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Utilizing focused field as a probe for shape determination of subwavelength structures via coherent Fourier scatterometry
Phys. Rev. Applied 23, 024016 – Published 6 February, 2025
DOI: https://doi.org/10.1103/PhysRevApplied.23.024016
Abstract
Nanopillars are widely used for various applications and require accurate shape characterization to enhance their performance and optimize fabrication processes. In this paper, we employ coherent Fourier scatterometry (CFS) combined with rigorous three-dimensional finite-difference time-domain simulations to accurately determine the shapes of nanopillars with various geometries, including cylindrical, triangular, square, and rectangular shapes. The nanopillars considered here have lateral dimensions () ranging from 100 to 1000 nm. Our methodology utilizes the preferential excitation of the nanostructures by a tightly focused beam and leverages their inherent symmetry to capture far-field signatures that vary periodically with rotation. This approach allows us to distinguish between different nanopillar shapes based on these rotational signatures. Our results demonstrate that the CFS method can reliably characterize nanopillars with lateral dimensions nm, surpassing the conventional diffraction limit of 351 nm. However, the method reaches its fundamental limits for nm, as also confirmed by simulations, where we approach the dipole approximation regime (). This constraint is not observed for rectangular nanopillars, owing to their constant breadth ( nm), which prevents such a regime. Furthermore, our method successfully differentiates nanopillars transitioning from rectangular to square shapes. We also explored the method’s limitations concerning nanostructure height (), finding that triangular and square nanopillars could be characterized accurately for nm and nm, respectively. Furthermore, the method remains robust against shape distortions such as edge roundness. The method is primarily effective in determining the lateral (top-down) shape of nanopillars, it does not resolve longitudinal features. The ability to accurately characterize nanostructure shapes has significant implications in fields such as photonics and biosensing, where geometry critically influences device performance.
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References (52)
- W.-Y. Chiu, T.-W. Huang, Y.-H. Wu, Y.-J. Chan, C.-H. Hou, H.-T. Chien, and C.-C. Chen, A photonic crystal ring resonator formed by SOI nano-rods, Opt. Express 15, 15500 (2007).
- H. Butt, Q. Dai, T. D. Wilkinson, and G. A. Amaratunga, Photonic crystals & metamaterial filters based on 2D arrays of silicon nanopillars, Prog. Electromagn. Res. 113, 179 (2011).
- H. Park and K. B. Crozier, Multispectral imaging with vertical silicon nanowires, Sci. Rep. 3, 2460 (2013).
- C. M. Lieber and Z. L. Wang, Functional nanowires, MRS Bull. 32, 99 (2007).
- C. M. Cobley, S. E. Skrabalak, D. J. Campbell, and Y. Xia, Shape-controlled synthesis of silver nanoparticles for plasmonic and sensing applications, Plasmonics 4, 171 (2009).
- M. Khorasaninejad, N. Abedzadeh, J. Walia, S. Patchett, and S. Saini, Color matrix refractive index sensors using coupled vertical silicon nanowire arrays, Nano Lett. 12, 4228 (2012).
- C. Lee, J. Thillaigovindan, C.-C. Chen, X. T. Chen, Y.-T. Chao, S. Tao, W. Xiang, A. Yu, H. Feng, and G. Lo, nanophotonics based cantilever sensor, Appl. Phys. Lett. 93, 113113 (2008).
- P. Yang, R. Yan, and M. Fardy, Semiconductor nanowire: What’s next? Nano Lett. 10, 1529 (2010).
- R. Kapadia, Z. Fan, K. Takei, and A. Javey, Nanopillar photovoltaics: Materials, processes, and devices, Nano Energy 1, 132 (2012).
- M. Kandziolka, J. J. Charlton, I. I. Kravchenko, J. A. Bradshaw, I. A. Merkulov, M. J. Sepaniak, and N. V. Lavrik, Silicon nanopillars as a platform for enhanced fluorescence analysis, Anal. Chem. 85, 9031 (2013).
- B. R. Murthy, J. Ng, E. Selamat, N. Balasubramanian, and W. Liu, Silicon nanopillar substrates for enhancing signal intensity in DNA microarrays, Biosens. Bioelectron. 24, 723 (2008).
