Nanostructures with steep side wall angles (swa) play a pivotal role in various technological applications. Accurate characterization of these nanostructures is crucial for optimizing their performance. In this study, we propose a far-field detection method based on coherent Fourier scatterometry (CFS) for accurate quantification of steep swa and heights in cliff-like nanostructures. Our approach introduces a parameter termed ‘visibility’, derived from the unique far-field signatures of cliff-like nanostructures. This parameter serves as a quantitative metric for the calibration of swa and heights. The heightened sensitivity of our method is demonstrated, particularly when the incident polarization is perpendicular to the invariant direction of the nanostructure for swa calibration, while both polarization states exhibit sensitivity to height calibration. Furthermore, a comprehensive sensitivity analysis reveals the stable nature of our method, showcasing that even with fluctuations of ±10 nm in the position of the nanostructure, the resulting swa remains stable within a range of ±0.5◦. The exponential variation of the visibility parameter with edge roundness is observed, with fluctuations in edge roundness within 10 nm resulting in swa variations within 1.7◦ for both polarization states. In experimental validations, our results demonstrate reasonable agreement between CFS-derived and AFM measurements. The AFM data for swa (77.99◦ ±1.37◦) and height (148.35 nm ±2.11 nm) are corroborated with CFS-derived value of swa (77.75◦ ±3.61◦, 78.36◦ ±3.89◦) and height (149.42 nm ±1.66 nm, 150.05 nm ±1.04 nm) obtained from calibration curves for TM and TE incident beams, respectively. Overall, our findings underscore CFS as a potential and reliable tool for nanostructure characterization, offering precise measurements that are pivotal for advancing nanotechnology.@en

In the semiconductor industry, the minimumelement size has stepped into nanometer level. To keep the functionality of fabricated nanostructures, there is a huge demand of a technique that can provide non-destructive inspection and allow for in-line or in-situ monitoring during the manufacturing process. Optical scatterometry, which uses the far-field optical scattering information to retrieve the geometrical features of a structure, is a suitable method. As a non-imaging technique, optical scatterometry does not produce images of the illuminated object. Optical scatterometry relies on retrieving nanostructure profile parameters by continuously comparing the given set of predicted signatures expected from a scattering experiment with the actual measured ones. Because we parametrize the structure with a limited set of parameters (i.e. we use prior knowledge of the structure), we can reconstruct the structure with a resolution beyond the diffraction limit. This technique is particularly valuable for characterizing micro- and nano-scale structures that are commonly found in semiconductor devices and integrated circuits ....@en

Optical singularities indicate zero-intensity points in space where parameters, such as phase, polarization, are undetermined. Vortex beams such as the Laguerre–Gaussian modes are characterized by a phase factor e^ilθ, and contain a phase singularity in the middle of its beam. In the case of a transversal optical singularity (TOS), it occurs perpendicular to the propagation, and its phase integral is 2π in nature. Since it emerges within a nano-size range, one expects that TOSs could be sensitive in the light-matter interaction process and could provide a great possibility for accurate determination of certain parameters of nanostructure. Here, we propose to use TOSs generated by a three-wave interference to illuminate a step nanostructure. After interaction with the nanostructure, the TOS is scattered into the far field. The scattering direction can have a relation with the physical parameters of the nanostructure. We show that by monitoring the spatial coordinates of the scattered TOS, its propagation direction can be determined, and as consequence, certain physical parameters of the step nanostructure can be retrieved with high precision.

@en

Accurate determination of the physical parameters of nanostructures from optical far-field scattering is an important and challenging topic in the semiconductor industry. Here, we propose a novel metrology method to determine simultaneously the height and side-wall angle of a step-shaped silicon nanostructure. By employing an optical singular beam into a typical coherent Fourier scatterometry system, both parameters can be retrieved through analyzing the intensity profile of the far-field scattering pattern. The use of singular beam is shown to be sensitive to slight changes of the parameters of the step. By changing the relative direction between the singularity and structure, the height and side-wall angle can both be retrieved with high precision. This new method is robust, simple, and can provide valuable means for micro-and-nano- metrologies.

