# Terahertz Detectors Using Microelectromechanical System Resonators

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{1/2}[36]), and outperform other room temperature detectors in terms of response time. However, Schottky diodes operate only at low frequencies (<1.5 THz) because the operation speed of rectification is limited by the transit time of carriers as well as the RC time constants of the device structures. The recent development of Fermi-Level managed barrier (FMB) diodes [37,38,39] utilizes the low barrier height of semiconductor heterojunctions to achieve lower NEP and a broader operation bandwidth than Schottky diodes. Nevertheless, the performance and efficiency of THz rectifiers tend to degrade as the frequency increases [36], which limits their usefulness for frequencies above 1.5 THz.

_{th}, and a heat sink (thermal reservoir) with temperature, T

_{s}, connected to the absorber by a thermal link with thermal conductance, G

_{th}. The incident radiation is absorbed to change the detector temperature, and the resultant changes in certain physical properties are finally output as detectable electrical signals. Representative devices of this type for THz detection include Golay cells, pyroelectric detectors, and bolometers [36].

^{5}–10

^{6}V/W) at room temperature but have a relatively long response time (typically, 15 ms). Other drawbacks, such as difficulty in assembling large arrays and sensitivity to mechanical vibrations, also limit the application potential of the Golay cell [44].

## 2. THz/IR Detection Based on MEMS/NEMS Resonators

^{1/2}and a NETD of 2 K for a 50-Hz noise bandwidth. Yamazaki et al. proposed a torsional resonator made of a tense thin film of polycrystalline Si [76], which exhibits a sensitivity of 30 Hz/K and a thermal coefficient of resonant frequency (TCF) of 830 ppm/K for IR detection. In their later work [75], this TCF is increased to 1000 ppm/K by using the metal-induced lateral crystallization of a hydrogenated amorphous Si (a-Si:H) thin film to form a tension-enhanced poly-Si film. Gokhale et al. [74], for the first time, demonstrate the use of gallium nitride (GaN)-based micromechanical resonator arrays as high-sensitivity, low-noise IR detectors, in which each individual pixel in the array is a thin-film resonator mechanically suspended by thin tethers. For a 100 mK radiation-induced temperature rise, it exhibits a radiant responsivity of 0.0168 W

^{−1}and a thermal time constant on the order of 556 µs. Zhang et al. [73] develop an IR bolometer based on a micrometer-sized torsional resonator with nanoscale supporting rods (~1 μm long and 50–100 nm in diameter). This nanoscale design provides both extraordinary thermal isolation and excellent torque sensitivities, resulting in a NETD of 390 mK. Moreover, they also mentioned that a room-temperature NETD below 10 mK appears feasible with further scaling and optimization.

^{8}pm W

^{−1}, corresponding to a NEP of 20 nW/Hz

^{1/2}at 2.5 THz, as well as a thermal response time of 2.5 µs.

^{1/2}and a detection speed of 40 Hz at room temperature, challenging the state-of-the-art bolometric detectors in the sub-THz range (140 GHz). Furthermore, Sadeghi et al. [83] demonstrate that further improvement in thermal responsivity can be achieved by embedding a phononic crystal membrane into a nanomechanical trampoline. Furthermore, based on silicon nitride, Piller et al. [79] propose a drum NEMS resonator for IR detection, as shown in Figure 1d, which is made of 50 nanometer-thick low-stress silicon comprising an absorber layer. Its working principle is also based on the thermally induced detuning of the resonance frequency. With an IR range of 5 to 20 µm, the drum NEMS resonator achieves a thermal time constant of 17 ms and a NEP of 320 pW/Hz

^{1/2}. It is worth noting that this NEP corresponds to the situation where the IR spot is fully filling the drum area. However, a smaller NEP of 30 pW/Hz

^{1/2}is feasible by optimizing the IR spot size. The electromechanical and thermal properties of the resonator might be deteriorated by the relatively bulky IR-absorbing material (or material stack) attached to the resonator body. To address this issue, a monolayer graphene sheet is utilized in lieu of a conventional metal film to fabricate the IR bolometer [78], as shown in Figure 1e, which is a thin graphene-aluminum nitride plate. Through this, the Q-factor and IR absorptance are improved by 12.6% and a factor of 10 (at 3.4 µm wavelength) and 138 (at 5 µm wavelength), respectively, compared with their metal-electrode counterparts. This results in a thermal time constant of ~0.53 ms and a NEP of ~47 nW/Hz

^{1/2}for the presented IR bolometer, which is a promising candidate for ultrafast and high-resolution NEMS IR detectors.

## 3. THz Bolometer Using GaAs Doubly Clamped MEMS Beam Resonators

#### 3.1. Working Principle and Fabrication of GaAs MEMS Bolometer

_{n}is the angular frequency of the nth vibrational mode, and t, L, and ρ represent the thickness, length, and density of the MEMS beam, respectively. E is the Young’s modulus of material. λ

_{n}is the nondimensional eigenvalue for the nth vibrational mode; the first few values are:

_{th}) the most. The resonance frequency of MEMS bolometers related to such thermal strain is given as [85]:

_{0}is the eigen-frequency (natural) frequency of the first bending mode. z is the beam center deflection. Here, ε

_{cr}is Euler’s critical buckling strain of the MEMS beam, which can be calculated by using the model developed in Refs. [86,87] as:

**Figure 2.**(

**a**) Schematic illustration of the doubly clamped MEMS beam resonator. The conduction layer and the top gates on both ends of the beam form two piezoelectric capacitors, C

_{1}and C

_{2}. A thin NiCr layer is deposited as a THz absorber and is used for calibrating the responsivity of the MEMS beam resonators. (

**b**) The calculated resonance frequency (ƒ/ƒ

_{0}) as a function of ε

_{th}/ε

_{cr}for various beam center deflections (z/t), the ƒ, ε

_{th}, and z are normalized by the natural frequencies, ƒ

_{0}, ε

_{th}, and beam thickness, t, respectively. (

**c**) Schematic illustrations of the beam structures that experience compressive stress (

**top**) and buckling (

**bottom**). Reprinted from [88], with the permission of AIP Publishing. (

**d**) Wafer structure used to fabricate the doubly clamped GaAs beam resonator. Reprinted from [59], with the permission of AIP Publishing.

_{th}but also z. Figure 2b shows the normalized resonance frequency (ƒ/ƒ

_{0}) and beam center deflection (z/t) as a function of ε

_{th}/ε

_{cr}. For an ideal, flat MEMS beam without center deflection (z = 0), as indicated by the top of Figure 2c, when ε

_{th}/ε

_{cr}< 1, the MEMS beam remains flat (z = 0), and f decreases with ε

_{th}and drops to zero at ε

_{th}/ε

_{cr}= 1. However, when ε

_{th}exceeds ε

_{cr}, the beam shows a deflection (z > 0) caused by buckling, as indicated by the bottom of Figure 2c, and the resonance frequency starts increasing with a further increase in ε

_{th}. It should be noted that the strain term remains ε

_{th}/ε

_{cr}= 1 after the buckling of the MEMS beam, which is because the excess ε

_{th}is translated to the increased beam deflection. In other words, the resonance frequency is only determined by z after the critical buckling condition, which can be expressed as:

_{0}is irradiated on the beam, the beam expands thermally, and compressive thermal strain, ε

_{th}, develops in the beam owing to the doubly-clamped structure, which causes the change in resonance frequency of the MEMS bolometer as shown in Figure 2b. Assuming the initial strain of the MEMS beam is zero, the thermal responsivity of MEMS bolometers, R, can be defined as the change in resonance frequency (Δf) with respect to unit incident power, which is expressed as [85]:

_{T}is the thermal expansion coefficient, κ is the thermal conductivity of the beam material, and w is the width of the beam. As we can see from Equation (6), the responsivity of a MEMS bolometer is proportional to the frequency shift with respect to unit incident power, i.e., the slope of the black curve in Figure 2b. Since the slope changes with the applied strain, the R is usually estimated by linear fitting within a small heating power range. From the perspective of dimensions, the responsivity is proportional to (L/t)

^{3}, so the sensitivity can be greatly increased by increasing the aspect ratio of the MEMS beam. However, a too large aspect ratio will make the MEMS beam very easily affected by the initial internal strain [85]. From the perspective of physical properties, the responsivity shown in Equation (6) is determined by the thermal expansion coefficient and thermal conductivity of the beam material in addition to the THz absorptance and the beam dimensions, thus allowing for good reproducibility of responsivity that does not rely on fabrication details of the device. Some feasible approaches to improving the responsiveness of MEMS bolometers will be discussed in detail in Section 4.

_{0.7}Ga

_{0.3}As sacrificial layer on a (100)-oriented semi-insulating GaAs substrate, the beam layer is formed by depositing a 100-nanometer-thick GaAs layer, a GaAs/Al

_{0.3}Ga

_{0.7}As superlattice structure, and a 1-micrometer-thick GaAs layer. Subsequently, a two-dimensional electron gas (2DEG) is formed by growing a 60-nanometer-thick Si-doped Al

_{0.3}Ga

_{0.7}As layer and a 10-nanometer-thick GaAs capping layer. The suspended beam structure is formed by selectively etching the sacrificial layer with diluted hydrofluoric acid (HF), as schematically shown in Figure 2a. The 2DEG layer and the top gate electrodes on the two ends of the beam form two piezoelectric capacitors, C

_{1}and C

_{2}. Utilizing the piezoelectric effect of GaAs developed by NTT Basic Research Laboratories [89], an AC voltage is applied to C

_{1}to drive the beam, and the induced oscillation signal is detected by C

_{2}. In order to obtain a broad sensitivity spectrum independent of wavelength, an impedance-matched NiCr layer is deposited on the MEMS beam as a THz absorber.

