1. Introduction

Recently, the optical properties of metallic, dielectric, and semiconductor nanoparticles have been investigated due to their potential for a controllable manipulation of optical fields at the nanoscale level. Single and multiple particles configurations enable the confinement and enhancement of optical effects [1,2] and the collective resonance response of nanoparticle arrays [3,4]. Resonant dielectric nanoparticles reduce dissipative loss and achieve directional light scattering [5–7]. Moreover, they can be used to design all-dielectric metamaterials for nanophotonic applications [8–9]. Semiconductor elements, due to their naturally optical resonances, have been used to enhance the performance of optoelectronic devices such as optical sources [10], photodetectors [11,12], and thermal emitters [13]. The optical properties are strongly dependent on the shape and size of the nanoparticles, on the interaction between nanoparticles, and on the polarization of the incident light [14,15].

In addition to the optical properties of all-dielectric nanoparticles, photothermal properties have also attracted attention recently [16–18]. The photothermal conversion process not only performs absorption of incident photons but also results in heat generation surrounding nanoparticle arrays. Because metal have a large number of free electrons, the plasmonic resonance in metallic nanoparticles significantly enhances the photothermal effect [18]. Numerous metallic nanostructures have been widely investigated in the wavelength range ranging from 300 nm to 2000nm. Indeed, plasmonic modes in metallic structures offer strong local heat due to the absorption of incident radiation and the transduction into thermal energy, which increase the temperature of nanoparticles and consequently to the surrounding medium.

The alternative approach to generate heat involves resonant modes in dielectrics nanoparticles with high refractive index. In particular, electric as well as magnetic optical resonances provide higher heat generation than that of metallic nanoparticles [19], which is of particular interest for advanced optical devices [8–9,20]. Nevertheless, the resonant photothermal properties of dielectric nanoparticles have not been yet studied, mainly because of the challenge that represents to quantitatively measure the temperature rise, the spatial distribution, and the actual temperature at the surface of nanoparticles. Some methods attempt to determine indirectly the temperature variation with the use of mode coupled theory [20] or with the observation of the power threshold in melting process [21]. This indirect measurement hinders, however, the fundamental physical mechanism for the understanding of energy flux transformation between the nanoparticle and the surrounding vapor/liquid phases at the nanoscale.

Here, we demonstrate theoretically and experimentally a platform for efficient optical nanoheating based on dielectric nanocuboids. The concept of thermal radiation sources is described for silicon nanocuboid illuminated with a polarized plane wave at normal incidence. The resonant conditions convert incident wave into internal energy and allow efficient dissipation of heat to the surroundings. Compared to nanospheres [22–25], the nanocuboids provide additional degrees of freedom to tune the resonant conditions along with a controllable fabrication method. Silicon is selected for its high refractive index in the visible range and its high melting point. Moreover, the thermal sensitivity of silicon to the Raman signal allows for thermometry during optical heating [26,27]. Consequently, we directly determine the temperature change inside silicon nanoparticles by measuring the Raman scattering with a spatial resolution at the nanoscale.

2. Results and discussions on resonant modes

In our calculations, electric vectors are obtained via Green’s tensor method by solving Maxwell's equations [28]. The temperature inside the nanocuboid is then obtained by solving heat equation via Green function method. The permittivity of monocrystalline silicon is from Palik’s handbook [29] and data of thermal properties from Chhabra’s handbook [30]. The nanoparticles in free space are illuminated by a normal incident y-polarized plane wave. All the calculated results are performed for nanoparticles at typical power intensity 1 mW/µm².

For a general case of complex permittivity, we calculate the heat conditions of dielectric nanoparticles illuminated with a plane wave at wavelength of 532 nm specifically, the temperature map inside a nanocuboid as a function of the real Re(ɛ) and imaginary Im(ɛ) parts of permittivity (Fig. 1b). A high real part of the dielectric permittivity determines the resonant modes, whereas the significantly lower imaginary part slightly contributes to the resonant intensity. The temperature map presents distinctive temperature peaks associated to resonant modes, particularly in materials with low imaginary part of the permittivity. Although the imaginary part of the dielectric permittivity is several orders of magnitude lower than that of metals, their absorption properties are effective for photothermal effect. For instance, monocrystalline silicon with complex relative permittivity 17.221 + i 0.373, produces significant temperature spots at the toroidal dipole (TD) resonant mode (Fig. 1b).

 

Fig. 1. Resonant optical nanoheating of dielectric nanocuboids. (a) Schematic of resonant thermal effect for nanoheating by a cuboid nanoparticle. (b) Theoretically calculated temperature map of cuboid nanoparticles as a function of the real and imaginary parts of complex permittivity. The nanocuboid, 150 nm by 150 nm and height 140 nm, is illuminated with a plane wave at wavelength 532 nm with unit power. ED, MD, and TD stand for electric, magnetic, and toroidal dipoles, respectively.

