric, operando SHG penetrates transparent optical windows to monitor the interfacial electric double layer (EDL) and chemical phase transformations in real time during charging and discharging. Evolution of the EFISH parabolic voltage curve reveals the onset of electrolyte reduction, passivation film maturation, and dead lithium dendritic growth non-invasively.