_{in}, where P

_{in}is generated by applying a DC voltage to the NiCr film in order to simulate heating by THz radiation. As seen in the figure, when the heating power is increased, the resonance frequency is reduced due to the thermal strain. The frequency shift keeps good linearity up to the mW-range, and the responsivity is estimated as ~79.5 W

^{−1}. This is typical for a MEMS beam with a geometry of 100 × 30 × 1.2 μm

^{3}. The Q-factor of the MEMS resonator is typically ~6000 for these GaAs MEMS resonators. at room temperature.

#### 3.2. Signal Readout and Operating Speed of MEMS Bolometer

_{D}= 16 mV, a 90° phase delay, and a 5 kHz demodulation bandwidth of the PLL. Figure 3c plots the output signal waveforms from the PLL under the conditions switched on and off at various f

_{m}(320–10,240 Hz) and an input heating power of P

_{in}= 32 μW. As seen, the signal amplitude displays a gradual decrease as f

_{m}approaches 5 kHz. The detection speed in the FM detection scheme is governed by two limiting factors. Firstly, the thermal time constant (τ

_{th}) of the system, represented by the ratio of heat capacitance (C

_{th}) to thermal conductance (G

_{th}) of the MEMS beam, significantly impacts the operational speed. The demodulation BW of the PLL circuit also plays a pivotal role in the detection speed of the system since it determines the ability of the PLL to track the frequency shift efficiently. A τ

_{th}of ~55 μs is estimated by using the finite element method calculation, corresponding to a −3 dB bandwidth of approximately 1/2 πτ

_{th}≈ 2.9 kHz. Interestingly, this estimation closely aligns with the measured −3 dB bandwidth of the present MEMS resonator, which is approximately 2.5 kHz. The MEMS bolometer deserves emphasis for its remarkable speed, surpassing that of conventional room-temperature THz thermal sensors. In comparison to the widely used pyroelectric detector [92,93] and the bolometers based on the phase transition in vanadium oxide (VOx) [94,95,96], the present MEMS bolometer shows a comparable responsivity while outperforming these conventional thermal sensors in terms of operation speed by more than 100 times. This outstanding performance underscores the promising potential of the present MEMS bolometer for fast THz imaging [97] and establishes it as a compelling candidate in the field.

#### 3.3. Sensitivity and Dynamical Range of MEMS Bolometer

_{f}represents the frequency noise spectrum. Figure 4 shows the frequency noise spectra as a function of f

_{m}at various driving voltages. As seen, in the case of V

_{D}≤ 8 mV, the n

_{f}roughly increases with the f

_{m}at a range of f

_{m}> 100 Hz, but the noise level is greatly reduced in the case of large driving voltages. In the FM detection mode, the n

_{f}is widely recognized to primarily come from two sources: thermal Brownian motion [99] and residual electrical noise generated by the buffer amplifier incorporated in the measurement circuit. The thermal Brownian motion contributes to white spectral noise, while the residual electrical noise introduces frequency noise that escalates proportionally with the f

_{m}. It is worth noting that both the two noise components exhibit an inverse relationship with the oscillation amplitude of the resonator. That is why the n

_{f}can be efficiently suppressed at a large driving voltage, as indicated by Figure 4. Consequently, a large and linear oscillation amplitude represents an effective approach to enhancing the performance of MEMS bolometers. The minimum n

_{f}obtained in Figure 4 is 3.5 mHz/Hz

^{1/2}at f

_{m}= 1 kHz in the case of V

_{D}= 64 mV. Furthermore, the NEP of the present MEMS bolometer can be estimated as ~90 pW/Hz

^{1/2}. This NEP value is comparable to that of the conventional pyroelectric and VOx sensors; however, the thermal response speed is more than 100 times faster. Furthermore, the NEP limited by the thermal fluctuation noise can be expressed as [100]:

_{B}is the Boltzmann constant and T is the temperature. The typical NEP

_{TF}is 20 pW/Hz

^{1/2}, which is in the same order of magnitude as the measured NEP, indicating that the sensitivity of the present MEMS bolometer is already close to the theoretical limit due to the thermal fluctuation noise [100,101].

_{th}≈ 1 μW, considering the small G

_{th}(~0.1 μW/K) [94]. By contrast, the presented MEMS bolometer works by frequency detection, maintaining good linearity across a wide heat range of 0–3 mW, as shown in Figure 3d. This range is approximately 3000 times larger than that achievable with VOx bolometers. In the case of a 1 Hz detection BW and an acceptable signal-to-noise ratio (SNR = 1), the minimum detectable power, P

_{min}, can be estimated as NEP × BW

^{0.5}× SNR = 90 pW, which gives a dynamic range of over 3 × 10

^{7}.

#### 3.4. Optical Characterization

_{amp}) of 1 s at 300 K. The output frequency (f

_{THz}) of the THz DFG is set to 250 GHz. Figure 5b shows a trace of Δf when a THz radiation of 0.44 μW is switched on and off, revealing a clear and periodic frequency shift. Since the output power of the THz DFG decreases significantly with increasing f

_{THz}[103]

_{,}a wide range is achieved by sweeping f

_{THz}from 250 GHz to 3 THz. In Figure 5c, the solid and dotted curves represent, respectively, the measured output THz power using a cryogenic Si composite bolometer and the MEMS bolometer as a function of the DFG frequency. Furthermore, Figure 5d plots the measured Δf as a function of the calibrated output power of the THz DFG source, determined with a cryogenic Si composite bolometer. As seen, Δf demonstrates a good linear response over a wide range of power levels. The optical P

_{min}of the MEMS bolometer, estimated from Figure 5d, is about 200 pW. Moreover, the optical NEP can be calculated as:

^{1/2}). This discrepancy primarily arises from the relatively small absorption coefficient of the NiCr THz absorber (~20%; calculated for the total power incident on the Si hyper-hemispherical lens) and potential losses in THz radiation collection. Enhancing the absorption coefficient can be achieved through the utilization of metamaterials [104,105] or a proper choice of substrate thickness [106].

## 4. Attempts at Improving the Performance of GaAs MEMS Bolometers

#### 4.1. Strain Tuning Effect on Responsivity

_{th}/ε

_{cr}= 1), as shown by the black curve of Figure 2b, suggesting that the responsivity becomes very large. Such a transition point is preferable for high-sensitivity sensing applications. Therefore, if a precise compressive strain is preloaded to induce the buckling of the MEMS beam, then the thermal responsivity of the MEMS beam can be greatly improved.

_{InAs}and α

_{GaAs}are the lattice constants of InAs and GaAs, respectively, and x represents the content of indium in In

_{x}Ga

_{1−x}As. To achieve the buckling condition of the MEMS beam (i.e., ε

_{l}= ε

_{cr}), one method is to precisely control the amount of indium; the other is to carefully vary the beam length due to the fact that ε

_{cr}is a function of beam length, as shown in Equation (4).

_{x}Ga

_{1−x}As and unstrained GaAs MEMS bolometers as a function of heating power, which both have a geometry of 120 (length) × 30 (width) × 1.2 (thickness) μm

^{3}. The indium content, x, in the In

_{x}Ga

_{1−x}As sample is 0.001. As seen, in comparison to the unstrained GaAs resonator, the resonance frequency of the In

_{x}Ga

_{1−x}As resonator shifts to the higher frequency side from the very beginning as heating power increases, indicating the In

_{x}Ga

_{1−x}As resonator is initially buckled. Under such an initial buckling condition, the In

_{x}Ga

_{1−x}As resonator shows a 3 times larger frequency responsivity (295 W

^{−1}) than that of the GaAs resonator (100 W

^{−1}), demonstrating that the introduction of buckling conditions is useful for achieving higher thermal sensitivity for MEMS bolometers.

_{x}Ga

_{1−x}As beam layer with a fixed indium concentration, x = 0.004, is grown, and then the unstrained GaAs and strained In

_{0.004}Ga

_{0.996}As MEMS beam resonators with various beam lengths, L (61–115 μm), are fabricated. Figure 6b shows the absolute value of responsivity, R, as a function of L for the GaAs and In

_{0.004}Ga

_{0.996}As beams (dots), together with theoretical expectations (solid line). As seen in Figure 6b, the In

_{0.004}Ga

_{0.996}As beams exhibit a much higher R than the GaAs beams with the same L. When the In

_{0.004}Ga

_{0.996}As MEMS beam achieves its buckling condition at L = 105 μm, it shows a R of 2400 W

^{−1}, which is 16 times higher than that of the GaAs sample of the same length (150 W

^{−1}). This result demonstrates that the introduction of a carefully designed compressive strain is useful for achieving high thermal responses for MEMS bolometers without deteriorating their detection speeds. Furthermore, the measured R is smaller than that of the theoretical expectation (red curve) due to a small initial deflection in the In

_{0.004}Ga

_{0.996}As MEMS beams. Consequently, a further increase in R is expected if the beam deflection can be suppressed.

#### 4.2. Control of Mechanical Nonlinearity in MEMS Bolometer

^{3}/12 for beams of rectangular cross-sections, with b and t being the width and thickness of the MEMS beam, respectively); T

_{0}is the inherent tension (positive for a tensile force and negative for a compressive force). Note that, here, the first bending mode of the MEMS beam is considered to study the mechanical nonlinearity. As seen in Equation (11), the cubic nonlinearity coefficient $\alpha =\frac{E}{2\rho L}\frac{{\left(\int {({\varphi}^{u})}^{2}du\right)}^{2}}{\int {\varphi}^{2}du}>0$ gives a hardening nonlinearity [127] and causes the resonance frequency to shift to the higher frequency side during the oscillation. However, once the symmetry of the MEMS beam is broken, e.g., if an initial center deflection exists in the MEMS beam, another quadratic (softening) nonlinearity will arise during the oscillation. As shown in Figure 7a, when the MEMS beam has an initial center deflection of z

_{0}in the steady state, it has a new equilibrium position (z

_{0}) for the oscillation. Thus, the change in beam length caused by oscillation must be calculated from this new equilibrium position. Since the MEMS beam has a steady deflection downward, the beam extends more (hardening) in the case of downward deflection but extends less (softening) when it deflects upward in the oscillation, giving a decrease in total nonlinearity.

