High sensitivity bolometers based on metal nanoantenna dimers with a nanogap filled with vanadium dioxide

One critical factor for bolometer sensitivity is efficient electromagnetic heating of thermistor materials, which plasmonic nanogap structures can provide through the electric field enhancement. In this report, using finite element method simulation, electromagnetic heating of nanorod dimer antennas with a nanogap filled with vanadium dioxide (VO2) was studied for long-wavelength infrared detection. Because VO2 is a thermistor material, the electrical resistance between the two dimer ends depends on the dimer’s temperature. The simulation results show that, due to the high heating ability of the nanogap, the temperature rise is several times higher than expected from the areal coverage. This excellent performance is observed over various nanorod lengths and gap widths, ensuring wavelength tunability and ultrafast operating speed, thereby making the dimer structures a promising candidate for high sensitivity bolometers.

www.nature.com/scientificreports/ about 18 times at the resonance, implying a high sensitivity of the end-to-end resistance to the LWIR irradiation. We also investigated the absorption and the field enhancement in the VO 2 nanogap to reveal the mechanism of the excellent bolometer performance and demonstrated resonance tuning and ultrafast pulse detection by changing the nanorod length and the gap width.

Results and discussion
We start this section by a brief explanation on the structure and the conditions we studied. Assuming high density array applications, a unit cell with a periodicity of 7 μm × 7 μm was considered. Figure 1 illustrates the unit cell for a gold dimer structure where the gap of 10 nm-width is filled with VO 2 . The length of the dimer was set to have a resonance in the LWIR range. In order to focus on the performance assessment of the dimer structure itself, we simplified supporting structures with a Si 3 N 4 membrane and two Si pillars. The Si pillars thermally and electrically connect the dimer structure ( Fig. S1 for the detailed pillar geometry) to a Si substrate which acts as a heat reservoir maintained at the room temperature, 293.15 K. Readout circuits can be formed on/inside the Si substrate but were omitted from this simulation for the sake of brevity. We also assumed convective heat dissipation with a typical transfer coefficient of 5 W/(m 2 K) for ambient air 22 . Setting the initial temperature at 293.15 K, we conducted electromagnetic heating simulation using a commercial finite element method software (COMSOL Multiphysics 5.5) within the LWIR range from 8 to 14 μm with a step size of 0.05 μm. Incident light was assumed to be a x-polarized plane wave propagating in the − z direction with a power of 5 nW/μm 2 (245 nW per unit cell). Periodic conditions were applied to the unit cell lateral boundaries. After obtaining the average temperatures of the gap and the rods in the simulation, the dimer resistance between the two ends was calculated as the sum of the three resistors shown in the circuit diagram in Fig. 1 exploiting the temperature dependent electrical conductivities of gold and VO 2 . Details of the material properties used in the calculation are presented in the "Methods" section.
To evaluate the bolometric response of the dimer, we calculated the temperature increase and the corresponding resistance when the incident LWIR power is 5 nW/μm 2 . As shown in Fig. 2, the VO 2 gap temperature increases by more than 4 K across the whole LWIR range. Especially, at the resonance wavelength of 9.05 μm, the temperature increases by nearly 14 K. Advantage of the dimer structure becomes evident when compared with a suspended perfect absorbing film which can be regarded as a simplified ideal of conventional optical cavity based bolometers 3,21 . For the comparison, we simulated temperature increase of a 50 nm-thick VO 2 film with the same unit cell dimension assuming all the incident energy is converted to heat in the film. The thermal time constant, or the ratio of the heat capacity of the suspended structure to the thermal conductance of the supporting pillars, was set to 38.2 μs which is equivalent to that of the dimer structure ( Fig. S2 for the simulation details). The simulation result for the perfect absorber is displayed as the red dashed line in Fig. 2 indicating that the VO 2 film temperature increases by only 0.77 K. Thus, the temperature increase of the dimer's VO 2 gap is at least 5 times larger than that of the perfect absorber throughout the LWIR range and reaches about 18 times at the resonance.
The dimer's normalized resistance shown as the blue solid line in Fig. 2 verifies the measurable resistance decrease. At the resonance, the dimer's resistance drops almost by 40%. This is because, although the width is only 10 nm, the VO 2 nanogap determines most of the total resistance. The resistance of the VO 2 nanogap drops as the temperature rises while the resistance of the gold parts constitutes a negligible portion. In contrast, the perfect absorber's resistance was calculated to decrease by only about 3%. Schematics of the unit cell structure under study. VO 2 (red) fills the gap between the two gold rods (yellow). The dimer is supported by a Si 3 N 4 layer (gray) and connected to a Si substrate by two Si pillars (dark blue). The substrate is assumed to be a heat reservoir maintained at 293.15 K. Red and blue arrows represent the incident direction and the polarization of LWIR, respectively. www.nature.com/scientificreports/ We investigated electromagnetic absorption of the dimer in the LWIR range to explain the efficient electromagnetic heating described above. Spectra of the total absorption and the absorption in the nanogap are displayed as the solid and dashed red lines in Fig. 3. Although the areal coverage of the structure is only 1.6% (= (4.01 μm × 200 nm)/(7 μm) 2 ), it absorbs 57% at the resonance and more than 16% over the whole LWIR range. In this absorption, the VO 2 nanogap makes a significant contribution. At the resonance, 13% absorption occurs in the nanogap whose areal coverage is only 0.0041% (= (10 nm × 200 nm)/(7 μm) 2 ). The contribution of the nanogap is more evident in the red side of the resonance, where the extinction coefficient of VO 2 increases, leading to a rebound of the total absorption. This enormous absorption in the VO 2 nanogap is attributed to the electric field enhancement by the capacitive charging of the nanogap structure 23 . The intensity enhancement, that is the electric field intensity in the nanogap normalized by the incident intensity, is plotted as the blue dashed line in Fig. 3. At the resonance, the field intensity is enhanced by five orders of magnitude. The cross-sectional electric field distribution at the resonance (inset in Fig. 3) clearly displays that the enhancement is concentrated at the vicinity of the gap where charges are accumulated.
We also studied wavelength tunability of the dimer structure which is important for performance optimization. Temperature changes for various nanorod lengths and gap widths are plotted in Fig. 4. As expected from the hybridization of plasmon modes 24 , longer nanorod lengths and narrower gap widths leads to redshift of the resonance. Since the heating efficiency is maintained about the same level, both the geometrical parameters can be exploited for wavelength tuning.
The high heating efficiency even for the gap width of 2 nm suggests that a substantial amount of absorption still occurs in the more compact VO 2 volume. Indeed, the 2 nm-gap absorbs 7.3% at the resonance, implying  www.nature.com/scientificreports/ that absorption in nanogap decreases only by less than the half while gap width is reduced to one fifth compared to the case of the 10 nm-gap. This absorption concentration into the thermistor region can be especially favorable for pulse detection. To demonstrate this point clearly, we studied time evolution of a VO 2 nanogap temperature and its width dependence assuming that resonant LWIR with a pulse energy of 5 fJ per unit cell is incident instantaneously at time zero. For simplicity and ease of simulation, we first obtained spatial absorption density distribution with a continuous wave scheme and converted it to temperature distribution at the time zero. Then, a heat transfer simulation was conducted to obtain the time evolution. Figure 5 shows that higher temperature changes and faster thermal relaxation are achieved in narrower gaps owing to the smaller thermal capacity of the gap. Although complete thermal relaxation requires several times the thermal time constant of 38.2 μs, which is determined by heat loss through the Si pillars, partial thermal relaxation by heat transfer to the gold and Si 3 N 4 parts can be accomplished on a picosecond scale as in the case of 2 nm-width, enabling ultrafast operation for pulse detection.

