Enhanced thermal sensitivity of MEMS bolometers integrated with two-dimensional phononic crystals

We have fabricated two-dimensional phononic crystal (PnC) structures on GaAs doubly-clamped microelectromechanical system (MEMS) beam resonators to modulate their thermal properties. Owing to the reduction in the thermal conductance of the MEMS beams by introducing the PnC structures, the MEMS bolometers with the PnC structures show 2-3 times larger thermal sensitivities than the unpatterned reference sample. Furthermore, since the heat capacitance of the MEMS beams is also reduced by introducing the PnCs, the thermal decay time of the patterned MEMS beams is increased only by about 30-40 %, demonstrating the effectiveness of the PnCs for enhancing the thermal sensitivities of bolometers without significantly deteriorating their operation bandwidths.


Micro-electromechanical system (MEMS) resonators 1-3 are very attractive for sensing
applications. Owing to their high quality (Q)-factors, the MEMS resonators can detect a small change in the resonance frequencies and can be used to detect changes in mass, 4-8 charge, 9,10 spin orientation, 11,12 and temperature 13,14 . Recently, we have developed an uncooled, sensitive and fast bolometer by using a doubly clamped GaAs MEMS beam resonator for terahertz (THz) sensing applications. [15][16][17] The MEMS resonator detects THz radiation by measuring the shift in the resonance frequency caused by heating of the MEMS beam. [15][16][17] Since the responsivity of the MEMS resonators is inversely proportional to the thermal conductance of the MEMS beam, GT, it is preferable to decrease G T for enhancing the responsivity. On the other hand, the thermal time constant D (= CT/GT; CT is the heat capacitance of the MEMS beam) increases when GT is decreased, leading to the reduction in the detection speed. This trade-off between the responsivity and the detection bandwidth exists in all kinds of thermal sensors.
The phononic crystals (PnCs) 18, 19 are the structures that have a periodic modulation in the elastic modulus and/or mass density. The PnC structures such as slabs with one-dimensional (1D) 20 or two-dimensional (2D) 21-23 hole arrays have been proposed to engineer the thermal properties of materials. The hole-array-based PnC structures are promising for improving thermal responsivities of the MEMS resonators; the PnC structure can reduce the thermal conductance, GT, of the MEMS beam by decreasing the cross section of the beam. Furthermore, the PnC structure reduces the heat capacitance of the beam, CT, by decreasing the material volume. Therefore, the increase in τD due to the decrease in GT is partly compensated by the reduction in CT and it is possible to enhance the thermal responsivity, while keeping a fast detection speed of the MEMS thermal sensors.
In this work, we have fabricated 2D PnC structures on the MEMS beam resonators to modulate their thermal properties. Homogenous hole arrays of square lattices were formed on the GaAs The wafer used for fabricating the doubly clamped MEMS beam resonators was grown by molecular beam epitaxy. 24 After growing a 200-nm-thick GaAs buffer layer and a 3-μm-thick Al0.7Ga0.3As sacrificial layer on a (100)-oriented semi-insulating GaAs substrate, the beam layer was formed by depositing a 50-nm-thick GaAs layer, a GaAs/Al0.3Ga0.7As superlattice structure, and a 400-nm-thick GaAs layer. We subsequently grew a 20-nm-thick Si-doped GaAs layer, a 70-nmthick Al 0.3 Ga 0.7 As layer and a 10-nm-thick GaAs capping layer. The fabrication process for the MEMS resonators with PnC structures were schematically shown in Fig. 1(a). The PnC structures of the square lattice were patterned on the beam by using electron-beam lithography. The holes were formed by using reactive ion etching with Cl2 gas and a rf power of 200 W at 50 C for 80 s.
