Bayram et al. Microsystems & Nanoengineering (2022) 8:8 Microsystems & Nanoengineeringhttps://doi.org/10.1038/s41378-021-00330-6 www.nature.com/micronano

ART ICLE Open Ac ce s s

Mechanical memory operations in piezotransistiveGaN microcantilevers using Au nanoparticle-enhanced photoacoustic excitationFerhat Bayram 1✉, Durga Gajula2, Digangana Khan1 and Goutam Koley1

AbstractNonlinear oscillations in micro- and nanoelectromechanical systems have emerged as an exciting research area inrecent years due to their promise in realizing low-power, scalable, and reconfigurable mechanical memory and logicdevices. Here, we report ultralow-power mechanical memory operations utilizing the nonlinear oscillation regime ofGaN microcantilevers with embedded piezotransistive AlGaN/GaN heterostructure field effect transistors as highlysensitive deflection transducers. Switching between the high and low oscillatory states of the nonlinear oscillationregime was demonstrated using a novel phase-controlled opto-mechanical excitation setup, utilizing a piezo actuatorand a pulsed laser as the primary and secondary excitation sources, respectively. Laser-based photoacoustic excitationwas amplified through plasmonic absorption in Au nanoparticles deposited on a transistor. Thus, the minimumswitching energy required for reliable memory operations was reduced to less than a picojoule (pJ), which translatesto one of the lowest ever reported, when normalized for mass.

IntroductionThe concept of mechanical computers has always fas-

cinated researchers throughout the evolution of com-puting, especially attracting research interest since thedemonstration of the first difference engine by CharlesBabbage almost two centuries ago1. Over the years, thedevelopment of efficient and sufficiently miniaturizedmechanical computing engines, a mechanical computerwith logic and memory operations capabilities, hasremained a challenging task for the research community,while silicon microelectronics-based memory cells andlogic devices have continued to experience a dramaticreduction in size and power consumption, resulting intheir widespread application in diverse fields2. With tra-ditional silicon-based transistor technologies approachingtheir fundamental size and power dissipation limits in

recent years, mechanical memory and logic devices, asalternatives to conventional computing, have once againstarted to garner significant research interest3. The cap-ability of operating in harsh environments and the pos-sibility of versatile logic operations in the same device aresome advantages of mechanical memory and logic devi-ces4,5. Considering the vast advancement in fabricationand instrumentation in recent years, memory and logicdevices based on micro/nanoelectromechanical systems(MEMS/NEMS) and resonators may compete againstcurrent electronic transistor-based computing systems interms of size, speed, and power consumption2,4,6–8.The demonstrated memory and logic operations utilizing

MEMS and NEMS are mainly based on their dynamicnonlinear behaviors originating from internal and externalfactors, such as large deformations and rotations9, boundaryconditions10, nonlinear damping11, and parametric excita-tions12, which result in the operation of the oscillator in thenonlinear regime and creation of two stable states – oneoscillatory and the other nonoscillatory, which facilitatesmemory operations. The transition between these stable

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Correspondence: Ferhat Bayram (fbayram@clemson.edu)1Holcombe Department of Electrical and Computer Engineering, ClemsonUniversity, Clemson, SC 29634, USA2School of Electrical and Computer Engineering, Georgia Institute ofTechnology, Atlanta, GA 30332, USA

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states is achievable through various procedures, includingchanging the frequency or amplitude of the external exci-tations. Nonlinearity-based mechanical memory and logicoperations have been investigated utilizing a single excita-tion source, including electrostatic13–19, electrothermal5,20,magnetomotive6, piezoelectric7,21, magnetic22,23, and piezoactuator-based actuations24,25. Regardless of the excitationsource, they are all grouped as mechanical memory due tothe mechanical oscillatory nature of the memory element.Most of these excitation techniques require either complexmicrofabrication processes and/or additional componentsto provide sufficient excitation, forcing the system tooscillate in the nonlinear regime26. In addition, changing thecurrent status of multiple resonators is not feasible andefficient with a single external resonating source. Toselectively operate an array of resonators for memory andlogic operations, two external actuation sources can beutilized, where the resonators can be sufficiently excited tooscillate in the bistable region using one (primary) externalsource, while the other (secondary) can be used to switchbetween stable states acting as a “set and reset operator for agiven resonator” using very little power. Optical excitationmethodologies using the photoacoustic effect offer a non-contact, simple actuation technique; therefore, they arehighly suitable for efficient dynamic mechanical memoryapplications.Light-driven resonators have become a promising

platform for developing photoacoustic spectroscopyapplications27–31, offering several advantages, includingnoncontact actuation, easy integration, and zero back-ground32. Photoacoustic excitation relies on the genera-tion of acoustic waves through periodic expansion andcontraction of photon absorbing media due to localizedheating caused by exposure to a pulsed light source. Thegenerated acoustic wave can be used to excite amechanical oscillator very efficiently if the pulsing fre-quency of the light source matches the resonance fre-quency of the oscillator. Despite its several advantagescompared to traditional excitation sources, the photo-acoustic excitation technique has not been utilized toinvestigate the intrinsic nonlinearities of MEMS devicesor their bistable operation.Here, we report, for the first time, the investigation of

dynamic mechanical memory operations utilizing ultra-sensitive AlGaN/GaN heterojunction field effect transis-tor (HFET)-embedded GaN microcantilevers driven withsingle and multiple external oscillation sources, includingprimary excitation with a piezo actuator and secondaryphotoacoustic actuation with a pulsed laser. An AlGaN/GaN HFET embedded at the cantilever base was utilizedto transduce microcantilever tip deflections into electricalsignals; hence, it is called a “piezotransistive” micro-cantilever. In the mode of a single excitation source, thetransition between the high and low stable states of the

GaN microcantilevers in their intrinsic nonlinear regimewas successfully demonstrated using either modulation ofthe piezo actuator bias, the laser beam location, or thelaser power. In addition to single excitation-basedswitching, we experimentally demonstrated for the firsttime that two different excitation sources could be com-bined utilizing constructive and destructive interferenceproperties to switch between the two stable states of thecantilever. While using the piezo actuator as the primaryexcitation source to oscillate the microcantilever in thebistable region, a pulsed laser-based secondary (photo-acoustic) excitation was used to perform switchingbetween the states. Moreover, the laser power to make thetransition between states was reduced to ultralow levelsfollowing the deposition of Au nanoparticles, whichstrongly augmented photoacoustic signal generation dueto plasmonic absorption.Previously, we have shown that the cantilever dimen-

sions have significantly affected the nonlinear cubic con-stant9,33, which determines the minimum excitationrequired to push an oscillator to the nonlinear regime34.Our results indicated that GaN microcantilevers withlarger widths (>70 μm) at a fixed length of 250 μm exhibitstrong softening-type nonlinearities where the resonancepeak shifted to lower frequencies. On the other hand,hardening-type nonlinearities, where the resonance peakmoves to higher frequencies, were dominant for canti-levers with smaller widths (<70 μm). Considering thoseearlier observations, two GaN microcantilevers, one withsoftening and one with hardening-type intrinsic non-linearities in the first flexural mode, were selected todemonstrate mechanical memory operations in thepresent study.