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The multiple resonance modes of silicon nanocuboid with different lateral sizes are marked in the 2D temperature map in Fig. 2(a). For particles with sizes less than 100 nm, the resonant magnetic dipole (MD) mode contributes to the temperature rising throughout the visible range, while the resonant TD mode produce temperature changes in wavelength shorter than green light. Moreover, the resonance modes redshift as lateral size increases. The nature of the resonance modes is distinguished by the distribution of electric and magnetic fields inside the particle [31] and is calculated by Green’s tensor method (Fig. 2b) [28]. Figure 2(c) shows the distribution of electric field vectors (red arrows) at resonant wavelength of 590 nm. Electric field vectors constitute two vortices (green circle) in x-y plane. The rotating vortices in opposite directions produce a magnetic vortex (blue line) in x-z plane. Consequently, the magnetic vortex induces an electric vector (green arrow) in the x direction. This configuration of electric field distribution is called toroidal dipole (TD) mode, which is generated by the oscillating current that flows along the meridians of a torus [31,32]. Toroidal dipole resonance results from the magnetoelectric effect, which is distinct from the magnetic and electric dipoles. Although the charge-current configurations of the TD modes are drastically different from their electric dipole (ED) counterparts, they have virtually identical far-field radiation properties.

 

Fig. 2. Resonant modes in cuboid nanoparticles. The dimensions of nanoparticles are characterized as L×L×H. (a) The calculation of temperature maps from Green tensor method for silicon cuboid nanoparticles with height (H) 140 nm as a function of lateral sizes (L). (b) Four selected temperature spectra of silicon cuboid nanoparticles with varying lateral side lengths. Resonance modes of a cuboid nanoparticle with size of (180×180×140) nm³ are calculated. The distributions of electric vectors give rise to (c) the toroidal dipoles (TD) mode at 590 nm and (d) the magnetic quadrupole (MQ) mode at 522 nm.

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At a wavelength 522 nm, electric field vectors form four primary electric vortices (green vortices in Fig. 2d). The spinning vortices produce four magnetic vectors (blue arrow) that give rise to a magnetic quadrupole (MQ) [31]. The MQ converts a larger amount of energy into heat than that converted by the TD mode at identical heat conditions. The temperature difference between the MQ and TD reaches up to 4 times, which is consistent with the prediction for a spherical silicon nanoparticle in Mie resonance [24]. At these resonant modes, the strong nanoparticles give rise to the heat generation. We also calculated the influence of the height on the photothermal effect (Fig. 3a). Likewise, a significant temperature rise is obtained at the excitation of resonant modes. Remarkably, we found a peak at an incident wavelength of 485 nm for a nanocuboid of height 60 nm, where there is a significant overlap between the MD and TD modes. The field distribution of this hybrid mode presents two spinning electric vortices that induce magnetic vectors (green and blue arrows, respectively in Fig. 3b). The projection of the electric field vectors into x-y plane coincide with the shadow of the TD mode as shown in Fig. 2(c) while the electric field vector projections onto the y-z plane are consistent with the field distribution of MD resonance in Fig. 3(c). The electric vortices (green circle) of MD resonance rotate along a same direction within the cuboid. In contrast to the temperature map of nanocubic with side length (S) (Fig. 3d), nanocuboid provides a degree of freedom to generate the resonant hybrid mode. Indeed, a high ratio L/H enables the coincidence of two kinds of resonant modes. As shown in Fig. 3(a), the higher-order resonant modes approach to the MQ mode for low ratio H/L. This hybrid mode not only leads to remarkable temperature enhancement but also broadens the heat band.

 

Fig. 3. Resonant hybrid modes in nanocuboid as a function of height. (a) Calculated normalized temperature maps for silicon nanocuboids with size of 150 nm. (b) The electric vector distributions of hybrid mode of a cuboid nanoparticle with sizes of (150×150×60) nm³ come from the overlap between the TD and MQ modes at 485 nm. (c) Charge-current distributions give rise to the MD mode in a nanocuboid at 600 nm. (d) Temperature map of cubic nanoparticles with varying side lengths.