- A. C. Ford, J. C. Ho, Y.-L. Chueh, Y.-C. Tseng, Z. Fan, J. Guo, J. Bokor, and A. Javey, Diameter-dependent electron mobility of nanowires, Nano Lett. 9, 360 (2009).
- D. Ma, C. Lee, F. Au, S. Tong, and S. Lee, Small-diameter silicon nanowire surfaces, Science 299, 1874 (2003).
- B. Tian, P. Xie, T. J. Kempa, D. C. Bell, and C. M. Lieber, Single-crystalline kinked semiconductor nanowire superstructures, Nat. Nanotechnol. 4, 824 (2009).
- S. M. Wells, I. A. Merkulov, I. I. Kravchenko, N. V. Lavrik, and M. J. Sepaniak, Silicon nanopillars for field-enhanced surface spectroscopy, ACS Nano 6, 2948 (2012).
- M. Rippa, R. Castagna, S. Brandi, G. Fusco, M. Monini, D. Chen, J. Zhou, J. Zyss, and L. Petti, Octupolar plasmonic nanosensor based on ordered arrays of triangular nanopillars for selective rotavirus detection, ACS Appl. Nano Mater. 3, 4837 (2020).
- V. Fuertes, N. Grégoire, P. Labranche, S. Gagnon, N. Hamada, B. Bellanger, Y. Ledemi, S. LaRochelle, and Y. Messaddeq, Cubic-shaped and rod-shaped YPO4 nanocrystal-doped optical fibers: Implications for next generation of fiber lasers, ACS Appl. Nano Mater. 6, 4337 (2023).
- O. Ergen, D. J. Ruebusch, H. Fang, A. A. Rathore, R. Kapadia, Z. Fan, K. Takei, A. Jamshidi, M. Wu, and A. Javey, Shape-controlled synthesis of single-crystalline nanopillar arrays by template-assisted vapor-liquid-solid process, J. Am. Chem. Soc. 132, 13972 (2010).
- R. Elbersen, W. Vijselaar, R. M. Tiggelaar, H. Gardeniers, and J. Huskens, Fabrication and doping methods for silicon nano-and micropillar arrays for solar-cell applications: A review, Adv. Mater. 27, 6781 (2015).
- L. Golobokova, Y. V. Nastaushev, F. Dultsev, D. Gulyaev, A. Talochkin, and A. Latyshev, Fabrication and optical properties of silicon nanopillars, J. Phys.: Conf. Ser. 541, 012074 (2014).
- S. Kodambaka, J. Tersoff, M. Reuter, and F. Ross, Germanium nanowire growth below the eutectic temperature, Science 316, 729 (2007).
- N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. Vladar, Metrology for the next generation of semiconductor devices, Nat. Electron. 1, 532 (2018).
- V. Rodríguez-Fajardo and A. Forbes, Measurement of nanometric heights by modal decomposition, Phys. Rev. Appl. 18, 064068 (2022).
- A. Paul, J. Rafighdoost, X. Dou, and S. F. Pereira, Investigation of coherent Fourier scatterometry as a calibration tool for determination of steep side wall angle and height of a nanostructure, Meas. Sci. Technol. 35, 075202 (2024).
- A. Villegas, M. H. Passos, S. F. Pereira, and J. P. Torres, Optimal parameter estimation of shaped phase objects, Phys. Rev. A 109, 032617 (2024).
- G. Freychet, D. Kumar, R. J. Pandolfi, P. Naulleau, I. Cordova, P. Ercius, C. Song, J. Strzalka, and A. Hexemer, Estimation of line cross sections using critical-dimension grazing-incidence small-angle x-ray scattering, Phys. Rev. Appl. 12, 044026 (2019).
- A. Vella, S. T. Head, T. G. Brown, and M. A. Alonso, Simultaneous measurement of multiple parameters of a subwavelength structure based on the weak value formalism, Phys. Rev. Lett. 122, 123603 (2019).
- N. Kumar, P. Petrik, G. K. Ramanandan, O. El Gawhary, S. Roy, S. F. Pereira, W. M. Coene, and H. P. Urbach, Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry, Opt. Express 22, 24678 (2014).
- P. Van Der Walle, E. Kramer, R. Ebeling, H. Spruit, P. Alkemade, S. Pereira, J. Van Der Donck, and D. Maas, in Metrology, Inspection, and Process Control for Microlithography XXXII (SPIE, San Jose, California, United States, 2018), Vol. 10585, p. 570.