_{T}, is expressed as [108]:

_{T}results from the compressive strain (ε) applied to the beam (z

_{0}→ z

_{T}). Compared with Equation (11), an additional quadratic nonlinear term $\beta =\frac{3{z}_{\mathrm{T}}E}{2\rho L}\frac{{\left(\int {({\varphi}^{u})}^{2}du\right)}^{2}}{\int {\varphi}^{2}du}=3{z}_{\mathrm{T}}\alpha $ arises, which compensates for the cubic hardening nonlinearity and leads to the suppression of the total nonlinearity [127]. Since β is proportional to z

_{T}and z

_{T}originates from the applied strain, the nonlinearity can be suppressed by precisely controlling the applied strain.

^{3}applied for the Young’s modulus and density of GaAs material. Figure 7b shows the calculated resonance frequency (ƒ/ƒ0) as a function of oscillation amplitude at various ε/ε

_{cr}values for z

_{0}/t = 0.1. As seen, when the compressive strain approaches the buckling condition (ε/ε

_{cr}= 0.72), the positive frequency shift reduces significantly and the frequency shift reaches a minimum at ε/ε

_{cr}= 0.66, which is because of the steep increase in β as shown in Figure 7c. This result shows that the nonlinearity of the MEMS beam can be well suppressed by approaching the buckling condition of the MEMS beam.

_{in}, to generate a thermal strain in the MEMS beam), the MEMS beam exhibits a ~300 nm linear oscillation amplitude in the case of P

_{in}= 8.4 mW (buckling condition: P

_{in}≈ 10 mW), as shown in Figure 8b, which is 10 times larger than that of the MEMS beam without thermal tuning.

_{0.004}Ga

_{0.996}As beams and then varying beam lengths (L = 51–111 μm). Figure 8c plots the measured resonance frequency shift (Δƒ) of In

_{0.004}Ga

_{0.996}As samples as a function of the oscillation amplitude with various L. As seen, the Δƒ changes from positive to negative as the beam length increases and reaches a minimum at L = 103 μm, giving a ~200 nm linear oscillation amplitude. Compared with that of the GaAs sample with the same beam length, the linear region is enhanced ~20 times. This result demonstrates the effectiveness of using lattice mismatch for controlling the mechanical nonlinearity of MEMS resonators.

#### 4.3. Use of the Internal Mode Coupling Effect

^{3}, giving a fundamental bending mode (f

_{b}) with the resonance frequency of 313.8 kHz and a fundamental torsional mode (f

_{t}) with the resonance frequency of 958.0 kHz. Although f

_{b}is slightly off by a third of f

_{t}, the larger frequency shift of f

_{b}in the nonlinear region enables us to achieve an integer ratio equal to 3 between f

_{t}and f

_{b}. Figure 9a shows the measured resonance spectrum of f

_{b}at V

_{D}= 200, 300, and 400 mV. When f

_{b}is increased to about 320 kHz, a small reduction in the resonance amplitude is observed in the spectrum, indicating that the vibrational energy of f

_{b}decreases under this condition. Figure 9b shows a blow-up of the spectrum in the mode-coupling region marked by the dotted red rectangle in Figure 9a. As seen, two clear drops in the amplitude appear at approximately 320.6 kHz and approximately 320.9 kHz, suggesting that internal mode coupling is formed between f

_{b}and f

_{t}. Once the two modes couple with each other, they are renormalized into two new eigenmodes, f

_{L}(320.6 kHz) and f

_{H}(320.9 kHz). The energy is transferred from f

_{b}to f

_{t}at these two new frequencies (f

_{L}and f

_{H}), causing two drops with a frequency difference (δ

_{f}) of 300 Hz in the resonance spectrum of the f

_{b}mode, as shown in Figure 9b.

_{m}, is applied to the MEMS beam. Figure 9c,d shows the measured frequency shift (Δf) of samples A and B as a function of f

_{m}at various driving voltages. As seen, when the f

_{m}reaches about 300 Hz under the internal-mode-coupling condition, a huge peak in the Δf is observed, as shown by the red and blue curves in Figure 9c. In comparison to the MEMS resonator that operates outside the mode-coupling region (V

_{D}= 283 mV), as indicated by the black curve in Figure 9c, the Δf in the mode-coupling region is, respectively, 17.5 (V

_{D}= 354 mV) and 25.0 (V

_{D}= 424 mV) times higher. For the sample B with a δ

_{f}= 500 Hz, the Δf is even enhanced by a factor of 60 with the internal mode coupling effect, as shown in Figure 9d. Using this sample B, the thermal responsivity and NEP of the MEMS bolometer are further estimated by applying a heating power of 2 to 10 nW. When sample B is operated in the mode-coupling region, it exhibits a responsivity of 10,000 W

^{−1}, which is almost 2 orders of magnitude higher than that of being operated outside the mode-coupling region. The corresponding NEP = 23 pW/Hz

^{1/2}is improved by a factor 6~7, which is found to be very close to the theoretical limits due to the thermal fluctuation noise of the MEMS beam.

#### 4.4. Responsivity Enhancement Using Nanometer-Scale Hole Array Structures

_{th}= C

_{th}/G

_{th}) and responsivity are inversely proportional to the thermal conductance (G

_{th}) of the MEMS bolometer. Longer MEMS beams offer a larger thermal response but also result in a longer response time. Thus, a route to circumvent the trade-off between detection speed and responsiveness is desirable for achieving highly sensitive sensing without deteriorating detection speed. Nano-porous structures, such as slabs with one-dimensional (1D) [139] or two-dimensional (2D) [140,141] hole arrays, have been proposed to engineer the thermal properties of materials, which is useful for improving thermal responsiveness while maintaining a fast detection speed [112]. With the hole array structure, the cross section of the beam is decreased, leading to a reduction in the thermal conductance of the MEMS beam and thus enabling it to improve thermal responsiveness. On the other hand, the material volume is also decreased by using the hole array structure, which results in a reduction in the heat capacitance of the beam, C

_{th}. Therefore, the increase in τ

_{th}due to the decrease in G

_{th}is partly compensated by the reduction in C

_{th}, resulting in maintaining a fast detection speed.

^{3}) with a 2D hole array structure. The inset of Figure 10a shows a blow-up of an SEM image of the hole array structure, allowing for a clear view of the homogeneous hole array. Two types of nanohole array structures, i.e., round hole array [112] and nano-mesh [111], have been fabricated on the MEMS beam. The thermal conductance of the MEMS beam has been measured to investigate how thermal sensitivity can be improved by porous structures. The red square dots in Figure 10b plot the normalized thermal conductance of the porous nano-mesh MEMS beams. For comparison, the thermal conductance at small porosities with a round-hole array is plotted as the black solid dots in Figure 10b. As seen, the thermal conductance is greatly reduced as the porosity increases. When the porosity increases to ~0.69, the thermal conductance of the porous nano-mesh beam has been reduced by over 90%. Since the thermal sensitivity is inversely proportional to the thermal conductance, an enhancement in the thermal sensitivity by over 10 times can be expected for high-porosity MEMS beams, whereas the detection speed is reduced by a factor of 3, giving an overall improvement in detection performance.

#### 4.5. Improving the Responsivity Spectrum of MEMS Bolometers

^{−1}and almost vanishes in the frequency range of 240–330 cm

^{−1}. This behavior arises from resonant absorption at the TO phonon frequency and the transition to a negative dielectric constant within the Reststrahlenband region (from the TO phonon to the LO phonon frequency), resulting in strong reflection of electromagnetic waves.

_{0.7}Ga

_{0.3}As are removed using a nonselective etching. The resulting wafer-bonded structure is shown in Figure 11c. The Δf-spectrum of the GaAs-based MEMS THz bolometer fabricated on a high-resistivity Si substrate is plotted by a blue curve in Figure 11a. Remarkably, the reduction or loss of sensitivity in the acoustic and optical phonon regions is no longer present, indicating a significant improvement in sensitivity and demonstrating the effectiveness of this wafer-bonding technique. Furthermore, a distinct feature is the presence of two sharp peaks near the TO and LO frequencies, which originate from an interplay between the strong reflection in the Reststrahlen band and the strong absorption at the TO phonon frequency in the thin GaAs MEMS beam structure.

