Investigation of AlGaN/GaN HFET and VO2 Thin Film Based Deflection Transducers Embedded in GaN Microcantilevers

The static and dynamic deflection transducing performances of piezotransistive AlGaN/GaN heterojunction field effect transistors (HFET) and piezoresistive VO2 thin films, fabricated on GaN microcantilevers of similar dimensions, were investigated. Deflection sensitivities were tuned with the gate bias and operating temperature for embedded AlGaN/GaN HFET and VO2 thin film transducers, respectively. The GaN microcantilevers were excited with a piezoactuator in their linear and nonlinear oscillation regions of the fundamental oscillatory mode. In the linear regime, the maximum deflection sensitivity of piezotransistive AlGaN/GaN HFET reached up to a 0.5% change in applied drain voltage, while the responsivity of the piezoresistive VO2 thin film based deflection transducer reached a maximum value of 0.36% change in applied drain current. The effects of the gate bias and the operation temperature on nonlinear behaviors of the microcantilevers were also experimentally examined. Static deflection sensitivity measurements demonstrated a large change of 16% in drain-source resistance of the AlGaN/GaN HFET, and a similarly high 11% change in drain-source resistance in the VO2 thin film, corresponding to a 10 μm downward step bending of the cantilever free end.


Introduction
Micro and nanoelectromechanical systems (M/NEMS) have been one of the major research areas spanning several decades due to many of their attractive attributes, including scalability, integration capability, reliability, and design variety [1,2]. Among M/NEMS devices, micro and nanocantilevers have been extensively studied, especially after their sensitivity and application potential was demonstrated by atomic force microscopy [3][4][5][6]. Besides material characterization applications, these structures, resembling tiny diving boards, have been incorporated into physical, chemical, and biological sensing applications, due to their ultra-high sensitivity to physical property changes [7][8][9]. The sensing operations with microcantilevers are based on tracking static or dynamic tip deflections, measured traditionally using optical read-out technologies. Even though optical deflection measurement offers very high resolution, excellent sensitivity, and low noise, it is not practical for an array of micro-resonators requiring simultaneous deflection measurements, as it would be immensely bulky and expensive [10]. In order to overcome the challenges associated with the traditional optical based detection methods, integrated photonic-based waveguide and optical cavity systems have been proposed [11][12][13][14]. Besides optomechanical deflection transducing techniques, recent research has The microcantilevers were operated in their dynamic oscillation mode. The AlGaN/GaN HFET embedded cantilever was excited by the piezoactuator under various alternating current (AC) biases, while a constant IDS of 200 μA was applied to the HFET drain from the SMU. The dynamic changes in the VDS (∆VDS), due to piezoactuator-based oscillations of the microcantilever, were measured using a lock-in amplifier (SR850 Stanford Research Systems, Sunnyvale, CA, USA), which was also used to bias the piezoactuator with a variable frequency sinusoidal AC voltage. Detailed experimental procedures of GaN microcantilever dynamic characterizations have been reported elsewhere [18][19][20]33,34]. To characterize the VO2 thin film embedded GaN microcantilever, a constant drain source voltage (VDS) of 20 V was applied to the drain contact of the VO2 thin film using the SMU. To measure alterations in the drain source current, IDS, due to the cantilever oscillation, the source contact was connected to a current pre-amplifier (SR570 Stanford Research Systems) to amplify the current readings. The amplified signal was fed to a lock-in amplifier that measured the AC changes in IDS. All the measurements were done on top of a hot plate, which enabled the temperature of the VO2 thin film to be controlled during the characterization experiments. The temperature measurements were  Figure 1e demonstrates the schematic of the experimental setup used to characterize the VO 2 transducer embedded GaN microcantilever. The fabricated chips containing AlGaN/GaN HFET and VO 2 thin film embedded cantilevers were attached (using a high temperature compatible epoxy) to a custom designed printed circuit board (PCB), to easily form electrical connections. A piezo actuator with dimensions of 5 × 5 × 2 mm (Model: PL055.3x from Physik Instrumente GmbH & Co., Karlsruhe, Germany) was attached under the PCB to actuate the microcantilevers. The cantilevers were placed on a hot plate as shown in the schematic. The same piezoactuator was employed in all characterization measurements of the AlGaN/GaN HFET and VO 2 thin film embedded GaN microcantilevers, to facilitate direct performance comparison between the two different transducers.
