1. Introduction

Efficient manipulation of light at the nanoscale using artificial nanostructures is of essence for the miniaturization of optical systems and integrated photonic circuits. In the past decades, plasmonic nanostructures have proven to be a promising candidate due to its capability of manipulating visible light at subwavelength scale by the collective oscillation of conduction electrons inside metals. With their unique optical properties, these nanostructures have demonstrated the potential for various applications such as optoelectronics [1–3], photocatalysis [4, 5], color printing [6], and chemo/bio-sensing [7, 8]. However, the performance of plasmonic nanostructures for practical applications is limited by their intrinsic absorption losses at the optical frequencies [9, 10]. An alternative solution to circumvent this obstacle is to use dielectric nanostructures with high refractive index instead. Unlike plasmonic nanostructures of the electrically dominated resonances, dielectric nanostructures allow for both electric and magnetic resonances. Essentially, the magnetic resonances of dielectric nanostructures arise from the excitation of circular displacement currents induced by the incident electric field which thus leads to much lower dissipative losses [11]. Therefore, dielectric nanostructures can serve as efficient magnetic scatters with strengthened manipulation ability, which can be used in various nanodevices such as photoelectric detectors, color filters and biochemical sensors.

Among dielectric materials, nanostructured silicon (Si) is the most promising building block for nanooptic elements because of its low cost, viable nanofabrication, and compatibility with the complementary metal-oxide-semiconductor (CMOS) processes. Since the first experimental demonstration of spherical Si nanoparticles with strong magnetic properties in the visible spectral range [12], numerous researches have been done on investigating the novel optical properties of Si nanostructures with different spherical sizes [13–15]. In contrast, Si nanocylinders have more degrees of freedom to manipulate the optical properties. For example, the tunable visible light scattering of Si cylindrical nanostructures has been demonstrated by varying the diameter and height of Si nanocylinders [16–18]. However, in previous work, either Si nanospheres prepared by laser ablation or Si nanocylinders prepared by lithographic methods present identical resonant responses with varying the excitation polarizations. Such isotropic optical resonance limits the tunability of light manipulation, thus to the potential applications such as polarization-dependent information encryption. Aiming at solving the issues mentioned above, dielectric meatasurfaces were constructed to realize the polarization-dependent electromagnetic responses through controlling the effective refractive indices along two different dimensions based on tuning the geometries, orientations and distributions of the units [19, 20]. Nevertheless, the polarization-dependent optical property of the dielectric metasurfaces is a global effect, and almost no work revealed the essence of the polarization-dependent response at the single particle resolution. In addition, most Si nanostructures in previous work are amorphous, in which the resonance performance is much weaker than that presented by crystallized Si nanostructures for practical applications [21].

In this work, we aim to investigate the polarization-dependent scattering properties of anisotropic single-crystalline Si nanocylinders. Robust vertical reactive ion etching combined with high-resolution electron-beam lithography process was developed to fabricate the unique Si nanostructures with high-fidelity geometry. Both simulations and experiments demonstrate that the lithographically defined Si nanocylindroids exhibit strong polarization-dependent scattering behavior. Finally, further numerical simulations with various parameters were conducted to clarify the magnetic and electronic resonances in the dielectric nanostructures, as well as the essence of the polarization-dependent optical properties.

2. Fabrication and optical measurement

Figure 1(a) illustrates the fabrication process of single-crystalline silicon nanocylinders. A commercial silicon-on-insulator (SOI) wafer with a 350-nm-thick single-crystalline Si layer on 1-µm silicon oxide (SiO₂) substrate was used. In a typical process, a hydrogen silsesquioxane (HSQ) resist layer was spin-coated on the wafer with a thickness of 30 nm, and then a Raith-150^TWO high-resolution electron-beam lithography (EBL) system was used to define the elliptical patterns, followed with a salty-solution development [22]. A robust cryogenic SF₆/O₂ chemistry process on an inductively coupled plasma reactive ion etching (ICP-RIE) system (Oxford Plasmalab System 100 ICP 180) was used for Si etching with the exposed HSQ patterns as the hard mask. Si nanocylinders with vertical sidewalls were successfully fabricated by optimizing the gas ratio of SF₆/O₂ (30/15 sccm) and substrate low frequency (LF) power (13 W) [23]. The etching would be self-terminated as soon as the oxide layer on SOI wafer was exposed. The HSQ mask on top is unnecessarily removed due to its transparency to the visible light.

 

Fig. 1 Fabrication process and dark-field scattering of the single-crystalline Si nanocylindroids. (a) Fabrication process of the Si nanostructures. (b) The experimental configuration for scattering measurements. (c) SEM images of an array of representative Si cylindroids, in which (l_x, l_y) = (200, 80) nm. (d) Experimental dark-field optical image of the corresponding array in (c) illuminated by unpolarized incident light.

