1. Introduction

A structure that is sufficiently smaller than the wavelength of light can exhibit a unique optical response that does not exist in bulk material. Artificial structures that show such a response are called metamaterials, and each structure that makes up the metamaterial is called a unit cell. The effective permittivity and permeability of the metamaterial can be controlled by designing the structure and arrangement of the unit cells, and as a result, it is possible to realize new materials that can control light as desired [1–5]. A typical example of artificial structures that compose metamaterials is a split-ring resonator (SRR), which strongly absorbs and scatters light at the resonant frequency [6–13]. However, when operating SRRs in the visible region, the conductor loss increases as the operating frequency becomes higher, and then the performance of the SRRs deteriorates.

In the high-frequency region, it has been proposed to construct metamaterials with high-permittivity dielectric spheres [14–16]. Figure 1 shows the resonant modes of the electromagnetic field in a dielectric sphere, which is explained by Mie theory [17]. In the lowest-order resonance mode, an electric field swirls in a dielectric sphere, and a magnetic field is generated through the center of the vortex (Fig. 1(a)). As a result, a magnetic dipole is formed in the axial direction of the vortex and causes a resonance phenomenon with the incident light, which is referred to as a magnetic dipole (MD) resonance. It has been reported that when silicon is chosen as the material of dielectric spheres with diameters of 100 to 200 nm, a magnetic field response occurs in the visible region [18]. There is another resonant mode, where the magnetic field swirls in the dielectric sphere and forms an electric dipole in the axial direction of the vortex, which is called an electric dipole (ED) resonance (Fig. 1(b)).

 

Fig. 1. Schematic diagrams of the (a) MD resonance and (b) ED resonance in dielectric spheres.

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The scattered light in the visible region is expected to be applicable to color filtering elements for painting, imaging, and display devices. Evlyukhin et al. experimentally demonstrated the magnetic dipole response in the visible range using laser induced transfer method for the first time [19]. Kuznetsov et al. also fabricated silicon nanospheres with diameters ranging from 100 to 200 nm using a laser ablation method and reported that the silicon nanospheres scattered light at specific wavelengths according to their diameter [20]. Zywietz et al. reported laser printing technique for fabrication of single silicon nanospheres with controllable positioning [21,22]. In addition to laser-assisted methods described above, lithography, chemical methods, dewetting, and combinations of these techniques have been proposed [23]. Laser-assisted methods have succeeded in producing a silicon sphere of an arbitrary size at an arbitrary location. However, it requires transparency of the collector substrate to the laser and cannot be applied to a device using an opaque semiconductor substrate. Lithography allows to fabricate two-dimensional nanostructures with desired sizes at desired positions on semiconductor substrates, while it is difficult to form three-dimensional nanospheres. Therefore, it is necessary to study a fabrication method of nanospheres using lithography.

Some researchers have reported hydrogen annealing as a method to process the shape of silicon surfaces [24–30]. Hydrogen annealing causes the self-diffusion of silicon atoms near the surface and smooths rough surfaces [31]. Hydrogen annealing also transforms rectangular cross-sectional structures into round cross-sectional structures [32]. Our group has developed a dedicated hydrogen annealing machine for microelectromechanical systems (MEMS) and silicon nanophotonic devices and has reported the fabrication method of X-ray mirrors and microatomic clocks with the hydrogen annealing method [33–35].

In this study, we propose a fabrication method of silicon nanospheres with diameters of 100-200 nm, which have a strong magnetic field response in the visible region, at arbitrary locations and in arbitrary sizes by using electron-beam (EB) lithography and hydrogen annealing. The smallest nanosphere fabricated by hydrogen annealing was reported to have a radius of 1 µm [32]; however, this size is too large for an optical cavity at visible wavelengths. In this paper, we succeeded in fabricating nanospheres of one-tenth its size. Additionally, we confirmed that scattered light was emitted from a single silicon nanosphere and was colored depending on the size of the nanosphere. It is worth mentioning that the hydrogen annealing method can be applied to nanostructures made by not only EB lithography but also deep-UV photolithography, which means large-scale devices can be produced by replacing the EB lithography step to deep-UV photolithography.

2. Optical design of silicon nanospheres

To confirm the electromagnetic field response of silicon nanospheres, we conducted simulations with the finite-difference time-domain (FDTD) method. FullWAVE provided by Synopsys, Inc. was used as the simulation software. The simulation model was set as shown in Fig. 2(a). A silicon sphere with a diameter of 100 nm was floated in free space with a refractive index of 1.0, and plane wave was incident from the −z direction. The incident light was absorbed in the light source region surrounding the sphere, and only the scattered light was transmitted outside the region. Then, the intensity of the scattered light was measured on the monitor surrounding the sphere. Note that the incident light was removed before reaching the monitor; thus, only the scattered light component was measured on the monitors. No reflection was set at the boundary of the computational domain. A grid of 5 nm was used to divide the computational domain.