@en

The sidewall angle (SWA) of a nanostructure exerts influence on the performance of the nanostructure and plays an important role in processing nano-structural chips. It is still a great challenge to determine steep SWAs from far field measurements especially when the SWAs are close to 90°. Here, we propose a far-field detection system to determine steep SWA of a cliff-shape step structure on a silicon substrate by combining a split detector with a scanning method. The far-field radiation field is asymmetric due to the scattering of the step structure, and further numerical analysis demonstrates the reliability of this far-field measurement method. In the simulations, two key variables, i.e. the polarization state and the focus position of the incident laser beam, are considered to explore their impacts. By scanning over the structure laterally and longitudinally with both TE and TM polarizations, polarization effects on the far-field occur. These effects show higher sensitivity to steep SWA variation for TM polarization as compared to TE. Furthermore, with a comprehensive longitudinal scanning analysis for the TM polarization case, a feasible focus interval can be optimized to retrieve the steep SWA. As the proposed method is fast, highly sensitive and easy to implement, it provides a powerful approach to investigate the scattering behavior of nanostructures.

@en

Optical tweezers and associated manipulation tools in the far field have had a major impact on scientific and engineering research by offering precise manipulation of small objects. More recently, the possibility of performing manipulation with surface plasmons has opened opportunities not feasible with conventional far-field optical methods. The use of surface plasmon techniques enables excitation of hotspots much smaller than the free-space wavelength; with this confinement, the plasmonic field facilitates trapping of various nanostructures and materials with higher precision. The successful manipulation of small particles has fostered numerous and expanding applications. In this paper, we review the principles of and developments in plasmonic tweezers techniques, including both nanostructure-assisted platforms and structureless systems. Construction methods and evaluation criteria of the techniques are presented, aiming to provide a guide for the design and optimization of the systems. The most common novel applications of plasmonic tweezers, namely, sorting and transport, sensing and imaging, and especially those in a biological context, are critically discussed. Finally, we consider the future of the development and new potential applications of this technique and discuss prospects for its impact on science.

@en

Nonzero transverse spin density, which describes phenomenon in which the electromagnetic fields of localized light spin in a plane containing its wavenumber vector, has gained enormous interest recently because of its useful applications like spin-direction coupling and routing. In this Letter, using the Richards–Wolf vectorial method for standard full Poincaré beams, we present an analytical model for the high-numerical-aperture focusing system to calculate all components of the electric and magnetic field strength vectors as well as spin density and Poynting vector. The role and contribution of the optical degrees of freedom including ellipticity, handedness, and orientation when the transverse spin density is present, are revealed based on this analytical model. Ellipticity affects the localization and magnitude of the transverse spin density for both transverse and longitudinal components. In contrast, handedness only affects the longitudinal component whereas orientation only affects the transverse component. Furthermore, the energy flux in the focal plane are also studied in detail for the standard full Poincaré beams. These findings may be help in spin-controlled directive coupling and optical tweezers.

@en

Improving the image quality of small particles is a classic problem and especially challenging when the distance between particles are below the optical diffraction limit. We propose a imaging system illuminated with radially polarized light combined with a suitable substrate that contains a thin dielectric layer to demonstrate that the imaging quality can be enhanced. The coupling between the evanescent wave produced in a designed thin dielectric layer, the small particles and the propagating wave forms a mechanism to transfer sub-wavelength information about the particles to the far field. The smallest distinguished distance reaches to 0.634λ, when the imaging system is composed of a high numerical aperture (NA=0.9) lens and the illumination wavelength λ = 632nm, beyond the diffraction limit 0.678λ. The lateral resolution can be further improved by combining the proposed structure with superresolution microscopy techniques.

@en

We show that elongating a tightly focused field in the direction perpendicular to the optical axis is possible. We demonstrate our approach by specially shaping the Pancharatnam–Berry (PB) phase. Moreover, the analytical formulae required to calculate the strength vectors and energy flux of the three-dimensional electromagnetic fields near the focus of an aplanatic optical system are derived using the Richards and Wolf vectorial diffraction methods. Calculations reveal that the transverse enhancement is controllable and depend on the phase index in the PB phase, thereby giving rise to a focus with tunable length and subwavelength width in the focal plane.

@en