1. Introduction

A bolometer is a temperature-sensitive electrical resistor. It can measure the temperature rise caused by the absorbed energy of the incident radiation. As such, bolometers are used as broadband detectors of infrared and terahertz waves. Modern bolometer technology development started in the early 1980s with the work of Honeywell on vanadium oxide (VO_x) [1] and Texas Instruments on amorphous silicon (a-Si) [2]. Thanks to the rapid development of Micro-Electro-Mechanical (MEMS) technology, very large format, low-cost, monolithic two-dimensional arrays of microbolometers have been constructed for military and high-end commercial applications with the highest possible performance. The array size of the state-of-art microbolometers based infrared imaging detectors has surpassed 1920 × 1080 (2 million), while the pixel size has been reduced to 8 µm [3]. Although microbolometer-based detectors present lower responsivity than photon detectors such as MCT and InSb detectors at certain spectral bands, they can achieve a D* > 10⁹ cm·Hz^1/2W^-1 across the spectrum [4], which is high enough for many applications. More importantly, they do not rely on cryogenic cooling and are thus more compact and cost-effective.

One critical limitation of microbolometer-based infrared detectors is that they lack pixel-level spectral selectivity and polarization selectivity [5]. Like other thermal detectors, their electrical output signals only represent the absorbed power of the incident light. But they are not capable of distinguishing the wavelengths and polarization states at the pixel level. Generally, there are four typical approaches to equip detectors with spectral selectivity and polarization selectivity. The first approach is to place separate components such as interference filters or wire-grid polarizers in front of the detectors [6–9]. This method is straightforward, but it inevitably increases the cost and complicates the device. The second approach is to take advantage of the intrinsic spectral and polarization selectivity of certain materials. For example, the asymmetrical structures of two-dimensional materials such as birefringent crystals [10], GeSe [11], GeSe₂ [12], black phosphorus [13], and ReS₂ [14] cause different responses to different polarization states of the incident light. As such, these materials can be used to construct polarization selective detectors (PSDs). However, the typical polarization extinction ratio of such PSDs is no more than 5 [11, 12], which is relatively low for efficient polarization selective detection.

The third approach is to directly integrate miropolarizers made of metal nanowires above the detector pixels [36–45]. This approach mitigates the need for separate polarizers and can reach high polarization extinction ratios. However, since a gap exists between the micropolarizer and the detector pixel, the obliquely incident light passing through the micropolarizer may arrive at the neighboring pixels and cause cross-talk [46]. Moreover, the spectral transmittance of the micropolarizer is usually flat in a broad spectral band, so this approach cannot resolve spectral bands and polarization states simultaneously.

The fourth approach is to tailor the spectral and polarization responses of the detector pixels using integrated optical metamaterials, which are essentially arrays of optical resonators with sub-wavelength dimensions and spacing [28,29,47–49]. The optical resonators can resonantly enhance the pixel-level light-matter interaction at a specific spectral band, and this mechanism equips the detector pixels with spectral selectivity. Furthermore, to enable polarization selectivity, one can use optical resonators with asymmetric structures, such as nanorods and nanostrips, to selectively enhance light with a specific polarization state. The four approaches are summarized in Appendix A.

Since the integrated optical metamaterials allow pixel level spectral selectivity and polarization selectivity simultaneously, they provide more degree of freedom than interference filters and wire-grid polarizers in tailoring the responses of detector pixels.

As summarized by Table 1, the concept of tailoring the detector pixels’ responses using optical metamaterials has been proposed for various types of infrared detectors, including both photon detectors and thermal detectors [5,15–35]. Particularly, for microbolometer-based detectors, the concept of metamaterial-enabled spectral selectivity has been demonstrated numerically and experimentally by several teams. However, microbolometers with metamaterial-enabled polarization selectivity are still missing. In this paper, we exploit the multifunctional ability of metamaterial absorbers to achieve a more versatile microbolometer that can simultaneously resolve the spectral bands and polarization states of light.

Table 1. Reported works on tailoring the detector pixel’s responses using metamaterials

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We have designed, simulated, and fabricated two types of metamaterial absorber (MA) based VO_x microbolometers for spectral and polarization detection in the spectral bands of 5.3 µm – 6.6 µm and 6.0 µm – 7.4 µm, respectively. As shown in Fig. 1(a), the MA integrated microbolometer consists of two parts: 1) A conventional VO_x microbolometers suspended by a freely standing Si₃N₄ thin film for thermal isolation. 2) A MA based on metal-insulator-metal (MIM) structure, consisting of a top layer of gold nanostrip antennas, a silicon nitride spacer, and a gold backplate. The absorption of incident light is caused by the localized surface plasmon resonance (LSPR) and magnetic dipole resonance excited in the metal-insulator-metal (MIM) structure. By adjusting the dimensions of nanostrip antennas and the thickness of silicon nitride spacer, the impedance of the MIM structure can match that of vacuum, leading to the spectrally selective and polarization selective light absorption [50–52]. To prevent the gold backplate of the MA from short-circuiting the microbolometers, a 100 nm thick silicon nitride insulating layer is inserted in between the microbolometer and the MA. The optical image of the fabricated detector pixel, including the VO_x microbolometers and the integrated MA is shown in Fig. 1(b), while the scanning electron microscopy (SEM) image of the gold nanostrip antennas in the MA is presented in Fig. 1(c).

