1 Introduction

There are growing interests for gas sensing such as greenhouse gas monitoring¹, indoor air quality supervision², automobile tail gas discharge detection³, toxic or flammable gases detection⁴, breath diagnostics⁵, industrial production⁶, etc. So far, several major approaches have been developed⁷, including electrochemical sensors⁸, calorimetric sensors⁹, acoustic sensors¹⁰ and optical sensors¹¹. Optical methods¹², in particular in the mid-IR range, are usually straightforward and have short response time, long lifetime, high sensitivity and selectivity. Generally, there are three mechanisms for optical gas sensing, including (i) refractive index (RI) sensing based on the real part of gas RI¹³, (ii) non-dispersive infrared (NDIR) absorption sensing based on the imaginary part of gas RI¹⁴, and (iii) spectroscopy based on the gas molecular spectral fingerprint¹⁵. The RI sensing method allows for characterization of nonreactive gases and very compact sensor design. However, this technique such as surface plasmon resonance (SPR)¹⁶ sensors that are widely used in liquid and solid detection suffers sensitivity issues for gas sensing due to the low RI difference (~10^-4 RIU) between various gases. For example, a localized SPR spectroscopy was developed with a detection limit level about 3×10^-4 RIU that only showed measurable signal between pure Ar and He¹⁷. An air-slot photonic crystal nanocavities was used to enhance the light-gas interaction, but a similar RI detection limit of 10^-5 RIU was estimated considering a 3 pm spectral measuring resolution¹⁸. As a result, some signal amplification techniques were developed. For example, silicon glycol copolymer was used in a standard SPR setup to enrich halothane and reduce the detection limit down to 80 ppm, where both thickness and RI of the copolymer are affected by the gas absorption¹⁹. Similarly, Pd²⁰, carbon nanotube²¹, and SnO₂ microspheres²² are also widely used to increase the RI variations by chemical reactions. In contrast, NDIR absorption sensing method is more popular²³. This technique is based on the Beer–Lambert Law, and thus the sensitivity can be increased by simply lengthening the optical path for light-gas interaction. For example, a detection limit for formaldehyde of 120 pptv was demonstrated by using an antimonide laser and a 1 m base-length cell with a multipass path lengths of 100 m by mirrors²⁴. Ethyl chloride gas at a 5 ppm concentration level was detected by using a distributed-feedback quantum cascade laser (QCL) coupled with a silica capillary with a length of 4 m²⁵. Instead of laser sources, the NDIR sensing system can also be built with a broadband source, narrowband filter and detector. For example, a detection limit of 50 ppm was predicted in an ellipsoid gas cell system with a LED source and PbSe detector²⁶. No matter which configuration, due to the low molecular absorption cross-sections of mid-IR vibrations (10⁻²⁰ cm²), the whole system is bulky to ensure a high sensitivity and therefore limited for integrated applications.

Recently, nanophotonic structures have attracted extensive interests in optical sensing fields^{27, 28}. Novel designs and excellent sensing performances have been demonstrated due to their remarkable electromagnetic field enhancement²⁹, spectral manipulating³⁰, chirality³¹ and phase³² engineering, etc. Some pioneered works have also explored mid-IR gas sensing. By manipulating the spatial electromagnetic field distribution, a detection limit of 60000 ppm for CO₂ was demonstrated in a 4 mm long gas cell device containing a metal microstructure array, which provides a 1100 times absorption enhancement in the optical path together with a porous metal-organic framework (MOF)³³. By engineering the emission spectrum, an NDIR sensor with a narrowband thermal emitter based on plasmonic crystal was demonstrated with a detection limit of 10000 ppm for CO₂ in a 7.5 mm gas cell³⁴. Similarly, the detection wavelength can also be engineered by integrating microstructure filters with the detector^{23, 25}, in which case it can form a sensing system with a low-cost broadband source. Although all these works demonstrated promising developments, the nanophotonic mid-IR gas sensors still suffer some major issues, 1) the detection limit is too high for low concentration gas detection, 2) the linewidth of either emitter or detector is too large with a quality (Q) factor < 10 and limits the device figure of merit, 3) a lack of spectroscopic analysis, and 4) the gas cell is still not compact.