At first, transistor and metal insulator transition characteristics were investigated for the embedded AlGaN/GaN HFET and VO 2 thin film, respectively. Figure 2a displays changes in AlGaN/GaN HFET drain-source current (I DS ), with the gate-source voltage (V GS ) at a constant drain-source voltage (V DS ) of 0.5 V. Drain currents below µA level in the cut-off region (V GS < −3 V) indicate excellent gate control. The inset of Figure 2a shows typical I-V characteristics of the AlGaN/GaN HFET. The effects of temperature on VO 2 thin film drain source resistance (R DS ) at a constant V DS of 20 V, applied using a source measurement unit (SMU) (B2902A Keysight Technologies Inc., Santa Rosa, CA, USA), are shown in Figure 2b. A photo of the VO 2 thin film embedded microcantilever on a hot plate, for temperature characterization, is shown in inset of Figure 2b. While the room temperature resistance of VO 2 thin film was found to be around~3 MΩ, the resistance reduced down to~60 kΩ at 80 • C. As the VO 2 thin film temperature reached the MIT temperature (which is typically found to be slightly above 60 • C for our films), the rate of decline in the R DS with temperature became sharper, as expected. We did not find the change to be very sharp, as observed for large area films on sapphire or SiO 2 /Si [35,36], possibly due to polycrystallinity and defects on the small area deposited VO 2 films.

Results and Discussion
We have demonstrated in our past studies that the deflection responsivity of the AlGaN/GaN HFET can be manipulated using the gate voltage [17,19,21,34]. On the other hand, we expected the sensitivity of the VO2 thin film deflection transducer to also be tunable based on the temperature of the film. To compare the deflection sensitivity of the AlGaN/GaN HFET and VO2 thin film in the microcantilevers' linear dynamic regime, the piezoactuator under the microcantilevers was biased at a constant AC voltage of 1 V. Figure 3a displays the experimental resonance characteristics of the AlGaN/GaN HFET embedded GaN microcantilever at various gate voltages, ranging from 0 to −2.6 V. The resonance frequency (f0) and the quality factor (Qf) of the HFET embedded microcantilever were determined from the measurements as 15.150 kHz and 80, respectively. As the channel resistance (RDS) increased due to higher gate biases, for a constant IDS of 200 μA, the ∆VDS corresponding to the mechanical oscillations of the microcantilever (at 1 V piezo excitation) also increased. Deflection sensitivity of the AlGaN/GaN HFET transducer at different gate voltages can be calculated using , where VDS is the drain source voltage at a particular gate voltage, and ∆VDS is the HFET resonance amplitude. As shown in Figure 3b, the deflection sensitivity of AlGaN/GaN HFET reaches its maximum point of a ~0.50% change in VDS, corresponding to a gate voltage of −2.5 V. The sensitivity reduced dramatically at gate voltages higher than this critical bias, even though VDS kept increasing, as shown in the right axis of Figure 3b. 0394 The deflection responsivity of the VO2 thin film deposited on the GaN microcantilever was also characterized at VPiezo = 1 V, at different measurement temperatures. Figure 3c demonstrates the resonance characteristics of the microcantilever with the VO2 piezoresistive transducer. The f0 and Qf of the VO2 thin film embedded GaN microcantilever were measured as 15.660 kHz and 85 at room temperature, respectively. At a constant VDS = 20 V, IDS was modified as the temperature changed, After characterizations of the AlGaN/GaN HFET and the VO 2 thin film, we investigated deflection transduction properties of these transducers embedded at the base of the GaN.