 

Fig. 1. (a) Schematic diagram of the fabricated metasurface integrated microbolometer for spectrum and polarization detection in this paper. (b)Optical image of the detector pixel taken by metalloscope. (c)SEM image of the nanostrip antennas in the MA.

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Since the nanostrip antenna based MIM absorber is essentially a polarization selective resonator, it can selectively absorb the incoming light in a designated spectral band with a designated polarization state. The absorbed light is converted into heat via the free carrier absorption in the gold nanostrip antennas and gold backplate. The generated heat is conducted to the VO_x layer below the MA via the silicon nitride insulating layer. The elevated temperature then causes the resistance of the VO_x layer to drop and the electrical output signal to increase. Thus, the MA integrated microbolometers only respond to light with the designated spectral band and polarization states. They can then be arranged as detector pixel arrays and resolve the full properties of light without separate spectral filters and polarizers.

2. Design and characterization of the metamaterial absorbers

The simplest version of the nanostrip antenna based MIM absorber has a top layer of single-sized nanostrips arranged in a periodic pattern. By tuning the width of the nanostrip and the period of the pattern, polarization selective near-unity absorption has been demonstrated across the infrared range [46]. However, the spectral absorption of the single-sized nanostrip antenna absorber is generally narrow. To broaden the spectral absorption band, multi-sized antenna absorber with different nanostrip widths in a unit cell can be used [53]. The design of multi-sized nanostrip antenna based MIM absorbers with a large number of nanostrips can be done by selecting an initial structure with a certain number of top nanostrip antennas in a unit cell and then fine-tune the spectral absorption by searching through the parameter space using computer algorithms such as particle swarm optimization (PSO) algorithm [46] or genetic algorithm (GA) [54]. Since the output wavelength range of the wavelength-tunable quantum cascade laser in our lab is from 5.291 µm to 6.098 µm, we designed two MIM absorbers with high absorption of TM mode in the spectral bands of 5.3 µm – 6.6 µm (MA₁) and 6.0 µm – 7.4 µm (MA₂), respectively. The bandwidths of the two MAs are about 1 µm, and only 3 nanostrips in a unit cell are needed. Thus the absorbers are designed by direct tuning of the nanostrip widths.

Here the TM mode is defined as the incident radiation with electric fields perpendicular to the nanostrip antennas. As shown by Fig. 2(a) and Fig. 2(b), the thicknesses of the gold backplate, the silicon nitride spacer, and the gold antennas of both the two MIM absorbers are 100 nm, 80 nm, and 50 nm, respectively. An extra layer of 5 nm to 10 nm chrome is added underneath the gold layers for process stability in the actual fabrication process. For MA₁, the period P₁ of the nanostrip antenna array is 4.2 µm, and the widths of the three nanostrip antennas (w₁, w₂, w₃) in one unit cell are 1.03 µm, 1.11 µm, and 1.19 µm, respectively. While for MA₂, the period P₂ is 5 µm and the widths of the nanostrip antennas (w₄, w₅, w₆) are 1.20 µm, 1.30 µm, and 1.40 µm, respectively. The simulated spectral absorption of MA₁ and MA₂ obtained by Lumerical FDTD, a finite-difference time-domain method based solver, are presented by Fig. 2(c) and Fig. 2(d).

 

Fig. 2. The designed metasurfaces for the two target wavebands. (a) The unit cell of the polarization-selective MA1. (b) The unit cell of the polarization-selective MA2. (c) The simulated spectral absorption curve of MA1 (d) The simulated spectral absorption curve of MA2.

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For MA₁, the simulated average absorption coefficient of TM and TE modes is 0.8322 and 0.0197, respectively, resulting in a polarization extinction ratio (PER) of 42.24. While for MA₂, the simulated average absorption coefficient of TM and TE modes is 0.7720 and 0.0181, respectively, and the corresponding PER is 42.65. Here, the polarization extinction ratio (PER) is defined as the ratio of the average absorption coefficient of TM and the average absorption coefficient of TE.

The designed MAs are fabricated by electron beam lithography and metal lift-off process and then characterized by scanning electron microscopy (SEM). (See section 3 for details about the fabrication process). The top nanostrip antenna arrays of the fabricated MA₁ and MA₂ are illustrated in Fig. 3(a) and Fig. 3(b), respectively. Since the thicknesses of the backplate, the spacer, and the nanostrip antennas in MA₁ and MA₂ are designed to be the same, and the only difference between MA₁ and MA₂ is the horizontal distribution of the nanostrip antennas, it is easy to integrate the two absorbers on the same focal plane array for dual-band polarization imaging. The measured period P₁ of the nanostrip antenna array in MA₁ is 4.2 µm, and the widths of the three nanostrip antennas are 1.06 µm, 1.14 µm, and 1.22 µm, respectively. While the measured period P₂ in MA₂ is 5 µm and the nanostrip widths are 1.24 µm, 1.30 µm, and 1.38 µm, respectively. Thus, the fabrication error of the nanostrip antennas is less than 40 nm, which corresponds to a relative error of < 4%.

 

Fig. 3. (a) SEM image of the MA1. (b) SEM image of the MA2. (c) Simulated and experimental absorption coefficient of MA1. (d) Simulated and experimental absorption coefficient of MA2.