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The morphology of a typical Si nanocylindroid array and its optical results are shown in Figs. 1(c) and 1(d), respectively. The diameters of cylinders along the major and minor axes are 200 and 80 nm, respectively. The inset in Fig. 1(c) displays the 30° tilted SEM images of individual Si nanostructure, showing vertical sidewall. The corresponding dark-field image illuminated by the unpolarized white light in Fig. 1(d) reveals the almost identical orange color of each Si nanocylindroid, indicating the high uniformity of their morphologies and sizes and thus the reliability of the fabrication process.

3. Results and discussion

To investigate the polarization-dependent scattering response, we designed and fabricated a series of Si nanocylinders with different oval cross sections. As shown by the SEM images in Fig. 2(b), with the minor axis of 80 nm fixed, the major axis of Si nanocylinders gradually increases from 80 to 200 nm with an increment of 20 nm. The range of dimensions was designed to ensure the resonance wavelength fell in the visible region [16, 24]. The incidence angle of 48° was employed here for the dark-field scattering measurements.

 

Fig. 2 Experimental results of the polarization response of individual Si nanocylindroids with varied value of l_x from 80 to 200 nm. The parameter l_y was set to 80 nm. (a) Scattering spectra of Si nanocylindroids excited by x-polarized excitation. (b) SEM images of the corresponding Si nanocylinders measured. (c) Scattering spectra of Si nanocylindroids with y-polarized excitation.

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Fig. 3 FDTD simulations of the polarization-dependent scattering spectra of the corresponding Si nanocylinders in Fig. 2 under (a) x-polarized and (b) y-polarized excitations.

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The spectral responses of individual Si nanocylinders for the incident light with polarization parallel to the major axis are shown in Fig. 2(a), and the normalized spectra are vertically offset for clarity. The Si nanocylinder with 80-nm diameter was used as a reference. For the x-polarized excitation, the scattering spectrum (red line) shows a stronger peak at 495 nm and a weaker peak at 460 nm. With the increased l_x, the peak at long wavelength clearly redshifts from 495 to 745 nm and gradually broadens simultaneously. Detailed analysis reveals that this peak results from the spectral overlapping of the magnetic dipole (MD) (peak 1) and electric dipole (ED) (peak 2) modes for the height we adopted, which will be discussed in Fig. 4. The size dependence of optical property of Si nanocylindroids is consistent with that of spherical nanoparticles or circular nanocylinders, as demonstrated in previous researches [13, 17].

 

Fig. 4 Absorption mapping of a typical Si nanocylindroids (l_x = 140 nm, l_y = 80 nm) as a function of height under various incident condition: (a, d) normal incidence, (b, e) oblique incidence (48°), and (c, f) horizontal incidence. Top row shows the simulation results under x-polarized excitation and bottom row displays the corresponding results under y-polarized excitation of the same structures. Two insets in panel (a) illustrate the electric-field distributions in the x-z plane at the marked dots. The slice in mapping denoted by two dashed lines in (b) and (e) are the corresponding spectra of the Si nanocylindroids with 350-nm height used in the experiment. The inset drawings in each figure show the geometry of structure, incident angle, and polarization feature of the light wave.

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In contrast, Si nanocylindroids excited by the y-polarized light show quite different optical responses, as exhibited in Fig. 2(b). The very similar scattering properties of the reference sample were observed for the x and y polarizations. For nanocylindroids, with the fixed diameters in the direction of driving field for y-polarization, the transition of MD (peak 1) and ED (peak 2) modes only slightly redshifted from 495 to 585 nm and 565 nm, respectively. The slight redshifts might be the consequences of increase in volume of structures [16]. Therefore, we can flexibly tune the wavelengths of the intrinsic modes in a wide range by varying the size of Si nanostructures. More importantly, distinct scattering properties and polarization-dependent scatters could be realized by separately varying the dimensions of the Si nanocylindroids in the major and minor axis.

Besides the two dominant resonances (peaks 1 and 2), a third peak (peak 3) was also visible in the high-frequency range. Further analysis (shown in Fig. 4) illustrates that this peak was relevant to the oblique incidence in experimental configuration, which is not the dominant resonance in dielectric structures. Therefore, this peak has not been taken into consideration in the discussion of polarization-dependent scattering for simplicity.

To further demonstrate the polarization and size dependence of Si nanocylindroids, simulations were carried out by three-dimensional finite-difference time-domain (FDTD) method. Figure 3 presents the simulated results of the corresponding Si nanocylinders in Fig. 2. The calculated results agree well with the experimental dark-field observations, clearly showing the dominant resonance peaks. For the x-polarization, the smallest cylinders feature two peaks in the scattering spectrum. As the size along the polarization axis increases, the peak at low energy redshifts to the side of the longer wavelength, accompanied by the splitting into two peaks (peaks 1 and 2) due to the different shift speeds of MD and ED resonances. Distinct optical response was found for the y-polarization in which the redshift range of the dominant MD and ED resonances was far narrower, confirming the anisotropic scattering properties of the Si nanocylindroids. The discrepancy in scattering intensity between experiment and simulation for large cylinders might be caused by the imperfections of structures and the suppressed intensity of the polarized light in experiment.