Conclusion
The nanorod dimer structure containing a VO 2 nanogap is demonstrated to absorb LWIR radiation efficiently, exceeding the areal coverage. The VO 2 nanogap provides, along with the high negative TCR, an enormous electromagnetic absorption by virtue of the capacitive charging, making the dimer structure attractive in bolometer applications. Because the resonance wavelength and the thermal relaxation are easily tunable by varying the nanorod length and the gap width, the dimer design is applicable in various spectral ranges and operating speeds. This study shows that VO 2 nanogap structures fabricated by atomic layer lithography can be used to achieve high performance in various bolometer applications, providing high heating efficiency and a small areal footprint particularly suitable for high sensitivity ultrafast microbolometer arrays.    32 . The thermal conductivities of Si 3 N 4 and Si were set to 0.15 and 1.0 W/(m·K), respectively, according to the measurements on thin films 33 . For the thermal properties of VO 2 , we used data measured at 291 K where the thermal conductivity, heat capacity, and density are 4.4 W/ (m·K), 647.5 J/(kg·K), and 4340 kg/m 3 , respectively 34 . Note that we assumed the thermal properties to be constant because they vary by less than 10% over the simulated temperature range.
After the simulation, temperature dependent electrical resistance of the VO 2 gap was calculated using a model for dc electric conductivity given by J. Ordonez-Miranda et al. 35 . The model is based on an effective medium theory and the conductivities of metallic and insulating domains are 84,175.1 S/m and 4.86 × 10 6 exp(− 3136.1/T) S/m, respectively, in the model. Resistance of the gold nanorods was calculated assuming the resistivity and the temperature coefficient of 2.44 × 10 -8 Ω·m and 3.4 × 10 -3 K -1 , respectively 36 .