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Siegel, P.H. Terahertz Technology. IEEE Trans. Microw. Theory Tech.
**2002**, 50, 910–928. [Google Scholar] [CrossRef] - Williams, G.P. Filling the THz Gap—High Power Sources and Applications. Rep. Prog. Phys.
**2005**, 69, 301. [Google Scholar] [CrossRef] - Smith, P.R.; Auston, D.H.; Nuss, M.C. Subpicosecond Photoconducting Dipole Antennas. IEEE J. Quantum Electron.
**1988**, 24, 255–260. [Google Scholar] [CrossRef] - Hu, B.B.; Nuss, M.C. Imaging with Terahertz Waves. Opt. Lett.
**1995**, 20, 1716–1718. [Google Scholar] [CrossRef] [Green Version] - Nagatsuma, T.; Ducournau, G.; Renaud, C.C. Advances in Terahertz Communications Accelerated by Photonics. Nat. Photon
**2016**, 10, 371–379. [Google Scholar] [CrossRef] - Sengupta, K.; Nagatsuma, T.; Mittleman, D.M. Terahertz Integrated Electronic and Hybrid Electronic–Photonic Systems. Nat. Electron.
**2018**, 1, 622–635. [Google Scholar] [CrossRef] - Ferguson, B.; Zhang, X.-C. Materials for Terahertz Science and Technology. Nat. Mater.
**2002**, 1, 26–33. [Google Scholar] [CrossRef] [PubMed] - Fischer, B.; Hoffmann, M.; Helm, H.; Modjesch, G.; Jepsen, P.U. Chemical Recognition in Terahertz Time-Domain Spectroscopy and Imaging. Semicond. Sci. Technol.
**2005**, 20, S246. [Google Scholar] [CrossRef] [Green Version] - Shalit, A.; Ahmed, S.; Savolainen, J.; Hamm, P. Terahertz Echoes Reveal the Inhomogeneity of Aqueous Salt Solutions. Nat. Chem.
**2017**, 9, 273–278. [Google Scholar] [CrossRef] - Wang, X.; Xia, F. Stacked 2D Materials Shed Light. Nat. Mater.
**2015**, 14, 264–265. [Google Scholar] [CrossRef] - Kato, M.; Tripathi, S.R.; Murate, K.; Imayama, K.; Kawase, K. Non-Destructive Drug Inspection in Covering Materials Using a Terahertz Spectral Imaging System with Injection-Seeded Terahertz Parametric Generation and Detection. Opt. Express
**2016**, 24, 6425–6432. [Google Scholar] [CrossRef] [PubMed] - Gezimati, M.; Singh, G. Advances in Terahertz Technology for Cancer Detection Applications. Opt. Quant. Electron.
**2023**, 55, 151. [Google Scholar] [CrossRef] [PubMed] - Yang, X.; Zhao, X.; Yang, K.; Liu, Y.; Liu, Y.; Fu, W.; Luo, Y. Biomedical Applications of Terahertz Spectroscopy and Imaging. Trends Biotechnol.
**2016**, 34, 810–824. [Google Scholar] [CrossRef] - Khushbu, S.; Yashini, M.; Rawson, A.; Sunil, C.K. Recent Advances in Terahertz Time-Domain Spectroscopy and Imaging Techniques for Automation in Agriculture and Food Sector. Food Anal. Methods
**2022**, 15, 498–526. [Google Scholar] [CrossRef] - Afsah-Hejri, L.; Akbari, E.; Toudeshki, A.; Homayouni, T.; Alizadeh, A.; Ehsani, R. Terahertz Spectroscopy and Imaging: A Review on Agricultural Applications. Comput. Electron. Agric.
**2020**, 177, 105628. [Google Scholar] [CrossRef] - Li, B.; Long, Y.; Liu, H.; Zhao, C. Research Progress on Terahertz Technology and Its Application in Agriculture. Trans. Chin. Soc. Agric. Eng.
**2018**, 34, 1–9. [Google Scholar] - Qin, J.; Ying, Y.; Xie, L. The Detection of Agricultural Products and Food Using Terahertz Spectroscopy: A Review. Appl. Spectrosc. Rev.
**2013**, 48, 439–457. [Google Scholar] [CrossRef] - Ren, A.; Zahid, A.; Fan, D.; Yang, X.; Imran, M.A.; Alomainy, A.; Abbasi, Q.H. State-of-the-Art in Terahertz Sensing for Food and Water Security—A Comprehensive Review. Trends Food Sci. Technol.
**2019**, 85, 241–251. [Google Scholar] [CrossRef] [Green Version] - Liu, H.-B.; Zhong, H.; Karpowicz, N.; Chen, Y.; Zhang, X.-C. Terahertz Spectroscopy and Imaging for Defense and Security Applications. Proc. IEEE
**2007**, 95, 1514–1527. [Google Scholar] [CrossRef] - Federici, J.F.; Schulkin, B.; Huang, F.; Gary, D.; Barat, R.; Oliveira, F.; Zimdars, D. THz Imaging and Sensing for Security Applications—Explosives, Weapons and Drugs. Semicond. Sci. Technol.
**2005**, 20, S266. [Google Scholar] [CrossRef] - Chen, Z.; Ma, X.; Zhang, B.; Zhang, Y.; Niu, Z.; Kuang, N.; Chen, W.; Li, L.; Li, S. A Survey on Terahertz Communications. China Commun.
**2019**, 16, 1–35. [Google Scholar] [CrossRef] - Sarieddeen, H.; Alouini, M.-S.; Al-Naffouri, T.Y. An Overview of Signal Processing Techniques for Terahertz Communications. Proc. IEEE
**2021**, 109, 1628–1665. [Google Scholar] [CrossRef] - Niu, Y.; Li, Y.; Jin, D.; Su, L.; Vasilakos, A.V. A Survey of Millimeter Wave Communications (MmWave) for 5G: Opportunities and Challenges. Wirel. Netw.
**2015**, 21, 2657–2676. [Google Scholar] [CrossRef] - Song, H.-J.; Nagatsuma, T. Present and Future of Terahertz Communications. IEEE Trans. Terahertz Sci. Technol.
**2011**, 1, 256–263. [Google Scholar] [CrossRef] - Giordani, M.; Polese, M.; Mezzavilla, M.; Rangan, S.; Zorzi, M. Toward 6G Networks: Use Cases and Technologies. IEEE Commun. Mag.
**2020**, 58, 55–61. [Google Scholar] [CrossRef] - Dang, S.; Amin, O.; Shihada, B.; Alouini, M.-S. What Should 6G Be? Nat. Electron.
**2020**, 3, 20–29. [Google Scholar] [CrossRef] [Green Version] - Faist, J.; Capasso, F.; Sivco, D.L.; Sirtori, C.; Hutchinson, A.L.; Cho, A.Y. Quantum Cascade Laser. Science
**1994**, 264, 553–556. [Google Scholar] [CrossRef] - Rogalski, A.; Sizov, F. Terahertz Detectors and Focal Plane Arrays: Opto-Electron. Rev.
**2011**, 19, 346–404. [Google Scholar] [CrossRef] - Sizov, F. THz Radiation Sensors. Opto-Electron. Rev.
**2010**, 18, 10–36. [Google Scholar] [CrossRef] [Green Version] - Lewis, R.A. A Review of Terahertz Detectors. J. Phys. D Appl. Phys.
**2019**, 52, 433001. [Google Scholar] [CrossRef] - Young, D.T.; Irvin, J.C. Millimeter Frequency Conversion Using Au-n-Type GaAs Schottky Barrier Epitaxial Diodes with a Novel Contacting Technique. Proc. IEEE
**1965**, 53, 2130–2131. [Google Scholar] [CrossRef] - Han, S.-P.; Ko, H.; Park, J.-W.; Kim, N.; Yoon, Y.-J.; Shin, J.-H.; Kim, D.Y.; Lee, D.H.; Park, K.H. InGaAs Schottky Barrier Diode Array Detector for a Real-Time Compact Terahertz Line Scanner. Opt. Express
**2013**, 21, 25874–25882. [Google Scholar] [CrossRef] - Brown, E.R.; Young, A.C.; Zimmerman, J.; Kazerni, H.; Gossard, A.C. Advances in Schottky Rectifier Performance. IEEE Microw. Mag.
**2007**, 8, 54–59. [Google Scholar] [CrossRef] - Semenov, A.; Cojocari, O.; Hübers, H.-W.; Song, F.; Klushin, A.; Müller, A.-S. Application of Zero-Bias Quasi-Optical Schottky-Diode Detectors for Monitoring Short-Pulse and Weak Terahertz Radiation. IEEE Electron Device Lett.
**2010**, 31, 674–676. [Google Scholar] [CrossRef] - Chahal, P.; Morris, F.; Frazier, G. Zero Bias Resonant Tunnel Schottky Contact Diode for Wide-Band Direct Detection. IEEE Electron Device Lett.
**2005**, 26, 894–896. [Google Scholar] [CrossRef] - Sizov, F. Terahertz Radiation Detectors: The State-of-the-Art. Semicond. Sci. Technol.
**2018**, 33, 123001. [Google Scholar] [CrossRef] - Ito, H.; Ishibashi, T. Fermi-Level Managed Barrier Diode for Broadband and Low-Noise Terahertz-Wave Detection. Electron. Lett.
**2015**, 51, 1440–1442. [Google Scholar] [CrossRef] - Ito, H.; Ishibashi, T. InP/InGaAs Fermi-Level Managed Barrier Diode for Broadband and Low-Noise Terahertz-Wave Detection. Jpn. J. Appl. Phys.
**2016**, 56, 014101. [Google Scholar] [CrossRef] - Ito, H.; Ishibashi, T. Low-Noise Heterodyne Detection of Terahertz Waves at Room Temperature Using Zero-Biased Fermi-Level Managed Barrier Diode. Electron. Lett.
**2018**, 54, 1080–1082. [Google Scholar] [CrossRef] - Kar, S. Chapter 5—Terahertz Technology—Emerging Trends and Application Viewpoints. In Terahertz Biomedical and Healthcare Technologies; Banerjee, A., Chakraborty, B., Inokawa, H., Nath Roy, J., Eds.; Elsevier: Amsterdam, The Netherlands, 2020; pp. 89–111. ISBN 978-0-12-818556-8. [Google Scholar]
- Rogalski, A. Progress in Performance Development of Room Temperature Direct Terahertz Detectors. J. Infrared Millim. Terahertz Waves
