Simplified Bond Hyperpolarizability Model Research Articles

A Novel Sensing Method to Detect Malachite Green Contaminant on Silicon Substrate Using Nonlinear Optics.

We propose a nonlinear-optics-based nanosensor to detect malachite green (MG) contaminants on semiconductor interfaces such as silicon (Si). Applying the simplified bond hyperpolarizability model (SBHM), we simplified the second-harmonic generation (SHG) analysis of an MG-Si(111) surface and were able to validate our model by reproducing experimental rotational anisotropy (RA) SHG experiments. For the first time, density functional theory (DFT) calculations using ultrasoft pseudopotentials were implemented to obtain the molecular configuration and bond vector orientation required by the SBHM to investigate and predict the second-harmonic generation contribution for an MG-Si 001 surface. We show that the SBHM model significantly reduces the number of independent components in the nonlinear tensor of the MG-Si(111) interface, opening up the possibility for real-time and non-destructive contaminant detection at the nanoscale. In addition, we derive an explicit formula for the SHG far field, demonstrating its applicability for various input polarization angles. Finally, an RASHG signal can be enhanced through a simulated photonic crystal cavity up to 4000 times for more sensitivity of detection. Our work can stimulate more exploration using nonlinear optical methods to detect and analyze surface-bound contaminants, which is beneficial for environmental monitoring, especially for mitigating pollution from textile dyes, and underscores the role of nonlinear optics in real-time ambient-condition applications.

Gas Adsorption Mechanism on 2D Materials: The Hyperpolarizability Evolution Analyzed by Nonlinear Optics

AbstractWhile understanding the competitive adsorption behavior of gas sensor is important, it is yet to be unraveled. Especially for the influence of water molecules to the gas adsorbed on 2D materials. This study explores the potential of layered 2D materials as a candidate material for gas sensing, employing non‐destructive measurement, and second harmonic generation (SHG). The investigation focuses on analyzing oxygen, ammonia, and water vapor adsorbed on a WS2 surface by studying the evolutions in electric dipole and electric field. Leveraging the simplified bond hyperpolarizability model (SBHM), a foundation is established for gas sensors utilizing high‐quality 2D materials. This approach facilitates the detection of material modifications in response to environmental influences, including the inevitable water molecules. The obtained hyperpolarizability from SBHM exhibits remarkable consistency with Langmuir's adsorption model, confirming the physical adsorption in the system. In addition, the competitive effects between gases are explored by comparing experimental results with theoretical predictions based on Boltzmann distribution and density functional theory (DFT) calculations. This highlights the effectiveness of SHG and SBHM in studying gas adsorption on layered van der Waals materials.

Bond model of second harmonic generation in tetragonal and orthorhombic perovskite structures

We apply the simplified-bond-hyperpolarizability model (SBHM) to investigate second harmonic generation (SHG) from tetragonal and orthorhombic methylammonium (MA) lead (Pb) iodide (I) perovskite structures. Assuming that the SHG radiation comes from the anharmonic charges parallel to the Pb-I covalent bond vectors, we show explicitly how the reflective rotational anysotropy SHG (RASHG) intensity profiles arise via dipole superposition from the perovskite surface and that their bulk contribution is zero for both the tetragonal and orthorhombic bulk structures if the contribution from MA molecules can be neglected. In addition, we compare the third order susceptibility tensor obtained from group theory and SBHM and calculate the values for the nonzero components as well as derive the SHG intensity field formulas. We found that the tetragonal and orthorhombic perovskite SHG intensity profiles are different. Furthermore, our results show that even in relative complex systems such as metal halide perovskites (MHPs), RASHG experimental data can be fitted using only one independent fitting parameter, which is the effective Pb-I nonlinear hyperpolarizability. Therefore, the analysis of perovskite using an anharmonic bond model can lead to better efficiencies of photovoltaic devices, while it will also pave a way for the use of SHG in MHP crystals as frequency conversion and optical signal processing.

Second harmonic generation and simplified bond hyperpolarizability model analyses on the intermixing of Si/SiGe stacked multilayers for gate-all-around structure