- S. Krämer, K. Kroth, T. Sure, and P. J. Klar, in Optical Measurement Systems for Industrial Inspection XIII (SPIE, Munich, Germany, 2023), Vol. 12618, p. 583.
- T. Käseberg, J. Grundmann, T. Siefke, P. Klapetek, M. Valtr, S. Kroker, and B. Bodermann, Mueller matrix ellipsometric approach on the imaging of sub-wavelength nanostructures, Front. Phys. 9, 814559 (2022).
- C. G. Frase, E. Buhr, and K. Dirscherl, CD characterization of nanostructures in SEM metrology, Meas. Sci. Technol. 18, 510 (2007).
- D. Hussain, K. Ahmad, J. Song, and H. Xie, Advances in the atomic force microscopy for critical dimension metrology, Meas. Sci. Technol. 28, 012001 (2016).
- P. Bazylewski, S. Ezugwu, and G. Fanchini, A review of three-dimensional scanning near-field optical microscopy (3D-SNOM) and its applications in nanoscale light management, Appl. Sci. 7, 973 (2017).
- M. H. Madsen and P.-E. Hansen, Scatterometry–fast and robust measurements of nano-textured surfaces, Surf. Topogr.: Metrol. Prop.. 4, 023003 (2016).
- R. J. Kline, D. F. Sunday, D. Windover, and B. D. Bunday, X-ray scattering critical dimensional metrology using a compact x-ray source for next generation semiconductor devices, J. Micro Nanolithogr. MEMS MOEMS 16, 014001 (2017).
- S. Liu, W. Du, X. Chen, H. Jiang, and C. Zhang, Mueller matrix imaging ellipsometry for nanostructure metrology, Opt. Express 23, 17316 (2015).
- C. Wang, X. Chen, C. Chen, S. Sheng, L. Song, H. Gu, H. Jiang, C. Zhang, and S. Liu, Reconstruction of finite deep sub-wavelength nanostructures by Mueller-matrix scattered-field microscopy, Opt. Express 29, 32158 (2021).
- S. Roy, A. C. Assafrao, S. F. Pereira, and H. P. Urbach, Coherent Fourier scatterometry for detection of nanometer-sized particles on a planar substrate surface, Opt. Express 22, 13250 (2014).
- A. Paul, D. Kolenov, T. Scholte, and S. F. Pereira, Coherent Fourier scatterometry: A holistic tool for inspection of isolated particles or defects on gratings, Appl. Opt. 62, 7589 (2023).
- J. J. Stamnes, Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves (Routledge, New York, USA, 2017).
- J. A. Stratton, Electromagnetic Theory (John Wiley & Sons, Hoboken, New Jersey, USA, 2007), Vol. 33.
- B. Richards and E. Wolf, Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system, Proc. R. Soc. London, A 253, 358 (1959).
- R. Dorn, S. Quabis, and G. Leuchs, The focus of light–linear polarization breaks the rotational symmetry of the focal spot, J. Mod. Opt. 50, 1917 (2003).
- A. A. Maradudin, Light Scattering and Nanoscale Surface Roughness (Springer Science & Business Media, New York, USA, 2007).
- P. Bobbert and J. Vlieger, Light scattering by a sphere on a substrate, Physica A 137, 209 (1986).
- G. W. Videen, W. L. Wolfe, and W. S. Bickel, Light scattering Mueller matrix for a surface contaminated by a single particle in the Rayleigh limit, Opt. Eng. 31, 341 (1992).
- R. Schmehl, B. M. Nebeker, and E. D. Hirleman, Discrete-dipole approximation for scattering by features on surfaces by means of a two-dimensional fast Fourier transform technique, J. Opt. Soc. Am. A 14, 3026 (1997).
- Ansys Lumerical FDTD solutions. Available from https://www.lumerical.com/.
- L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, New York, USA, 2012).
- İ. R. Çapoğlu, J. D. Rogers, A. Taflove, and V. Backman, The microscope in a computer: Image synthesis from three-dimensional full-vector solutions of Maxwell’s equations at the nanometer scale, Prog. Opt. 57, 1 (2012).
- G. Videen, M. G. Turner, V. J. Iafelice, W. S. Bickel, and W. L. Wolfe, Scattering from a small sphere near a surface, JOSA A 10, 118 (1993).