ResultsDevice characterizationFigure 1a and Fig. S1a show scanning electron micro-

scope (SEM) images of fabricated microcantilevers withdimensions (length × width) of 250 × 100 μm and 150 ×50 μm, respectively. The microcantilevers were testedusing the generic experimental setup illustrated inFig. 1b, where the microcantilevers were attached to alinear piezo actuator with dimensions of 5 × 5 × 2 mm.For our studies, the microcantilevers were placed insidea home-built vacuum chamber setup, as shown inFig. S2, at a pressure of ~1 mTorr. Figure 1c and Fig. S1bdisplay the I-V (current-voltage) characteristics of theAlGaN/GaN HFETs embedded at the bases of theaforementioned microcantilevers. When the micro-cantilevers were excited into oscillations (i.e., using apiezo actuator), alterations in the HFET drain-sourcevoltage (VDS) caused by piezo-induced modulations oftwo-dimensional electron gas (2DEG) located at theAlGaN/GaN interface were measured using a lock-in

Bayram et al. Microsystems & Nanoengineering (2022) 8:8 Page 2 of 14

amplifier35–37. Detailed investigations and analysis of thedeflection transduction mechanism in AlGaN/GaNHFET-embedded GaN microcantilevers can be foundelsewhere35–39. A schematic of the experimental setupused for piezo actuator-based excitation is shown in Fig.S3. The resonance characteristics of the microcantileversin the linear regime were measured by applying a 4 mVac (rms) bias to the piezo actuator, as shown in the insetof Fig. 1c and Fig. S1b. Increasing the drive amplitudesforced the microcantilevers to enter their intrinsic non-linear territories. Figure 2a displays the resonance curvesof the microcantilever with dimensions 250 × 100 μm atvoltages (VPiezo) of 10, 20, 40, and 60 mV (rms) applied tothe piezo actuator, indicating that softening-type non-linearities are dominant at higher drive strengths,observable for 20 mV bias and beyond. On the otherhand, hardening nonlinearity was exhibited from themicrocantilever with dimensions of 150 × 50 μm at piezoactuator biases of 200 and 300 mV, as shown in Fig. S3a.

Memory operations utilizing piezo actuator-basedexcitationsTwo distinct features of Duffing-type nonlinearities,

bifurcations and hysteresis, have been observed with GaNmicrocantilevers in the frequency domain9,33,34. In thenonlinear regime, two stable states coexist, and a hysteresisloop becomes distinguishable at a constant frequency below(for softening type) or above (for hardening type) the criticalfrequency at which the bifurcations start to occur. Since twostable states are attainable due to hysteresis, changing theamplitude of the external force enables switching betweenthese states for memory operations3,34. In addition, theoscillations in these two states after switching in betweencan be sustained with the same excitation force amplitude.The insets of Fig. 2a and Fig. S4a display the hysteresisresponses of the microcantilevers under sweep-up (solidline) or sweep-down (dashed line) settings of the piezoactuator voltage at constant frequencies of 15.688 and42.379 kHz, respectively.

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Fig. 1 Experimental setup and characterization of GaN microcantilevers. a SEM image of the microcantilever (top) and photo of the piezoactuator attached underneath the microcantilever chip (bottom). b Schematic diagram of the experimental setup showing simultaneous piezo chipand photoacoustic excitation (using a pulsed laser) to switch cantilever states. c Electrical (IDS−VGS) and mechanical (resonance, inset) characteristicsof a microcantilever with dimensions of 250 × 100 µm. The resonance frequency and the quality factor of the resonator are determined to be15.690 kHz and 9600, respectively

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To investigate the piezo actuator-based switchingbehavior of the cantilever with a softening nonlinearity, aconstant VPiezo= 28mV (rms) signal with a frequency of15.688 kHz was applied to the piezo actuator. Then, thesteady-state VPiezo excitation signal was increased ordecreased by 8mV for a duration of 100ms to switchbetween the stable states of the microcantilever. Figure 2bdemonstrates the piezo actuator-based memory operationperformances of the GaN microcantilevers, where the toppanels show the variation in VDS (proportional to oscilla-tion amplitude), and the bottom panels show the ±8mVVPiezo triggers for 100ms around the mean value of 28mV.Figure S4b shows similar switching behavior betweenstable states triggered by VPiezo= ±6mV, around the meanvalue of 157mV for a duration of 500ms. We note thathigher piezo actuator biases were required for the canti-lever with dimensions 150 × 50 μm to operate in thenonlinear regime since the critical amplitude to drive themicrocantilever in the hysteresis region is higher.

Memory operations utilizing photoacoustic excitationsIn addition to piezo actuator-based excitation, GaN

microcantilevers can be excited through photoacousticwaves generated near the cantilever base using a pulsedlaser36,37. Pulsed laser irradiation-induced periodic heat-ing and cooling of the localized region results in expan-sions and contractions, which create acoustic waves in thestructure. Hence, these pulsed laser-based excitations arecalled photoacoustic excitations. Details of the photo-acoustic generation in the microcantilever are reportedelsewhere29,31,36. A pulsed 520 nm laser was focused near

the cantilever HFET using an X-Y-Z micropositioner, asshown in Fig. S5, and the resonance characteristics of themicrocantilevers were recorded at different power set-tings. The results are presented in Fig. 3a and Fig. S4c,where the softening and hardening characteristics ofmicrocantilevers, similar to the piezo actuator-basedexcitations, can be clearly seen beyond a certain laserpower (0.3 and 0.7 mW, respectively). Keeping the laserpulsing frequency constant and sweeping the laser powerhigher and lower resulted in a similar hysteresis responseas those obtained with the piezo ac bias sweep; the resultsare shown in the insets of Fig. 3a and S3c. Takingadvantage of these hysteresis characteristics, multiplememory switching operations were demonstrated at afixed frequency of 15.669 kHz by changing the laser powerfor 30ms to switch on/off the microcantilever, as shownin Fig. 3b. The laser with a 520 nm wavelength was kept ata base power of 960 μW to operate the microcantilever inits hysteresis regime. The laser power was increased by580 μW for 30ms to reach the high state from the lowstate, while a 380 μW reduction in laser power resulted inswitching from the high to the low state. Figure S4d showslaser-based memory operations using the microcantileverwith hardening characteristics, where the operations wereperformed with a base laser power of 550 μW andswitching was achieved by changing the power up anddown by 500 and 450 μW, respectively, for ~100ms.For photoacoustic-based excitations, the location of the

focused beam is crucial to reveal microcantilevers’intrinsic nonlinearities. The bistable regime, defined asthe frequency difference between drop and jump

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Fig. 2 Memory operations using a piezo actuator. a Softening-type nonlinear resonance characteristics of the microcantilever under differentpiezo actuator biases. The inset shows the hysteresis behavior at a fixed frequency of 15.688 kHz. b Switching the cantilever’s stable states using thepiezo actuator. A piezo bias of 28 mV was used to keep the cantilever in the bistable region. A bias differential of ±8 mV was added to the signal for100 ms to switch the cantilever from one bistable oscillatory state to another. Due to intrinsic softening properties, all resonance curves in (a) wereswept from high to low frequencies (sweep-down)