Si/SiGe stacked multilayers are key elements in fabrication of gate-all-around (GAA) structures and improvement of electrical properties, with the evolution of the Si/SiGe interfaces playing a crucial role. In this work, a model is developed based on the simplified bond hyperpolarizability model (SBHM) to analysis the anisotropic reflective second harmonic generation (Ani-RSHG) on a three-period stacked Si/Si1−x Ge x multilayer, which builds on Si(100) diamond structures. The C 4v symmetry of the Si(100) structure enables the second harmonic generation (SHG) contribution from the bonds to be simplified and the effective hyperpolarizabilities of the interfacial and bulk sources to be obtained. The effective interface dipolar and bulk quadrupolar SHG hyperpolarizabilities in the Si1−x Ge x sample with various Ge concentration profiles are modeled by interpreting the concentration of a component element as the probability of the element occupying an atomic site. On the basis of the developed model, the Ani-RSHG spectra of the as-grown samples with various Ge ratios for each layer and the samples annealed at 850 °C and 950 °C are analyzed to inspect the change in Ge distribution and its gradient in depth. The ani-RSHG analysis on as-grown samples showed difference in Ge distribution in samples with the multi Si/SiGe structure, which is not well observed in synchrotron x-ray diffraction (XRD) spectra. For the annealed samples, the response to changes in Ge concentration and its gradient in depth reveal the Si/Si1−x Ge x interface intermixing. Results of high-angle annular dark-field scanning transmission electron microscopy and energy dispersive x-ray spectroscopy agree well with the Ani-RSHG with SBHM findings. Compared with the Raman and synchrotron XRD spectra, the Ani-RSHG with SBHM simulation result demonstrates much better response to changes in compositions of the Si/Si1−x Ge x stacked multilayered structures, verifying the potential for characterizing the concentration distribution in stacked multilayered thin films for GAA structures.

Structure of an In Situ Phosphorus-Doped Silicon Ultrathin Film Analyzed Using Second Harmonic Generation and Simplified Bond-Hyperpolarizability Model

In fabricating advanced silicon (Si)-based metal-oxide semiconductors, the ability to inspect dopant distribution in Si ultrathin films (tens of nm) is crucial for monitoring the amount of dopant diffusion. Here, we perform an anisotropic reflective second harmonic generation (SHG) measurement to demonstrate the sensitivity of SHG to phosphorus (P) concentration within the range of 2.5×1017 to 1.6×1020 atoms/cm3. In addition, we propose an analysis method based on a simplified bond-hyperpolarizability model to interpret the results. The bond vector model that corresponds to the P vacancy clusters is built to calculate the SHG contribution from substitutionally incorporated P atoms. The effect of incorporating P into the Si lattice is reflected in the effective hyperpolarizability, lattice tilt, and deformation of this model. The fitting results of the intuitively defined coefficients exhibit a high correlation to the P concentration, indicating the potential of this model to resolve the properties in complex material compositions. Finally, a comparison with Fourier analysis is made to evaluate the advantages and disadvantages of this model. Combined anisotropic reflective SHG (Ani-RSHG) and the simplified bond-hyperpolarizability model (SBHM) can analyze the crystal structure of doped ultrathin films and provide a non-destructive nanophotonic way for in-line inspection.

Zn dots coherently grown as the seed and buffer layers on Si(111) for ZnO thin film: Mechanism, in situ analysis, and simulation

In conventional ZnO/Si heterostructures, a buffer layer is usually required to compensate the mismatch between the host substrate and the grown thin film. However, poor quality of buffer layers might lead to severe crystalline misorientation and defects. In this work, we demonstrate that collective oxidized Zn dots act as buffer and seed layers for the growth of high surface quality ZnO thin films on Si(111) by rf-sputtering, and we further in situ analyze the structural evolution by reflective second harmonic generation (RSHG). The collective Zn dots grown on Si(111) were oxidized with exposure to ozone gas under proper Ultraviolet-C (UVC) irradiation, and then these ZnO shells formed seed layers to promote the nucleation process for subsequent ZnO thin film growth. Besides, RSHG was performed in situ to observe the net symmetrical dipole contribution at each fabrication steps and analyzed the surface quality of the ZnO thin film. Consistent with the analyses of synchrotron x-ray diffraction and atomic force microscopy, the RSHG results analyzed with simplified bond-hyperpolarizability model fitting revealed that well oxidized Zn dot-embedded ZnO films grown on Si(111) exhibit a 3m-symmetrical surface structure, and that excessive oxidation time led to ZnO2 formation and higher roughness. Our results demonstrate the efficient approach toward high-surface-quality ZnO thin film by rf-sputtering, verifying that the quality of ZnO shell covering Zn dot grown on Si(111) is the focal factor for the sequent ZnO thin film growth.

Quo Vadis Nonlinear Optics? An Alternative and Simple Approach to Third Rank Tensors in Semiconductors

It is well understood that nonlinear optical (NLO) phenomena are deeply related to the material’s symmetry. Mathematically, the material symmetry can be described in terms of the nonzero parameters in the nonlinear susceptibility tensors. Generally, more complex structures involve more nonzero parameters in the tensor. The number of parameters increases rapidly if higher NLO orders are considered, complicating the physical analysis. Conventionally, these parameters are obtained via abstract symmetry analysis, e.g., group theory (GT). This work presents a novel theoretical analysis to approach the nonlinear tensor using the simplified bond hyperpolarizability model (SBHM) and compare it with GT. Our analysis is based on a light–matter interaction classical phenomenological physical framework. Rather than just looking at the symmetry of the crystal, the model applies physical considerations requiring fewer independent parameters in the tensor than GT. Such a simplification significantly improves the determination of the surface–bulk SHG contribution factors, which cannot be extracted from the experiment alone. We also show for the case of perovskite that the SHG contribution can be addressed solely from their surface dipoles with only one independent component in the tensor. Therefore, this work may open the path for a similar analysis in other complicated semiconductor surfaces and structures in the future, with potential applications to nanoscale surface characterization and real-time surface deposition monitoring.