The microcantilevers were operated in their dynamic oscillation mode. The AlGaN/GaN HFET embedded cantilever was excited by the piezoactuator under various alternating current (AC) biases, while a constant I DS of 200 µA was applied to the HFET drain from the SMU. The dynamic changes in the V DS (∆V DS ), due to piezoactuator-based oscillations of the microcantilever, were measured using a lock-in amplifier (SR850 Stanford Research Systems, Sunnyvale, CA, USA), which was also used to bias the piezoactuator with a variable frequency sinusoidal AC voltage. Detailed experimental procedures of GaN microcantilever dynamic characterizations have been reported elsewhere [18][19][20]33,34]. To characterize the VO 2 thin film embedded GaN microcantilever, a constant drain source voltage (V DS ) of 20 V was applied to the drain contact of the VO 2 thin film using the SMU. To measure alterations in the drain source current, I DS , due to the cantilever oscillation, the source contact was connected to a current pre-amplifier (SR570 Stanford Research Systems) to amplify the current readings. The amplified signal was fed to a lock-in amplifier that measured the AC changes in I DS . All the measurements were done on top of a hot plate, which enabled the temperature of the VO 2 thin film to be controlled during the characterization experiments. The temperature measurements were made using a standard thermocouple (k type) and data-acquisition equipment (34972A from Agilent Technologies Inc., Santa Clara, CA, USA).
In addition to dynamic characterization experiments, the static deflection transducing performances of the AlGaN/GaN HFET and the VO 2 thin film were measured by deflecting the microcantilevers' free ends by 10 µm downward. A tungsten needle with a tip radius of 7 µm (72T-J3/70 Creative Devices Inc., Middletown, DE, USA) was attached to a computer-controlled nanopositioner (P-611.Z Physik Instrumente GmbH & Co., Karlsruhe, Germany) for the bending experiments. The same constant biases of I DS = 200 µA and V DS = 20 V used in the dynamic resonance measurements were also applied to the HFET and VO 2 thin film (using the SMU), respectively. The changes in the V DS of the HFET and the I DS of the VO 2 thin film, due to the 10 µm downward bending of the microcantilever tip, were recorded.

Results and Discussion
We have demonstrated in our past studies that the deflection responsivity of the AlGaN/GaN HFET can be manipulated using the gate voltage [17,19,21,34]. On the other hand, we expected the sensitivity of the VO 2 thin film deflection transducer to also be tunable based on the temperature of the film. To compare the deflection sensitivity of the AlGaN/GaN HFET and VO 2 thin film in the microcantilevers' linear dynamic regime, the piezoactuator under the microcantilevers was biased at a constant AC voltage of 1 V. Figure 3a displays the experimental resonance characteristics of the AlGaN/GaN HFET embedded GaN microcantilever at various gate voltages, ranging from 0 to −2.6 V. The resonance frequency (f 0 ) and the quality factor (Q f ) of the HFET embedded microcantilever were determined from the measurements as 15.150 kHz and 80, respectively. As the channel resistance (R DS ) increased due to higher gate biases, for a constant I DS of 200 µA, the ∆V DS corresponding to the mechanical oscillations of the microcantilever (at 1 V piezo excitation) also increased. Deflection sensitivity of the AlGaN/GaN HFET transducer at different gate voltages can be calculated using Sensitivity (%) = , where V DS is the drain source voltage at a particular gate voltage, and ∆V DS is the HFET resonance amplitude. As shown in Figure 3b, the deflection sensitivity of AlGaN/GaN HFET reaches its maximum point of ã 0.50% change in V DS , corresponding to a gate voltage of −2.5 V. The sensitivity reduced dramatically at gate voltages higher than this critical bias, even though V DS kept increasing, as shown in the right axis of Figure 3b.