In this article, a novel mid-IR gas sensor consisting of a narrowband plasmonic absorber integrated with a thermal detector is proposed to address these issues. The shallow metal grating structure is adopted and found to provide a high Q factor resonance and strongly localized resonant field, which ensures a high sensitivity even at a limited light-gas interaction length. The combination of the optical resonator and thermal detector offers on-chip direct readout for portable gas sensors. Thoughtful investigation based on both optical and thermal simulation reveals the significant enhancement on the sensitivity via both SPR and MOF. The on-chip spectroscopy with an ultrahigh spectral resolution is also demonstrated by using a narrowband sensor array with the help of compressive sensing algorithm. In addition, the size effect existing in most periodic plasmonic structure is investigated considering the practical applications and a potential solution is discussed.

2 Mechanism and design

2.1 Mechanism

Conventionally, the gas sensing system needs a bulky gas chamber to ensure a strong light-gas interaction for low detection limit^36-38. As is well known, micro-resonators are usually used to enhance the light-matter interaction³⁰, which is able to reduce the sensor dimensions for distributed or low-load platform while keeping a high performance. To construct a high sensitivity, compact gas sensor for on-site application, it is important to integrate separated elements into a single multi-functional component. Moreover, the performance is maintained or even improved by an optimal combination of different functions. Inspired by the previous work on microfluidic integrated metamaterial 'flowing through' sensor²⁹ and color routing metal scatters integrated silicon optoelectronic device³⁹, a novel mid-IR gas sensor is proposed as shown in Fig. 1(a), where an optical resonator such as metal covered subwavelength periodic gratings integrates with thermal resistance material. It can be seen as a monolithic combination of a resonant sensor and a thermal detector. The incident light is coupled to the surface resonant mode by the gratings and the on-resonance absorption generates heat mainly in metal, which is transmitted to the adjacent thermal resistive materials. The operating mechanism as shown in Fig. 1(b) is that the environment gas variation modifies the light absorption of the resonator and thus changes the temperature of the sensing element with a result of an electric signal by the thermal resistance of VO₂. As a result, it is possible to achieve chip scale gas sensing system, possessing a compact device dimension due to the enhanced light-matter interaction and the novel combination of sensing and transducing elements.

Fig. 1. (a) Schematic of a multilayer stack (Au/Si₃N₄/VO₂/Si₃N₄) coated silicon gratings for on-chip gas sensing. (b) Sensing mechanism. The variation of gas concentration induces an increase/decrease of light absorbance of the microstructures and then causes a temperature increase/decrease, which generates an electrical signal via VO₂.

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For a high sensing performance, it needs to optimize both optical and electrical design to integrate efficiently. From the optical sensing perspective, the larger change of the light absorption at the same gas concentration variation, the stronger the detection signal. To achieve this, a resonator with a narrowband and efficient absorption is required in a broadband wavelength range. The wavelength selective detection also increases the gas selectivity. From the electrical transducing perspective, although the photodetectors based on compound semiconductors usually have high detectivity in the mid-IR range⁴⁰, it is too expensive and not compatible to the CMOS process. Thermal detectors with a reasonably good sensitivity attract lots of attention due to the simplicity and low cost⁴¹. Obviously, the more efficient of the heat induced resistance variation, the stronger electric current signal, i.e. the device is more sensitive. To achieve this, a thermal resistance material with a large temperature coefficient of resistance and low 1/f noise such as VO₂ is chosen and fabricated adjacent to a thermal source. To connect optical and electrical perspectives, the on-resonance light absorption is converted to photocurrent in such a Au/Si₃N₄/VO₂/Si₃N₄ multilayer thermal resistor.

However, it is not straightforward to achieve a narrowband resonant absorption with a large Q factor. In fact, the Q factors are very low for most plasmonic and metamaterial absorbers based on periodic metal structures although they usually have strong light-matter interaction^{29, 42}. For example, the microfluidic metamaterial sensor has a resonant absorption with a Q factor less than 10²⁹ and a SPR photodetector has a resonant absorption with a Q factor about 15⁴³. Fano resonance⁴⁴, asymmetrical unit cell⁴⁵ and even gain material⁴⁶were used to increase the Q factor. Generally, the Q factor associates with radiation loss and absorption loss in a resonant system^{16, 47}. It is important to reduce both losses to realize a high Q factor. The absorption is associated with the ohmic loss. Although TiN, AZO and graphene have been investigated as alternative plasmonic materials, noble metals are still the main materials to construct plasmonic or metamaterial absorbers, where Au and Ag have relatively low absorption loss. On the other hand, the radiation loss can be reduced to zero in a flat layered structure. Therefore, the radiation loss in a resonator configuration as shown in Fig. 1(a) can be suppressed by decreasing the grating depth. However, the grating depth cannot be too small because the light absorption of such a resonator depends on the optical coupling. Based on the coupled mode theory, the maximum absorption occurs at the critical coupling condition when the radiation loss equals the absorption loss²⁶. Therefore, a systematic investigation is required to optimize the optical design of gas sensor.

