Second Harmonic Generation Rotational Anisotropy Research Articles

Spatial dispersion contribution to second harmonic generation in inversion-symmetric materials

It is well known that second harmonic generation (SHG) from dipoles within the bulk vanishes in inversion-symmetric semiconductor materials as a consequence of parity symmetry. Hence SHG is then ascribed in the form of either surface dipole effects or bulk-related electric quadrupole or magnetic dipole effects. By incorporating the redefined spatial dispersion into the simplified bond-hyperpolarizability model, we show that the SHG spatial dispersion contribution for Si(001) and Si(111) facet orientations can be reformulated by a third-rank tensor containing one independent parameter, namely, the complex SHG spatial dispersion hyperpolarizability. Our results show that certain unexplained rotational anisotropy SHG intensity features for different incoming light wavelengths or optical penetration depths can be well reproduced only if the contribution from spatial dispersion is incorporated.

Spin-orbit-enhanced magnetic surface second-harmonic generation in Sr2IrO4

An anomalous optical second-harmonic generation (SHG) signal was previously reported in Sr$_2$IrO$_4$ and attributed to a hidden odd-parity bulk magnetic state. Here we investigate the origin of this SHG signal using a combination of bulk magnetic susceptibility, magnetic-field-dependent SHG rotational anisotropy, and overlapping wide-field SHG imaging and atomic force microscopy measurements. We find that the anomalous SHG signal exhibits a two-fold rotational symmetry as a function of in-plane magnetic field orientation that is associated with a crystallographic distortion. We also show a change in SHG signal across step edges that tracks the bulk antiferromagnetic stacking pattern. While we do not rule out the existence of hidden order in Sr$_2$IrO$_4$, our results altogether show that the anomalous SHG signal in parent Sr$_2$IrO$_4$ originates instead from a surface-magnetization-induced electric-dipole process that is enhanced by strong spin-orbit coupling.

Second harmonic generation as a probe of broken mirror symmetry

The notion of spontaneous symmetry breaking has been used to describe phase transitions in a variety of physical systems. In crystalline solids, the breaking of certain symmetries, such as mirror symmetry, is difficult to detect unambiguously. Using 1$T$-TaS$_2$, we demonstrate here that rotational-anisotropy second harmonic generation (RA-SHG) is not only a sensitive technique for the detection of broken mirror symmetry, but also that it can differentiate between mirror symmetry-broken structures of opposite planar chirality. We also show that our analysis is applicable to a wide class of different materials with mirror symmetry-breaking transitions. Lastly, we find evidence for bulk mirror symmetry-breaking in the incommensurate charge density wave phase of 1$T$-TaS$_2$. Our results pave the way for RA-SHG to probe candidate materials where broken mirror symmetry may play a pivotal role.

Fourier domain rotational anisotropy-second harmonic generation.

We describe a novel scheme of detecting rotational anisotropy-second harmonic generation (RA-SHG) signals using a lock-in amplifier referenced to a fast scanning RASHG apparatus. The method directly measures the nth harmonics of the scanning frequency corresponding to SHG signal components of Cn symmetry that appear in a Fourier series expansion of a general RA-SHG signal. GaAs was used as a test sample allowing comparison of point-by-point averaging with the lock-in based method. When divided by the C∞ signal component, the lock-in detected data allowed for both self-referenced determination of ratios of Cn components of up to 1 part in 104 and significantly more sensitive measurement of the relative amount of different Cn components when compared with conventional methods.

Modeling Fourth Harmonic Generation in a Non-Vicinal (111) Diamond Lattice

In this work it is shown how Rotational Anisotropy Fourth Harmonic Generation (RAFHG) data from nonvicinal (111) diamond lattice obtained by M. Downer Group can be very well modelled using the modified nonlinear bond model. Extending the bond model previously developed for second harmonic generation to higher harmonics is straightforwardly achieved by modification of the nonlinier susceptibility in the form of adding more direct product of bond vectors. Because a diamond latttice is centrosymmetric, FHG radiation measured in reflection should mainly come from the interface because it is bulk forbidden due to parity simmetry. Previous work showed that the nonlinear bond model can very well describe Rotational Anisotropy Second Harmonic Generation (RASHG) and Rotational Anisotropy Third Harmonic Generation (RATHG) data and here I present similar agreement for FHG.