 

Fig. 2. (a) Schematic diagram of the simulation model. (b) Calculated scattering spectrum of a silicon nanosphere with a diameter of 100 nm. (c) Electric and (d) magnetic fields in the nanosphere at the MD resonance (λ = 470 nm). Amplitudes of the magnetic field in the x-y cross section through the center of the sphere at (e) λ = 470 nm and at (f) λ = 700 nm.

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Figure 2(b) shows the calculated intensity change in the scattered light when the incident light wavelength, λ, was changed from 400 nm to 750 nm in 10 nm increments. At a wavelength of approximately 470 nm, the lowest-order resonance mode (MD resonance) was triggered. At a wavelength of approximately 420 nm, another resonant mode (ED resonance) was triggered.

Figure 2(c) shows the electric field vectors in the x-z cross section through the center of the sphere when the incident wavelength was 470 nm. The electric field vectors swirled around the center of the sphere. Figure 2(d) shows the magnetic field vectors in the x-y cross section through the center of the sphere when the incident wavelength was 470 nm. A magnetic field formed a dipole through the center of the sphere. These results correspond to the electromagnetic field at the MD resonance, as described in Mie theory [17].

Figures 2(e) and 2(f) show the amplitude of the y-axis component of the magnetic field in the x-y cross section through the center of the sphere at the MD-resonant wavelength (λ = 470 nm) and nonresonant wavelength (λ = 700 nm), respectively. At the MD resonance, the magnetic field inside the sphere increased 30 times as large as the surrounding area. On the other hand, at nonresonance, no magnetic field enhancement appeared. These results indicate that silicon nanospheres produce high field enhancement with the MD-resonant wavelength.

3. Fabrication

Figure 3 shows the fabrication process of silicon nanospheres using EB lithography and hydrogen annealing. A silicon-on-quartz (SOQ) substrate with a 100-nm-thick silicon layer was used. The SOQ substrate was provided by Canon Inc. and made by its epitaxial layer transfer method. First, EB resist (ZEP520A, ZEON Corporation) and water-soluble conductive polymer were spin-coated on the SOQ substrate. The thickness of the EB resist was adjusted to approximately 200 nm by diluting it with anisole so that the EB resist pattern would not collapse. Second, the EB resist was patterned using an EB lithography system (JBX5000LSS, JEOL). The acceleration voltage was 50 kV, and the current value was 10 pA. Third, the silicon layer was etched by fast atom beam etching [36,37]. The flow rate of SF₆ gas was 12 sccm, the voltage was 2.0 kV, the current was 20 mA, and the etching time was 8 min. Cylindrical columns made of silicon were formed on the quartz layer. Fourth, the quartz layer beneath the silicon columns was partly underetched by soaking the substrate in hydrofluoric acid (HF) diluted 50 times with pure water for 6 min. This step is necessary to bring the final structure closer to a perfect sphere. Finally, the substrate was hydrogen-annealed using a dedicated hydrogen annealing machine built in our laboratory [33]. The preannealing temperature and time were set as 400°C and 10 min, respectively. After hydrogen gas was introduced, the retention temperature, time, pressure, and flow rate were set as 940°C and 40 min, 50 kPa, and 0.3 L/min, respectively. The silicon columns transformed into silicon nanospheres due to the self-diffusion of silicon atoms.

 

Fig. 3. Fabrication process of the silicon nanospheres.

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Figures 4(a), 4(b) and 4(c) show the scanning electron microscopy (SEM) images of silicon columns with different diameters before hydrogen annealing. The silicon columns were supported by quartz posts made by the underetching process. Figures 4(d), 4(e) and 4(f) show the SEM images of the silicon nanospheres after hydrogen annealing, which correspond to Figs. 4(a), 4(b) and 4(c), respectively. The diameters of the nanospheres shown in Fig. 4(d), 4(e) and 4(f) were 114 nm, 158 nm and 200 nm, respectively. The heights of the nanospheres shown in Figs. 4(d), 4(e) and 4(f) were 130 nm, 143 nm and 155 nm, respectively. These results indicate that the silicon columns could be transformed into nanospheres while the sphericities varied. The nanosphere shown in Fig. 4(d) was shaped like a vertically long spheroid, while the nanospheres shown in Figs. 4(e) and 4(f) were shaped like a horizontally long spheroid. One reason for the difference in the shape between the nanospheres is because the aspect ratios of the height to the diameter of silicon columns were different between the silicon columns. A large aspect ratio leads to a vertically long shape, while a small aspect ratio leads to a horizontally long shape. Another reason is that the boundary between the nanosphere and quartz post remains flat. If the diameter of the silicon column is much larger than the underetch length, then the boundary where self-diffusion does not occur disturbs the spheroidization, and then the structure becomes horizontally long.

 

Fig. 4. SEM images of silicon columns with diameters of (a) 114, (b) 158, (c) and 200 nm. Silicon nanospheres after hydrogen annealing of the columns with diameters of (d) 114, (e) 158, (f) and 200 nm. (g) Periodically arranged silicon nanospheres with a period of 800 nm.