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.

Generation, reflection and transmission of nonlinear harmonic waves by direct superposition of anharmonic dipoles

It is well known that the linear and nonlinear light reflection and transmission formula can be obtained from the standard macroscopic Maxwell equation. In the past, a microscopic approach based on the Ewald–Oseen extinction theorem to derive the reflection and transmission formula by direct dipole summation has been performed by Fearn et al where they successfully derived the Fresnel formula in linear optics. In this work, we extend their work for the first time to derive the nonlinear reflection and transmission formula by direct summation of anharmonically oscillating dipoles for the case of a normal incidence wave, yielding similar results with coupled-mode-theory (CMT). We demonstrate for a decaying incoming field that dipolar radiation is no longer forbidden inside the bulk of a centrosymmetric material. Using the simplified bond hyperpolarizability model (SBHM), we find that these additional bulk dipole contribution must be accounted along with the surface dipoles and bulk quadrupolar contribution to explain recent rotational anisotropy SHG intensity experimental data of Si(111) with high precision.

Bond model of second-harmonic generation in wurtzite ZnO(0002) structures with twin boundaries

We describe second-harmonic generation (SHG) in ZnO(0002) wurtzite structures with [11¯00]/(1102) twin boundaries using the simplified bond hyperpolarizability model (SBHM). We show explicitly how the reflective second-harmonic generation (RSHG) intensity profile for the s-incoming fundamental and s-outgoing SHG polarized light arise via superposition of the SHG dipole fields. The nonlinear fields originate from anharmonic motions of electric charges along each bond. The total dipole fields from within the ZnO bulk sum up to zero but produce a constructive SHG radiation from the unreduced surface and twin boundary. In addition, we compare the third-order susceptibility tensor obtained from group theory and the SBHM and calculate the values for the nonzero components. We found that the off-resonance RSHG intensity data in diatomic wurtzite structures even with the presence of twin boundaries can be modeled using only three independent fitting parameters, namely, the effective bulk, reduced surface, and twin boundary SHG hyperpolarizability. The results show that the SBHM can be used to investigate impurities and surface defects in ZnO as well as their contribution to nonlinear radiation with potential application to frequency conversion in nanoscale optical circuitry.

Third harmonic generation in ZnO semiconductor using the simplified bond hyperpolarizability model

We describe the fourth rank tensor and the related third harmonic generation (THG) light intensity profile in a (0002) wurtzite structure using the simplified bond hyperpolarizability model (SBHM). We show that the resulting THG intensity is isotropic e.g., does not depend on the azimuthal rotation angle of the material. Assuming that THG inside wurtzite structures are dominated solely by bulk dipoles, only one fitting parameter in terms of the effective THG hyperpolarizability is required to generate the Rotational Anisotropy THG (RATHG) experiment result.

Isotropic and Anisotropic Parts for the Susceptibility Tensor Calculated Using Simplified Bond-Hyperpolarizability Model

In this paper we discuss the importance of separating the susceptibility tensor in the isotropic and anisotropic parts, we show how to do that and what is the contribution from each part to the nonlinear polarizability. Specific examples are given for second harmonic generation in the surface of Si(001) and for third harmonic generation in bulk silicon along (001) direction. Our calculations are performed using simplified bond-hyperpolarizability model.

Bulk quadrupole contribution to second harmonic generation from classical oscillator model in silicon.

We predict the frequency-dependent bulk quadrupole contribution to second harmonic generation in silicon quantitatively from the linear susceptibility by means of a generalized classical anharmonic oscillator model and the simplified bond hyperpolarizability model. We show that in single-beam setups the main contribution is found for the silicon (111) surface, and only a minor contribution for the (001) and (011) facets. The dipole contribution obtained from our model is compared to literature values for SiC, AlAs and GaAs to demonstrate the viability of the method.

Nonlinear ellipsometry of Si(111) by second harmonic generation

In this paper we present experimental and simulated data of the second harmonic response for arbitrarily oriented linear input polarization and output polarization on Si(111) surfaces. In contrast to other nonlinear optical ellipsometry experiments (e.g. nonlinear optical null ellipsometry) we azimuthally rotate the sample for additional analysis of the crystal structure. In our study, we used the simplified bond hyperpolarizability model (SBHM) to simulate the observed angular shifts of the nonlinear peaks and the change of symmetry features related to a modification of the beam polarizations. Our findings help to identify the corresponding interface dipolar and bulk quadrupolar SHG sources.