VO₂ is a typical thermal resistance material, which has attracted great interest for several decades due to its metal-semiconductor transition around 60℃ (Supporting Information Fig. S1). It has been widely used in infrared detectors^{48, 49}. For example, the commercial VO₂ infrared detector can detect a temperature variation as low as 30 mK⁵⁰. To enable the on-chip direct readout of the mid-IR gas sensing signal, VO₂ is deposited close to the metal layer and is separated by a Si₃N₄ layer to avoid shortcut as shown in Fig. 1(a). Apart from the electric insulation, it is also important to reduce the thermal conductance of the transducer. It can be realized by fabricating the Au/Si₃N₄/VO₂/Si₃N₄ multilayer stack on a silicon membrane by removing the silicon handle layer at the back of a silicon-on-insulator (SOI) wafer. It is important to optimize the device structure by the thermal modeling to reduce heat dissipation and ensure a large variation of electric resistance.

2.2 Optical design

The optical model of the gas sensor is shown in Fig. 1(a), where the silicon gratings with slope sidewalls (θ=54.7°) were used to consider the practical fabrication process by wet etching. The numerical simulation is based on the finite-difference time-domain algorithm and the material parameters are from literatures⁵¹. First, the periodic boundary condition with a plane wave source is used to model the optical properties of infinite periodic structure. The structure dimensions are optimized to achieve a single resonant peak in the mid-IR absorption spectra with low background absorption. As shown in Fig. 2(a), the resonant wavelength λ_r increases with the environmental RI n_gas, where λ_r = 3300 nm at n_gas = 1 and λ_r = 3333 nm at n_gas = 1.01. Therefore, the high sensitivity S = 3300 nm/RIU is achieved. The large sensitivity is associated with the strong confinement of the resonant mode on the surface of the sensor as shown in Fig. 2(c), which provides a strong near-field light-gas interaction. Moreover, the absorption peaks are narrow with an average FWHM of approximately 13 nm and consequently the Q factors are around 250 as shown in Fig. 2(b), which is one order of magnitude larger than that of conventional plasmonic and metamaterials absorbers⁴². As a result, a figure of merit FoM=S/FWHM > 200 and a FoM*= (dI/dn)/I > 96 (I is the light intensity, dI is the variation of intensity for a change of RI dn) are achieved⁵². In contrast, the FoM and FoM* are 60 and 55, respectively, in plasmonic Mach-Zehnder interferometer gas sensor⁵³.

Fig. 2. (a) Simulated absorption spectra at different n_gas for the device structure in Fig. 1(a). The period of gratings P = 3.3 µm, the grating depth h_g = 160 nm, and the grating width w_g = (w₁+w₂)/2 = 3 µm. (b) Q factor and FoM at various n_gas. (c) The electric field distribution at the resonance peak (λ = 3.3 μm) at n_gas = 1. (d) Poynting vector at the resonance. (e) The calculated absorption spectra as functions of wavelength and incident angle. (f) Sensitivities of different order modes versus the incident angle.

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It is important to understand the physics governing the light coupling to the high Q surface resonant mode. In such a continuous metal film coated grating structure, propagating SPR modes are supported. Therefore, the resonance wavelength of the diffractive coupled surface propagating mode can be de determined by the momentum matching conditions:

1$k\sin ({\theta _{in}}) + mG = \pm {k_{sp}}, $

where θ_in is the incident angle, G=2π/P is the grating constant, k=2πn_gas/λ is the wave vector, and k_sp is the wave vector of SPR mode. Since ultra-shallow (H < λ/20) grooves can be considered as very small perturbations to the flat metal surface, k_sp can be approximately calculated using the dispersion relationship of SPR mode supported by a flat Au/dielectric interface. In addition, m is an integer representing the diffraction order while '+' and '-' signs in the right side of the equation correspond to diffracted waves of orders m > 0 (positive order) and m < 0 (negative order), respectively. In Fig. 2(e), the resonance wavelength versus the incident angle predicted by SPR coupling formulas (Eq. (1)) is superimposed over the numerical absorption spectra of the multilayer grating structure. The theoretical prediction shows reasonable agreement with the numerical calculations with regards to the similar band shift upon changing incident angle or RI of the incident medium. The findings above offer a convincing proof that the observed absorption anomaly stems from the diffractive character of the periodic structures. It is interesting to quantitatively determine the theoretical maximum RI sensitivity for a specific diffraction order coupled SPP mode in such a device configuration. As illustrated in Fig. 2(f), the RI sensitivity at normal incidence is 3300 nm/RIU for the first diffraction order and decreases by half for the second order, which is close to P/|m|. As the angle of incidence increases, the diffractive coupled SPP mode splits into two modes linked to positive or negative orders. From Fig. 2(f), it is observed that the RI sensitivities of positive and negative orders have opposite dependency on the incident angle. With the increasing incident angle, the sensitivity of the negative order grows while the one of the positive order reduces. For extremely large incident angles, the RI sensitivity of the first negative order mode is approaching a remarkable value of 6580 nm/RIU.

For on-chip electrical readout, it is preferred to have a high resonant light absorption so that large electrical output signal can be realized by the temperature variation associated with light absorption. As mentioned above, the maximum absorption occurs at the critical coupling condition when the radiation loss equals the absorption loss. By finely tuning the grating depth, high absorption above 96% at the resonances is obtained as shown in Fig. 2(a). Figure 2(d) shows the corresponding Poynting vector plot at the resonance for the critical coupling case. As indicated by the arrows, the electromagnetic energy flows are primarily trapped on the top of the gratings with the formation of the vortex-like Poynting vector profiles, resulting in the significantly suppressed reflection loss. In this scenario, most of the incident energy will be efficiently absorbed by the Au layer and generates heat that raises the temperature of the Au/Si₃N₄/VO₂/Si₃N₄/Si stack.

2.3 Thermal analysis

As described in the device mechanism, photothermal conversion is a key step to connect the gas induced light absorption to the on-chip electrical readout. There are two major factors for the efficient photothermal conversion in this proposed gas sensor. One is the heat capacity and the other is the heat dissipation. The smaller the heat capacity and the slower the heat dissipation, the higher temperature difference can be realized in the VO₂ layer, i.e. a higher sensing performance. An SOI wafer based fabrication process is straightforward in this case by integrating the transducer in the silicon device layer and removing the backside silicon handle layer to form a membrane. As shown in Fig. 3(a), the grating structure is fabricated on the silicon device layer and then covered with the Au/Si₃N₄/VO₂/Si₃N₄ stack. By removing the backside silicon handle layer, a combined sensing and transducing element is achieved including a multilayer stack of Au/Si₃N₄/VO₂/Si₃N₄/Si/SiO₂. This dual functional element is electrically connected with two electrodes on the surrounding silicon mesa by Au wires with a width of 20 µm. As seen, the transducer is surrounded by air in both up and down directions. Moreover, the heat dissipation channel in the plane is governed by the thin SiO₂ film. Therefore, it is expected to have an obvious temperature variation under illumination. The sensing area covers a size of 330 µm × 330 µm, including 100 periods of gratings. There is a buffer area with 500 µm width between the sensing window and the surrounding mesa. In the thermal simulation, the grating region of the structure can be treated as a heat source with a power density determined by the illumination and light absorption from the optical simulation above. Open boundary conditions are set at the four lateral surfaces of the structure and convection boundary conditions are used for the rest, where the heat transfer coefficient is set to be 3 W/(m²×K). The thermal conductivity and heat capacity of various materials are from the literature⁵⁴ and the material database of COMSOL software.

Fig. 3. (a) Schematic of on-chip mid-IR gas sensor based on an SOI platform, where the silicon substrate in the area underneath the sensor is removed to reduce the thermal dissipation. The thickness of each layer in the Au/Si₃N₄/VO₂/Si₃N₄/Si stack is 200 nm, 50 nm, 100 nm, 500 nm and 4 μm, respectively. The thickness of the oxide layer is 1 µm. P = 3.3 µm, h_g = 220 nm, w_g = 3 µm. (b) Simulated temperature distribution across the sensor with the illumination on and off when the power density of light is 3.75 W/cm² at 3.348 μm and corresponding absorption efficiency is 58%. (c) Temperature maximum under different wavelength illumination at the same power density and the absorption spectra of the gratings. The period number of the grating is 100. (d) Absorption spectra for variation of different environmental RI. (e) Absorption at 3.345 µm illumination and the associated device temperature versus the variation of different environmental RI.