The deflection responsivity of the VO 2 thin film deposited on the GaN microcantilever was also characterized at V Piezo = 1 V, at different measurement temperatures. Figure 3c demonstrates the resonance characteristics of the microcantilever with the VO 2 piezoresistive transducer. The f 0 and Q f of the VO 2 thin film embedded GaN microcantilever were measured as 15.660 kHz and 85 at room temperature, respectively. At a constant V DS = 20 V, I DS was modified as the temperature changed, therefore the sinusoidal change in I DS (∆I DS ), captured with the lock-in amplifier (proportional to the amplitude) at the microcantilever resonance, was also altered. As shown in right axis of Figure 3d, the I DS of the VO 2 thin film increased with the rise in temperature at constant V DS as R DS reduces. This increase in I DS resulted in a higher resonance amplitude. The deflection sensitivity calculated using the formula: Sensitivity (%) = ∆I DS × 100 I DS , reached~0.36% in the range of 65-75 • C, where the metal insulator transition of the VO 2 thin film takes place. Increasing the temperature beyond the critical MIT temperature reduces the displacement sensitivity of VO 2 thin film, as clearly evident from Figure 3d. We noted that the resonance frequency of the VO 2 thin film deposited cantilever shifted significantly to lower frequencies as the temperature increased. Reduction in elastic modulus, which directly determines the spring constant of the cantilever, due to an increase in temperature, was a major reason for the observed red shift in resonance frequency [37]. The HFET VDS variation due to the gate bias is shown in the right axis. (c) Effects of the temperature on the dynamic resonance behavior of the VO2 thin film embedded GaN microcantilever, while the piezoactuator was biased at 1 V. (d) VO2 thin film deflection sensitivity calculated at various temperatures. As the temperature increases, resistance of the VO2 thin film reduces. Therefore, at a constant VDS of 20 V, IDS increases with temperature, as shown in the right axis.
We also investigated the sensitivities of the AlGaN/GaN HFET and VO2 thin film deflection transducers at various piezoactuator biases ranging from 1 V to 5 V, which shifted the resonance mode of the microcantilevers from the linear to non-linear regime. The non-linear operation is particularly interesting due to its wide potential applications in designing ultra-high sensitivity sensors [38,39]. Figure 4a shows resonance curves of the GaN microcantilever with the AlGaN/GaN HFET transducer biased at IDS = 200 mA and VGS = −2.5 V. Increasing the drive amplitudes (excited by the piezo chip) revealed Duffing type intrinsic nonlinearities of the microcantilever in the fundamental resonance mode. Softening type nonlinearity, shifting the resonance frequency to lower values, was found to be dominant in the first mode, as seen in Figure 4a. According to our previous studies, GaN microcantilevers with widths greater than 70 μm and a length of 250 μm exhibit softening type nonlinearities in their first resonance modes [34]. Therefore, the AlGaN/GaN HFET embedded GaN microcantilever with dimensions of 100 × 250 μm utilized in this study could be expected to manifest softening type nonlinearities at high deflection amplitudes, which was indeed observed in the present study.
The tip oscillation amplitude (x0) at the resonance frequency of ω0 is given by = ( ) where FPiezo is the external effective force applied by the piezoactuator, and keff is the effective spring constant, given as = (m is the effective mass). The external force applied by the piezo actuator is defined as FPiezo = mω0 2 VPiezoGPiezo where VPiezo and GPiezo are the applied piezo bias and the constant piezo displacement coefficient, respectively [34]. Therefore, substituting the piezo force into the deflection equation, we get = . The amplitude of the tip deflections at the resonance frequency is independent of the intrinsic nonlinearities, including geometric and inertial We also investigated the sensitivities of the AlGaN/GaN HFET and VO 2 thin film deflection transducers at various piezoactuator biases ranging from 1 V to 5 V, which shifted the resonance mode of the microcantilevers from the linear to non-linear regime. The non-linear operation is particularly interesting due to its wide potential applications in designing ultra-high sensitivity sensors [38,39]. Figure 4a shows resonance curves of the GaN microcantilever with the AlGaN/GaN HFET transducer biased at I DS = 200 mA and V GS = −2.5 V. Increasing the drive amplitudes (excited by the piezo chip) revealed Duffing type intrinsic nonlinearities of the microcantilever in the fundamental resonance mode. Softening type nonlinearity, shifting the resonance frequency to lower values, was found to be dominant in the first mode, as seen in Figure 4a. According to our previous studies, GaN microcantilevers with widths greater than 70 µm and a length of 250 µm exhibit softening type nonlinearities in their first resonance modes [34]. Therefore, the AlGaN/GaN HFET embedded GaN microcantilever with dimensions of 100 × 250 µm utilized in this study could be expected to manifest softening type nonlinearities at high deflection amplitudes, which was indeed observed in the present study.
