Supplementary Figures

Supplementary Figure 1 | 3D representation of an AlN NPR with bottom inter-digital transducers and top floating metal plate. The 2D FEM simulated lateral-extensional mode of vibration (total displacement) is superimposed to the AlN film.


Supplementary Note 1. AlN nano-plate resonator
The core of the proposed nanoplasmonic piezoelectric IR detector is an aluminum nitride (AlN) nanoplate resonator (NPR). Supplementary Fig. 1 illustrates a 3-dimensional (3D) representation of a conventional AlN NPR using a lateral field excitation (LFE) scheme ( Supplementary Fig. 2). (2) In particular the device equivalent motional resistance, R m , is inversely proportional to the k t 2 ⋅Q product (Supplementary Eq. 1). The achievement of a low value of motional resistance, in a radio frequency electromechanical resonator, is of crucial importance for the direct interface of the device with compact and low-power 50-Ω electronics 3 . Therefore, the figure of merit (FOM) of an electromechanical resonator is defined as the k t 2 ⋅Q product.
It is worth to note that the fabrication process of an AlN nano-plate resonator is post-CMOS compatible.
"post-CMOS compatible process" means that the micro-fabrication process starts with a CMOS wafer and only uses materials which are post CMOS compatible (can be deposited with temperature < 400 °C and dry etched using standard CMOS tools). Previous paper 4 has shown that the current AlN resonant technology employed in this work is post-CMOS compatible. Note that the platinum bottom electrode and gold structures can easily be replaced with standard CMOS metals, such as titanium, titanium nitride, and tungsten.

Supplementary Note 2. Design considerations
The proposed plasmonic piezoelectric NEMS resonant IR detector is modeled with a two-port network with both electrical and mechanical inputs, as shown in Fig. 5a in the main text. When the IR radiation is absorbed by the plasmonically enhanced resonant nano-plate, the temperature of the device increases according to where Q p is the incident IR power, h is the absorption coefficient of the plasmonic resonant nano-plate, ω is the modulation frequency of the incident IR radiation, G th and C th are the thermal conductance and thermal capacitance of the device, respectively. Such IR induced temperature rise results in a shift, ∆f, in the mechanical resonance frequency of the structure (Fig. 1a in the main text), given by which arises due to the intrinsically large temperature coefficient of frequency of the piezoelectric resonant nano-plate (the TCF of AlN resonators is typically in the order of -30 ppm·K -1 for AlN plates thinner than 1 µm). Using these expressions, the detector overall responsivity for slowly modulated impinging IR radiation can be expressed as where R th is the thermal resistance of the device (R th =1/G th ). A crucial parameter that ought to be considered for the design and optimization of the proposed resonant IR detector is the noise equivalent power (NEP), defined as the noise-induced frequency fluctuation f n divided by the responsivity of the detector: Among different noise sources, the fundamental limit to frequency stability of a thermal resonant sensor is given by: (1) the thermal fluctuation noise associated with the spontaneous temperature fluctuations of the detector element due to the finite heat conductance G th to the surroundings, (2) the background fluctuation noise due to radiative heat exchange with the environment, and (3) the thermomechanical noise originated from thermally driven random motion of the mechanical structure. Therefore, the minimization of the NEP associated with each of these three fundamental noise contributions 13 (respectively NEP th , NEP rad , NEP mec ) can be used to drive the design of the IR detector. These NEPs can be expressed by where K B is the Boltzmann constant, T 0 is the temperature of the resonator, A is the area of the device, ε is the emissivity, σ is the Stefan-Boltzman constant, P c is power used to drive the mechanical resonance in the structure, Q is the resonator's quality factor. The total NEP can be expressed as Supplementary Eq. 8 and 9 indicate that minimum NEP, thus a high resolution resonant IR detector, can be achieved by maximizing the device thermal resistance R th , absorption coefficient h, temperature coefficient of frequency, TCF, quality factor Q, and power handling P c .
Another crucial parameter to be considered is the detector response time, which is limited by the thermal time constantof the device th th C R ⋅ = t (10) Supplementary Eq. 8-10 indicate that by improving the thermal isolation of the sensing element from the heat sink (hence increasing R th ) the NEP of the device is reduced but its response time is increased. Therefore, a trade-off between these two important performance metrics needs to be generally considered for the design of the detector. Nevertheless, for a given thermal resistance (guaranteeing a satisfactory NEP) the response time of the sensor can be reduced by minimizing its thermal capacitance, which directly translates to reducingthe volume of the resonant structure.