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The spectral reflectance of the two fabricated MAs are characterized using a Fourier transform infrared (FTIR) spectrometer (NICOLET 5700 from Thermo Electron) combined with an IR microscope (Continu-µm). The area size of each MA fabricated on top of the microbolometer is 500 µm × 500 µm, and the aperture size of the IR microscope is 100 µm × 100 µm. The measured spectral reflection R is normalized to a gold mirror (Thorlabs, PF05-03-M01), while the spectral transmission T is zero due to the 100 nm thick gold backplate. Thus, the spectral absorption is calculated as A = 1 – R. Since the FTIR is not installed with a polarizer, the infrared light beam incident on the sample is un-polarized. In this case, we can only measure the average of the actual absorption of TE mode A_TE and the actual absorption of TM mode A_TM, i.e., A_average = (A_TE + A_TM)/2.

In Fig. 3(c) and 3(d), the dash-dot lines show the simulated spectral absorption of TM mode (red) and TE mode (blue) for the two MAs using the measured antenna sizes. The refractive index of silicon nitride used in the simulation is fixed at 1.85 (see Appendix B for discussion). For MA₁, the average of the fitted spectral absorption coefficient of TM and TE modes is 0.8300 and 0.0201, respectively, resulting in a PER of 41.29. While for MA₂, the average of the fitted spectral absorption coefficient of TM and TE modes is 0.7969 and 0.0181, respectively, resulting in a PER of 44.03. For simplicity, we consider the actual absorption of TE mode A_TE to be zero. Then the actual absorption of TM mode can be derived from the measured average absorption using A_TM = 2 × A_average, as shown by the solid black lines in Fig. 3(c) and 3(d). We can see that the experimentally obtained absorption spectra of the TM mode agree well with the simulated curves.

3. Fabrication of the metasurface integrated microbolometer

Figure 4(a) presents the fabrication process of the MA integrated microbolometers. Step I, a 500 µm thick silicon wafer with 200 nm thick silicon nitride layers deposited by low pressure chemical vapor deposition (LPCVD) on both sides, is chosen as the substrate. The silicon nitride layer on the top side acts as the supporting layer, holding up the entire microbolometer. While the silicon nitride layer on the backside protects the silicon substrate from being etched by the potassium hydroxide (KOH) solution in the releasing step. Step II, the thermal-sensitive areas are produced using photolithography to define the square patterns, followed by ion beam sputtering to deposit 120 nm thick vanadium oxide layer and subsequent lift-off process to remove the unwanted vanadium oxide. The size of the vanadium oxide square is 700 µm × 700 µm, and the properties of the VO_x film can be found in our previous publication [55]. Step III, the electrodes used to read out the electrical signals from the thermal-sensitive areas are produced by using photolithography to define the patterns, followed by electron beam evaporation (EBE) to deposit 10 nm thick chrome adhesion layer and 100 nm thick gold layer, and subsequent lift-off process. Step IV, a 100 nm thick silicon nitride passivation layer is deposited by plasma enhanced chemical vapor deposition (PECVD), followed by photolithography and subsequent inductively coupled plasma (ICP) etching to generate the pattern. The silicon nitride passivation layer prevents the vanadium oxide from oxidation. It also acts as the electrical isolation layer between the underneath vanadium oxide layer and the gold backplate of the MA atop. Step V, the backplate of the MA is produced by using photolithography to define the patterns, followed by electron beam evaporation (EBE) to deposit 10 nm thick chrome adhesion layer and 100 nm thick gold layer, and subsequent lift-off process. Step VI, the spacer of the MA is produced by depositing an 80 nm thick silicon nitride layer using plasma enhanced chemical vapor deposition (PECVD), followed by photolithography and subsequent ICP etching to generate the pattern. The area sizes of the gold backplate and silicon nitride spacer are both 500 µm × 500 µm. Step VII, the nanostrip antennas of the MA are produced by using electron beam lithography (EBL) to define the patterns, followed by EBE to deposit 5 nm thick chrome adhesion layer and 50 nm thick gold layer, and subsequent lift-off process. Step VIII, the silicon substrate beneath the MA integrated microbolometers is removed to reduce the thermal capacity and thermal conductivity. This is done by first patterning the silicon nitride layer on the backside of the substrate using photolithography and ICP etching to generate a release window for wet etching, and then immersing the chip in a 40% mass fraction of potassium hydroxide (KOH) solution, which is heated in a water bath at 85 °C for about 8 hours. During the wet etching process, the structures on top of the substrate should be protected by a certain layer, such as silicon nitride or photoresist, which are easily removed afterward. In our experiment, we used PECVD to deposit 80 nm thick silicon nitride as the protection layer. We choose the thickness of 80 nm based on the measured etching rate of SiN in KOH solution. Ideally, the SiN protection layer should also be removed during the wet-etching of the silicon substrate with KOH. In practice, the SiN protection layer might remain after the wet-etching (under-etching), but based on the simulation shown by Fig. 17 in Appendix I, the spectral absorption of the MAs is not affected too much. At the end of the process, the microbolometer region is covered by drop-casted photoresist while the potentially remaining protection layer on the electrodes are selectively removed by inductively coupled plasma (ICP) etching to ensure electrical connection.

 

Fig. 4. (a) Fabrication process of the metasurface integrated microbolometer. (b) SEM image of the fabricated detector. (c)Resistance of the pixels as a function of temperature.