nonlinearities [40,41]. Since the cantilever tip deflections are directly proportional to the applied piezo bias, VPiezo was included in the sensitivity equation. The AlGaN/GaN HFET deflection sensitivity at high oscillation amplitudes was calculated using the formula: . Figure 4b shows changes in sensitivity of the AlGaN/GaN HFET at different excitation biases. The sensitivity was 0.42% at VPiezo = 1 V. Increasing the piezo biases gradually reduced the deflection sensitivity of the HFET transducer. At VPiezo = 5 V, the sensitivity decreased to 0.37%. In addition to the AlGaN/GaN HFET deflection characteristics at high oscillation amplitudes, resonance curves of the VO2 thin film embedded GaN cantilever at room temperature are shown in Figure 4c. Similarly to the HFET cantilever, the VO2 cantilever with the same dimensions features similar softening type nonlinearities in the first resonance mode. The deflection sensitivity of VO2 thin film calculated using (%) = ∆ × at various VPiezo voltages is shown in Figure 4d. The responsivity of the piezoresistive VO2 deflection sensor also reduced monotonically, like the HFET embedded cantilever, as the piezoactuator bias increased. While the resonance amplitude at VPiezo = 1 V was measured as a 0.12% change in IDS at a constant VDS of 20 V, only a 0.08% change in IDS was produced due to cantilever oscillations at VPiezo = 5 V. These reductions in the sensitivities of piezotransistive AlGaN/GaN HFET and piezoresistive VO2 thin film deflection transducers at high drive amplitudes might arise from other factors such as nonlinear damping, The tip oscillation amplitude (x 0 ) at the resonance frequency of ω 0 is given by where F Piezo is the external effective force applied by the piezoactuator, and k eff is the effective spring constant, given as k eff = mω 2 0 (m is the effective mass). The external force applied by the piezo actuator is defined as F Piezo = mω 0 2 V Piezo G Piezo where V Piezo and G Piezo are the applied piezo bias and the constant piezo displacement coefficient, respectively [34]. Therefore, substituting the piezo force into the deflection equation, we get x 0 = V Piezo G Piezo Q f . The amplitude of the tip deflections at the resonance frequency is independent of the intrinsic nonlinearities, including geometric and inertial nonlinearities [40,41]. Since the cantilever tip deflections are directly proportional to the applied piezo bias, V Piezo was included in the sensitivity equation. The AlGaN/GaN HFET deflection sensitivity at high oscillation amplitudes was calculated using the formula: Figure 4b shows changes in sensitivity of the AlGaN/GaN HFET at different excitation biases. The sensitivity was 0.42% at V Piezo = 1 V. Increasing the piezo biases gradually reduced the deflection sensitivity of the HFET transducer. At V Piezo = 5 V, the sensitivity decreased to 0.37%.