The suspended beam structure was formed by selectively etching the sacrificial layer with diluted hydrofluoric acid 24 . Figure 1(b) shows an optical microscope image of a fabricated MEMS beam resonator (100300.6 m 3 ) with a 2D PnC structure of a hole diameter d = 500 nm and the neck size (the distance between neighboring holes) n = 500 nm. The inset of Fig. 1(b) shows a blow-up of an SEM image of the PnC structure, showing that the fabricated hole array is homogeneous. We fabricated MEMS beams with the PnC structures of various sizes, i. e., d/n = 500 nm/500 nm, 500 nm/400 nm, 500 nm/300 nm, 300 nm/300 nm, and 300 nm/200 nm. In addition, we fabricated a reference sample without a PnC structure. The Si-doped GaAs layer and the top metal gates (15-nm-thick NiCr) on the two ends of the MEMS beam form two piezoelectric capacitors. An ac voltage was applied to one of the piezoelectric capacitors to drive the beam and the induced resonant beam motion was monitored by a laser Doppler vibrometer, as schematically shown in Fig.1(c). The resonance signal is input to a phase locked loop (PLL) to provide a feedback control for maintaining a self-oscillation, as we reported elsewhere 17 . On the MEMS beam, we deposited a 15-nm-thick NiCr layer as a heater for calibrating the responsivity of the MEMS resonator, whose sheet resistance was ~500 /. All the measurements were performed in a vacuum (~10 -4 torr) at room temperature. When an input power to the NiCr film, Pin, is increased from 0 to 50 μW, f0 is reduced due to the thermal stress of the beam. Figure 2(b) shows the normalized frequency shift, Δf/f0, as a function of the input heating power, Pin, for two MEMS resonators with PnC structures (d/n = 300 nm/300 nm and 300 nm/200 nm) and a reference MEMS resonator without the PnC. From the slope of the frequency shift shown in Fig. 2(b), we determined the thermal responsivity, R  Δf/f0Pin, for the samples. R is increased from ~393 W -1 for the reference sample to ~712 W -1 for d/n = 300 nm/300 nm and ~892 W -1 for d/n = 300 nm/200 nm, indicating that the PnC is effective in increasing the thermal responsivity of the MEMS detectors.
To back up our interpretation, we have calculated the thermal conductance of the unit cell of the square PnC lattice, gT. Here, we introduce the porosity of the beam, p, which is defined by the ratio of the material volume removed from the beam to the volume of the beam before fabricating PnC structures 21 , . ( As seen in Eq. (1), p is determined only by the ratio n/d. In the calculation, we assumed that the left and right boundaries of the PnC unit cell has a temperature difference, T, and we calculated the heat where f0 is the frequency shift when the heat modulation frequency fm = 0. GPLL(fm) expresses the circuit response of the PLL.
We first characterized GPLL(fm) to calibrate the effect of the demodulation bandwidth (BW) of the PLL. We input a frequency-modulated (FM) ac signal (amplitude = 1V, carrier frequency = 200 kHz, and FM depth 1 kHz) to the PLL to simulate the signal from the MEMS bolometer. 17 We swept fm and measured the demodulated output of the PLL to obtain GPLL(fm). Then, we can obtain the intrinsic frequency response of the beams as f(fm)/GPLL(fm), which is only determined by the thermal decay process in the MEMS beam. Figure 4(a) plots f(fm)/GPLL(fm) for a reference MEMS resonator without the PnC and typical two MEMS resonators with PnC structures (d/n = 300 nm/300 nm and 300 nm/200 nm). As seen in the figure, the signals for the PnC samples decrease slightly faster than that of the reference sample, indicating that the thermal decay times, τD, are slightly increased by introducing the PnC structures.
By using numerical fitting of Eq. (2) to f(fm)/GPLL(fm), we obtained τD for the MEMS beams with the PnCs and that for the reference MEMS beam. Figure 4(b) plots τD of the MEMS beams with PnC structures as a function of p. τD is increased from ~75.8 μs for the reference sample to ~97.4 μs for d/n = 300 nm/300 nm and ~112.5 μs for d/n = 300 nm/200 nm. From Fig. 4(b), we see that the increase in τ D by introducing the PnC structures is typically 30-40%. Compared with the improvement in responsivity (2-3 times), the reduction in the thermal BW is smaller, demonstrating effectiveness of the PnCs for partly resolving the trade-off between the responsivity and the bandwidth of the thermal sensors.
Finally, we have characterized the noise equivalent power (NEP) of the MEMS beam resonators.
We drove the MEMS beam resonators in a self-oscillation mode by using a PLL with a demodulation band width of 1 kHz and measured the frequency noise spectra, nf.  to provide a feedback control for maintaining the self-oscillation.   Fig. 4(b), as a function of the porosity of the PnC structure.