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Figure 4(g) shows the SEM image of the periodically aligned silicon nanospheres. The period of the nanospheres was 800 nm, which was consistent with the design value. The SEM images show that all silicon columns on the substrate were transformed into nanospheres at once by hydrogen annealing. These results indicate that the proposed fabrication method enables the fabrication of silicon nanospheres at arbitrary positions with arbitrary periods.

4. Measurement of the scattered light

We observed scattered light from the silicon nanospheres under a dark-field illumination microscope. First, to distinguish the scattered light from each nanosphere clearly, we fabricated nanospheres arranged at a period of 3 µm by changing the diameter of the nanosphere. Figures 5(a), 5(b) and 5(c) show the observation results from nanospheres with diameters of 114, 158 and 200 nm, where the nanospheres are colored blue, green and red, respectively. This result indicates that a resonance occurs, that the field inside the nanosphere is enhanced in the visible region, and that the resonant wavelength shifts to longer wavelengths as the diameter increases. Note that the upper left part of all the structures appeared to be blue due to the lens aberration of the measurement system.

 

Fig. 5. Dark-field illumination microscopic images of scattered light from silicon nanospheres with diameters of (a) 114, (b) 158, (c) and (c) 200 nm. (d) Periodically arranged silicon nanospheres with a period of 500 nm.

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Next, to prove that the observed scattered light is not due to the guided-mode resonance caused by the periodicity of the structure but the resonance of each unit cell, we fabricated nanospheres arranged at a period of 500 nm where the diameter of the nanosphere differs from the adjacent structure on either side. Figure 5(d) shows the observation result of the scattered light under a dark-field illumination microscope. If the scattered light is due to the periodicity of the structure, then it comes from not each nanosphere but the entire structure. However, we could observe that each nanosphere emits scattered light corresponding to its size, where the adjacent structures emit different colors of scattered light from each other. Therefore, it was confirmed that the observed light was scattered light from each nanosphere, not due to the periodicity.

To investigate in more detail, we measured the spectra of the scattered light from each nanosphere shown in Figs. 5(a), 5(b) and 5(c) and compared them with the corresponding spectra calculated in the simulation. The measured spectra were obtained from a spectroscope (Ocean Optics, HR2000) through an optical fiber connected to a dark-field illumination microscope. The core diameter and total length of the optical fiber were 400 µm and 2 m, respectively. Only scattered light emitted from a single nanosphere was measured by adjusting the field of view of the dark-field illumination microscope. The calculated spectra were obtained using the FDTD simulation method, as shown in Fig. 2(a), where the models were replaced from perfect spheres to spheroids. The heights and diameters of the spheroids were the same as those of the spheroids shown in Figs. 4(d), 4(e) and 4(f). Note that the spheroids were considered to be floated in free space; therefore, the effect of the substrate was not considered in this simulation as well as the simulations performed in Section 2 because it was difficult to build a simulation model that includes the substrate and measures only scattered light.

Figures 6(a), 6(b) and 6(c) show the measured and calculated spectra obtained from nanospheres corresponding to Figs. 4(d), 4(e) and 4(f), respectively. Both the measured and calculated spectra show that the peak position of the spectra redshifted as the diameter of the nanosphere increased, which agrees with the color change in the nanospheres along the diameter. However, there are also differences between the measured and calculated spectra. For example, some peaks observed in the calculated spectra were weakened in the measured spectra. Additionally, compared to the calculated spectra, the measured spectra were blueshifted. A possible reason for this shift is because the actual structures were not spheroids as modeled in the simulations but were polyhedrons composed of crystalline surfaces. Another reason may be structural asymmetry due to fabrication errors. Moreover, the substrate was not considered in the simulations, which also affects the shape of the spectra [19,20]. These factors may have caused the differences in the measured and calculated spectra. Further development is required to design nanospheres with arbitrary spectral shapes as well as at arbitrary locations.

 

Fig. 6. Measured and calculated scattering spectra of silicon nanospheres with diameters of (a) 114, (b) 158, (c) and 200 nm.

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5. Conclusions

In this paper, we proposed a fabrication method for silicon nanospheres at arbitrary locations using EB lithography and hydrogen annealing method. It was confirmed by FDTD simulations that silicon nanospheres showed a strong magnetic field response. Then, silicon columns were fabricated on SOQ substrates by EB lithography and were transformed into nanospheres by hydrogen annealing. Fabricated nanospheres had diameters of 114, 158 and 200 nm and were arranged with a designed period; this means that silicon nanospheres can be formed in the desired size and location. The light scattered from the fabricated nanospheres was observed by dark-field illumination microscopy. Silicon nanospheres with diameters of 114, 158 and 200 nm emitted scattered light in the visible region and were colored blue, green and red, respectively. It was also confirmed that the scattered light was not due to the periodicity of the structure but was emitted from each single nanosphere. The spectra of the scattered light were measured by a spectrometer and were compared with the calculated spectra obtained in the simulation. The peak position of both the measured and calculated spectra redshifted as the diameter of the nanosphere increased, which was consistent with the observed color of the scattered light.