Due to the overlapped spectra of the MD and ED resonances for the height adopted here, it is hard to distinguish the dominant resonances from the electric and magnetic field distributions at the resonance wavelength. Herein, systematic calculations were carried out by sweeping a series of height parameter of Si nanocylindroids to gain a deeper insight into the resonance modes of peaks 1 and 2. The oblique-incident source in experimental configuration was decomposed into the horizontal and vertical components in simulations in order to reveal different resonance modes. Therefore, three illumination conditions including the normal incidence, oblique incidence (48°) and horizontal incidence were taken into account. Considering the negligible effect of the SiO₂ substrate on the optical properties of the Si structures [25], the substrate was neglected for simplicity in the simulations in this section. Several high-order resonances involved in the spectra result in indistinguishable scattering peaks. For a large particle, optical absorption has a dominant effect relative to scattering in the high-order resonances. Hence, absorption cross sections instead of scattering were used here to identify the resonance peaks of the electric and magnetic dipole/multipole modes, which is essential to the precise determination of the electromagnetic modes in our structures.

In Fig. 4, we chose the typical Si nanocylinders with 140 nm in l_x and 80 nm in l_y as the sample for further study. A series of resonances including the dipole modes and high-order modes could be distinguished from the absorption mapping in Fig. 4(a). In order to understand the MD and ED modes better, the insets in the top-right corner of Fig. 4(a) show the electric field distributions of a 140-nm-height nanocylinder (orange and magenta dots) in the x-z plane. A linear electric field at λ = 500 nm reveals the ED mode, as indicated by the topper inset. Conversely, there is a vortex-like electric field associated with a displacement current loop at λ = 595 nm (bottom inset), indicating the MD mode. The MD and ED resonances show a clear redshift with the increase of height, and the two branches start to cross for higher cylinders. The red shift of ED is a result of radiative damping while the shift of MD is due to the fact that the current loop fits better inside higher structure, as observed in previous work by adjusting the height-to-diameter aspect ratio [17, 26]. This feature remains for the oblique incidence (48°), and the red dashed line corresponding to the height of 350 nm in Fig. 4(b) explains the spectral overlap of MD and ED in experiment. The overlap of the electric and magnetic dipole resonances has been proven to be crucial in directional visible light scattering and metasurfaces [15, 27].

For the horizontal incidence (Fig. 4(c)), the driving field orientation is vertical rather than horizontal. The ED resonance shifts to a shorter wavelength while MD mode occurs at the same wavelength compared with that induced by the horizontal electric field, which agrees well with the observations [16]. For the oblique incidence of 48°, both vertically and horizontally oriented E-components exist in the source. As a consequence, two series of electric resonances were simultaneously excited inside the nanocylinder. The electric resonances at the shorter wavelength merge with the other high-order resonances and cause a constructive interference, as shown in the area emphasized by a black dashed circle of Fig. 4(b). Finally, the interference resonances could result in a composite peak that has been demonstrated as the peak 3 in Fig. 3.

Likewise, the analysis above can hold for the y-polarization. As shown in Fig. 4(d), two branches of MD and ED resonances could be distinguished. A similar redshift trend is observed and the red dashed line in Fig. 4(e) demonstrates the more apparent merging of two dominant resonances in experiment. The intensity of ED reduces with the increase of incidence angle (Fig. 4(e)) and finally disappears for the horizontal incidence (Fig. 4(f)). A similar compound peak is also found for the y-polarization with the oblique incidence, as indicated by the black dashed circle in Fig. 4(e). Based on above analysis, it is reasonable to conclude that for a particular anisotropic structure, the absorption is dramatically different under x- and y-excitations, confirming the polarization-dependent optical properties of our Si nanocylindroids. The as-fabricated anisotropic Si nanostructures provide more flexibility in the design of optical devices and possess potential applications in scenarios with requirement for polarization control. One of the significant applications is polarization-dependent information encryption, as demonstrated by previous plasmonic structure [28,29]. In our current designed system, encoding microscopic images with two color states or the specific images that emerge at particular polarization can be realized by constructing Si nanostructure arrays with various geometries and orrientations.

4. Conclusion

In conclusion, we have presented a systematic investigation on the polarization- and size-dependent visible light scattering of Si nanocylindroids. High-resolution electron-beam lithography in combination with robust vertical dry etching process was utilized to fabricate the Si nanostructures with high-fidelity profile. Both experimental and simulated scattering spectra demonstrate the different scattering responses of Si nanocylindroids for two linearly polarized excitations. Further numerical simulations clarified the MD and ED resonance modes in the spectra and revealed that the two dominant resonances spectrally overlapped for the height adopted here. The unique anisotropic optical property of Si nanocylindroids provides a promising candidate for on-chip control and manipulation of visible light with extra freedom for various applications such as bio-imaging, sensing, high-efficiency metasurfaces and integrated optical devices.