Supplementary Note 3. Optimization of the nanoplasmonic piezoelectric metasurface
The spectrally selective plasmonic resonant NEMS structure consists of two functional parts defined by  Fig. 4a and b). The three nanoplasmonic resonators were tested in a RF probe station and their electrical admittances versus frequency were measured using a vector network analyzer (as described in the methods section of the main text  Fig. 4c and d). Following these results, the coverage of the plasmonic nanostructures on the top metal layer of the plasmonic piezoelectric NEMS resonator prototype discussed in the main text was set to 80% given the demonstrated capability ofachieving high absorption coefficient while maintaining high electromechanical transduction efficiency when this configuration is employed.

Supplementary Note 4. Estimation of the device thermal properties by 3D FEM simulation
The  Supplementary Fig. 5d.

Supplementary Note 5. Experimental characterization of the noise equivalent power (NEP)
The NEP of the fabricated device was experimentally characterized by measuring all the determining parameters in Supplementary Eq. 7: Frequency noise spectral density, f n : A frequency noise spectral density of f n~1 .46 Hz·Hz -1/2 at 100 Hz was extracted from the measurement by monitoring the short term frequency instability. The resonator was excited at a single frequency, f c = 161.5 MHz, for which the slope of admittance amplitude curve versus frequency is maximum (Fig. 7 in methods in the main text). The peak to peak admittance amplitude fluctuation was recorded (11.7 mdB) and converted to peak to peak frequency fluctuation (96 Hz) by dividing it by the slope (121.3 dB·MHz -1 ). Then, the root mean square (rms) noise was calculated by dividing the peak to peak frequency fluctuation by 6.6 for a 99.9% confidence, and found to be 14.55 Hz. Finally, the frequency noise spectral density was calculated by dividing the rms frequency noise by the square root of the measurement bandwidth (100 Hz), and found to be f n~1 .46Hz·Hz -1/2 .
Mechanical resonance frequency, f 0 : The resonator admittance versus frequency was measured, as described in the main text, showing a resonance frequency f 0~1 61.4 MHz (see Fig. 3a in the main text).
Absorption coefficient h: The IR spectral absorptance of the fabricated structure was experimentally characterized, as described in the main text, showing h~80% for an optimized spectral bandwidth around 8.8 µm (see Fig. 2 in the main text).
Temperature coefficient of frequency, TCF: the resonator frequency sensitivity to temperature was characterized using a temperature controlled radio frequency (RF) probe station, obtaining TCF~23 ppm·K -1 (see Supplementary Fig. 6), which matches the typical TCF values recorded for 500 nm thick AlN contour-mode resonators 5 .
Thermal resistance, R th : The device thermal resistance, in air and at room temperature, was directly extracted from the measurement of the admittance amplitude-frequency (A-f) nonlinearity induced by self-heating 6 . The source of admittance A-f nonlinearities in AlN contour-mode MEMS resonators is attributed to the softening of the equivalent Young's modulus due to self-heating effects. Therefore, the thermal resistance of the device can be experimentally extracted by measuring the A-f response of the resonator for different input IR powers, according to where ∆f is resonance frequency shift, ∆P c is the input RF power to the resonator, Γ = (Z -Z 0 )/(Z + Z 0 ) is the reflection coefficient (Z 0 = 50 Ω), k IF is a constant introduced to take into account the effect of the sampling speed of the network analyzer (k IF = 1 for IF bandwidth of 100 Hz used in the measurement), TCF is the temperature coefficient of frequency, f 0 is the resonance frequency of the resonator. The thermal resistances of two devices, with same geometries but different anchors (Detector1 is with Pt anchors and Detector2 is with conventional AlN/Pt anchors) were extracted based on this method. The measured A-f response and extracted thermal resistance are shown in Supplementary Fig.7  The mismatch between the FEM simulated results and the experimentally measured results is attributed to the heat conduction through air, as the experiment was conducted in air and FEM simulation did not include the contribution of heat transfer from air conduction (simulating the case of vacuum). Basically, the measured R th is a parallel combination of the thermal resistance related to the anchors of the resonator and the thermal resistance associated with the air between the resonator and the Silicon substrate, as illustrated in Supplementary Fig. 8. Based on the measured and simulated R th , the R Air of the two devices can be extracted and found to be 5.3 ×10 4 K·W -1 and 5.0 ×10 4 K·W -1 , respectively. Considering the thermal conductivity of air at 1 atm, and the geometries of the resonator, the average air gap between the resonator and Si substrate can be extracted to be ~20 μm, which is reasonable for a typical XeF 2 isotropic etching of Si to completely release the resonator.
The thermal resistance of the IR detector is limited by the finite thermal resistance of the air gap between the resonator and Si substrate when it is tested in air. Supplementary Fig. 9a shows that the maximum thermal resistance of the IR detector in air at 1 atm (air thermal conductivity of 0.024 Wm -1 K -1 ) is