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frequencies (due to the hysteresis between forward andbackward resonance curves), was mapped by measuringthe resonance curves at various locations on and near thebase of the cantilever, as illustrated in Fig. 4a. An SEMimage of the cantilever with dimensions 250 × 100 µm isused as background, and the center points of highlightedsquares are ~25 µm apart from each other. Figure 4bdemonstrates the bistability measurements of the micro-cantilever. The highest bistability (~230 Hz) was observedwhen the laser beam was focused on the microcantileverHFET. Moving the laser beam away from the cantileverbase reduces the bistable region as the effective amplitudeof the acoustic waves reaching the cantilever decreaseswith increasing distance from the cantilever base. Thisdependence of the bistability on the laser beam locationcan also be used to demonstrate memory operations.Figure 4c displays switching between the cantilever statesin the bistable regime utilizing different laser beam loca-tions. The laser beam was first focused near the cantileverwith some bistability for steady-state operations, as illu-strated with the red dot in Fig. 4b. To switch the canti-lever from the low to the high state, the laser beam wasmanually moved for 1 s toward the microcantilever HFET,where the bistability is higher, as shown by the blue arrowin Fig. 4b. On the other hand, when the laser beam wasmoved for 1 s to another position away from the micro-cantilever, as shown by the black arrow in Fig. 4b, thecantilever switched from the high to the low oscillatorystate. Fig. S6 shows laser location-based memory opera-tions utilizing hardening-type nonlinearities of themicrocantilever with dimensions of 150 × 50 μm.

Combining two piezo actuator excitations to switchmicrocantilever oscillationFollowing demonstration of memory operations sepa-

rately through the piezo actuator and photoacoustic-based excitation of the GaN microcantilevers with soft-ening and hardening nonlinearities, we examined bistablememory operations with two excitation sources—a pri-mary and a secondary source. As mentioned earlier, asingle excitation source (piezo actuator or laser) is notvery efficient for developing a mechanical memory wheremultiple resonators need to be separately switched backand forth between the bistable states independently. Toovercome this limitation, surface waves created by thesetwo excitation sources (piezo actuator-based and photo-acoustic-based) can be optimized to exploit constructiveand destructive interference. To verify this concept, wefirst used a second piezo actuator attached to a printedcircuit board (PCB) on which the first piezo actuator withthe microcantilever (250 × 100 μm) was placed. The firstpiezo actuator was attached directly under the micro-cantilever, while the second piezo actuator was positioned~2 cm away from the microcantilevers (see Fig. S7). Thefirst (primary) piezo actuator was used to maintain thecantilever oscillation in the bistable regime, while thesecond piezo actuator was employed to switch betweenthe microcantilever states by adding or removing acousticpower through constructive or destructive interference.Both provided excitation at 15.974 kHz. Figure 5ademonstrates the memory operations using two piezoactuators. The second piezo actuator was turned on for100ms (duration of gate pulse) to change the cantilever’s

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Fig. 3 Memory operations using photoacoustic excitation by a pulsed laser at 520 nm. a Softening-type nonlinearities exhibited by the GaNmicrocantilever for different laser powers. The inset shows the hysteresis behavior at a frequency of 15.669 kHz. b Photoacoustic switching operationsof the GaN microcantilever. A laser power of 0.9 mW was used to keep the cantilever in the bistable region, while differential power of 0.6 mW (up)and 0.4 mW (down) was used to make the transitions. Because of the softening-type intrinsic properties, all resonance curves in (a) were swept fromhigh to low frequencies (sweep-down)

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current status. To switch from the low state to the highstate, the effective phase of the signal applied to the sec-ond piezo chip (ϕeffective) was kept at 0° relative to the firstpiezo actuator signal. Therefore, the magnitude of surfacewaves reaching the microcantilever was enhanced due toconstructive interference. On the other hand, to changethe cantilever state from high to low, an effective phase of180° relative to the first piezo actuator was utilized, whichresulted in destructive interference and a reduction in theoverall excitation. We also used different effective phasesto verify the concept of constructive and destructiveinterference of two excitations. As seen from Fig. 5b, thesignals with 90° and 135° phase differences did not changethe cantilever status from the high oscillatory state, as

sufficient reduction in the overall excitation was notachieved for these phases.

Switching enabled by a combined piezo actuator andphotoacoustic excitationThe second piezo actuator that was used for switching

can be replaced with photoacoustic excitation induced bya pulsed laser. However, exposing nearby locations of amicrocantilever HFET to the laser can cause shifts in thefundamental frequency due to localized thermal effects.Such effects can be clearly seen in Figs. 2a and 3a of thelow amplitude resonance curves. While the resonancefrequency of the microcantilever recorded under excita-tion from the piezo actuator (biased at 10 mV rms) was

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Fig. 4 Switching the microcantilever oscillation state in the bistable region by changing the laser excitation location. a Red squares indicatethe grids for the laser beam locations used for bistability mapping, superimposed on the SEM image of the cantilever under study. b Bistability mapof the frequency gap (between up transition and down transition) of the photoacoustically excited microcantilever. As the laser location approachesthe cantilever HFET (higher excitation), the bistability frequency gap increases. c Switching the cantilever repeatedly by manually adjusting the laserlocations away from the cantilever base. To go from the low to high state, the laser beam focused on the cantilever surface, indicated by the red dotin (b), was moved to the higher bistable region (blue dot) for a second and brought back to its original position, as shown by the blue arrow in (b).The same moving procedure to the lower bistable region (marked by the black dot) was performed to switch the cantilever off, as shown by theblack arrow in (b)

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~15.690 kHz, the resonance frequency measured for thephotoacoustically excited microcantilever (with 60 μWlaser power) was certainly below 15.690 kHz, indicating aresonance shift. Alterations in the resonance frequenciesof the GaN microcantilevers with dimensions of 250 ×90 μm, 250 × 100 μm, and two dimensions of 150 × 50 μmafter 520 nm laser exposure for ~500ms are shown inFig. 6a. We find that microcantilevers demonstratingsoftening-type intrinsic nonlinearities (250 × 90 μm and250 × 100 μm) exhibit a reduction in resonance frequency,

while the resonance frequencies of the microcantileverswith hardening-type intrinsic nonlinearities (150 × 50 μm)shift to higher frequencies after exposure to the laser. Tofurther verify these temperature-related resonance shifts,a microcantilever with dimensions 250 × 100 μm wasattached on top of a ceramic heater. The ceramic heaterwas turned on for 3.5 and 5 seconds to provide pulsedheating, and the resonance shifts were subsequentlymeasured. As seen in Fig. S8a, the resonance frequencyinitially decreased as the microcantilever temperature

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Fig. 5 Switching the microcantilever oscillatory states using constructive and destructive interference from two excitations. a Memoryoperations utilizing two identical piezo actuators when piezo actuator #1 was attached directly under the microcantilever, while piezo actuator #2was positioned ~2 cm away from the microcantilever. Piezo actuator #1 (15.974 kHz, 100 mV) was used to maintain microcantilever oscillations in thebistable region, while piezo actuator #2 (15.974 kHz, 800 mV) was employed to change the cantilever’s current state. To magnify the surface acousticwave reaching the microcantilever to switch from the low state to the high state, the effective phase of the bias applied to the second piezo chip(φeffective) was set as 0° relative to the first piezo actuator signal. To reset the cantilever state, an effective phase of 180° relative to the first piezoactuator signal was employed. b Effects of the different effective phases of the piezo actuator #2 bias on the cantilever current state. The signals with90° and 135° effective phase differences did not change the cantilever status from the high oscillatory state, as the differential excitation energy wasnot enough to enable phase transition

