Abstract
The light reflection properties of Ge disk lattices on Si substrates are studied as a function of the disk height and the gap width between disks. The interdisk spacing effect is observed even at such large gap widths as 500 nm. The gap width decrease leads to the appearance of the reflection minimum in the short wavelength region relative to one originated from the magnetic and electric dipole resonances in individual Ge disks, thereby essentially widening the antireflection properties. This minimum becomes significantly deeper at small gap widths. The observed behavior is associated with the features of the resonant fields around closely spaced disks according to numerical simulation data. The result shows the importance of using structures with geometrical parameters providing the short-wavelength minimum. This can essentially enhance their other resonant properties, which are widely used for applications, in particular, based on collective lattice resonances.
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Introduction
The efficiency of optoelectronic devices, such as solar cells and photodetectors, depends on their surface properties related to light reflection and transmission1,2. To reduce reflection, surface texturing and coating with antireflection dielectric films are usually used3,4. Recently, intensive research has been carried out on coatings of metal and/or dielectric particles as an alternative to continuous antireflection films5,6,7,8,9. Their action is based on the excitation of plasmonic10,11 or electromagnetic (EM) resonances12,13,14,15 in metal and dielectric particles, respectively. Compared to continuous films, the capabilities of antireflection coatings made of particles are wider. They can be less dependent on the EM radiation incidence angle5. In addition, they can be more broadband5,9, or, on the contrary, have a greater spectral selectivity6,8,16,17 due to using various resonance effects.
The characteristics of optical resonances are well studied for individual dielectric particles, while their arrays are used for practical applications. An experimental study of metal particle arrays revealed the effects of collective lattice resonances which provide laser generation17,18, biosensing applications19,20 and amplification of light radiation21,22,23. In addition to creating antireflection coatings, arrays of ordered dielectric particles can be used in optical waveguides24,25 and also as metasurfaces and metamaterials23,26. Particular attention is paid to the study of the interaction of resonant modes, excited in individual dielectric particles, with lattice modes. In this case, it is reasonable to expect that the role of lattice modes will increase with a decrease in the interparticle spacing as a result of an increase in the overlap of their fields and the appearance of diffraction effects27,28,37. Despite the absence of narrow minima due to collective lattice resonances, their effect, nevertheless, manifests itself in a greater depth of the efficient broad minimum in the short-wavelength region of our spectra. This agrees to the results of38, which showed that the scattering maxima caused by lattice resonances can be located far from the strongest EM resonances of individual particles, which, in our case, are of the dipole type located in the region of relatively longer wavelengths.
Conclusion
In this study we found that the influence of the close spacing of dielectric disks in their lattices on the reflection spectra is observed even at such large gap widths between the disks as 500 nm. The gap width value effect turns out to be stronger in the short-wavelength region of the measured spectra. According to our numerical simulations, this is due to the participation of quadrupole resonances and stronger resonant fields in the disk area caused by the close proximity of the disks. As a result, at small gap widths, the appearing reflection minimum in the short-wavelength region of the spectra is essentially deeper than the minimum in their long-wavelength region, which originated from magnetic and electric dipole resonances in individual dielectric disks. The stronger gap width value that influences the reflection in the short-wavelength region should be taken into account both in the manufacture of antireflection coatings and sensors which operation is based on the use of local resonant EM fields. As for collective lattice resonances designed for the conditions of the short-wavelength reflection minimum, they can be more efficient in their various applications, compared to those created for the conditions of magnetic and electric dipole resonances.
Methods
Ge disk fabrication
Ge disk arrays were fabricated on Si substrates coated with a 5 nm thick thermal SiO2 film, similar to how it was made in14. After a positive resist PMMA 950 K A4 film deposition on the substrate, it was exposed to a 20 keV electron beam at the aperture of 10 μm using the Raith PIONEER lithography system. Circle-shaped holes were formed by selective dissolving the PMMA films in the methyl isobutyl ketone and isopropyl alcohol (IPA) solution taken as 1:3, respectively, at room temperature for 30 s. The fabricated masks consisted of holes of about 200 nm in diameter arranged in a square lattice. The distance between hole centers was varied from about 250 to 700 nm. Ge films of different thicknesses were deposited onto the prepared samples by the Ge evaporation from a Knudsen cell in an Omicron ultrahigh vacuum system. To obtain Ge disk arrays, excess Ge was removed from the sample surface through the lift-off process in an ultrasonic bath with acetone for 1 min.
Methods of characterization
The shape of Ge disks after their formation and the distance between them were determined using the PIONEER lithography system (in the microscope mode) or a scanning electron microscope (SEM) manufactured by Hitachi (SU 8020). The reflection spectra at a normal light incidence were measured with the microscope-spectrophotometer MSFU-K supplied with a 40 × objective (WD = 0.6 mm, NA = 0.65). This optical setup collects reflected light within the objective aperture angle α = 40.5°. The sample position was shifted about 0.2 mm relative to the objective focal plane for the irradiation of a wide (~ 80 μm) area containing a large number of Ge disks. The reflection spectra for Ge disk arrays were normalized to those of bare substrates.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
The work is supported by the Ministry of Science and Higher Education of the Russian Federation, project # 075-15-2020-797 (13.1902.21.0024). The authors acknowledge the Shared Equipment Centers CKP “NANOSTRUKTURY” of the Rzhanov Institute of Semiconductor Physics SB RAS and CKP “VTAN” (ATRC) of the NSU Physics Department for the instrumental and technological support.
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A.A.S. and D.E.U. fabricated the structures and carried out the experimental measurements. A.V.T., S.A.K. and K.V.A. performed the numerical simulation. All authors discussed the results and analyzed the data. A.A.S. wrote the paper. A.V.L. reviewed the manuscript.
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Shklyaev, A.A., Utkin, D.E., Tsarev, A.V. et al. Interdisk spacing effect on resonant properties of Ge disk lattices on Si substrates. Sci Rep 12, 8123 (2022). https://doi.org/10.1038/s41598-022-11867-5
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DOI: https://doi.org/10.1038/s41598-022-11867-5
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