Nonlinear ellipsometry of Si(111) by second harmonic generation

Reitböck, Cornelia; Stifter, David; Alejo-Molina, Adalberto; Hardhienata, Hendradi; Hingerl, Kurt

doi:10.1016/j.apsusc.2016.10.131

Cited by 5 publications

(17 citation statements)

References 18 publications

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“…In the experiment, the RA-SHG response of a Si(1 1 1) sample investigated with an incident radiation at a wavelength of 800 nm reflects the underlying bond symmetry. As seen in figure 10(a), the shape of the angular SHG response is six-fold for ps, ss and three-fold for pp, sp polarization combinations, and the pattern could succesfully be explained in the context of the SBHM introduced above, including only surface dipole contributions [82].…”

Section: Semiconductorsmentioning

confidence: 89%

“…In this context, it was shown that the SHG response for the pp polarization combination is a result of interference between bulk and surface nonlinear contributions [83]. With the help of the SBHM, the different contributions originating from dipolar surface and quadrupolar bulk contributions could successfully be separated, also by evaluating measurements at arbitrary polarization orientations of the input raditation, exemplified for a fundamental wavelength of 890 nm in [82,84]. In figure 11, the RA-SHG response from Si(1 1 1) for the pp polarization combination is plotted, for the first time, for several different wavelengths of the fundamental radiation in the range between 750 nm and 1050 nm.…”

Section: Semiconductorsmentioning

confidence: 99%

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Material characterisation with methods of nonlinear optics

Prylepa

Reitböck

Cobet

et al. 2018

J. Phys. D: Appl. Phys.

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In this review, we present nonlinear optical methods, based on the second and third order nonlinear polarization, especially in the context of material characterization tasks outside the area of life sciences-for which these techniques are mostly designed. An overview of application studies reported to date is given, together with a discussion on the advantages and limits of the individual methods. Furthermore, new ways of experimentally combining different optical concepts are introduced, and their potential for characterisation and inspection tasks is evaluated in the context of various case studies, including the investigation of semiconductor surfaces, metals and related corrosion products, as well as of organic materials.

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Section: Semiconductorsmentioning

confidence: 89%

Section: Semiconductorsmentioning

confidence: 99%

Material characterisation with methods of nonlinear optics

Prylepa

Reitböck

Cobet

et al. 2018

J. Phys. D: Appl. Phys.

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“…At the SiO 2 /Si interface and defect sites, the dominant SHG source is the dipolar terms, which can be modeled in the SBHM via [ 17 , 32 , 33 , 34 ]:

whereas the quadrupolar term that dominates in the bulk can written in the following form [ 33 , 35 ]:

where

and

are the third and fourth rank susceptibility tensors, respectively;

and

are the E field of the incident wave and its gradient, respectively;

is the volume;

is the total number of bonds inside the considered unit cells;

is the bond unit vector;

is the dipolar SHG hyperpolarizability that corresponds to

, and

is the quadrupolar SHG hyperpolarizability that is consistent with all the bonds in the bulk term. The gradient of the E field along the direction of the incident wave,

, takes the form

where

is a complex fitting number [ 24 , 25 ]. In the subsequent fitting, we adopted the value fitted out for the Si in the previous work [ 24 , 25 ].…”

Section: Theorymentioning

confidence: 99%

“…The gradient of the E field along the direction of the incident wave,

, takes the form

where

is a complex fitting number [ 24 , 25 ]. In the subsequent fitting, we adopted the value fitted out for the Si in the previous work [ 24 , 25 ]. The E field of the incident wave is determined by the angle of incidence,

, and the polarization,

, (0 for s - and 90 for p -polarization), such that

where

is the field amplitude in the air, and

and

are the Fresnel transmission coefficients for the p - and s -polarization of the interfaces between the air and the SHG source, respectively.…”

Section: Theorymentioning

confidence: 99%

“…However, a model that can analyze the Ani-RSHG spectrum to determine detailed changes in the structure with various dopants remains lacking. Through the introduction of the simplified bond-hyperpolarizability model (SBHM), the number of independent second harmonic generation (SHG) susceptibility coefficients can be reduced by categorizing the bonds [ 24 ], allowing the analysis of the Ani-RSHG spectrum to be excited with the arbitrary polarization [ 24 , 25 ]. Furthermore, by comparing with Fourier analysis, which is conventionally used for the quantitative depiction of Ani-RSHG spectra [ 26 , 27 ], the fitting for the parameters defined on the basis of the SBHM makes the interpretation more intuitive.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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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.

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

et al. 2023

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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−xGex multilayer, which builds on Si(100) diamond structures. The C4v 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−xGex 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−xGex 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−xGex stacked multilayered structures, verifying the potential for characterizing the concentration distribution in stacked multilayered thin films for GAA structures.

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Nonlinear ellipsometry of Si(111) by second harmonic generation

Cited by 5 publications

References 18 publications

Material characterisation with methods of nonlinear optics

Material characterisation with methods of nonlinear optics

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

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

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