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continued to rise slowly following the initial heating,reaching the lowest value of −2.2 Hz at ~110 s and thenrecovered slowly back to its initial value as the tempera-ture rise in the cantilever subsided. Although at firstglance, this temperature change might be perceived as anundesirable side effect of any potential laser-based exci-tation, in reality, this resonance shift due to heating can beutilized to perform memory operations for both hard-ening and softening types of microcantilevers under study.This is because as the resonance frequency decreases formicrocantilevers with softening characteristics, the bis-table regime also shifts equivalently. Thus, if the micro-cantilever oscillates at its lower branch of the bistableregion, then the deflection amplitude moves to theoscillatory state due to heating, as the operating frequencyis no longer in the bistable region of the cantilever. As thecantilever cools down, the state of the cantilever remainsin the high state of the bistable regime since it was alreadyin the oscillatory state due to the heating effect. Thecantilever switching effect caused by a heat pulse is shownschematically in Fig. S8b. This was also verified experi-mentally using the setup illustrated in Fig. S9, and theresults are shown in Fig. S8c, where following the initial3.5 s heat pulse provided by the heater (between 8 and12 s), the amplitude of the cantilever kept rising slowlyuntil it suddenly jumped into the high oscillatory state at~45 s and then remained there until it was brought downto the low oscillatory state by the second piezo actuator

providing excitation at 180 phase difference with the firstpiezo actuator.Utilizing the thermal effects and destructive inter-

ference, memory operations with a piezo actuator as theprimary source of excitation and two lasers (520 nm and790 nm) providing photoacoustic excitation, as well as theassociated heating effect, are experimentally demon-strated in Fig. 6b. The experimental schematic is shown inFig. S10. A low-power (~50 μW) laser with a 790 nmwavelength was focused on the microcantilever HFET,while the 520 nm laser (600 μW) was carefully focused~100 μm away from the cantilever base to ensure negli-gible thermal effects. Even though the power of the790 nm laser was low, it was able to shift the resonancefrequency of the microcantilever (see Fig. S11). Themicrocantilever with dimensions 250 × 100 μm wasmaintained in the bistable regime using the piezo actuatorbiased with a constant VPiezo of 44 mV ac at 15.684 kHz.To change the cantilever current state from low to high,the 790 nm laser (steady, no pulsing) was kept on for300ms (duration of gate pulse) to heat the cantilever. Thiscaused a shift in the oscillatory status of the cantileverfrom low to high. On the other hand, the 520 nm laserwith a pulsed frequency of 15.684 kHz and 180° phaseshift relative to the piezo actuator signal was kept on for a50ms gate pulse duration to make the cantilever switchfrom the high state to the low state by destructive inter-ference (as discussed above regarding the second piezo

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Fig. 6 Utilizing the thermal effects for mechanical switching. a Shift in the resonance frequency as a function of time due to heating themicrocantilever using a continuous laser. The microcantilevers were heated for 0.5 s. Due to heating, the resonance frequency temporarily switches tohigher or lower frequencies depending on the cantilever dimension. b Switching the cantilever with heating effects (to switch on) and destructiveinterference (to switch off). The microcantilever with dimensions 250 × 100 μm was maintained in the bistable regime using the piezo actuatorbiased with a constant VPiezo of 44 mV ac at 15.684 kHz. The 790 nm laser (~50 μW) was turned on for 300 ms (duration of gate pulse) to switch thecantilever ON, while the 520 nm laser was pulsed at a frequency of 15.684 kHz (with a phase of 180°) and a pulse width of 50 ms (duration of gatepulse) to turn the cantilever OFF. The switch-on operation is driven solely by heating effects, while destructive interference was utilized for theswitch-off operation

Bayram et al. Microsystems & Nanoengineering (2022) 8:8 Page 8 of 14

actuator-based excitation). The lasers were exchanged forthe microcantilever with dimensions of 150 × 50 μm. A520 nm laser (focused on the cantilever HFET) wasemployed to change the cantilever oscillatory status fromlow to high utilizing the thermal effects, while destructiveinterference-based switching from the high to low statewas achieved using a 790 nm laser focused ~100 μm awayfrom the cantilever. The results are shown in Fig. S12.

Enhancing photoacoustic excitation with plasmonics toreduce switching powerOptimizing the power and the beam location of the

lasers is necessary not only to dilute the thermal effectsbut also to switch efficiently between the bistable states,expending the lowest possible energy. Figure 7a shows theswitching characteristics of the microcantilever with awidth of 100 μm. Shifts in the resonance frequency due tothermal effects were avoided by using the low-power790 nm laser focused slightly away from the cantileverHFET. The 790 nm laser with a pulse width of 400 ms,

frequency of 15.330 kHz, and power of 45 μW wasoperated under constructive and destructive interferencesettings to change the cantilever current state, while thepiezo actuator was biased at a frequency of 15.330 kHzand VPiezo= 34mV was utilized as the primary excitationsource to sustain the bistable oscillations (see Fig. 1b forexperimental diagram). The inset of Fig. 7a displays for-ward and backward sweeps. To reduce the requiredswitching laser power of 45 μW, the absorption propertiesof the surface can be improved, which would thenenhance the amplitude of the photoacoustic waves. Verysignificant enhancement in photon absorption andenhancement in the photoacoustic signal is possible by athin Au nanoparticle coating on the surface, which hasbeen observed to amplify the photoacoustically generatedsignal by up to two orders of magnitude37,40. Accordingly,we deposited 1.5 nm Au on the top surface of the entirechip containing the GaN microcantilevers to reduce thelaser power required for switching. The resonance fre-quency of the microcantilever was increased by ~6 Hzfollowing Au nanoparticle deposition, as the surface stresschanged significantly, overcoming any mass loading effect,in agreement with our earlier observations31. FollowingAu nanoparticle (NP) deposition, switching betweenstates utilizing the 790 nm laser could be realized with asignificantly reduced power of 6 μW (compared to 45 μWprior to Au deposition), as observed from the inset (left)pulse magnitudes of Figs. 7a, b. The right inset of thefigures shows the hysteresis region between the forwardand backward curves, which can be seen to be approxi-mately the same before and after gold deposition. How-ever, the amplitude difference between the low and highstates is lower than the difference before Au coating sincea lower VDS (0.22 V compared to 0.28 V before, withVGS=−2.6 V and a constant IDS= 100 µA) was measuredafter Au deposition, possibly due to minor alterations inthe conductivity of the HFET due to Au NP deposition(the HFET and resonance characteristics before and afterAu NP deposition are shown in Fig. S13). Therefore, thesinusoidal changes in VDS are also lower following Audeposition.To estimate the lowest energy needed to make the

transition from a nonoscillatory to an oscillatory state andvice versa, the minimum piezo actuator amplitude todrive the microcantilevers in the bistable regime must becalculated. Therefore, we first estimated the nonlinearcubic constant (α) from experimental piezo actuator-based forward and backward curves using the modifiedDuffing equation discussed in detail in SupplementaryDiscussion I. The minimum piezo actuator bias to excitethe cantilever (dimensions of 250 × 100 μm) with bifur-cations was calculated to be ~13.5 mV, as discussed inSupplementary Discussion I, using the estimated cubicconstant. The critical bifurcation frequency where drop