Resonance-type thickness dependence of optical second-harmonic generation in thin films of the topological insulatorBi2Se3

Optical second-harmonic generation (SHG) has been measured in a reflection from the nanometer-thick films (6 to 40 nm) of the topological insulator $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$ using 1.51 eV (820 nm) Ti:Sapphire laser photons and revealed a strong dependence of the integral SHG intensity on the film thickness. The integral SHG intensity was determined by area integration of the SHG rotational anisotropy patterns measured for different input-output light polarization geometries. A \ensuremath{\sim}100-fold enhancement of the integral SHG intensity with decreasing film thickness has been suggested to result from the dc-electric-field-induced SHG (EFISHG) effects. Two sources of dynamically created dc electric field were proposed: (i) the capacitor-type dc electric field that gradually increases with decreasing film thickness from 40 to 6 nm due to a dynamical imbalance of photoexcited long-lived carriers between the opposite-surface Dirac surface states and (ii) a dc electric field associated with a nonlinearly excited Dirac plasmon, which is responsible for the resonant enhancement of the integral SHG intensity for the 10 nm thick film with a Lorentz-shaped resonance of \ensuremath{\sim}1.6 nm full width at half maximum. In addition to the general SHG enhancement trends with decreasing film thickness, a relative decrease of the out-of-plane contribution with respect to the in-plane contribution was observed. Using a theoretical treatment of the measured SHG rotational anisotropy patterns, this effect has been suggested to result from the joint contributions of the linear and quadratic dc electric field effects to the EFISHG response.

Optical second-harmonic generation induced by electric current in graphene on Si and SiC substrates

We find that the flow of direct electric current (dc) through graphene on substrate enhances surface optical second-harmonic generation (SHG) from the graphene/substrate system. The current can enhance surface SHG by about 300% for a chemical-vapor-deposition (CVD) graphene monolayer on a SiO${}_{2}/\mathrm{Si}(001)$ substrate, and by about 25% for an epitaxial four-layer-graphene film on a 3.5\ifmmode^\circ\else\textdegree\fi{}-miscut vicinal SiC(0001) substrate. The enhancement in both the CVD and epitaxial graphene samples is due to electric field-induced SHG, which is produced by the current-associated vertical electric field at the SiO${}_{2}/$Si interface or at the graphene/SiC interface. Measurements of rotational-anisotropy SHG (RA-SH) from both samples revealed that the current-induced SHG varies strongly with the measurement location along the current flow direction. By measuring RA-SH from the vicinal SiC(0001) substrate, we determined all three second-order susceptibility tensor elements (${d}_{33}$ = \ensuremath{-}52.0 pm/V, ${d}_{15}$ = 20.0 pm/V, and ${d}_{31}$ = 18.7 pm/V) that characterize the SHG response of hexagonal SiC at the fundamental wavelength of 740 nm. We further determined the three effective susceptibility tensor elements (${d}_{33}$ = \ensuremath{-}135.8 pm/V, ${d}_{15}$ = 18.5 pm/V, and ${d}_{31}$ = 14.6 pm/V) that characterize the surface SHG from the graphene/vicinal-SiC(0001) sample and finally showed that the current-dependent tensor element ${d}_{33}$ can be enhanced to a large value of ${d}_{33}$ = \ensuremath{-}199.0 pm/V by electric current in epitaxial graphene.

Photoreactivity of Si(111)−H in Ambient

Second harmonic generation rotational anisotropy (SHG-RA) provides a convenient means to monitor the chemical state of the Si surfaces and to follow the conversion of a H-terminated surface to SiO2 by oxidation as a function of time in ambient. SHG at 800 nm is sensitive to changes in the surface electronic properties induced by oxidation, and it probes both the initial stage of oxidation and the logarithmic oxide growth. We found that intense, ultrashort (4 ps) 800 nm laser pulses accelerate the initial stage of oxidation of Si(111)−H in ambient. The cross-section of the photoinduced process was found to be (1.7 ± 0.5) × 10-23 cm2. A mechanism involving drift of photoexcited electrons toward the surface is proposed to explain the photooxidation.

Optical Recognition of Surface Chirality at Au(hkl) Single Crystalline Surfaces by Second Harmonic Generation Rotational Anisotropy

Two-dimensional chirality at naturally chiral gold single crystalline surfaces was detected and characterized using optical second harmonic generation (SHG) measurements. SHG rotational anisotropy (SH-RA) patterns at Au(643)S and Au(643)R surfaces were mirror symmetric to each other. Systematic SH-RA measurements at chiral Au(hkl) surfaces with the same step and kink structures but different (111) terrace widths showed a linear correlation between surface step density and SH-RA fitting parameters arising from defects. These results indicate that SH-RA measurements provide information not only on surface chirality but also on density of surface defects.