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As shown in Fig. 3(c), the peak absorption is 58% due to the limited area (100 gratings) with a FWHM of 18 nm. Illuminated at a resonance wavelength of 3.348 µm, the active region shows a temperature distribution between 300 K and 332 K as shown in Fig. 3(b). By tuning the illumination wavelength, the temperature varies accordingly with the same trend of the absorption spectrum, which means that the photothermal effect is dominated by the surface mode of the grating structures. In fact, gas detection based on RI has a long history although the RI variation of gas with the concentration is not as large as liquid. In 1982, SPP has been applied for halothane detection with the sensitivity of 3×10^-5 deg/ppm¹⁹. Recently, an extremely low detection limit < 10^-8 RIU was demonstrated in a 30 mm all-fiber gas sensor⁵⁵. It is interesting to know how much the temperature can be affected by the gas environment in the proposed sensor with a size less than 2 mm² and its sensitivity. As shown in Fig. 3(d), the resonance wavelength shifts from 3348.0 nm at n_gas = 1 to 3349.3 nm at n_gas = 1.0004, which indicates the wavelength sensitivity S = 3250 nm/RIU. Considering the spectral resolution (~0.5 cm^-1) of commercial Fourier transfer infrared (FTIR) spectrometers, it can measure a minimum RI change of 1.7×10^-4 RIU that is much larger than the counterpart in the visible range. It is obviously not enough for gas sensing. With the resonance shift, the absorption changes as well. For example, the absorption at 3.345 µm decreases from 51.8% at n_gas=1 to 46.7% at n_gas=1.0004, with the amplitude sensitivity S*= ΔI/Δn = 127.5%/RIU. This change of light absorption results in a temperature variation of 2.7 K as shown in Fig. 3(e). Considering the detection resolution of 30 mK of commercial VO₂ thermal detector⁵⁰, the RI detection limit of such an on-chip gas sensor is expected to be 4.4×10^-6 RIU. This value gives a detection limit of approximately 29000 ppm for CO₂ in a Ar/CO₂ mixture, which is compatible to previous works^{33, 34}. It is noted that the analysis of the sensing performance in this section only considers the real part of the gas RI, i.e. this technique can be carried out for all kinds of gases that have no absorption at this wavelength. The advantage is that the similar sensing experiment can be conducted for various gases without matching the laser source to the gas absorption peaks. In practical terms, there are requirements on low concentration gas detection or multiplexing gas detection from gas mixture. It is needed to further reduce the detection limit and improve the resolving capability. The former can be improved by optimized thermal design and gas enrichment strategy. The latter can be realized by matching the laser wavelength to the unique absorption peak of the target gas or enable on-chip spectroscopy by a transducer array.

3 Results and discussion

3.1 Thermal optimization and gas enrichment

To further improve the sensitivity, optimizing thermal design and introducing gas enrichment are both potential solutions. Actually, the device structure in Fig. 3(a) has relatively high heat dissipation via the large area membrane and it is not easy to fabricate an array of such a cell structure due to the wet etching for removing the silicon handle layer. Thus, an optimized air bridge structure commonly used in thermal focal plane array⁵⁶ are investigated, where the Au/Si₃N₄/VO₂/Si₃N₄ stack with gratings is supported by the Si₃N₄/W air bridge as shown in Fig. 4(a). This configuration provides an excellent thermal insulation due to the narrow heat dissipation path and is easy to form a transducer array for multiplex sensing or on-chip spectroscopy. The simulation setting is similar to the one in Fig. 3. As shown in Fig. 4(c), the temperature distributions clearly show the limited heat dissipation along the supporting arms and uniformity across the transducing element. For a transducer with a size of 330 µm (100 gratings) × 50 µm, the temperature of the membrane increases approximately 34℃ if illuminated at a wavelength of 3.345 µm with a power density of 1 W/cm². Considering the smaller thermal source and the lower illumination power than that in Fig. 3(a), the heating efficiency is approximately 30 times higher. For the environment gas RI changing from 1 to 1.0004, the temperature variation is 3.5 K. Considering the temperature detection limit of 30 mK of conventional VO₂ thermal detector⁵⁰, the RI sensing limit of this sensor is approximately 3.4×10^-6 RIU for the device working at the semiconductor phase of VO₂. For a Ar/CO₂ mixture, a detection limit of 22550 ppm can be estimated from this value.