20

b

5

10

15

20

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8

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S(m

V)

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φ = 0°, ~400 ms

φ = 180°, ~400 ms

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DS

Fig. 7 Effect of 1.5 nm gold plasmonic layer deposition on thephotoacoustic state transition in the microcantilever. a Before1.5 nm gold deposition, a 790 nm laser with a power of 45 µW (for400 ms gate pulse duration) at phases 0 and 180° was employed toswitch the cantilever state from OFF to ON, and vice versa, while themicrocantilever was excited using the piezo actuator at 34 mV bias.b After 1.5 nm of gold deposition on the cantilever surface, only 6 µWlaser power was required to switch between the cantilever bistablestates. Insets show the forward (green) and backward (blue) resonancecurves of the cantilever at the piezo bias used in the switchingoperations. High and low states are shown with black double-sidedarrows, corresponding to operational frequencies of 15.330 and15.338 kHz for (a) and (b), respectively

Bayram et al. Microsystems & Nanoengineering (2022) 8:8 Page 9 of 14

and jump frequencies compose an inflection point ispredicted to be 15.344 kHz at this excitation voltage usingthe Duffing equation33,34. However, exciting the micro-cantilever at the critical frequency will very likely result innoise-assisted stochastic switching between the states25.Frequency fluctuations due to external and internalsources, including thermomechanical noise41 and damp-ing noise42, considerably affect the stability of the canti-lever at its current state43. Thus, consistent memoryoperations can only be performed while exciting themicrocantilever at marginally lower Δf (depending on theinstrument and noise limitations) below the critical fre-quency, since softening nonlinearities are dominant for

this cantilever. Hence, frequency fluctuations at drop andjump frequencies were measured at a piezo actuator biasof 24 mV, which exceeds the critical amplitude of 13.5 mVto obtain a clear difference between bifurcation fre-quencies, with reference to the hysteresis curve shown inFig. 8a. We considered 100 cases of jump-up and jump-down transitions, and the frequency distributions areplotted in Fig. 8b. There are two histograms that wereseparately fit with Gaussian curves, which exhibitedstandard deviations (σ) of 67 mHz and 94 mHz for dropand jump frequency fluctuations, respectively. The bis-table regime of the microcantilever as a function of thepiezo actuator bias VPiezo, defined as the region between

0

15.345

σ= 67 mHz

15.336 15.348

Drop frequency fluctuations

Sweep-up

Sweep-down

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fluctuations

ForwardBackward

σ= 94 mHz

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φ = 0°, ~ 400 ms

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60 75

2 mV~300 nW

0.9 mV~135 nWb

c

d

Fig. 8 Theoretical and experimental demonstration of the minimum laser power required to switch between the high (ON) and low (OFF)states of microcantilever oscillation. a Typical sweep-up and sweep-down resonance characteristics of the microcantilever with excitation from apiezo actuator at a bias of 24 mV. b Transition frequency distribution around the “OFF to ON” (shown by blue bars) and “ON to OFF” (shown by redbars) determined for 100 transitions each. Each distribution was fitted with Gaussian curves to yield standard deviations σ of 67 and 94 mHz. c Leftpanel: A bistable frequency plot was generated from Equations S6 and S7, as discussed in the supplemental section, with the upper white region>95% confidence interval (frequency difference of 4 times averaged σ) in switching transitions. Right panel: Magnified section of the bistablefrequency plot (dotted rectangle) shows the differential VPiezo values needed to make the ON and OFF transitions, which are 2 and 0.9 mV,respectively. The corresponding laser estimation is also shown as 300 and 135 nW. d Switching the microcantilever using the 790 nm laser set at 800nW power. The inset shows the forward (green) and reverse (blue) resonance curves of the cantilever at the piezo bias (20 mV ac rms) used toperform the switching experiments. The high and low states of 2.1 and 4.3 mV are shown with the double-headed arrow at a resonance frequency of15.335 Hz

Bayram et al. Microsystems & Nanoengineering (2022) 8:8 Page 10 of 14

bifurcation points (drop and jump frequencies), wasnumerically calculated using the estimated value of α(nonlinearity parameter) = −9.20 × 106, using EquationsS6 and S7 in the supplementary discussion, and the resultis shown in Fig. 8c. To avoid frequency fluctuations forthe sake of stability, the frequency difference betweendrop and jump frequencies needs to be ~4σ to assure a95% confidence interval. The 4σ frequency interval wascalculated by averaging the standard deviations for jumpand drop frequency fluctuations, which yielded 4((67+94)/2) mHz = 0.322 Hz. The minimum operation VPiezo

bias satisfied the 95% confidence interval (0.322 Hz fre-quency difference between the blue (jump frequency) andred (drop frequencies) lines in Fig. 8c) for memoryoperations is 20.2 mV, which is shown by the dotted linein Fig. 8c. The operation frequency was computed as15.3429 kHz, which is the mean of the drop and the jumpfrequencies at VPiezo= 20.2 mV determined from thetheoretically calculated bistability diagram. From Fig. 8c,we find that to perform switching operations at the centerfrequency of 15.3429 Hz, a 2 mV increase in VPiezo isrequired to switch from the low to high state, while a0.9 mV reduction in VPiezo is necessary to make thetransition from the high state to the low state, as shown inFig. 8c. The equivalent laser powers corresponding tothese calculated VPiezo biases (i.e., 2 mV to set to high and0.9 mV to reset to low) can be estimated by comparing theresonance amplitudes of the photoacoustic and piezoactuator-based excitations, as discussed below.Direct comparison of the microcantilever resonance

amplitude caused by the piezo actuator and photo-acoustic excitation can offer a reliable estimate of theconversion factor since the deflection sensitivity of themicrocantilever HFET does not change with the excita-tion source, even though laser-based photoacousticexcitation may shift the resonance frequency slightly36.Comparing the experimental resonance characteristicscaused by the two excitation techniques (plotted in Fig.S14), we find that the resonance amplitude resultingfrom photoacoustic excitation with an 800 nW laser(790 nm) will be equivalent to the resonance behaviorobtained from a piezo actuator bias VPiezo= 5.0 mV.Then, in Fig. 8c, the VPiezo bias increase of 2 mV asneeded to reach the “high” oscillatory state would beequivalent to operating the laser with ~300 nW power inthe constructive interference setting (primary excitationstill being the piezo actuator). On the other hand, VPiezo

can be decreased by 0.9 mV, or equivalently by a laserpower of ~135 nW under destructive interference con-ditions, to reach the “low” oscillatory state. Taking thehigher of these two as the power to make a reliabletransition, we determine 300 nW as the minimum powerof the 790 nm laser at this specific laser beam locationfor memory operations.