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3. Experiment verification

The Si nanocuboids were fabricated with the use of electron-beam lithography (EBL) and reactive ion etching (RIE) on a monocrystalline silicon thin-film on glass substrate (Borofloat 33). Polymethyl methacrylate (PMMA) was used as electron beam resist. After pattern exposition, the resist was developed in methyl isobutyl ketone and isopropanol solution (MIBK:IPA, 1:3). To stop the developing process, we immersed into IPA for 15 s. A 50-nm-thick layer of aluminum (Al) was then deposited with the use of electron beam evaporation and the lift-off was done in acetone to remove the residual PMMA and Al and therefore, to form an Al hard mask for RIE. A fluoride plasma was used to transfer the pattern into the Si layer. Finally, Al hard mask was removed with acid solution.

Crystalline silicon produces a strong Raman signal at room temperature and therefore, Raman thermometry is used to directly measure optical heating [24,27]. Consequently, we used Raman thermometry to measure the temperature increase in our fabricated silicon nanocuboid illuminated under different incident power densities. It is known that the frequency shift of the light scattering spectrum of silicon exhibits a quadratic dependence on a temperature ranging from 5 K to 1400 K due to the lattice vibrations of the anharmonic effects [27]. The Raman frequency shift induced by a temperature increase ($\varDelta$T) within a crystalline silicon nanoparticle is given by:

The direct relation between Raman frequency shift and temperature change provides thermometry at the nanoscale. The resolution for the reconstruction of temperature distribution is determined by the microscopic confocal Raman. The silicon cuboid nanoparticles are illuminated at 532 nm with linearly increasing powers. In Fig. 4(a) we plotted the measured Raman shift induced by optical heating. The linear relation between temperature change $\varDelta$T and Raman wavelength, obtained with the use of Eq. (1), is also plotted. We measured a temperature rise of up to $\varDelta$T ≈ 200 K at a frequency shift of 515 cm⁻¹. As we increased the incident power of the source, the Raman spectrum shifts, which implies a temperature rise (Fig. 4b). The experimental temperature increase is thus linearly proportional to the incident power intensity and agrees with the theoretical calculations (Fig. 4c). In Fig. 4(d), we present the measurement subsequently obtained for a silicon nanocuboid of size 250 nm by 250 nm by 140 nm, precisely, we increase and then decrease the incident power with no significant difference. Additionally, we noted that the temperature rise ($\varDelta$T) is higher for small nanocuboid (i.e. cuboid of 200 nm by 200 nm by 140 nm) than that for a larger nanocuboid (i.e. 250 nm by 250 nm by 140 nm). We attribute the temperature difference of 100 K to the hybridization of MQ mode and high-order modes (Fig. 2a).

 

Fig. 4. Experiment verification of photothermal effect from dielectric nanoparticles. (a) Measured Raman signal for a cuboid nanoparticle at power 2.0 mW. Relation between ΔT and corresponding Raman signal is inserted. (b) Shifting of Raman signal for a cuboid nanoparticle indicates a temperature increasing. The nanoparticle is heated by a 532 nm wavelength laser with increasing powers. (c) Experimental data from a cuboid nanoparticle with sizes of (200 × 200 × 140) nm³. Inset: SEM image of a fabricated cuboid nanoparticle. (d) Nanocuboid is measured without obvious heating retardation for a repeated temperature increasing up to 200 K. Inset: temperature distribution field within a cuboid.

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Raman thermometry is thus a useful tool for the measurements of the temperature changes and does not cause any irreversible changes in the silicon nanoparticle. In turn, crystalline silicon is suitable material for nanoscale thermometry and optical heating due to its high thermal sensitivity and high melting threshold (1685 K). On the opposite side, plasmonic nanoparticles based on noble metals often suffer from the problem of low melting points, approaching the melting points of bulk Au (1336 K) and Ag (1234 K) [16]. As a consequence, the light-induced heating for metal nanostructures reshapes the nanoparticles in few nanoseconds, even at low incident intensities [33,34], which results in a melting process in the regions of plasmonic hotspots owing to enhanced light absorption [35,36].

4. Conclusion

In conclusion, we present a platform for an efficient heating generation based on resonant modes in all-dielectric nanocuboids. We found that the temperature increase is efficiently obtained with dielectric nanoparticles with low imaginary part and high real part of the dielectric permittivity. In contrast to spherical dielectric nanoparticles, cuboid dielectric nanoparticles provide the degrees of freedom to tune the resonant conditions. Indeed, the ratio height to length allows us to generate a superposition of the toroidal and magnetic dipoles, as well as the overlap between the magnetic quadrupole and higher-order modes. We conclude that the efficient photothermal effect is a direction consequence of the mode coupling. In particular, mode coupling in the fabricated silicon nanocuboids efficiently produced heat up to a temperature increase of 300 K with low incident power densities. The thermal-induced Raman shifting is an excellent tool for the measurement of the photothermal effect of our nanoheating platform. This platform would suit the heat rise requirements for several biomedical applications.