Fig. 4. (a) Schematic of on-chip mid-IR gas sensor array based on an air bridge structure. The grating region has a size of 330 µm × 50 µm. The Au/Si₃N₄/VO₂/Si₃N₄ stack is shown in the inset and the thicknesses are 200 nm/50 nm/100 nm/500 nm, respectively. The stack is supported by the Si₃N₄/W bridges on Si substrate. (b) Temperature and relative electrical resistance variation of the sensors versus the variation of different environment gas RI. 'PD' means the power density of the incident light. (c) Simulated temperature distribution across the sensor with and without illumination at a wavelength of 3.348 µm with a power density of 1 W/cm² and the absorption is 58%.

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3.2 Absorptive gas sensing and on-chip spectroscopy

It is noted that only pure RI sensing is discussed above, which has no gas selection. The molecular absorption fingerprints of gases are actually very important for gas detection and identification. The common way is to choose a laser with an emission wavelength matching one absorption peak of the target gas and monitor the absorption variation. As discussion in literatures^{23, 33}, MOF and polymer can be used to enrich the gas and thus increase the absorption. Gas enrichment technique was also used in refractive index sensing by coating MOF on metal nanoparticles⁵⁷. Moreover, the greatly localized field of SPP as shown in Fig. 2(c) further improves the influence of the enriched gas in the MOF or polymer if it is close to the plasmonic structure. Similarly here, a MOF (zeolitic imidazolate framework, ZIF-8) with selective adsorption of CO₂⁵⁸ with a thickness of 2.7 μm is placed on top of the sensor. The void fraction of ZIFs is approximately 0.47⁵⁹. The refractive index of the gas adsorbed MOF is given in Supplementary Information Section 2. In thermal simulation, the thermal conductivity and heat capacity at constant pressure of MOF are from literatures^{60, 61}.

As shown in Fig. 5(a), the simulation shows that an absorption variation as high as 37% for 10% CO₂ in a Ar/CO₂ mixture can be obtained for the MOF and plasmonic absorber composite structure at 2.71 μm compared to 0.0046% for the pure CO₂ with the same optical interaction length. As shown by the red and green lines, the pure RI variation in the real part induces a change of 27.8% in absorption, which is the working mechanism of sensors in Fig. 3 and 4. In addition, the absorption of CO₂ further enlarges the absorption variation shown by the blue line. As a result, in such a plasmonic absorber based gas sensor, both real and imaginary parts of RI of the target gas contribute to the sensing signal and thus improve the sensing performance by an enhancement factor as high as 8043. The performance may be further improved if the device is set to work at the CO₂ absorption peak for example 4.4 μm. As shown in Supplementary Information Section 3, it is easy to tune the device resonance to various gas absorption peaks. At the same illumination power and the membrane size as Fig. 4(b), the temperature raises by 31.44 K due to large absorption variation. Consequently, the detection limit of 95 ppm is evaluated considering the 30 mK resolution of conventional VO₂ detector. This value is very promising considering a very compact light-gas int eraction length of 2.7 µm in the proposed configuration that is three orders of magnitude smaller than the previous works^{32, 52}. Moreover, in the above case the VO₂ film is in the semiconductor phase. As shown in Fig. 4(b), if the illumination power increases to 1.25 W/cm² and 3.75 W/cm², the temperature of the membrane approaches 65 and 155℃ respectively as shown in Fig. 4(b) and thus the VO₂ film is in the phase transition region and the metallic phase respectively. First, the rates of change in temperature at the same gas RI variation in phase transition region (33062 K/RIU) is about 4 times larger than that in the semiconductor phase (8745 K/RIU). Assuming the same temperature measuring resolution, the gas concentration detection limit can be reduced to 24 ppm if the sensor is working at the VO₂ phase transition region. Moreover, the temperature resolution of 30 mK is for the VO₂ detector working in the semiconductor phase. As shown in Fig. 4(b), the relative electrical resistance variation in the phase transition region is two orders of magnitude larger than that in the semiconductor phase. Although a small working temperature range and the much lower temperature resolution are expected if the VO₂ thermal detection is developed in its phase transition region. As a result, a sub-ppm detection limit may be realized by all these strategies for extremely low concentration of target gas.