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Figure 4(b) shows the SEM image of the fabricated detector pixels on the same chip. The colored pixel in the upper left corner is the image taken by a metalloscope with the same scale bar. After the fabrication process is completed, the electrical resistances of the 8 MA integrated microbolometers on the same chip as a function of the temperature are measured by using a hotplate to control the temperature of the chip. As presented in Fig. 4(c), the electrical resistances of the microbolometers decrease as the temperature increases, which is typical of vanadium oxide. It is also seen that the value of resistance varies from pixel to pixel, mainly caused by the non-uniformity of the fabrication process. The high-temperature process such as PECVD will also affect the resistance of the deposited vanadium oxide layer. Here we define the temperature coefficient of resistance (TCR) α as:

4. Spectral responses of the MA integrated microbolometers

The experimental setup to characterize the spectral responses of the MA integrated microbolometers is presented in Fig. 5(a). The light source is a wavelength-tunable quantum cascade laser (QCL) from Block engineering, with a wavelength tuning range from 5.291 µm to 6.098 µm. The output beam of the QCL is collimated and linear polarized, and the relative orientation between the detector pixel and the QCL is adjusted so that the light beam incident on the MA is polarized perpendicular to the nanostrip antennas (TM mode). The fabricated detector chip is vacuum packaged with a 700 µm thick germanium (Ge) substrate as the IR transparent window to minimize the heat loss into ambient conditions and mounted on a printed circuit board for electrical connections, as shown in Fig. 5(b). The optical window of the packaged detector chip is customized so that the average transmittance in the spectral band from 5 µm to 12 µm is 92.62%. When the wavelength is below 2 µm, the light transmittance is close to 0, so it is impossible to see the interior of the packaged detector through the optical window in visible light. Thus we use a thermal infrared camera to picture the packaged detector chip, as shown in Fig. 5(c). The infrared image that reveals the interior of the detector chip is then used to facilitate the alignment between the light beam from the QCL and the detector pixels.

 

Fig. 5. (a) The experiment setup to characterize the wavelength response property of the MA integrated microbolometer. (b) The optical image of the packaged detector after being soldered onto a PCB board. (c) The infrared image of the packaged detector. (d) The responsivity of detector 1 as a function of wavelength. (e) The responsivity of detector 2 as a function of wavelength.

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The spectral responsivity of the MA integrated microbolometers is defined as:

5. Polarization response of the metasurface integrated microbolometers

As shown in Fig. 6(a), a SiC blackbody and a BaF₂ polarizer are used to characterize the voltage responses of the MA integrated microbolometers as a function of the polarization state. The blackbody (SLS203L, Thorlabs) has a total output power above 1.5 W and a spectral peak at around 2.5 µm. The holographic wire grid polarizer (WP25H-B, Thorlabs) has a polarization extinction ratio over 300:1 in the spectral band from 5 µm to 10 µm. To avoid a destructive temperature rise of the detector pixel, the output beam from the blackbody is not focused by a lens. Instead, the beam passes through the polarizer and directly illuminates the detector chip. The polarization angle θ of the light arriving at the detector chip is varied from 0° to 350° with a step of 10°, by rotating the wire-grid polarizer, and the output voltage $\Delta V$ of the detector pixel is recorded at each angle of polarization. Here θ is the angle between the polarizer’s wire-grids and the MA’ nanostrip antennas, as shown by the inset in Fig. 6(a).

 

Fig. 6. (a) The experiment setup to characterize the polarization response property of the MA integrated microbolometer. (b) The experimental data and the calculated fitting curve as a function of polarizer angle.

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Since the light beam is not focused, the silicon nitride membrane around the MA will also absorb the incident radiation and generate an additional temperature rise which is independent of the angle of polarization. As such, the relative output voltage ΔV/V is a linear function of cos²θ, with an additional constant determined by the absorption of silicon nitride membrane, and the detailed derivation can be found in Appendix D. By using the least square method, the measured ΔV/V of detector 1 as a function of cos²θ is found to be:

To find out the additional constant in ΔV/V caused by the absorption of silicon nitride membrane, we assume that the ratio of ΔV/V caused by TM mode to that caused by TE mode is equal to 41.29, which is the polarization extinction ratio of the integrated MA. The additional constant in ΔV/V caused by the absorption of silicon nitride membrane is then calculated to be -0.00547. After removing this constant, the relationship between ΔV/V and cos²θ can be rewritten as:

6. Characterization of the time constant and noise

The time constants of the two detectors are measured to be 1.67 ms and 1.78 ms. While the achieved highest specific detectivity D* are 6.94×10⁵ cm·Hz^1/2W^-1 at 11 Hz for detector 1 and 9.95×10⁵ cm·Hz^1/2W^-1 at 36 Hz for detector 2, respectively. (See Appendix E and F for the details about the measurement of time constant and noise).

The measured D* of our devices are relatively low comparing with commercial microbolometers, and this is attributed to two factors: (1) The size of the vanadium oxide square (the pixel size) is 700 µm × 700 µm, which is larger than the typical sizes of commercial microbolometers. It is expected that when the pixel size is scaled down to a few tens of micrometers to achieve smaller thermal capacitance and thermal conductance, the responsivity and ${\textrm{D}^\mathrm{\ast }}$ can be higher [20]. (2) No integrated read-out circuit (ROIC) is used during the noise measurement. In practical applications, proper ROIC can improve the responsivity and D* as well.