Optical second harmonic generation studies of ultrathin high-k dielectric stacks

We report an investigation of charge transfer in high-k dielectric stacks on Si by second harmonic generation (SHG). Ultrathin (2–6 nm) films of HfO2, ZrO2, and Al2O3 grown on Si surfaces by atomic layer deposition were investigated and compared to conventional SiO2-based gate dielectrics. From the SHG rotational anisotropy (SHG-RA) of Si-(high-k) and Si–SiO2 systems, optical roughness of the films was found to increase in the following order: SiO2, Al2O3, and (ZrO2 and HfO2). The optical roughness is regarded as a quantity describing the nonuniformity in the distribution of interfacial defects capable of charge trapping. Time dependent second harmonic generation (TD-SHG) measurements were carried out to understand charge trapping and detrapping dynamics and trapped charge densities. Relative comparison of the four dielectrics revealed that Al2O3 films have the highest densities of trapped and fixed charge while silicon oxides exhibited less charge trapping, consistent with electrical measurements performed on similar structures. In contrast to SiO2 films, detrapping was significantly suppressed in the high-k films due to significantly reduced leakage currents. We also observed ambient effects in charge trapping at the dielectric/air(vacuum) interface that could be significantly reduced by covering the dielectric film with a thin (semitransparent) metal (aluminum) overlayer.

Selective surface/interface characterization of thin garnet films by magnetization-induced second-harmonic generation

Magnetization-induced second-harmonic generation (SHG) has been used for the study of thin garnet films. The strong optical absorption of these films at the second harmonic frequency provides a unique possibility to study magnetic and structural properties of the film surface and film/substrate interface separately. When studied in transmission at normal incidence all relevant elements of the crystallographic part of the nonlinear optical susceptibility tensor vanish identically, while a magnetization-induced contribution remains. The purely magnetic origin of SHG from the interface is unambiguously demonstrated. From measurements of the SHG rotational anisotropy and magnetic field dependence, the surface is found to have inclusions which act as nonmagnetic sources of SHG, while the anisotropy causing easy in-plane magnetization is found to be stronger at the interface with the substrate than at the surface of the film.

In situ second-harmonic generation measurements of the stability of Si(111)–H and kinetics of oxide regrowth in ambient

The oxidation of H terminated silicon surfaces is a significant and controversial problem in silicon device fabrication. Second-harmonic generation rotational anisotropy (SHG–RA) provides a convenient means to monitor the chemical state of the Si surfaces, and to follow the conversion of H terminated surface to SiO2 by oxidation as a function of time in ambient. The change in SHG–RA of Si(111)–H was shown to correlate well with the ellipsometric thickness. SHG is sensitive to the initial stage of oxidation (induction period) as well as to the logarithmic oxide growth. SHG is sensitive to the electronic properties of the surface, therefore it is a sensitive probe of the quality of H terminated Si(111) surface. Under ambient conditions, (20% relative humidity, 23 °C) the initial oxidation rate is at most 2×10−6 ML/s.

Optical characterisation of anodic sulphide films on Hg 1− xCd xTe (MCT) grown by the potential step method

The growth of native sulphide films on Hg 1− x Cd x Te (MCT) by potential steps to two different electrochemical growth regions has been studied by in-situ ellipsometry, photocurrent spectroscopy and second harmonic generation (SHG) rotational anisotropy. Films grown at −0.4 V versus SCE were porous and consisted mainly of cubic close packed (ccp) CdS. The photocurrent spectrum of the film exhibited a cut-off which closely conformed to the expected bandgap of CdS. The gradual increase in SH intensity as the sulphide film thickened was due to a contribution to the overall SH signal from the CdS film itself. No evidence of any hcp species was apparent in the rotational anisotropy patterns, with the four-fold pattern expected for the vicinal MCT surface being maintained even after film growth. When the potential was stepped to −0.3 V, the film grown absorbed the ellipsometer radiation once a thickness of 86 nm was reached. Photocurrent measurements showed a tail extending into the red region of the spectrum. These phenomena have been attributed to the incorporation of ccp HgS into the sulphide film as at this potential, the electrochemical reaction of the HgTe component of MCT can occur. SHG rotational anisotropy confirmed the four-fold symmetry of the ccp surface film.

Ambient stability of chemically passivated germanium interfaces

The stability of any semiconductor surface passivating layer is key to applications. Second harmonic generation (SHG) can be used to probe the chemical state of semiconductor interfaces, as well as investigate the mechanisms of chemical transformation. While the SHG rotational anisotropy changes upon sulfidation or alkylation of Ge surfaces, SHG appears far less sensitive to H and Cl passivation of germanium surfaces than to silicon surfaces. Investigation of the stability of chemically modified germanium surfaces using a number of additional techniques, including atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS), reveals that H- and Cl-terminated Ge(1 1 1) rapidly re-oxidize in ambient. S- and alkyl-terminations are more robust, showing little sign of oxide formation after a month in ambient.