Fig. 5. (a) Absorption spectra of a similar sensor as shown in Fig. 4 with an additional MOF layer placed on the top surface in pure Ar₂ and a mixture of Ar(90%)/CO₂(10%). The result in a mixture of Ar(90%)/CO₂(10%) ignoring the absorbance of CO₂ is also shown for comparison. P = 1.99 µm, h_g = 100 nm, w_g = 1.25 µm. RIs of CO₂ and MOF refer to literatures^{57, 60}. For a same membrane size (330 μm×50 μm) with the one in Fig. 4, there are 165 gratings in this case. (b) Simulated temperature distribution across the sensor illuminated at a wavelength of 2.71 µm with a power density of 1 W/cm² in a mixture of Ar(90%)/CO₂(10%).

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Although the narrowband detector and the MOF have some selectivity of target gas, the fault alarm could still occur using the non-dispersive method if different gases with similar absorption wavelengths or adsorption coefficients are mixed. Spectroscopy is an excellent way to address this issue because each gas has unique absorption fingerprints associated with the molecular rotation and vibrational frequency, but the current commercial spectrometers are too large and expensive for on-site application and the spectral resolution (0.5 cm^-1) is limited to resolve fine gas energy level. As the proposed plasmonic gas sensor has tunable absorption wavelength by simply changing the grating period, on-chip spectroscopy can be realized if a series of sensors with different absorption wavelengths are arranged into an array. Using a broadband source, each sensor detects the signal of the target gas absorption spectrum in a certain wavelength range. By combining all these signals, the whole absorption spectral information can be obtained by using the compressive sensing algorithm (Fig. 6(a)), resulting in significantly improved spectral resolution^62-67. For example, quantum dot absorptive filters⁶³, plasmonic grating filters⁶⁴ and multimode fibers⁶² have been explored to construct the microspectrometer. To verify this idea, 80 gas sensors similar to the one in Fig. 4(a) are designed with the spectral response shown in Fig. S3(c), which can be patterned in a single lithography process step. The spectra of illumination source, CO₂ absorption and 80 sensors are given in Supplementary Information Section 4. Generally, the resonance linewidths of these absorption spectra are approximately 10 nm (0.014 cm^-1), but their spectral resolution can be very high by calibrating via tunable QCLs. The CO₂ molecular absorption coefficient (red line in Fig. S3(b)) is obtained from the HITRAN database⁵⁹. The black and blue lines in Fig. 6(b) are simulated via a Gaussian model with a setting of spectral resolution of 0.5 cm^-1 and 0.1 cm^-1, i.e., they mimic the measured spectra of FTIR at the corresponding resolution. As seen, there are actually 7 peaks between 2673.9 nm to 2676.3 nm with an average linewidth of the absorption peaks of approximately 0.1 nm, which is far beyond the capability of the state-of-the-art spectrometer (0.5 cm^-1). The mimic measured spectrum at a resolution of 0.5 cm^-1 cannot accurately resolve each absorption peak. Please note that the resolution of 0.1 cm^-1 is beyond the state-of-the-art of FTIR. To reconstruct the fingerprint absorption spectrum using the sensor array, first the integrations of the broadband source spectrum, CO₂ absorption spectrum and the sensor spectral responses are calculated, which in fact associate with the electrical readouts of the sensor array. Similar data without CO₂ absorption can also be obtained. Using the L1 minimization algorithm, the CO₂ molecular absorption spectrum can be reconstructed with the calibrated sensor spectral response and the two integration array above (Fig. 6(b)). As seen, the reconstructed spectrum almost overlaps with the original signal with the resolution of approximately 0.01 nm that is far better than the commercial spectrometer. Therefore, the proposed mid-IR gas sensing technique not only provides potential high sensitivity for gas sensing but also an excellent on-chip spectroscopic function for fingerprint identification. Note that the spectral resolution of such technique associates with quite a few factors including the spectral correlation between the adopted filters, the accuracy of the calibrated filtering responses, the reconstruction algorithm itself, etc. Moreover, the actual measured spectral resolution is largely limited by various noises in the measuring system. It is found that the noise tolerance highly depends on the algorithm used for the signal recovery, which can be improved by using a quadratic instead of the equality constraint⁶⁸.