7. Conclusions and outlook

To conclude, we have designed two MAs based on MIM structure with nanostrip antennas as the top layer. The average absorption of the TM polarized light of the two MAs are 0.8300 in the spectral band of 5.3 µm – 6.6 µm, and 0.7969 in the spectral band of 6.0 µm – 7.4 µm respectively. The PERs of the two designed MAs are 41.29 and 44.03, respectively. The two designed MAs are integrated with VOx microbolometers for spectral selective and polarization selective detection. The measured spectral responses and polarization responses of the MA integrated microbolometers agree well with the spectral selectivity and polarization selectivity of the integrated MAs.

As a comparison, reference 20 experimentally demonstrated amorphous silicon microbolometers integrated with a metamaterial absorber based on a metal-insulator-metal structure with a measured peak responsivity of 4 mV/W at 1 kHz. The sizes of the fabricated microbolometers range from 0.2mm to 2mm. When operating at the lower frequency such as a few hertz, the responsivity is expected to be one to two orders higher, which is comparable to our results (∼1V/W).

Spectral imaging and polarization imaging are two very advanced detection schemes that are useful in applications such as remote sensing [56], biological and medical imaging [57–59], and facial recognition [60]. Polarization state of the light can provide more information of surface topography and scattering, which can be applied for target detection in defense and biomedical applications [61]. While a high-resolution spectral information provides details on the material composition for the assessment of food quality, artwork authentication and many other applications [62]. When the information carried by spectral bands or the polarization states of light alone is not adequate enough to distinguish the targets, combining the two modalities (spectro-polarimetry) can provide a more complete picture about the targets [63,64]. Our work demonstrates that, the spectral and polarization responses of VO_x microbolometers can be simultaneously tailored using integrated MAs, thus mitigating the need for separate spectral filters and polarizers. Since VO_x microbolometers have enabled the construction of large format infrared focal plane array detectors that operate in the room temperature, our strategy allows each pixel in the focal plane array to have its own spectral response and polarization response, as shown by Fig. 7, which in turn enables a variety of new detection schemes, such as polarization imaging detection in multiple designated spectral bands. We therefore envision that, when fully developed, the demonstrated multifunctional microbolometers will allow the implementation of spectral imaging and polarization imaging using a unified and compact platform.

 

Fig. 7. Metamaterial integrated VOx superpixel for spectral and polarization detection

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Appendix A: approaches towards spectral and polarization detection

Figure 8 summarizes the four major approaches to achieve spectral and polarization detection. The first approach is to place separate optical components such as interference filters or wire-grid polarizers in front of the detectors [6–9]. The second approach is to take advantage of the intrinsic spectral and polarization selectivity of certain photosensitive materials [10–14]. The third approach is to directly integrate transmissive micro-filters or miro-polarizers made of nanostructures above the detector pixels [36–45]. The fourth approach is to tailor the spectral and polarization responses of the detector pixels using integrated optical metamaterials [28,29,47–49].

 

Fig. 8. The four approaches to achieve spectral and polarization detection.

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Appendix B: refractive index of the silicon nitride spacer

In the visible and near infrared spectral range, the refractive index of silicon nitride can be measured using ellipsometer. In longer wavelengths, the refractive index fitted by Kevin [65] using Sellmeier equation is shown in Fig. 9(a). Kischkat also measured the refractive index of silicon nitride under different deposition conditions [66], as shown in Fig. 9(b). It is seen that the refractive index of silicon nitride ranges from 1.5 to 2.4 in the spectral range of 5 µm - 7.5 µm. Due to the lack of spectroscopic ellipsometer that can measure refractive indices in the mid-infrared band, we assume the refractive index of silicon nitride in the fabricated MA to be 1.85, which can make simulated spectral absorption close to the measured spectral absorption.

 

Fig. 9. (a) Dispersive refractive index of silicon nitride in the infrared band reproduced using the data in Ref. [65]. (b) Refractive index of silicon nitride deposited under different conditions, data from reference [66].

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Appendix C: calculation of detector responsivity

The thermal balance equation of microbolometer is:

(6)$$\mathrm{\beta P\ =\ C}\frac{{\textrm{dT}}}{{\textrm{dt}}}\mathrm{\ +\ G\Delta T}\textrm{.}$$

where P is the incident power, β is the product of the optical window’s transmittance ${\textrm{t}_\textrm{w}}$ and the absorption coefficient $\mathrm{\eta }$ of the MA, C is the thermal capacity, G is the thermal conductance, ΔT is the temperature change, and dT/dt is the change rate of the temperature T. In the steady state, the temperature doesn’t change with time and dT/dt = 0. Equation (6) then simplifies to:

(7)$$\mathrm{\Delta T\ =\ }\frac{{\mathrm{\eta }{\textrm{t}_\textrm{w}}\textrm{P}}}{\textrm{G}}\textrm{.}$$

The definition of TCR α is:

(8)$$\mathrm{\alpha =\ }\frac{{\textrm{dR}}}{{\textrm{RdT}}}\textrm{.}$$

The temperature change ΔT is relatively low, so that α can be regarded as a constant. Equation (8) can be rewritten as:

(9)$$\mathrm{\alpha = }\frac{{\mathrm{\Delta R}}}{{\mathrm{R\Delta T}}}\textrm{.}$$

The change in the microbolometer’s output voltage is:

(10)$$\mathrm{\Delta V\ =\ i\Delta R}\textrm{.}$$

Where i is the bias current of the microbolometers. The detector’s responsivity is defined as the ratio of voltage change $\varDelta V$ to incident power P. The responsivity can be expressed from Eq. (6)-(10) as:

(11)$${\textrm{R}_\textrm{v}}\textrm{ = }\frac{{\mathrm{\Delta V}}}{\textrm{P}}\textrm{ = }\frac{{\mathrm{iR\alpha \eta }{\textrm{t}_\textrm{w}}}}{\textrm{G}}\textrm{.}$$

Appendix D: voltage change as a function of the polarization angle

Since the SiC blackbody source used to measure the detector’s polarization response is not focused, the detector pixel and the silicon nitride around will receive the incident radiation at the same time, causing the temperature rise of the pixel. The power received by the pixel is a function of the polarization angle due to the integrated MA, while the power absorbed by the area that is not covered by the MA is polarization-independent. The total power causing the temperature rise by can be expressed as:

(12)$${\textrm{P}_\textrm{t}}\textrm{ = }{\mathrm{\eta }_{\textrm{TM}}}{\textrm{P}_\textrm{p}}\textrm{co}{\textrm{s}^\textrm{2}}\mathrm{\theta +\ }{\mathrm{\eta }_{\textrm{TE}}}{\textrm{P}_\textrm{p}}\textrm{si}{\textrm{n}^\textrm{2}}\mathrm{\theta +\ }{\mathrm{\eta }_{\textrm{SiN}}}{\textrm{P}_{\textrm{SiN}}}\textrm{.}$$

where P_p and P_SiN are the power incident on the pixel and the silicon nitride around, respectively. η_TM and η_TE are the average absorption coefficient of TM mode and TE mode, respectively. θ is the polarization angle and η_SiN is the average absorption coefficient of silicon nitride around. The polarization extinction ratio (PER) is defined as:

(13)$$\textrm{PER = }\frac{{{\mathrm{\eta }_{\textrm{TM}}}}}{{{\mathrm{\eta }_{\textrm{TE}}}}}\textrm{.}$$

According to Eq. (6), (7) and (12), the temperature change is:

(14)$$\mathrm{\Delta T\ =\ }\frac{{{\textrm{P}_\textrm{t}}}}{\textrm{G}}\textrm{.}$$

The voltage change can be expressed from Eq. (9), (10) and (14) as:

(15)$$\mathrm{\Delta V\ =\ }\frac{{\mathrm{i\alpha R}{\textrm{P}_\textrm{t}}}}{\textrm{G}}\textrm{.}$$

So the relative change rate of voltage can be expressed from Eq. (12) and (15) as:

(16)$$\frac{{\mathrm{\Delta V}}}{\textrm{V}}\textrm{ = }{\textrm{k}_\textrm{1}}\textrm{co}{\textrm{s}^\textrm{2}}\mathrm{\theta +\ }{\textrm{k}_\textrm{2}}\textrm{.}$$

The constants ${\textrm{k}_1}$ and ${\textrm{k}_2}$ are:

(17)$${\textrm{k}_\textrm{1}}\textrm{ = }\frac{{\mathrm{\alpha }{\mathrm{\eta }_{\textrm{TM}}}{\textrm{P}_\textrm{p}}({\textrm{1 - }{\textrm{1} / {\textrm{PER}}}} )}}{\textrm{G}}\textrm{.}$$

(18)$${\textrm{k}_\textrm{2}}\textrm{ = }\frac{{\mathrm{\alpha }({{{{\mathrm{\eta }_{\textrm{TM}}}{\textrm{P}_\textrm{p}}} / {\textrm{PER}}}\textrm{ + }{\mathrm{\eta }_{\textrm{SiN}}}{\textrm{P}_{\textrm{SiN}}}} )}}{\textrm{G}}\textrm{.}$$

Appendix E: time constant measurement

The thermal time constant τ is defined as the time required for the temperature change to reach 63.2% of the maximum temperature rise. It can be expressed as the ratio of thermal capacity C to thermal conductance G. During the test, τ can be measured by changing the modulation frequency of the light source.

If the light is modulated by an angular frequency $\mathrm{\omega } = 2\mathrm{\pi f}$, the Eq. (6) can be rewritten as:

(19)$$\mathrm{\beta Pexp(i\omega t)\ =\ C}\frac{{\textrm{dT}}}{{\textrm{dt}}}\mathrm{\ +\ G\Delta T}\textrm{.}$$

And the solution is:

(20)$$\mathrm{\Delta T\ =\ }\frac{{\mathrm{\beta P}}}{\textrm{G}} \cdot \frac{{{\textrm{e}^{\mathrm{i(\omega t\ +\ \varphi )}}}}}{{\sqrt {\textrm{1 + }{\mathrm{\omega }^\textrm{2}}{\mathrm{\tau }^\textrm{2}}} }}$$

Where φ and τ are defined as:

(21)$$\mathrm{sin\varphi =\ }\frac{{\mathrm{\ -\ \omega \tau }}}{{\sqrt {\textrm{1 + }{\mathrm{\omega }^\textrm{2}}{\mathrm{\tau }^\textrm{2}}} }}$$

(22)$$\textrm{cos}\mathrm{\varphi =\ }\frac{\textrm{1}}{{\sqrt {\textrm{1 + }{\mathrm{\omega }^\textrm{2}}{\mathrm{\tau }^\textrm{2}}} }}$$

(23)$$\mathrm{\tau =\ }\frac{\textrm{C}}{\textrm{G}}$$

The amplitude of ΔT is:

(24)$$|{\mathrm{\Delta T}} |\textrm{ = }\frac{{\mathrm{\beta P}}}{\textrm{G}} \cdot \frac{\textrm{1}}{{\sqrt {\textrm{1 + }{\mathrm{\omega }^\textrm{2}}{\mathrm{\tau }^\textrm{2}}} }}$$

The voltage change ΔT and responsivity R_v can also be expressed as:

(25)$$\mathrm{\Delta V\ =\ i\Delta R\ =\ i\alpha R}|{\mathrm{\Delta T}} |\textrm{ = }\frac{{\mathrm{i\alpha R\beta P}}}{\textrm{G}} \cdot \frac{\textrm{1}}{{\sqrt {\textrm{1 + }{\mathrm{\omega }^\textrm{2}}{\mathrm{\tau }^\textrm{2}}} }}$$

(26)$${\textrm{R}_\textrm{v}}\textrm{ = }\frac{{\mathrm{\Delta V}}}{\textrm{P}}\textrm{ = }\frac{{\mathrm{i\alpha R\beta }}}{\textrm{G}} \cdot \frac{\textrm{1}}{{\sqrt {\textrm{1 + }{\mathrm{\omega }^\textrm{2}}{\mathrm{\tau }^\textrm{2}}} }}$$

When the modulation frequencies are ω₁ and ω₂, the corresponding voltage changes are ΔV₁ and ΔV₂. According to Eq. (25), the relationship between them is:

(27)$$\frac{{\mathrm{\Delta }{\textrm{V}_{\textrm{1}}}}}{{\mathrm{\Delta }{\textrm{V}_{\textrm{2}}}}}\textrm{ = }\frac{{\sqrt {\textrm{1} + \omega _{\textrm{2}}^{\textrm{2}}{\mathrm{\tau }^{\textrm{2}}}} }}{{\sqrt {\textrm{1} + \omega_{\textrm{1}}^{\textrm{2}}{\mathrm{\tau }^{\textrm{2}}}} }}$$

We select four frequencies to calculate τ, and the test results are presented in Table 2. The configuration of the measurement system is shown in Fig. 10. τ is calculated according to Eq. (27) by selecting any two frequencies. For detector 1, the calculated results are 1.64 ms, 1.72 ms, 1.65 ms, 1.67 ms, 1.69 ms and 1.65 ms, with a mean value of 1.67 ms. For detector 2, the calculated results are 1.67 ms, 2.46 ms, 1.66 ms, 1.92 ms, 2.02 ms, and 1.65 ms. We dropped 2.46 ms because it deviates too much from the other five numbers, resulting a mean value of 1.78 ms.

Table 2. Voltage change of the two detectors at different frequencies

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Fig. 10. The configuration of the system used to measure the time constant

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In Fig. 11, the black dots represent the measured AC signals, and the red dotted lines are the fitting curves based on the calculated time constants.

 

Fig. 11. Measured and fitted AC response for (a) detector 1 and (b) detector 2.

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Appendix F: noise measurement

We consider three main types of noise in the microbolometer, including Johnson noise, 1/f noise, and temperature fluctuation noise [67].

• (1) Johnson noise is caused by the random thermal disturbance of carriers, also known as thermal noise. Johnson noise is a kind of white noise that is independent of frequency. According to Nyquist theorem, the root mean square Johnson noise voltage in a bandwidth of Δf is:

  (28)$${\textrm{V}_\textrm{j}}\textrm{ = }\sqrt {\mathrm{4kTR\Delta f}} $$

  k is Boltzmann constant with the value of 1.38×10⁻²³ J/K. T is the temperature, and R is the resistance.
• (2) 2) The resistance of thermal-sensitive film usually shows a fluctuation, which is reflected as additional voltage noise when there is a bias current. The main additional voltage noise is 1/f noise. At the frequency of f with a bandwidth of 1Hz, 1/f noise is:

  (29)$${\textrm{V}_{{\textrm{1} / \textrm{f}}}}\textrm{ = V}\sqrt {\frac{{{\textrm{k}_{{\textrm{1} / \textrm{f}}}}}}{\textrm{f}}} $$

V is the voltage and k_1/f is the coefficient which is usually on the magnitude of 10⁻¹³ for vanadium oxide microbolometer.

• 1. 3) There is random temperature fluctuation in any thermal system, including microbolometer. This noise is called temperature fluctuation noise, and the root-mean-square of the noise voltage is:

  (30)$${\textrm{V}_\textrm{t}}\textrm{ = }{\textrm{R}_{\textrm{v0}}}\sqrt {\frac{{\textrm{4kG}{\textrm{T}^\textrm{2}}}}{{\textrm{1 + }{\mathrm{\omega }^\textrm{2}}{\mathrm{\tau }^\textrm{2}}}}} $$

R_v0 is the voltage responsivity when the source is not modulated.

The noise voltage of the detectors V_noise is measured by a lock-in amplifier (Stanford Research System SR830). The measured data is presented in Table 3, and the configuration of the noise measurement system is presented in Fig. 12.