Growth of the anodic sulfide film on Hg 1− xCd xTe (MCT) by the potential step method into the electrochemical passivation region

The growth of the anodic sulfide film on Hg 1− x Cd x Te (MCT) by a potential step directly into the electrochemical passivation region is reported. Second harmonic generation (SHG) was employed to analyse the film during and subsequent to the growth. The analysis of the surface structure by SHG rotational anisotropy showed that the thin sulfide film formed by the potential step method did not lead to changes in the surface symmetry. However, increasing the film thickness by a voltage scan negative from the passive region led to an almost complete loss of the SH intensity which has been attributed to absorption of the fundamental and SH signals by the β-HgS present in the sulfide film. The anisotropy pattern of the film here showed strong deviations from the four-fold symmetry expected for the vicinal (1 0 0) surface. On the other hand, where current oscillations were observed during the cathodic voltage sweep from the passivation region, no reduction in the SH intensity was observed even for thicker sulfide films, signifying that the β-HgS had been removed from the layer. The close conformity in the anisotropy patterns between the original MCT surface and that for the sulfide-covered MCT surface confirms that the sulfide film is epitaxial, maintaining the ccp structure of the MCT substrate.

Second-harmonic generation from chemically modified Ge(111) interfaces

Second-harmonic generation (SHG) was used to investigate chemically modified surfaces of Ge(111). Chemical modification was achieved by wet-chemical covalent binding of decyl and sulfur directly to the Ge interface after oxide stripping. Chemical modification of the interface substantially changes the second harmonic response. The decyl and sulfur terminations are stable in ambient during several weeks, as judged by SHG and XPS measurements. The SHG rotational anisotropy patterns were analyzed to estimate the relative values of the nonlinear susceptibilities describing the surface and bulk response. The choice of fundamental/SHG polarization combinations for accessing various nonlinear coefficients is presented. The factors affecting the relative values of the surface-to-bulk contributions to SHG and their changes upon chemical modification of the surface are discussed. In particular, it was found that the higher the electronegativity of chemically attached species, the higher the contribution of the surface-originating nonlinear terms to the overall response. Also, it was found that the relative contribution of surface versus bulk to SHG is different for different polarization combinations: the surface contribution to the p-in/p-out response is the greatest.

In-situ evaluation of the anodic oxide growth on Hg1−xCdxTe (MCT) using ellipsometry and second harmonic generation

In-situ measurements of ellipsometry and second harmonic generation (SHG) were carried out to monitor the electrochemical growth of native anodic oxide films on Hg1−xCdxTe (MCT). Growth of the anodic oxide was performed using two different methods viz., by linear sweep voltammetry and by applying a constant current density. The influence of scan rate and the magnitude of the applied current density on the properties of the growing films were examined. From the ellipsometry data, we have shown that the measured refractive index value of 2.19 for the oxide film remains unchanged for moderate and high oxide growth rates. Only at very slow growth rates were significant increases in the refractive index observed (n=2.4), indicating an increase in the compactness of the layer. For film thicknesses in excess of ∼1200 A, a non-zero value for the extinction coefficient was found, indicating the incorporation of HgTe particles within the anodic oxide film. SHG rotational anisotropy measurements, performed on the MCT with and without an anodic oxide film showed only the four-fold symmetry associated with the MCT and so confirmed that the oxide was centrosymmetric. However, an increase in the SH intensity was observed in the presence of the oxide and this has been attributed to multiple reflections in the thin oxide film and also to the increase in the χ(2) non-linear susceptibility tensor as a result of charge accumulation at the MCT/anodic oxide interface.

Nonlinear Optics of Magnetic Crystals

Nonlinear optics of magnetic crystals is a very recent field that exhibits a number of unusual optical phenomena. Using the electric dipole approximation we discuss the crystallographic and magnetization-induced nonlinear susceptibilities that coexist in magnetic crystals. It is the interference between the nonlinear optical waves of different origin that is the source of novel magneto-optical effects, such as transversal linear in M effect at normal incidence, circular magnetic dichroism with no equivalence between light helicity and magnetization direction change, etc., that have no equivalent in linear optics. As a model system for experimental studies we used thin epitaxial films of magnetic garnets grown on substrates with different crystallographic orientations. The second harmonic generation (SHG) was studied in the spectral range of 0.71-0.84 μm. These experiments were done in both transverse and longitudinal geometries. The experimental data on the SHG rotational anisotropy perfectly confirm the predicted effects.