**2022**, 43, 709–727. [Google Scholar] [CrossRef] - Zahl, H.A.; Golay, M.J.E. Pneumatic Heat Detector. Rev. Sci. Instrum.
**1946**, 17, 511–515. [Google Scholar] [CrossRef] [PubMed] - Khanna, V.K. Practical Terahertz Electronics: Devices and Applications, Volume 2: Optical Devices and Applications; IOP Publishing: Bristol, UK, 2021; ISBN 978-0-7503-4886-7. [Google Scholar]
- Desmaris, V.; Rashid, H.; Pavolotsky, A.; Belitsky, V. Design, Simulations and Optimization of Micromachined Golay-Cell Based THz Sensors Operating at Room Temperature. Procedia Chem.
**2009**, 1, 1175–1178. [Google Scholar] [CrossRef] [Green Version] - Müller, R.; Gutschwager, B.; Hollandt, J.; Kehrt, M.; Monte, C.; Müller, R.; Steiger, A. Characterization of a Large-Area Pyroelectric Detector from 300 GHz to 30 THz. J. Infrared Millim. Terahz Waves
**2015**, 36, 654–661. [Google Scholar] [CrossRef] [Green Version] - Hu, F.; Sun, J.; Brindley, H.E.; Liang, X.; Lucyszyn, S. Systems Analysis for Thermal Infrared ‘THz Torch’ Applications. J. Infrared Millim. Terahz Waves
**2015**, 36, 474–495. [Google Scholar] [CrossRef] [Green Version] - Li, W.; Liang, Z.; Wang, J.; Gou, J.; Jiang, Y. A Direct Method of Thermal Time Constant Measurement for Lithium Tantalate Based Terahertz Pryroelectric Detectors. J. Mater. Sci. Mater. Electron.
**2016**, 27, 9996–10002. [Google Scholar] [CrossRef] - Seliverstov, S.; Maslennikov, S.; Ryabchun, S.; Finkel, M.; Klapwijk, T.M.; Kaurova, N.; Vachtomin, Y.; Smirnov, K.; Voronov, B.; Goltsman, G. Fast and Sensitive Terahertz Direct Detector Based on Superconducting Antenna-Coupled Hot Electron Bolometer. IEEE Trans. Appl. Supercond.
**2015**, 25, 1–4. [Google Scholar] [CrossRef] - Timofeev, A.; Luomahaara, J.; Grönberg, L.; Mäyrä, A.; Sipola, H.; Aikio, M.; Metso, M.; Vesterinen, V.; Tappura, K.; Ala-Laurinaho, J.; et al. Optical and Electrical Characterization of a Large Kinetic Inductance Bolometer Focal Plane Array. IEEE Trans. Terahertz Sci. Technol.
**2017**, 7, 218–224. [Google Scholar] [CrossRef] - Galeazzi, M.; McCammon, D. Microcalorimeter and Bolometer Model. J. Appl. Phys.
**2003**, 93, 4856–4869. [Google Scholar] [CrossRef] [Green Version] - Alsop, D.C.; Inman, C.; Lange, A.E.; Wilbanks, T. Design and Construction of High-Sensitivity, Infrared Bolometers for Operation at 300 MK. Appl. Opt.
**1992**, 31, 6610–6615. [Google Scholar] [CrossRef] - Mauskopf, P.D.; Bock, J.J.; Castillo, H.D.; Holzapfel, W.L.; Lange, A.E. Composite Infrared Bolometers with Si
_{3}N_{4}Micromesh Absorbers. Appl. Opt.**1997**, 36, 765–771. [Google Scholar] [CrossRef] - Schmidt, D.R.; Lehnert, K.W.; Clark, A.M.; Duncan, W.D.; Irwin, K.D.; Miller, N.; Ullom, J.N. A Superconductor–Insulator–Normal Metal Bolometer with Microwave Readout Suitable for Large-Format Arrays. Appl. Phys. Lett.
**2005**, 86, 053505. [Google Scholar] [CrossRef] - Oda, N.; Kurashina, S.; Miyoshi, M.; Doi, K.; Ishi, T.; Sudou, T.; Morimoto, T.; Goto, H.; Sasaki, T. Microbolometer Terahertz Focal Plane Array and Camera with Improved Sensitivity at 0.5–0.6 THz. In Proceedings of the 2014 39th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), Tucson, AZ, USA, 14–19 September 2014; pp. 1–2. [Google Scholar]
- Oda, N. Uncooled Bolometer-Type Terahertz Focal Plane Array and Camera for Real-Time Imaging. Comptes Rendus Phys.
**2010**, 11, 496–509. [Google Scholar] [CrossRef] - Simoens, F.; Meilhan, J. Terahertz Real-Time Imaging Uncooled Array Based on Antenna- and Cavity-Coupled Bolometers. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2014**, 372, 20130111. [Google Scholar] [CrossRef] [Green Version] - Vicarelli, L.; Tredicucci, A.; Pitanti, A. Micromechanical Bolometers for Subterahertz Detection at Room Temperature. ACS Photonics
**2022**, 9, 360–367. [Google Scholar] [CrossRef] [PubMed] - Liu, J.; Chomet, B.; Beoletto, P.; Gacemi, D.; Pantzas, K.; Beaudoin, G.; Sagnes, I.; Vasanelli, A.; Sirtori, C.; Todorov, Y. Ultrafast Detection of TeraHertz Radiation with Miniaturized Optomechanical Resonator Driven by Dielectric Driving Force. ACS Photonics
**2022**, 9, 1541–1546. [Google Scholar] [CrossRef] - Zhang, Y.; Hosono, S.; Nagai, N.; Song, S.-H.; Hirakawa, K. Fast and Sensitive Bolometric Terahertz Detection at Room Temperature through Thermomechanical Transduction. J. Appl. Phys.
**2019**, 125, 151602. [Google Scholar] [CrossRef] - Liu, A.Q.; Zhu, W.M.; Tsai, D.P.; Zheludev, N.I. Micromachined Tunable Metamaterials: A Review. J. Opt.
**2012**, 14, 114009. [Google Scholar] [CrossRef] [Green Version] - Demir, K.; Unlu, M. Miniature MEMS: Novel Key Components Toward Terahertz Reconfigurability. J. Microelectromechanical Syst.
**2020**, 29, 455–467. [Google Scholar] [CrossRef] - Ekinci, K.L.; Huang, X.M.H.; Roukes, M.L. Ultrasensitive Nanoelectromechanical Mass Detection. Appl. Phys. Lett.
**2004**, 84, 4469–4471. [Google Scholar] [CrossRef] [Green Version] - Dohn, S.; Sandberg, R.; Svendsen, W.; Boisen, A. Enhanced Functionality of Cantilever Based Mass Sensors Using Higher Modes. Appl. Phys. Lett.
**2005**, 86, 233501. [Google Scholar] [CrossRef] [Green Version] - Jensen, K.; Kim, K.; Zettl, A. An Atomic-Resolution Nanomechanical Mass Sensor. Nat. Nanotech.
**2008**, 3, 533–537. [Google Scholar] [CrossRef] [PubMed] - Onomitsu, K.; Mahboob, I.; Okamoto, H.; Krockenberger, Y.; Yamaguchi, H. Ferromagnetic-Induced Component in Piezoresistance of GaMnAs. Phys. Rev. B
**2013**, 87, 060410. [Google Scholar] [CrossRef] - Masmanidis, S.C.; Tang, H.X.; Myers, E.B.; Li, M.; De Greve, K.; Vermeulen, G.; Van Roy, W.; Roukes, M.L. Nanomechanical Measurement of Magnetostriction and Magnetic Anisotropy in (Ga,Mn)As. Phys. Rev. Lett.
**2005**, 95, 187206. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Cleland, A.N.; Roukes, M.L. A Nanometre-Scale Mechanical Electrometer. Nature
**1998**, 392, 160–162. [Google Scholar] [CrossRef] - Knobel, R.; Yung, C.S.; Cleland, A.N. Single-Electron Transistor as a Radio-Frequency Mixer. Appl. Phys. Lett.
**2002**, 81, 532–534. [Google Scholar] [CrossRef] [Green Version] - Wang, X.; Wei, X.; Pu, D.; Huan, R. Single-Electron Detection Utilizing Coupled Nonlinear Microresonators. Microsyst. Nanoeng.
**2020**, 6, 78. [Google Scholar] [CrossRef] - Larsen, T.; Schmid, S.; Grönberg, L.; Niskanen, A.O.; Hassel, J.; Dohn, S.; Boisen, A. Ultrasensitive String-Based Temperature Sensors. Appl. Phys. Lett.
**2011**, 98, 121901. [Google Scholar] [CrossRef] - Pandey, A.K.; Gottlieb, O.; Shtempluck, O.; Buks, E. Performance of an AuPd Micromechanical Resonator as a Temperature Sensor. Appl. Phys. Lett.
**2010**, 96, 203105. [Google Scholar] [CrossRef] [Green Version] - Laurent, L.; Yon, J.-J.; Moulet, J.-S.; Roukes, M.; Duraffourg, L. 12—μm-Pitch Electromechanical Resonator for Thermal Sensing-Pitch Electromechanical Resonator for Thermal Sensing. Phys. Rev. Appl.
**2018**, 9, 024016. [Google Scholar] [CrossRef] [Green Version] - Zhang, X.C.; Myers, E.B.; Sader, J.E.; Roukes, M.L. Nanomechanical Torsional Resonators for Frequency-Shift Infrared Thermal Sensing. Nano Lett.