In addition to the AlGaN/GaN HFET deflection characteristics at high oscillation amplitudes, resonance curves of the VO 2 thin film embedded GaN cantilever at room temperature are shown in Figure 4c. Similarly to the HFET cantilever, the VO 2 cantilever with the same dimensions features similar softening type nonlinearities in the first resonance mode. The deflection sensitivity of VO 2 thin  Figure 4d. The responsivity of the piezoresistive VO 2 deflection sensor also reduced monotonically, like the HFET embedded cantilever, as the piezoactuator bias increased. While the resonance amplitude at V Piezo = 1 V was measured as a 0.12% change in I DS at a constant V DS of 20 V, only a 0.08% change in I DS was produced due to cantilever oscillations at V Piezo = 5 V. These reductions in the sensitivities of piezotransistive AlGaN/GaN HFET and piezoresistive VO 2 thin film deflection transducers at high drive amplitudes might arise from other factors such as nonlinear damping, which can reduce the quality factor of the resonator at higher amplitudes, thus reducing the normalized resonance amplitude as the applied external force increases [40][41][42].
As mentioned earlier, the gate bias can be used to tune the sensitivity of the HFET deflection transducer. Figure 5a demonstrates the gate bias effects on the resonance curves the of AlGaN/GaN HFET embedded GaN microcantilever, excited in the nonlinear regime at V Piezo = 5 V. Backward frequency sweep setting was utilized in all nonlinear curves, since there is a hysteresis between forward and backward curves. For resonators demonstrating softening type nonlinearities, only backward sweep direction exposes a total shift in the resonance frequency [40]. On the other hand, forward frequency sweep needs to be used to identify the frequency shift in hardening dominated nonlinear curves, where the resonance frequency moves to higher frequencies. Higher gate biases result in the enhancement of the HFET resonance amplitude as the sensitivity of the AlGaN/GaN HFET increases. However, the drop frequency, which is a significant feature of these Duffing type nonlinear behaviors, remains stable at 15.00 kHz, as displayed by the dotted line in Figure 5a. The results indicate that the gate bias modifying sensitivity of the HFET based deflection transducer does not affect nonlinear characteristics of the GaN microcantilever. On the other hand, the operating temperature of the piezoresistive VO 2 thin film transducer can be changed to tune its deflection sensitivity.
Micromachines 2020, 11, x 8 of 12 which can reduce the quality factor of the resonator at higher amplitudes, thus reducing the normalized resonance amplitude as the applied external force increases [40][41][42].
As mentioned earlier, the gate bias can be used to tune the sensitivity of the HFET deflection transducer. Figure 5a demonstrates the gate bias effects on the resonance curves the of AlGaN/GaN HFET embedded GaN microcantilever, excited in the nonlinear regime at VPiezo = 5 V. Backward frequency sweep setting was utilized in all nonlinear curves, since there is a hysteresis between forward and backward curves. For resonators demonstrating softening type nonlinearities, only backward sweep direction exposes a total shift in the resonance frequency [40]. On the other hand, forward frequency sweep needs to be used to identify the frequency shift in hardening dominated nonlinear curves, where the resonance frequency moves to higher frequencies. Higher gate biases result in the enhancement of the HFET resonance amplitude as the sensitivity of the AlGaN/GaN HFET increases. However, the drop frequency, which is a significant feature of these Duffing type nonlinear behaviors, remains stable at 15.00 kHz, as displayed by the dotted line in Figure 5a. The results indicate that the gate bias modifying sensitivity of the HFET based deflection transducer does not affect nonlinear characteristics of the GaN microcantilever. On the other hand, the operating temperature of the piezoresistive VO2 thin film transducer can be changed to tune its deflection sensitivity. Such changes in the operating temperature of the VO2 thin film also caused alterations in nonlinear resonance curves as shown in Figure 5b, which was not observed for the HFET embedded cantilever. Even though the sensitivity of the VO2 thin film increased towards the critical MIT temperature, the cantilever resonance frequency also shifted to lower frequencies, since utilizing the hot plate to control the VO2 thin film temperature also regulated the cantilever temperature. The temperature dependence of elastic modulus, which resulted in red shift of the resonance frequency for linear regime oscillations, as noted in our above discussions, can also change the non-linear behavior of the resonators [37]. In addition, dimensional changes of the cantilever due to temperature rise can modify the intrinsic nonlinearities [34]. A combination of these factors likely resulted in the shift in the drop frequency of oscillations in the nonlinear region, as observed in Figure 5b.