For experimental verification of the lower power limitdetermined above for memory operations, we reduced thelaser power to 800 nW to the minimum value possible,limited by the instrument and the measurement setup.The 790 nm laser was carefully focused near the micro-cantilever HFET to obtain the highest resonance ampli-tude. Switching operations were performed with an 800nW laser (with primary excitation from the piezo actuatorbiased at 20 mV ac, rms), which was turned on and off for400ms, with phases of 0 and 180° to make transitionsfrom low to high and vice versa. The results are shown inFig. 8d. The inset shows the forward (green) and back-ward (blue) resonance curves of the cantilever at a piezobias of 20 mV. From Fig. 8d, reliable bistable switchingoperations can be observed using 800 nW laser power,much above the noise limit, supporting the validity of ourtheoretical estimate. Further reduction in the minimumlaser power required for switching operations can beachieved by selecting a more appropriate laser wavelengththat is better absorbed in the substrate or through higherplasmonic amplification, which can lead to higher pho-toacoustic excitation.The minimum laser power determined via theoretical

and experimental means, as discussed above, is only anexternal estimate limited by the experimental andinstrument setup. It does not provide a reliable estimate ofthe actual energy required by the microcantilever toswitch from one state to another. Indeed, only a very smallfraction of the energy provided by the 790 nm laser isabsorbed by the GaN microcantilever since a large frac-tion is reflected back (especially when the laser is focusedon the HFET with metal contacts), and from theremainder, only very little is absorbed by the material, asthe bandgap of GaN (~3.42 eV) is much larger than thephoton energy at 790 nm. The absorption of opticalenergy is mostly facilitated by plasmonic absorption37,which is difficult to estimate accurately. Therefore, wecalculated the switching power/energy utilizing acousticwave equations starting from an estimation of the canti-lever oscillation amplitude. The amplitude of the photo-acoustic wave generated with an 800 nW laser at themicrocantilever base is first estimated using the conver-sion factor. We note that the photoacoustic waves gen-erated with the 790 nm laser, operating at a power of 800nW, caused a similar response generated by the piezoactuator excitation at VPiezo= 5 mV, and since the laserbeam was focused on the cantilever fixed end, theamplitude of the base displacement can be assumed to beequal to the piezo actuator displacement at a 5 mV bias.The displacement at a bias of 5 mV ac rms is 110 pmusing the following relationship, i.e., piezo actuator dis-placement (δPiezo) = GPiezo VPiezo, where GPiezo and VPiezo

are the displacement coefficient of the piezo actuator(2.2 × 10−8m/V provided by the manufacturer) and the

Bayram et al. Microsystems & Nanoengineering (2022) 8:8 Page 11 of 14

amplitude of the ac bias (5 mV), respectively. Utilizing aplane progressive acoustic soundwave assumption, theacoustic power (Pac) can be calculated using the equa-tion39,44, Pac= δ2 ω2 Z A, where δ is the particle dis-placement and ω and A are the excitation frequency andthe area of the laser exposure (~20 µm diameter circle atthe focal point, provided by laser manufacturer WorldStarTech), respectively. Z is the acoustic impedance of GaN,calculated using Z= p c, where ρ is the density of GaN(6.15 × 103 kg/m3)45 and c is the sound velocity in GaN(8000m/s)45,46, which yields Z = 49.2 × 106 kgm−2s−1.Using the values of Z, ω = 96.36 kHz, and the area of thelaser exposure, in the equation for acoustic power Pac, wedetermine that the switching power needed to be 1.74 ×10−12W, which corresponds to an acoustic energy of 7 ×10−13 J considering a 400ms exposure time.

DiscussionIn general, memory and logic operations based on

resonators are operated in dynamic mode taking advan-tage of resonance and nonresonance modes3. Amongdifferent techniques switching from on-resonance to off-resonance behaviors, a significant amount of work hasbeen reported on mechanical memory and logic opera-tions in the nonlinear regime, taking advantage of theexistence of two different stable oscillatory states at thesame frequency (bistability)3. A comprehensive list ofmemory and logic operations reported in the literatureutilizing MEMS and NEMS, including double clampedbeams, nano and microcantilevers, and comb drives, ispresented in Supplementary Table II to put the currentwork in perspective with the best results in this area. Withregard to the performance analysis of memory devices, thepower/energy requirement per switching cycle is animportant parameter to consider, in addition to size andoperational complexities. From Supplementary Table II,we find that the lowest reported energy consumption forelectrostatically actuated doubly clamped nanobeams andnanocantilevers scaled down to the range of 10−11 –10−17 J7,14,18,19,47, which is very comparable to memorydevices based on CMOS transistor technology, which istypically in the range of 10−16 – 10−18 J3. We note that theminimum switching energy for our GaN microcantileversthrough photoacoustic excitation is ~10−13 J, which,although low, is still several orders of magnitude higherthan the lowest switching energy reported for NEMSdevices. This is expected, however, since the size and massof our GaN microcantilevers are much larger than thoseof nanoresonators with reported ultralow power perfor-mances3,19,47. To account for this variation, we haveincluded a column in Supplementary Table II showingcalculations of switching energy per unit mass per cyclefor the selected resonators. Normalization was performedby simply dividing the required switching energy by the

resonator mass. The normalized switching energy permass of the GaN microcantilevers is on the order of10−3 J/kg, which is very comparable, if not better than thebest reported experimental results in the literature,spanning various length scales, excitation techniques, andreadout schemes.Another notable feature presented in the table is the

readout methodology used in mechanical memory andlogic operations. Optical transduction methods were gen-erally employed to readout the position of the resonators.Transducing tip oscillations directly into electrical signalsusing an embedded HFET offers a significant advantage forour system since the usage of optical deflection transduc-tion schemes makes the system complex and cumbersome,especially when applied to an array of resonant devices. Inaddition to the readout methodology, the excitation sourceof the resonator is a key factor in memory/logic operationsperformed in a nonlinear regime. Electrostatic actuation iscommonly used since an electrostatic force can be easilyapplied to the system, and it can be used as a sensingmechanism. The required switching energy with the elec-trostatic actuation method is quite small for memory andlogic operations because of the extremely small capacitiveterm in the formulation14,19. However, the main drawbackof electrostatic actuation is the requirements of large acand dc voltages (tens of V) to reach the nonlinear regime.The required signals to drive GaN microcantilevers in theirnonlinear regime are considerably lower with the piezoactuator (mV regime) and photoacoustic-based excitationmethods. In addition, photoacoustic-based switching offersmany advantages in mechanical memory operations,including position-controlled switching, which is trulyunique among all competing excitation techniques and isreadily applicable to array-based operation. In addition,electrostatic excitation introduces additional spring soft-ening effects into the resonance characteristics, which aretypically used to manipulate intrinsic nonlinearities43,48–50.As an alternative to regulating the nonlinear characteristicswith electrostatic actuation, both softening and hardeningnonlinearities are readily accessible with GaN micro-cantilevers with different dimensions34.In addition, utilizing two different phase-controlled

actuation methods in dynamic memory operations, i.e.,the piezo actuator-based primary excitation to oscillatethe microcantilever in the bistable regime and the pho-toacoustic secondary excitation to switch between thestable states, underlines the versatility of our system andits applicability for resonator arrays. This phase-controlled dual-mode excitation can unlock the truepotential of these resonators for practical applicationsthrough the realization of complex mechanical memoryoperations and computation. This is because multipleresonators with similar resonance and nonlinearityproperties can be assembled on the same piezo actuator,

Bayram et al. Microsystems & Nanoengineering (2022) 8:8 Page 12 of 14

and a tracking system can be used to move the laser beamwith a microscale resolution to set or reset the micro-cantilever oscillatory states as desired. In the case of asingle external actuation force-based memory and logicoperations, controlling each resonator requires separateexcitation and detection mechanisms, which can make theprocess quite cumbersome.Another important factor to be considered in MEMS/