**2013**, 13, 1528–1534. [Google Scholar] [CrossRef] [Green Version] - Gokhale, V.J.; Rais-Zadeh, M. Uncooled Infrared Detectors Using Gallium Nitride on Silicon Micromechanical Resonators. J. Microelectromechanical Syst.
**2014**, 23, 803–810. [Google Scholar] [CrossRef] - Jeong, J.; Kumagai, S.; Yamashita, I.; Uraoka, Y.; Sasaki, M. Micromechanical IR Thermal Detector Using Torsional Oscillation: Improvement of Resonator Profile for High Sensitivity. Jpn. J. Appl. Phys.
**2015**, 54, 04DE07. [Google Scholar] [CrossRef] - Yamazaki, T.; Ogawa, S.; Kumagai, S.; Sasaki, M. A Novel Infrared Detector Using Highly Nonlinear Twisting Vibration. Sens. Actuators A Phys.
**2014**, 212, 165–172. [Google Scholar] [CrossRef] [Green Version] - Froberger, K.; Walter, B.; Lavancier, M.; Peretti, R.; Ducournau, G.; Lampin, J.-F.; Faucher, M.; Barbieri, S. SOI-Based Micro-Mechanical Terahertz Detector Operating at Room-Temperature and Atmospheric Pressure. Appl. Phys. Lett.
**2022**, 120, 261103. [Google Scholar] [CrossRef] - Qian, Z.; Hui, Y.; Liu, F.; Kang, S.; Kar, S.; Rinaldi, M. Graphene–Aluminum Nitride NEMS Resonant Infrared Detector. Microsyst. Nanoeng.
**2016**, 2, 16026. [Google Scholar] [CrossRef] [PubMed] - Piller, M.; Luhmann, N.; Chien, M.-H.; Schmid, S. Nanoelectromechanical Infrared Detector. In Proceedings of the Optical Sensing, Imaging, and Photon Counting: From X-Rays to THz 2019, San Diego, CA, USA, 14–15 August 2019; Volume 11088, pp. 9–15. [Google Scholar]
- Blaikie, A.; Miller, D.; Alemán, B.J. A Fast and Sensitive Room-Temperature Graphene Nanomechanical Bolometer. Nat. Commun.
**2019**, 10, 4726. [Google Scholar] [CrossRef] [Green Version] - Belacel, C.; Todorov, Y.; Barbieri, S.; Gacemi, D.; Favero, I.; Sirtori, C. Optomechanical Terahertz Detection with Single Meta-Atom Resonator. Nat. Commun.
**2017**, 8, 1578. [Google Scholar] [CrossRef] [Green Version] - Zhu, H.; Wang, K.; Liu, G.; Wang, G.; Mou, J.; Zhang, W.; Wei, G. A Terahertz Optomechanical Detector Based on Metasurface and Bi-Material Micro-Cantilevers. Micromachines
**2022**, 13, 805. [Google Scholar] [CrossRef] - Sadeghi, P.; Tanzer, M.; Luhmann, N.; Piller, M.; Chien, M.-H.; Schmid, S. Thermal Transport and Frequency Response of Localized Modes on Low-Stress Nanomechanical Silicon Nitride Drums Featuring a Phononic-Band-Gap Structure. Phys. Rev. Appl.
**2020**, 14, 024068. [Google Scholar] [CrossRef] - Yamaguchi, H. GaAs-Based Micro/Nanomechanical Resonators. Semicond. Sci. Technol.
**2017**, 32, 103003. [Google Scholar] [CrossRef] [Green Version] - Qiu, B.; Zhang, Y.; Akahane, K.; Nagai, N.; Hirakawa, K. Effect of Beam Deflection on the Thermal Responsivity of GaAs-Based Doubly Clamped Microelectromechanical Beam Resonators. Appl. Phys. Lett.
**2020**, 117, 203503. [Google Scholar] [CrossRef] - Kim, C.S.; Dickinson, S.M. The Flexural Vibration of Slightly Curved Slender Beams Subject to Axial End Displacement. J. Sound Vib.
**1986**, 104, 170–175. [Google Scholar] [CrossRef] - Nayfeh, A.H.; Kreider, W.; Anderson, T.J. Investigation of Natural Frequencies and Mode Shapes of Buckled Beams. AIAA J.
**1995**, 33, 1121–1126. [Google Scholar] [CrossRef] - Zhang, Y.; Hosono, S.; Nagai, N.; Hirakawa, K. Effect of Buckling on the Thermal Response of Microelectromechanical Beam Resonators. Appl. Phys. Lett.
**2017**, 111, 023504. [Google Scholar] [CrossRef] - Mahboob, I.; Yamaguchi, H. Bit Storage and Bit Flip Operations in an Electromechanical Oscillator. Nat. Nanotech.
**2008**, 3, 275–279. [Google Scholar] [CrossRef] - Albrecht, T.R.; Grütter, P.; Horne, D.; Rugar, D. Frequency Modulation Detection Using High-Q Cantilevers for Enhanced Force Microscope Sensitivity. J. Appl. Phys.
**1998**, 69, 668. [Google Scholar] [CrossRef] [Green Version] - Andronov, A.A.; Vitt, A.A.; Khaikin, S.E. Theory of Oscillators: Adiwes International Series in Physics; Elsevier: Amsterdam, The Netherlands, 2013; ISBN 978-1-4831-9472-1. [Google Scholar]
- Liu, S.T.; Long, D. Pyroelectric Detectors and Materials. Proc. IEEE
**1978**, 66, 14–26. [Google Scholar] [CrossRef] - Muralt, P. Micromachined Infrared Detectors Based on Pyroelectric Thin Films. Rep. Prog. Phys.
**2001**, 64, 1339. [Google Scholar] [CrossRef] - Oda, N.; Yoneyama, H.; Sasaki, T.; Sano, M.; Kurashina, S.; Hosako, I.; Sekine, N.; Sudoh, T.; Irie, T. Detection of Terahertz Radiation from Quantum Cascade Laser Using Vanadium Oxide Microbolometer Focal Plane Arrays. In Proceedings of the Infrared Technology and Applications XXXIV, Orlando, FL, USA,16–20 March 2008; SPIE: Bellingham, WA, USA, 2008; Volume 6940, pp. 982–993. [Google Scholar]
- Cole, B.E.; Higashi, R.E.; Ridley, J.A.; Wood, R.A. Integrated Vacuum Packaging for Low-Cost Lightweight Uncooled Microbolometer Arrays. In Proceedings of the Infrared Technology and Applications XXVII, Orlando, FL, USA, 16–20 April 2001; SPIE: Bellingham, WA, USA, 2001; Volume 4369, pp. 235–239. [Google Scholar]
- Jerominek, H.; Picard, F.; Vincent, D. Vanadium Oxide Films for Optical Switching and Detection. Opt. Eng.
**1993**, 32, 2092–2099. [Google Scholar] [CrossRef] - Morohashi, I.; Zhang, Y.; Qiu, B.; Irimajiri, Y.; Sekine, N.; Hirakawa, K.; Hosako, I. Rapid Scan THz Imaging Using MEMS Bolometers. J. Infrared Millim. Terahz Waves
**2020**, 41, 675–684. [Google Scholar] [CrossRef] - Richards, P.L. Bolometers for Infrared and Millimeter Waves. J. Appl. Phys.
**1994**, 76, 1–24. Available online: https://aip.scitation.org/doi/10.1063/1.357128 (accessed on 16 April 2023). [CrossRef] [Green Version] - Fukuma, T.; Kimura, M.; Kobayashi, K.; Matsushige, K.; Yamada, H. Development of Low Noise Cantilever Deflection Sensor for Multienvironment Frequency-Modulation Atomic Force Microscopy. Rev. Sci. Instrum.
**2005**, 76, 053704. [Google Scholar] [CrossRef] [Green Version] - Low, F.J. Low-Temperature Germanium Bolometer. J. Opt. Soc. Am.
**1961**, 51, 1300–1304. [Google Scholar] [CrossRef] - Mather, J.C. Bolometer Noise: Nonequilibrium Theory. Appl. Opt.
**1982**, 21, 1125–1129. [Google Scholar] [CrossRef] [PubMed] - The THz Source Used in This Work Was Tera-Master, from Spectra Quest Lab, Inc. Available online: https://spectraquestlab.com/system.html (accessed on 21 June 2023).
- Betta, G.-F.D. Advances in Photodiodes; BoD—Books on Demand: Norderstedt, Germany, 2011; ISBN 978-953-307-163-3. [Google Scholar]
- Aydin, K.; Ferry, V.E.; Briggs, R.M.; Atwater, H.A. Broadband Polarization-Independent Resonant Light Absorption Using Ultrathin Plasmonic Super Absorbers. Nat. Commun.