 

Fig. 12. The configuration of the noise measurement system

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Table 3. Measured noise voltage of the two detectors

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The specific detectivity D* is described as:

(31)$$\mathrm{D\ast{=}\ }\frac{{\sqrt {{\textrm{A}_\textrm{d}}\mathrm{\Delta f}} }}{{\textrm{NEP}}}\textrm{ = }\frac{{{\textrm{R}_\textrm{v}}\sqrt {{\textrm{A}_\textrm{d}}\mathrm{\Delta f}} }}{{{\textrm{V}_{\textrm{noise}}}}}$$

R_v is the voltage responsivity, and A_d is the pixel area. According to Eq. (26), D* can be rewritten as:

(32)$$\mathrm{D\ast{=}\ }\frac{{{\textrm{R}_{\textrm{v0}}}}}{{{\textrm{V}_{\textrm{noise}}}}} \cdot \frac{{\sqrt {{\textrm{A}_\textrm{d}}\mathrm{\Delta f}} }}{{\sqrt {\textrm{1 + }{\mathrm{\omega }^\textrm{2}}{\mathrm{\tau }^\textrm{2}}} }}$$

Figure 13 shows the calculated noise voltage and the measured noise voltage, as well as the corresponding D*. The parameters used in the calculation are shown in Table 4.

 

Fig. 13. Calculated noise voltage, measured noise voltage, and corresponding ${\textrm{D}^\mathrm{\ast }}$ of detector 1(a) and detector 2(b).

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Table 4. Parameters used in the calculation

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Detector 1 achieves the highest ${\textrm{D}^\mathrm{\ast }}$ of 6.94×10⁵ cmHz^1/2/W at 11 Hz, and detector 2 achieves the highest ${\textrm{D}^\mathrm{\ast }}$ of 9.95×10⁵ cmHz^1/2/W at 36 Hz.

The measured D* of our devices is relatively low compared with commercial microbolometers, and this is attributed to two factors: (1) The size of the vanadium oxide square (the pixel size) is 700 µm × 700 µm, which is larger than the typical sizes of commercial microbolometers. It is expected that when the pixel size is scaled down to a few tens of micrometers to achieve smaller thermal capacitance and thermal conductance, the responsivity and D* can be higher [20]. (2) As shown in Fig. 14, no integrated read-out circuit (ROIC) is used during the noise measurement. In practical applications, proper ROIC can improve the responsivity and D*.

 

Fig. 14. The packaged detector without any ROIC

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Appendix G: simulation of heat generation profiles

To find out the effect of nanostrip antennas’ period and stripe widths on the heat generation profiles, we conducted the thermal simulation of the MA integrated microbolometer using DEVICE - a multiphysics simulator from Lumerical Inc. The configuration of the simulation region is shown in Fig. 15(a) and 15(b). To save simulation time, we set the sizes of the free-standing silicon nitride supporting layer, the vanadium oxide square, and the area of nanostrip antennas to be 80 µm, 70 µm, and 50 µm, respectively. The silicon nitride supporting layer is suspended by a 10 µm thick Si framework made by removing the silicon underneath the 80 µm × 80 µm free-standing silicon nitride layer. The bottom sides of the Si framework are set as heat sinks. The nanostrip antennas are selected as the heat source with a total thermal power of 20 nW. The only difference between the two detectors is the arrangement of the nanostrip antennas. It is seen from the simulated heat generation profiles in Fig. 15(c) and 15(d) that the two microbolometers’ temperature profiles are nearly identical but the maximum temperature rises are 9 mK and 8 mK for the two detectors, respectively, confirming that the arrangement of the nanostrip antennas will cause different temperature rises, which in turn contributes to the difference in detector responses.

 

Fig. 15. (a)(b) Configuration of the thermal simulation. (c) Temperature rise of VOx for detector 1. (d)Temperature rise of VOx for detector 2.

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Appendix H: simulation of the local electromagnetic fields

Figure 16 presents the local distribution of magnetic field intensity |H| of the TM polarization at the resonant wavelengths of MA1 and MA2, respectively. It is clearly shown that at each resonance, the local magnetic fields are mainly confined in the spacer under one nanostrip and the local fields under other nanostrips are weak. As the resonant wavelength increases, the concentrated local magnetic fields move from the leftmost nanostrip to the rightmost nanostrip. Correspondingly, the optical energy loss is mainly concentrated in one nanostrip and the backplate below that nanostrip at each resonance [46,54]. Therefore, the broadened absorption of the TM polarization is a combined effect of the excited LSPR in the MIM structure with muli-width nanostrip antennas.

 

Fig. 16. (a)∼(c) The distribution of magnetic field intensity |H| in MA1 at the absorption peak of λ₁ = 5.52 µm, λ₂ = 5.83 µm, and λ₃ = 6.12 µm, respectively. (d)∼(f) The distribution of magnetic field intensity |H| in MA2 at the absorption peak of λ₁ = 6.20 µm, λ₂ = 6.62 µm, and λ₃ = 7.01 µm, respectively.

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Appendix I: impact of the SiN protection layer on the MAs’ spectral absorption

 

Fig. 17. Impact of the SiN protection layer on the MAs’ spectral absorption. (a) under-etching case and (c) the corresponding spectral absorption. (b) Over-etching case and (d) the corresponding spectral absorption.

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Funding

National Natural Science Foundation of China (11774112, 12174135); National Key Research and Development Program of China (2019YFB2005700); The Fundamental Research Initiative Funds for Huazhong University of Science and Technology (2017KFYXJJ031, 2018KFYYXJJ052, 2019KFYRCPY122).

Acknowledgments

We thank Xu Wei engineer and Li Pan engineer in OMFCF of WNLO for their EBE and EBL fabrication support. We thank Zhang Guangxue and Huang Guang engineers in OMFCF of WNLO for their support in the photolithography process. We thank Lai Jianjun and Cao Weijie in WNLO for the support of the deposition of vanadium oxide.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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