Bulk quadrupole and interface dipole contribution for second harmonic generation in Si(111)

The second harmonic generation (SHG) response was measured for arbitrarily oriented linear input polarization on Si(111) surfaces in rotational anisotropy experiments. We show for the first time, using the simplified bond hyperpolarizability model (SBHM), that the observed angular shifts of the nonlinear peaks and symmetry features—related to changes in the input polarization—help to identify the corresponding interface dipolar and bulk quadrupolar SHG sources, yielding excellent agreement with the experiment. Additionally, we evaluate for the s-in/p-out (sp) and p-in/p-out (pp)-polarization SHG intensities the contributions from the individual Si bonds. Furthermore, a relation between the four parameters arising from SBHM and six coefficients of the phenomenological SHG theory needed to reproduce experimental data is established.

Bulk dipolar contribution to second-harmonic generation in zincblende

We present a comprehensive analysis of second-harmonic generation (SHG) in a diatomic zincblende crystal based on the simplified bond hyperpolarizability model (SBHM) and compare the result with two rotational anisotropy (RA)SHG experiments on a nonvicinal zincblende lattice. We show that bulk dipolar sources alone are sufficient to describe the experimental data by implementing the SBHM previously applied for silicon surfaces to bulk lattices containing two different atoms, e.g., Ga and As. It is shown that a second-rank tensor for a Td point group has only one independent component and this tensor is equivalent to the one derived by the SBHM model using an effective bulk hyperpolarizability αGaAs=(αGa−αAs). In addition, SBHM gives an excellent fit with the RA-SHG experiments of GaAs using a single fitting parameter if Fresnel transmission factors are also incorporated in the model, suggesting strongly that bulk dipolar contribution is the dominant SHG source in a zincblende lattice.

The role of Kleinman Symmetry in the Simplified Bond Hyperpolarizability Model

We have shown previously in [J. Opt. Soc. Am. 31, 526-533 (2014)] that Kleinman symmetry plays an important role when comparing the third rank tensor associated with Second Harmonic Generation (SHG) obtained from the Simplified Bond Hyperpolarizability Model (SBHM) and from group theory (GT) for diamond and zincblende lattice. In this work we show that the third rank tensor derived from the SBHM has inherently the assumption of Kleinman symmetry.

Model of third harmonic generation and electric field induced optical second harmonic using simplified bond-hyperpolarizability model

We report for the first time a comprehensive study of the fourth rank tensor describing third harmonic generation (THG) and electric field induced second harmonic (EFISH) in centrosymmetric material from two different viewpoints: Group Theory (GT) and the Simplified Bond Hyperpolarizability Model (SBHM). We show that the fourth rank tensor related to THG and direct current (DC) EFISH can be reduced to two independent elements whereas SBHM always gives only one, reproducing perfectly well EFISH experimental results in Metal Oxyde Semiconductor (MOS). We argue that it is possible to reduce the fourth rank tensor describing EFISH to a third rank tensor and further deliver a classical explanation of EFISH regarding symmetry breaking where the term containing $r^3$ in the potential immediately leads to second harmonic generation (SHG).

Simplified bond-hyperpolarizability model of second harmonic generation, group theory, and Neumann’s principle

We discuss the susceptibility third-rank tensor for second harmonic and sum-frequency generation, associated with low index surfaces of silicon (Si(001), Si(011), and Si(111)), from two different approaches: the simplified bond-hyperpolarizability model (SBHM) and group theory (GT). We show that the SBHM agrees very well with the experimental results for simple surfaces because the definitions of the bond vectors implicitly include the geometry of the crystal and therefore the symmetry group. However, for more complex surfaces it is shown that one can derive from GT the SBHM tensor, if Kleinman symmetry is allowed.

Simplified bond-hyperpolarizability model of second-harmonic-generation in Si(111): theory and experiment

Second-harmonic-generation (SHG) in centrosymmetric material such as Si(111) is usually understood either from the phenomenology theory or more recently using the simplified bond-hyperpolarizability model (SBHM) [G. D. Powell, J. F. Wang, and D. E. Aspnes, Phys. Rev. B 65, 205320/1 (2002)]. Although SBHM is derived from a classical point of view, it has the advantage over the former that it gives especially for lower symmetry systems a clear physical picture and a more efficient explanation of how nonlinearity is generated. In this paper we provide a step-by-step description of the SBHM in Si(111) for the linear and second harmonic case. We present a SHG experiment of Si(111) and show how it can be modelled by summing up the contribution of the fields produced by the anharmonic motion of the charges along the bonds.