**2011**, 2, 517. [Google Scholar] [CrossRef] [Green Version] - Landy, N.I.; Sajuyigbe, S.; Mock, J.J.; Smith, D.R.; Padilla, W.J. Perfect Metamaterial Absorber. Phys. Rev. Lett.
**2008**, 100, 207402. [Google Scholar] [CrossRef] - Hilsum, C. Infrared Absorption of Thin Metal Films. J. Opt. Soc. Am.
**1954**, 44, 188–191. [Google Scholar] [CrossRef] - Qiu, B.; Zhang, Y.; Nagai, N.; Hirakawa, K. Enhancing the Thermal Responsivity of Microelectromechanical System Beam Resonators by Preloading a Critical Buckling Strain. Appl. Phys. Lett.
**2021**, 119, 153502. [Google Scholar] [CrossRef] - Li, C.; Qiu, B.; Yoshioka, Y.; Hirakawa, K.; Zhang, Y. Mechanical Control of Nonlinearity in Doubly Clamped MEMS Beam Resonators Using Preloaded Lattice-Mismatch Strain. Phys. Rev. Appl.
**2023**, 19, 024025. [Google Scholar] [CrossRef] - Zhang, Y.; Yoshioka, Y.; Iimori, M.; Qiu, B.; Liu, X.; Hirakawa, K. Thermal Tuning of Mechanical Nonlinearity in GaAs Doubly-Clamped MEMS Beam Resonators. Appl. Phys. Lett.
**2021**, 119, 163503. [Google Scholar] [CrossRef] - Zhang, Y.; Kondo, R.; Qiu, B.; Liu, X.; Hirakawa, K. Giant Enhancement in the Thermal Responsivity of Microelectromechanical Resonators by Internal Mode Coupling. Phys. Rev. Appl.
**2020**, 14, 014019. [Google Scholar] [CrossRef] - Yamamoto, R.; Kojima, A.; Koshida, N.; Morohashi, I.; Hirakawa, K.; Zhang, Y. Thermal and Optical Properties of Porous Nanomesh Structures for Sensitive Terahertz Bolometric Detection. Sensors
**2022**, 22, 5109. [Google Scholar] [CrossRef] - Zhang, Y.; Qiu, B.; Nagai, N.; Nomura, M.; Volz, S.; Hirakawa, K. Enhanced Thermal Sensitivity of MEMS Bolometers Integrated with Nanometer-Scale Hole Array Structures. AIP Adv.
**2019**, 9, 085102. [Google Scholar] [CrossRef] [Green Version] - Niu, T.; Morais, N.; Qiu, B.; Nagai, N.; Zhang, Y.; Arakawa, Y.; Hirakawa, K. GaAs-Based Microelectromechanical Terahertz Bolometers Fabricated on High-Resistivity Si Substrates Using Wafer Bonding Technique. Appl. Phys. Lett.
**2021**, 119, 041104. [Google Scholar] [CrossRef] - Antonio, D.; Zanette, D.H.; López, D. Frequency Stabilization in Nonlinear Micromechanical Oscillators. Nat. Commun.
**2012**, 3, 806. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhang, Y.; Yoshioka, Y.; Morohashi, I.; Liu, X. 1:1 Internal Mode Coupling Strength in GaAs Doubly-Clamped MEMS Beam Resonators with Linear and Nonlinear Oscillations. Appl. Phys. Express
**2020**, 14, 014001. [Google Scholar] [CrossRef] - Younis, M.I. MEMS Linear and Nonlinear Statics and Dynamics; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2011; ISBN 978-1-4419-6020-7. [Google Scholar]
- Lurie, A.I. Theory of Elasticity; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2010; ISBN 978-3-540-26455-2. [Google Scholar]
- Meirovitch, L. Analytical Methods in Vibrations. Electron. Power
**1967**, 13, 480. [Google Scholar] - Feng, X.L.; He, R.; Yang, P.; Roukes, M.L. Very High Frequency Silicon Nanowire Electromechanical Resonators. Nano Lett.
**2007**, 7, 1953–1959. [Google Scholar] [CrossRef] [Green Version] - Sazonova, V.; Yaish, Y.; Üstünel, H.; Roundy, D.; Arias, T.A.; McEuen, P.L. A Tunable Carbon Nanotube Electromechanical Oscillator. Nature
**2004**, 431, 284–287. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Harouni, M.B.; Vaseghi, M. Preparation of Vibrational Quantum States in Nanomechanical Graphene Resonator. Laser Phys.
**2016**, 26, 115204. [Google Scholar] [CrossRef] [Green Version] - Jiang, J.-W.; Wang, B.-S.; Wang, J.-S.; Park, H.S. A Review on the Flexural Mode of Graphene: Lattice Dynamics, Thermal Conduction, Thermal Expansion, Elasticity and Nanomechanical Resonance. J. Phys. Condens. Matter
**2015**, 27, 083001. [Google Scholar] [CrossRef] [Green Version] - Hajjaj, A.Z.; Hafiz, M.A.; Younis, M.I. Mode Coupling and Nonlinear Resonances of MEMS Arch Resonators for Bandpass Filters. Sci. Rep.
**2017**, 7, 41820. [Google Scholar] [CrossRef] [Green Version] - Tajaddodianfar, F.; Yazdi, M.R.H.; Pishkenari, H.N. Nonlinear Dynamics of MEMS/NEMS Resonators: Analytical Solution by the Homotopy Analysis Method. Microsyst. Technol.
**2017**, 23, 1913–1926. [Google Scholar] [CrossRef] - Hayashi, C. Nonlinear Oscillations in Physical Systems; Princeton University Press: Princeton, NJ, USA, 2014; ISBN 978-1-4008-5287-1. [Google Scholar]
- Lifshitz, R.; Cross, M.C. Chapter 1—Nonlinear Dynamics of Nanomechanical and Micromechanical Resonators. In Rev. Nonlinear Dyn. Complex; Schuster, H.G., Ed.; Wiley: Weinheim, Germany, 2008; pp. 1–52. ISBN 978-3-5274-0729-3. [Google Scholar]
- Neumeyer, S.; Sorokin, V.S.; Thomsen, J.J. Effects of Quadratic and Cubic Nonlinearities on a Perfectly Tuned Parametric Amplifier. J. Sound Vib.
**2017**, 386, 327–335. [Google Scholar] [CrossRef] [Green Version] - Westra, H.J.R.; Poot, M.; van der Zant, H.S.J.; Venstra, W.J. Nonlinear Modal Interactions in Clamped-Clamped Mechanical Resonators. Phys. Rev. Lett.
**2010**, 105, 117205. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Matheny, M.H.; Villanueva, L.G.; Karabalin, R.B.; Sader, J.E.; Roukes, M.L. Nonlinear Mode-Coupling in Nanomechanical Systems. Nano Lett.
**2013**, 13, 1622–1626. [Google Scholar] [CrossRef] [Green Version] - Houri, S.; Hatanaka, D.; Asano, M.; Yamaguchi, H. Demonstration of Multiple Internal Resonances in a Microelectromechanical Self-Sustained Oscillator. Phys. Rev. Appl.
**2020**, 13, 014049. [Google Scholar] [CrossRef] [Green Version] - Afaneh, A.A.; Ibrahim, R.A. Nonlinear Response of an Initially Buckled Beam with 1:1 Internal Resonance to Sinusoidal Excitation. Nonlinear Dyn.
**1993**, 4, 547–571. [Google Scholar] [CrossRef] - Czaplewski, D.A.; Strachan, S.; Shoshani, O.; Shaw, S.W.; López, D. Bifurcation Diagram and Dynamic Response of a MEMS Resonator with a 1:3 Internal Resonance. Appl. Phys. Lett.
**2019**, 114, 254104. [Google Scholar] [CrossRef] - Samanta, C.; Yasasvi Gangavarapu, P.R.; Naik, A.K. Nonlinear Mode Coupling and Internal Resonances in MoS2 Nanoelectromechanical System. Appl. Phys. Lett.
**2015**, 107, 173110. [Google Scholar] [CrossRef] [Green Version] - Pu, D.; Wei, X.; Xu, L.; Jiang, Z.; Huan, R. Synchronization of Electrically Coupled Micromechanical Oscillators with a Frequency Ratio of 3:1. Appl. Phys. Lett.
**2018**, 112, 013503. [Google Scholar] [CrossRef] - Lan, C.; Qin, W.; Deng, W. Energy Harvesting by Dynamic Unstability and Internal Resonance for Piezoelectric Beam. Appl. Phys. Lett.
**2015**, 107, 093902. [Google Scholar] [CrossRef] - Güttinger, J.; Noury, A.; Weber, P.; Eriksson, A.M.; Lagoin, C.; Moser, J.; Eichler, C.; Wallraff, A.; Isacsson, A.; Bachtold, A. Energy-Dependent Path of Dissipation in Nanomechanical Resonators. Nat. Nanotech.
**2017**, 12, 631–636. [Google Scholar] [CrossRef] [Green Version] - Bhardwaj, A.; Kaur, J.; Wuest, M.; Wuest, F. In Situ Click Chemistry Generation of Cyclooxygenase-2 Inhibitors. Nat. Commun.
**2017**, 8, 1. [Google Scholar] [CrossRef] [Green Version] - Arı, A.B.; Çağatay Karakan, M.; Yanık, C.; Kaya, İ.İ.; Selim Hanay, M. Intermodal Coupling as a Probe for Detecting Nanomechanical Modes. Phys. Rev. Appl.
**2018**, 9, 034024. [Google Scholar] [CrossRef] [Green Version] - Yanagisawa, R.; Maire, J.; Ramiere, A.; Anufriev, R.; Nomura, M. Impact of Limiting Dimension on Thermal Conductivity of One-Dimensional Silicon Phononic Crystals. Appl. Phys. Lett.
**2017**, 110, 133108. [Google Scholar] [CrossRef] - Song, D.; Chen, G. Thermal Conductivity of Periodic Microporous Silicon Films. Appl. Phys. Lett.
**2004**, 84, 687–689. [Google Scholar] [CrossRef] - Maire, J.; Anufriev, R.; Yanagisawa, R.; Ramiere, A.; Volz, S.; Nomura, M. Heat Conduction Tuning by Wave Nature of Phonons. Sci. Adv.
**2017**, 3, e1700027. [Google Scholar] [CrossRef] [Green Version] - Zhang, Y.; Watanabe, Y.; Hosono, S.; Nagai, N.; Hirakawa, K. Room Temperature, Very Sensitive Thermometer Using a Doubly Clamped Microelectromechanical Beam Resonator for Bolometer Applications. Appl. Phys. Lett.
**2016**, 108, 163503. [Google Scholar] [CrossRef] - Mooradian, A.; Wright, G.B. First Order Raman Effect in III–V Compounds. Solid State Commun.
**1966**, 4, 431–434. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Schematic illustration of a typical resonator based on torsional mode. (