NEMS-based dynamic memory and logic operations is theswitching rate, which is limited by the rise and fall time14,51.The theoretical switching rate is given by Γ= fo/Q

3,8, wheref0 and Q are the resonance frequency and quality factor ofthe resonator, respectively. The estimated operation ratesare 1.625 s and 0.11 s for the GaN microcantilevers withdimensions of 250 × 100 μm and 150 × 50 μm, respectively.The ambient pressure around the microcantilever can bechanged to control the quality factors of the resonators andoptimize the switching rate. Raising the pressure, whichreduces the quality factor, not only improves the switchingrate but also decreases the frequency fluctuations41, whichwill reduce the minimum laser power to switch the canti-lever status. However, a higher microcantilever excitationwill be needed to operate them in the nonlinear regime athigher pressure.In summary, we have demonstrated for the first time

dynamic memory operations involving bistable states inGaN piezotransistive microcantilevers operated in theirintrinsic nonlinear regime. A novel multimodal excitationscheme involving a piezo actuator and a laser, acting asprimary and secondary excitation sources to performconstructive and destructive interference based on theirphase relationships, was used to demonstrate hardeningand softening nonlinearities in these cantilevers and switchbetween the high and low oscillatory states in the bistableregime, respectively. In addition to phase, variation wasalso demonstrated to be an alternative method to performrepeatable switching, which is unique to the photoacousticmethod among all other methods reported in the literature.The minimum energy required for reliable memoryoperations utilizing secondary photoacoustic excitation wasdetermined to be less than a picojoule, utilizing plasmonicamplification of the signal by Au nanoparticles depositednear the cantilever, which resulted in a several-fold increasein the photoacoustic signal magnitude. When normalizedfor cantilever mass and resonance frequency, the switchingenergy was estimated to be one of the lowest reported thusfar for oscillators with various dimensions, excitationsources, and readout schemes.

Materials and methodsDevice structure and fabricationA high-quality epitaxial wafer, which consists of 20 nm

AlxGa1-xN (x = 0.25), 1 μm GaN, 0.3 μm buffer layer, and675 μm Si layers, was purchased from NTT Advanced

Technology Corporation. AlGaN/GaN HFET-embeddedGaN microcantilevers were fabricated at the Institute forElectronics and Nanotechnology at the Georgia Instituteof Technology. A brief fabrication procedure is as follows:first, AlGaN and GaN layers are etched using the Plasma-Therm inductively coupled plasma (ICP) tool to definethe HFET and microcantilever areas, respectively. Afterdeposition of the metal stack of Ti (20 nm)/Al (100 nm)/Ti (45 nm)/Au (55 nm) using a CHA e-beam evaporator,HFET ohmic contacts were formed with a rapid thermalannealing process (SSI RTP). Schottky-metal contacts ofNi (25 nm)/Au (375 nm) and the probe metal stack of Ti(20 nm)/Au (150 nm) were deposited using the e-beamconsecutively. Finally, deep Si etching with the Boschprocess (STS ICP) was used to release the micro-cantilevers. Au layers for plasmonic amplification weredeposited using an electron beam deposition system (CCSCA-40 e-beam evaporator).

CharacterizationThe fabricated microcantilevers were placed on a linear

piezo actuator (PL055 from Physik Instrumente) withdimensions of 5 × 5 × 2mm. For electrical connection, thepiezo actuator and the cantilevers were attached to acustom-designed printed circuit board (PCB), and theHFET probe contacts were wire-bonded to the PCB. Aconstant drain current (IDS) of 100 μA was supplied to thecantilever HFET under study using a source measurementunit (Keysight 2902 A), while the gate was biased at anappropriate gate voltage. Two temperature-compensatedpulsed laser systems with wavelengths of 520 and 790 nm,purchased from WorldStar Tech, were employed forphotoacoustic excitation. Sinusoidal changes in the drain-source voltage of the HFET were measured using a lock-inamplifier (Stanford Research Systems, SR850). Forswitching experiments with multiple excitation sources,two signal generators (Keysight 33210 A) were used topulse the laser(s) and the piezo chip. The optical power ofthe laser used in our experiments was measured at thesame pulsing settings and conditions using a photodiode(Newport 880-SL) and an optical power meter (Newport1918-R) immediately after the switching experiment. Allthe characterization and switching experiments werecarried out at room temperature and at ~1mTorr pres-sure in a homemade vacuum chamber (fitted with a two-stage mechanical/turbomolecular pump) with opticalviewports and electrical feedthrough.

AcknowledgementsThis research was financially supported by the National Science Foundation,grant numbers ECCS-1809891 and IIP-1602006.

Conflict of interestThe authors declare no competing interests.

Bayram et al. Microsystems & Nanoengineering (2022) 8:8 Page 13 of 14

Supplementary information The online version contains supplementarymaterial available at https://doi.org/10.1038/s41378-021-00330-6.

Received: 16 March 2021 Revised: 21 August 2021 Accepted: 13 October2021

References1. Swade, D. & Babbage, C. In Difference engine: Charles Babbage and the quest to

build the First Computer (Viking Penguin, 2001).2. Rueckes, T. et al. Carbon nanotube-based nonvolatile random access memory

for molecular computing. Science 289, 94–97 (2000).3. Ilyas, S. & Younis, M. I. Resonator-based M/NEMS logic devices: Review of

recent advances. Sens. Actuators A: Phys. 302, 111821 (2020).4. Lee, T. H., Bhunia, S. & Mehregany, M. Electromechanical computing at 500

degrees C with silicon carbide. Science 329, 1316–1318 (2010).5. Kazmi, S. N. et al. Tunable nanoelectromechanical resonator for logic com-

putations. Nanoscale 9, 3449–3457 (2017).6. Badzey, R. L., Zolfagharkhani, G., Gaidarzhy, A. & Mohanty, P. A controllable

nanomechanical memory element. Appl. Phys. Lett. 85, 3587–3589 (2004).7. Mahboob, I. & Yamaguchi, H. Bit storage and bit flip operations in an elec-

tromechanical oscillator. Nat. Nanotechnol. 3, 275–279 (2008).8. Hafiz, M. A. A., Kosuru, L. & Younis, M. I. Microelectromechanical repro-

grammable logic device. Nat. Commun. 7, 1–9 (2016).9. Villanueva, L. et al. Nonlinearity in nanomechanical cantilevers. Phys. Rev. B 87,

024304 (2013).10. Moon, F. C. & Shaw, S. W. Chaotic vibrations of a beam with non-linear

boundary conditions. Int. J. Non-Linear Mech. 18, 465–477 (1983).11. Eichler, A. et al. Nonlinear damping in mechanical resonators made from

carbon nanotubes and graphene. Nat. Nanotechnol. 6, 339–342 (2011).12. Turner, K. L. et al. Five parametric resonances in a microelectromechanical

system. Nature 396, 149–152 (1998).13. Guerra, D. N., Imboden, M. & Mohanty, P. Electrostatically actuated silicon-

based nanomechanical switch at room temperature. Appl. Phys. Lett. 93,033515 (2008).