In Figure 6, the static bending experiment results of the AlGaN/GaN HFET and VO2 thin film deflection transducers are presented. A schematic of the experimental setup used for the VO2 thin film embedded GaN microcantilever is presented in Figure 6a. When the tip of the GaN microcantilever was bent 10 μm downward, the VDS of the HFET, under a constant bias of IDS = 200 Such changes in the operating temperature of the VO 2 thin film also caused alterations in nonlinear resonance curves as shown in Figure 5b, which was not observed for the HFET embedded cantilever. Even though the sensitivity of the VO 2 thin film increased towards the critical MIT temperature, the cantilever resonance frequency also shifted to lower frequencies, since utilizing the hot plate to control the VO 2 thin film temperature also regulated the cantilever temperature. The temperature dependence of elastic modulus, which resulted in red shift of the resonance frequency for linear regime oscillations, as noted in our above discussions, can also change the non-linear behavior of the resonators [37]. In addition, dimensional changes of the cantilever due to temperature rise can modify the intrinsic nonlinearities [34]. A combination of these factors likely resulted in the shift in the drop frequency of oscillations in the nonlinear region, as observed in Figure 5b.
In Figure 6, the static bending experiment results of the AlGaN/GaN HFET and VO 2 thin film deflection transducers are presented. A schematic of the experimental setup used for the VO 2 thin film embedded GaN microcantilever is presented in Figure 6a. When the tip of the GaN microcantilever was bent 10 µm downward, the V DS of the HFET, under a constant bias of I DS = 200 µA and V GS = 0 V, was reduced by 0.15%. As shown in Figure 6b, increasing the deflection sensitivity of the AlGaN/GaN HFET, by tuning the gate bias, yielded 1% and 16% reductions in the V DS at gate biases of V GS = −2 V and V GS = −2.5 V, respectively. As the cantilever bends downward, effective tensile stress increases the 2DEG density of the AlGaN/GaN HFET, leading a reduction in the channel resistance of R DS [18]. At a constant I DS , the HFET channel voltage of V DS also decreases by a percentage directly proportional to the R DS reduction, as the cantilever undergoes a downward bending. Figure 6c demonstrates changes in I DS of the VO 2 thin film under an applied drain bias of V DS = 20 V in response to 10 µm downward step bending at various temperatures. While the I DS of VO 2 thin film reduces 0.3% at a room temperature of 22 • C, increasing the temperature towards the MIT temperature enhances the static deflection sensitivity of VO 2 thin film. As shown in Figure 6c, 10 µm downward step bending yielded 3% and 10% decreases in the I DS of the VO 2 thin film transducer at temperatures of 40 • C and 65 • C, respectively. At a constant V DS , reduction in the I DS due to downward bending corresponds to an increase in the R DS . This behavior was expected since the resistance of VO 2 thin film increases due to band structure changes when the VO 2 thin film is subjected to a tensile stress [43]. Figure 6d displays the sensing results in Figure 6b,c in terms of normalized R DS changes, (∆R DS /R DS ) in the AlGaN/GaN HFET (red circles), and VO 2 thin film (blue squares), at selected V GS and temperatures, respectively.