**b**) Schematic of the cantilever geometry with all relevant dimensions. The Al antennas are 80 nm thick. The inset shows a SEM image of the fabricated device. Reprinted from [77], with the permission of AIP Publishing. (

**c**) Schematic illustration of a trampoline membrane resonator and its working principle. Reprinted from [57], with the permission of Vicarelli et al. (

**d**) Schematic drawing of the silicon nitride drum resonator. The detector is based on a 50-nanometer-thick drum resonator made of silicon nitride, comprising an absorber layer. The absorber’s thin film thermalizes part of the radiation. The resulting photothermal heating of the nanoelectromechanical drum causes a measurable detuning of the drum’s resonance frequency. Reprinted from [79] with the permission of Piller et al. (

**e**) A false-colored tilted SEM image of a fabricated G-AlN NEMS resonant IR detector. The device is 75 μm wide and 200 μm long. Reprinted with permission from [78]. Copyright 2016 Qian et al. (

**f**) Schematic of the optomechanical system, with indications of the RF voltage and THz radiation. Reprinted with permission from [58]. Copyright 2022 American Chemical Society.

**Figure 3.**(

**a**) Schematic diagram of the FM detection. Reprinted from [59], with the permission of AIP Publishing. (

**b**) Circuit illustration of the FM detection. The MEMS beam resonator achieves a self-sustained oscillation mode with a PLL. The modulated voltages with various modulation frequencies f

_{m}are applied to the NiCr heater. Reprinted from [59], with the permission of AIP Publishing. (

**c**) The Signal waveforms in the case of being switched on and off at f

_{m}= 320–10,240 Hz, with the initial conditions: V

_{D}= 16 mV, P

_{in}= 32 µW, and the demodulation bandwidth of the PLL is 5 kHz. Reprinted from [59], with the permission of AIP Publishing. (

**d**) The normalized measured frequency shift as a function of P

_{in}, using the FM detection mode. Reprinted from [59], with the permission of AIP Publishing.

**Figure 4.**The measured frequency noise, n

_{f}, as a function of the heat modulation frequency, f

_{m}, at various driving voltages (V

_{D}= 2, 4, 8, 16, 32, and 64 mV). The demodulation bandwidth of the PLL is set to be 1 kHz. Reprinted from [59], with the permission of AIP Publishing.

**Figure 5.**(

**a**) A schematic diagram for the optical measurements that use a monochromatic THz DFG source. LD1 and LD2 are two tunable lasers that have a lasting frequency difference in the THz range. A uni-traveling-carrier photodiode (UTC-PD) is used to generate THz radiation by using the mixed output of LD1 and LD2. The MEMS resonator is mounted on a silicon hyper-hemispherical lens to focus the incident THz radiation on the MEMS beam. Reprinted from [59], with the permission of AIP Publishing. (

**b**) The detected frequency shift of the MEMS bolometer when the output THz power of the DFG source is switched on and off. The output frequency of the THz DFG, f

_{THz}, is set to be 250 GHz. The THz radiation is modulated at 400 Hz. The output power, P

_{THz}, is 0.44 μW. The MEMS resonator was operated in FM detection mode with a PLL demodulation bandwidth of 1 kHz. Reprinted from [59], with the permission of AIP Publishing. (

**c**) THz power measured by a Si composite bolometer as the THz DFG frequency is scanned from 250 GHz to 3.0 THz. The THz output power decreases from 0.44 μW to 80 pW as the DFG frequency increases. The dots show the measured frequency shift, Δf, of the MEMS bolometer. Δf is measured by using a lock-in time constant, τ

_{amp}, of 1 s at 300 K. Reprinted from [59], with the permission of AIP Publishing. (

**d**) Output signal of the MEMS bolometer, Δf, as a function of P

_{THz}. The noise floor of the present MEMS bolometer is ~1.8 mHz. Using this value, the minimum detectable power, P

_{min}, is determined to be ~200 pW. Reprinted from [59], with the permission of AIP Publishing.

**Figure 6.**(

**a**) The normalized frequency shifts are plotted as a function of the input heating power for the GaAs beam (open circles) and the In

_{x}Ga

_{1−x}As beam (full circles). Reprinted from [88], with the permission of AIP Publishing. (

**b**) The absolute value of the thermal responsivities of the In

_{0.004}Ga

_{0.996}As and GaAs beams is plotted as a function of the beam length. Dots: experiment; line: theory. The In

_{0.004}Ga

_{0.996}As beams longer than 105 μm are buckled, and the polarity of their responsivities is inverted (red triangles). Reprinted from [107], with the permission of AIP Publishing.

**Figure 7.**(

**a**) Schematic diagram of a MEMS beam with a center deflection z

_{0}in the steady state, which induces a quadratic softening nonlinearity in oscillation. Adapted with permission from [108]. Copyright 2023 American Physical Society. (

**b**) The calculated resonance frequency (ƒ/ƒ

_{0}) as a function of oscillation amplitude at various ε/ε

_{cr}values; the initial center deflection is z

_{0}/t = 0.1. The frequency is normalized by the natural frequency ƒ

_{0}without oscillation. Reprinted with permission from [108]. Copyright 2023 American Physical Society. (

**c**) The calculated α and β as a function of the compressive strain (ε/ε

_{cr}) at z

_{0}/t= 0.1.

**Figure 8.**(

**a**) The measured resonance spectra of the sample without thermal tuning at various driving voltages (V

_{D}= 20–90 mV). The red curve shows that the resonance frequency shifts toward the higher frequency with increasing oscillation amplitude. Reprinted from [109], with the permission of AIP Publishing. (

**b**) The measured resonance spectra of the MEMS beam with thermal tuning. Reprinted from [109], with the permission of AIP Publishing. (

**c**) The measured resonance frequency shifts (Δƒ) of In

_{0.004}Ga

_{0.996}As samples with various L. Adapted with permission from [108]. Copyright 2023 American Physical Society.

**Figure 9.**(

**a**) The measured resonance spectra at V

_{D}= 200, 300, and 400 mV. Reprinted with permission from [110]. Copyright 2020 American Physical Society. (

**b**) A blow-up of the spectrum in the mode-coupling region marked by a dotted rectangle in (

**a**). Reprinted with permission from [110]. Copyright 2020 American Physical Society. (

**c**) Thermally induced frequency shift, Δf, for sample A as a function of heat modulation frequency, f

_{m}, measured at p = 25 nW. The black, blue, and red curves plot the results when V

_{D}= 283, 354, and 424 mV, respectively. Reprinted with permission from [110]. Copyright 2020 American Physical Society. (

**d**) Thermally induced frequency shift, Δf, for sample B as a function of heat modulation frequency, f

_{m}, measured at p = 20 nW. The black and red curves plot the results when V

_{D}= 650 and 820 mV, respectively. Reprinted with permission from [110]. Copyright 2020 American Physical Society.

**Figure 10.**(

**a**) Microscope image of a fabricated GaAs MEMS beam resonator (100 × 30 × 0.6 μm

^{3}) with a 2D hole array structure of a hole diameter d = 500 nm and a neck size n = 500 nm. Reprinted with permission from [112]. Copyright 2019 Zhang et al. (

**b**) The normalized thermal conductance of the porous nano-mesh MEMS beams. The calculated thermal conductance of the round hole and the mesh hole is shown by the dotted line and the solid line, respectively. The square red plots are nano-mesh porous MEMS with 0.44, 0.64, and 0.69 porosities, respectively. The black dots show the thermal conductance at small porosities with a round-hole array structure. Reprinted from [111], with the permission of Yamamoto et al.

**Figure 11.**(

**a**) Output Δf-spectra of the MEMS bolometers fabricated on a high-resistivity Si substrate (blue) and on a GaAs substrate (red). Vertical dashed lines indicate the TO and LO frequencies in GaAs. The inset shows a schematic illustration of a MEMS bolometer mounted on a Si lens. Reprinted from [113], with the permission of AIP Publishing. (

**b**) The wafer structure grown for the wafer bonding process. Reprinted from [113], with the permission of AIP Publishing. (

**c**) Wafer-bonded structure used to fabricate the GaAs-based MEMS THz bolometer on a Si substrate. Reprinted from [113], with the permission of AIP Publishing.

Physical Principle | Frequency Range | τ_{th} | Responsivity | NEP | Reference |
---|---|---|---|---|---|

Torsional mode | IR | - | - | 27 pW/Hz^{1/2} | [72] |

Torsional mode | IR | - | - | 30 Hz/K | [76] |

Torsional mode | IR | - | - | 1000 ppm/K | [75] |

Torsional mode | IR | 556 µs | 0.0168 W^{−1} | - | [74] |

Torsional mode | IR | - | 10^{−7} rad/Hz^{1/2} | - | [73] |

Bending mode | 2–3.5 THz | 2.5 µs | 1.5 × 108 pm/W | 20 nW/Hz^{1/2} | [77] |

Bending mode | 250 GHz–3 THz | 55 μs | ~100 W^{−1} | 500 pW/Hz^{1/2} | [59] |

Trampoline membrane | 140 GHz | 25 ms | - | 100 pW/Hz^{1/2} | [57] |

Trampoline membrane | Light | 2.4 μs | - | 2 pW/Hz^{1/2} | [80] |

Drum | 5–20 µm | 17 ms | 343 W^{−1} | 320 pW/Hz^{1/2} | [79] |

Thin plate | IR | 0.53 ms | - | 47 nW/Hz^{1/2} | [78] |

Optical read out | 2.5 THz | 1.2 μs | 30 pm/nW | - | [58] |

Optical read out | 2.6 THz | 3 μs | - | 16 nW/Hz^{1/2} | [81] |

Optical read out | 3.24–3.98 THz | 100 ms | 24.8 µm/µW | 38.2 pW/Hz^{1/2} | [82] |

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**MDPI and ACS Style**

Li, C.; Zhang, Y.; Hirakawa, K.
Terahertz Detectors Using Microelectromechanical System Resonators. *Sensors* **2023**, *23*, 5938.
https://doi.org/10.3390/s23135938

**AMA Style**

Li C, Zhang Y, Hirakawa K.
Terahertz Detectors Using Microelectromechanical System Resonators. *Sensors*. 2023; 23(13):5938.
https://doi.org/10.3390/s23135938

**Chicago/Turabian Style**

Li, Chao, Ya Zhang, and Kazuhiko Hirakawa.
2023. "Terahertz Detectors Using Microelectromechanical System Resonators" *Sensors* 23, no. 13: 5938.
https://doi.org/10.3390/s23135938