14. Guerra, D. N. et al. A noise-assisted reprogrammable nanomechanical logicgate. Nano Lett. 10, 1168–1171 (2010).

15. Noh, H., Shim, S., Jung, M., Khim, Z. G. & Kim, J. A mechanical memory with adc modulation of nonlinear resonance. Appl. Phys. Lett. 97, 033116 (2010).

16. Uranga, A. et al. Exploitation of non-linearities in CMOS-NEMS electrostaticresonators for mechanical memories. Sens. Actuators A: Phys. 197, 88–95(2013).

17. Yao, A. & Hikihara, T. Logic-memory device of a mechanical resonator. Appl.Phys. Lett. 105, 123104 (2014).

18. Hafiz, M. A. A., Kosuru, L., Ramini, A., Chappanda, K. N. & Younis, M. I. In-planeMEMS shallow arch beam for mechanical memory. Micromachines 7, 191(2016).

19. Chappanda, K. et al. A single nano cantilever as a reprogrammable universallogic gate. J. Micromech. Microeng. 27, 045007 (2017).

20. Al Hafiz, M. A., Kosuru, L. & Younis, M. I. Electrothermal frequency modulatedresonator for mechanical memory. J. Microelectromech Syst. 25, 877–883(2016).

21. Mahboob, I., Mounaix, M., Nishiguchi, K., Fujiwara, A. & Yamaguchi, H. Amultimode electromechanical parametric resonator array. Sci. Rep. 4, 4448(2014).

22. Onuta, T., Wang, Y., Long, C. J., Lofland, S. E. & Takeuchi, I. Dynamic stateswitching in nonlinear multiferroic cantilevers. Appl. Phys. Lett. 101, 043506(2012).

23. Onuta, T., Wang, Y., Lofland, S. E. & Takeuchi, I. Multiferroic operation ofdynamic memory based on heterostructured cantilevers. Adv. Mater. 27,202–206 (2015).

24. Venstra, W. J., Westra, H. J., van der Zant & Herre, S. J. Mechanical stiffening,bistability, and bit operations in a microcantilever. Appl. Phys. Lett. 97, 193107(2010).

25. Venstra, W. J., Westra, H. J., Van Der Zant & Herre, S. J. Stochastic switching ofcantilever motion. Nat. Commun. 4, 2624 (2013).

26. Gao, N., Zhao, D., Jia, R. & Liu, D. Microcantilever actuation by laser inducedphotoacoustic waves. Sci. Rep. 6, 1–7 (2016).

27. Koskinen, V., Fonsen, J., Roth, K. & Kauppinen, J. Progress in cantileverenhanced photoacoustic spectroscopy. Vibrational Spectrosc. 48,16–21 (2008).

28. Chamassi, K. et al. Capacitive silicon micro-electromechanical reso-nator for enhanced photoacoustic spectroscopy. Appl. Phys. Lett. 115,081106 (2019).

29. Khan, D., Li, H., Gajula, D., Bayram, F. & Koley, G. H2 detection using plasmo-nically generated surface photoacoustic wave in Pd nanoparticle depositedGaN Microcantilevers. ACS sensors (2020).

30. Wu, Q. et al. Photoacoustic microbeam-oscillator with tunable resonancedirection and amplitude. Opt. Commun. 407, 381–385 (2018).

31. Khan, D., Li, H., Bayram, F., Gajula, D. & Koley, G. Photoacoustic detection of H2and NH3 using plasmonic signal enhancement in GaN microcantilevers.Micromachines 11, 680 (2020).

32. Tomberg, T., Vainio, M., Hieta, T. & Halonen, L. Sub-parts-per-trillion levelsensitivity in trace gas detection by cantilever-enhanced photo-acousticspectroscopy. Sci. Rep. 8, 1–7 (2018).

33. Lifshitz, R. & Cross, M. Nonlinear dynamics of nanomechanical and micro-mechanical resonators. Rev. nonlinear Dyn. Complex. 1, 1–52 (2008).

34. Bayram, F., Gajula, D., Khan, D., Gorman, S. & Koley, G. Nonlinearity inpiezotransistive GaN microcantilevers. J. Micromech. Microeng. 29,125011 (2019).

35. Qazi, M., DeRoller, N., Talukdar, A. & Koley, G. III-V Nitride based pie-zoresistive microcantilever for sensing applications. Appl. Phys. Lett.99, 193508 (2011).

36. Talukdar, A. et al. Piezotransistive transduction of femtoscale displacement forphotoacoustic spectroscopy. Nat. Commun. 6, 1–10 (2015).

37. Khan, D. et al. Plasmonic amplification of photoacoustic waves detected usingpiezotransistive GaN microcantilevers. Appl. Phys. Lett. 111, 062102 (2017).

38. Bayram, F., Khan, D., Li, H., Hossain, M. M. & Koley, G. Piezotransistive GaNmicrocantilevers based surface work function measurements. Jpn. J. Appl. Phys.57, 040301 (2018).

39. Talukdar, A., Qazi, M. & Koley, G. High frequency dynamic bending response ofpiezoresistive GaN microcantilevers. Appl. Phys. Lett. 101, 252102 (2012).

40. Gao, N., Zhao, D., Jia, R., Zhang, D. & Liu, D. Plasmonic Microcantilever withRemarkably Enhanced Photothermal Responses. Sci. Rep. 7, 1–7 (2017).

41. Roy, S. K., Sauer, V. T. K., Westwood-Bachman, J. N., Venkatasubramanian, A. &Hiebert, W. K. Improving mechanical sensor performance through largerdamping. Science 360, https://doi.org/10.1126/science.aar5220. Epub 2018 Jun14 (2018).

42. Maillet, O. et al. Measuring frequency fluctuations in nonlinear nanomecha-nical resonators. ACS nano 12, 5753–5760 (2018).

43. Sansa, M. et al. Frequency fluctuations in silicon nanoresonators. Nat. Nano-technol. 11, 552 (2016).

44. Rienstra, S. W. & Hirschberg, A. An introduction to acoustics. Eindh. Univ.Technol. 18, 19 (2004).

45. Levinshtein, M. E., Rumyantsev, S. L. & Shur, M. S. in Properties of AdvancedSemiconductor Materials: GaN, AIN, InN, BN, SiC, SiGe (John Wiley & Sons, 2001).

46. Rais-Zadeh, M. et al. Gallium nitride as an electromechanical material. J.Microelectromech Syst. 23, 1252–1271 (2014).

47. Wenzler, J., Dunn, T., Toffoli, T. & Mohanty, P. A nanomechanical Fredkin gate.Nano Lett. 14, 89–93 (2014).

48. Agarwal, M. et al. Optimal drive condition for nonlinearity reduction in elec-trostatic microresonators. Appl. Phys. Lett. 89, 214105 (2006).

49. Kacem, N., Arcamone, J., Perez-Murano, F. & Hentz, S. Dynamic rangeenhancement of nonlinear nanomechanical resonant cantilevers for highlysensitive NEMS gas/mass sensor applications. J. Micromech. Microeng. 20,045023 (2010).

50. Tiwari, S. & Candler, R. N. Using flexural MEMS to study and exploit non-linearities: a review. J. Micromech. Microeng. 29, 083002 (2019).

51. Aldridge, J. & Cleland, A. Noise-enabled precision measurements of a duffingnanomechanical resonator. Phys. Rev. Lett. 94, 156403 (2005).

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