Comparing the sensitivities of the VO 2 thin film and AlGaN/GaN HFET integrated cantilevers, we find that their maximum static and dynamic deflection sensitivities are very similar. In the linear dynamic regime, oscillation amplitudes of the cantilevers under study were expected to be the same, since they had the same dimensions and the same piezoactuator was utilized to excite them. Optimizing the sensitivity tuning parameters, namely, gate bias for AlGaN/GaN HFET, and temperature for VO 2 thin film, led to the maximum sensitivity values of 0.5% (change in HFET V DS at a constant I DS ), and 0.35% (change in VO 2 thin film I DS at constant V DS measured in linear regime applying 1 V to the piezoactuator), respectively. Both types of GaN microcantilevers also exhibited softening type nonlinearities at large deflection amplitudes. While the gate bias for the AlGaN/GaN HFET embedded microcantilever did not affect the intrinsic nonlinearities of the microcantilever at higher excitation amplitudes, increasing the operation temperature to modify the sensitivity of the VO 2 thin film embedded microcantilever had a considerable influence over the nonlinear behavior, as discussed above. Moreover, the responses of the AlGaN/GaN HFET and VO 2 thin film to 10 µm static downward bending support the experimental results observed in dynamic oscillation mode. Even though the AlGaN/GaN HFET and the VO 2 thin film demonstrated opposite resistance change behaviors (decrease in R DS for AlGaN/GaN HET, and increase in R DS for the VO 2 thin film) in response to the applied tensile stress, corresponding to a 10 µm step bending, their peak deflection transduction performances (16% change in R DS for AlGaN/GaN HFET and 11% change in R DS for VO 2 thin film), at their optimized strain sensing conditions, are quite comparable.
downward step bending yielded 3% and 10% decreases in the IDS of the VO2 thin film transducer at temperatures of 40 °C and 65 °C, respectively. At a constant VDS, reduction in the IDS due to downward bending corresponds to an increase in the RDS. This behavior was expected since the resistance of VO2 thin film increases due to band structure changes when the VO2 thin film is subjected to a tensile stress [43]. Figure 6d displays the sensing results in Figure 6b,c in terms of normalized RDS changes, (∆RDS/RDS) in the AlGaN/GaN HFET (red circles), and VO2 thin film (blue squares), at selected VGS and temperatures, respectively. Comparing the sensitivities of the VO2 thin film and AlGaN/GaN HFET integrated cantilevers, we find that their maximum static and dynamic deflection sensitivities are very similar. In the linear dynamic regime, oscillation amplitudes of the cantilevers under study were expected to be the same, since they had the same dimensions and the same piezoactuator was utilized to excite them. Optimizing the sensitivity tuning parameters, namely, gate bias for AlGaN/GaN HFET, and temperature for VO2 thin film, led to the maximum sensitivity values of 0.5% (change in HFET VDS at

Conclusions
In conclusion, we successfully compared the performances of piezotransistive AlGaN/GaN HFET and piezoresistive VO 2 thin film based deflection transducers embedded on GaN microcantilevers in static and dynamic modes. Microcantilevers with similar nominal dimensions, when excited similarly with a piezoactuator, exhibited very similar maximum deflection sensitivities in the linear oscillation regime, which were tuned using gate bias and operation temperature, for AlGaN/GaN HFET and VO 2 thin film transducers, respectively. In the linear dynamic regime, while the deflection sensitivity of the AlGaN/GaN HFET reached up to 0.5% change in V DS at an appropriate gate bias of −2.5 V, the VO 2 thin film deflection transducer demonstrated a maximum sensitivity of 0.36% change in I DS around the MIT temperature of 65-75 • C. When operated in the non-linear regime, using higher excitation from the piezoactuator, a gradual reduction in sensitivities of the transducers was observed with both deflection transducers, while the VO 2 embedded one showed variation drop frequencies at varying temperatures, due to changes in elastic modulus and dimensions. Comparable static deflection sensitivities were observed for the AlGaN/GaN HFET and the VO 2 thin film when the microcantilevers were subjected to static bending. While a 10 µm downward tip bending resulted in a 16% change in R DS of the AlGaN/GaN HFET at an optimal gate bias of −2.5 V, the maximum change in R DS of the VO 2 thin film, corresponding to the same downward step bending, was found to be 11%, at the critical MIT temperature of~65 • C. Funding: This research was funded by the National Science Foundation, grants number ECCS-1809891 and IIP-1602006.

Conflicts of Interest:
The authors declare no conflict of interest.