Fig. 6. Gas molecular fingerprint spectrum reconstruction with the monolithically integrated plasmonic gas sensor array Φ(λ). (a) Schematic of the reconstruction process for an unknown input signal X(λ), where the photoelectric signal Y of each sensor is recorded. (b) The recovered spectrum (red line) and the reference spectra by simulation based on HITRAN database (black and blue lines).

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As seen, a large number of sensors in an array are required to construct the spectra although the number can be further reduced by optimizing the reconstruction algorithm. It is also preferred to reduce the size of each sensor to improve the mechanical stability of the membrane structure. In our case each sensor has a sensing area of 330 μm×50 μm at a cost of absorption as shown in Fig. 3(c) and that in literature³⁵ is even 1000 µm × 1000 µm. It is important to know the fundamental reason of the size effect and find a way to solve it. As discussed in Fig. 2(e), the light absorption is dominated by the SPP mode. The incident light is coupled into the in-plane surface wave by the gratings and absorbed during its propagation along the metal surface. If the grating region is not large enough to cover the attenuation length of the surface wave, the light absorption is not complete, which is the reason of the reduced absorption. This value is further reduced to 30% if there are only 60 periods as shown in Fig. S4. This size effect exists at any wavelength range and is worse in the structure with a larger Q factor. As seen, the absorption drops from 93% to 60% when the grating number is reduced to 50 in a wavelength range around 9 µm as shown in Fig. S4(b). There are two ways to reduce the size of transducer element without sacrificing the resonant absorption. One is to increase the attenuation coefficient such as using lossy materials and the other is to increase the effective propagating length of the surface wave such as adopting a lateral cavity, both of which increases the absorption at a certain device size. However, the former is not preferred because it reduces the Q factor of the resonance simultaneously. Alternatively, the latter can be realized by adding two reflective structures at both ends of the gratings as shown in the inset of Fig. S4(c). By fabricating a metal coated step with a depth h=9.9 µm at both ends of the gratings, the resonant absorption reaches as high as 88%. This remarkable suppression of the size effect comes from the efficient reflection of the surface propagating mode. As shown in Fig. 2(c), the main out-of-plane field of the surface propagating mode extends to a distance more than one period of the grating. Thus, the depth of the reflectors should be larger than one period. If the reflectors are too small to reflect all the surface propagating modes as shown by the blue and red lines in Fig. S4(c), the light absorption drops. In addition, the length of the transducing elements along the grating direction can be further reduced as well. As shown in Fig. S4(d), a length of 5 µm is enough to ensure a high absorption efficiency above 85%. Therefore, the transducing element can be as small as 50 µm × 5 µm, which is more than 400 times smaller than the sensing region in Fig. 3(a) and very important for multiplexing and on-chip spectroscopy. How to fabricate such a structure is still an open question for future work.

4 Conclusions

In conclusion, we proposed and demonstrated numerically a novel plasmonic mid-IR gas sensor, which shows a remarkable gas absorption enhancement factor over 8000 in an ultracompact optical interaction length of only several microns. Moreover, on-chip readout and spectroscopy have been achieved by integrating optical sensing, photothermal detection and compressive sensing algorithm. In particular, the estimated spectral resolution as high as 0.01 nm is quite promising to use in gas identification with such a portable device. The unity integration idea of active and passive optical components provides a novel technique for on-chip sensing. The shallow metal grating structure in the proposed sensor also provide an excellent platform combining both localized electromagnetic field and high Q factor.

5 Acknowledgements

We are grateful for financial supports from National Key Research and Development Program of China (No. 2019YFB2203402), National Natural Science Foundation of China (Nos. 11774383, 11774099 and 11874029), Guangdong Science and Technology Program International Cooperation Program (2018A050506039), Guangdong Natural Science Founds for Distinguished Young Scholars (No. 2020B151502074), Pearl River Talent Plan Program of Guangdong (No. 2019QN01X120), Fundamental Research Funds for the Central Universities, Royal Society Newton Advanced Fellowship (No. NA140301) and Key Frontier Scientific Research Program of the Chinese Academy of Sciences (No. QYZDBSSW-JSC014).

6 Author contributions

Q. Chen and L. Wen conceived the work and proposed the design. L. Liang, L. Wen and Q. L. Zheng conducted the simulation. Q. Chen wrote the paper. All authors discussed the results and commented on the manuscript.

7 Competing interests

The authors declare no competing financial interests.

8 Supplementary information