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1 Sensors 1, 1, ; doi:1.339/s17744 OPEN ACCESS sensors ISSN Article Investigation o the Frequency Shit o a SAD Circuit Loop and the Internal Micro-Cantilever in a Gas Sensor Liu Guan, Jiahao Zhao*, Shijie Yu, Peng Li and Zheng You Department o Precision Instruments and Mechanics, Tsinghua University, Beijing 184, China; s: guanl4@mails.tsinghua.edu.cn (L.G.); yu-sj@tsinghua.edu.cn (S.Y.); yz-dpi@mail.tsinghua.edu.cn (Z.Y.) * Author to whom correspondence should be addressed; zhaojh@mails.tsinghua.edu.cn; Tel.: ; Fax: Received: 15 June 1; in revised orm: 3 June 1 / Accepted: 1 July 1 / Published: 3 July 1 Abstract: Micro-cantilever sensors or mass detection using resonance requency have attracted considerable attention over the last decade in the ield o gas sensing. For such a sensing system, an oscillator circuit loop is conventionally used to actuate the micro-cantilever, and trace the requency shits. In this paper, gas experiments are introduced to investigate the mechanical resonance requency shits o the micro-cantilever within the circuit loop(mechanical resonance requency, MRF) and resonating requency shits o the electric signal in the oscillator circuit (system working requency, SWF). A silicon beam with a piezoelectric zinc oxide layer is employed in the experiment, and a Sel-Actuating-Detecting (SAD) circuit loop is built to drive the micro-cantilever and to ollow the requency shits. The dierences between the two resonating requencies and their shits are discussed and analyzed, and a coeicient related to the two requency shits is conirmed. Keywords: micro-cantilever; gas sensor; requency shit; oscillator loop 1. Introduction Micromachined resonant devices are attracting increasing interest in the ield o chemical sensor applications, due to some o their interesting properties such as sensitivity, compactness and low
2 Sensors 1, energy consumption [1]. Helped by an actuating and detecting circuit loop, the working requency o the MEMS resonant devices can be ollowed automatically, and thus the analyte quantity can be determined []. In the study o Zhou et al. o Tsinghua University, a gas sensor based on a MEMS cantilever was introduced [3-4]. In their work, a piezoelectric micro-cantilever was used, with a sensitive layer deposited on the tip to adsorb gas molecules. The adsorption modiies the mechanical properties o the structure, and thereore the resonance requency shits accordingly [5,6]. As the micro-cantilever has no detection structure, a sel-actuating and detecting (SAD) circuit loop was designed speciically or this single-port device. The SAD circuit loop drives the micro-cantilever and traces the working requency r o the circuit. The details o the SAD circuit loop will be introduced in Section.1. Most o the actual studies ollow the same pattern as presented previously [7-14]: on exposure to an analyte vapor, the additional mass loading o the polymer layer decreases the mechanical resonance requency (MRF) o the micro-cantilever. This MRF shit, noted, should be proportional to the mass loading m, and thus proportional to the change in the gas concentration c [1]. Nevertheless, in real world applications, as MRF usually is not available in operation, the system working requency (SWF) shit o the actuating and detecting circuit loop, noted as r in this study, is measured instead. The MRF shit and SWF shit are not actually identical. Li et al. irst reerred to the dierence between the MRF shit and SWF shit, in a simulation approach [4]. An investigation is perormed in this paper to demonstrate the existence o a coeicient α, which makes r = α. The experimental investigation consists o an open-loop test, where the MRF shit is measured, and a close-loop test, where the SWF shit r is recorded. The origin o this coeicient is also discussed. The results indicate that the conventional usage o SWF shit as a measurement o gas concentration is not appropriate, as the SWF shit is not identical to MRF shit. Instead, SWF shit measured should be revised by a coeicient to approach the MRF shit. The urther discussion in this work also proves that this inding can be applied to all the sensing system using an actuating-detecting oscillator loop.. Experimental Details.1. Brie Description o the SAD Circuit Loop With a presumption o small deormation, an electrical model o a piezoelectric micro-cantilever is developed [3]. Figure 1. Electrical model o piezoelectric micro-cantilever.
3 Sensors 1, The mechanical unction analogy o the electrical components is presented in Equation (1). Where m eect is the eective mass o the micro-cantilever, k is the spring constant, c is the static capacitance o the piezoelectric layer, is the damping coeicient. The k 1, k are proportionality constants: C1 k1k meect L1 kk1k km R1 kk1k C c k k 1 Thereore, the electrical components in the model can be determined by the mechanical properties o the beam, among which C1 and C can be seen as a constant, R1 and L1 will vary with the requencies. Furthermore, the impedance o the micro-cantilever can be determined, as shown in Figure. As the impedance o C is much smaller than that o C1-R1-L1 branch, the impedance o the micro-cantilever is rather determined by that o C, and has only a local minimum at the MRF. This means the micro-cantilever does not have a good capability o selecting the resonance requency. eect Figure. Impedance o the piezoelectric micro-cantilever. (1) Thereore, or ameliorating the requency selection perormance o the beam, a requency selection network module is designed. The constant capacitor C in the electrical model was compensated by an external tunable capacitor. In an ideal situation, the output o the network should perorm as a band-pass ilter, having maximum amplitude at the mechanical resonance requency (see Figure 3).
4 Sensors 1, Figure 3. Frequency selection network module. Figure 4 shows the block diagram o the SAD circuit loop. The micro-cantilever is integrated in the module o requency selection network, which constitutes the requency determining unit o the oscillator circuit, and serves like a band-pass ilter with a central requency equal to. The output signal o the requency selection network is ampliied and then adjusted by the ollowing phase compensator. An amplitude limiting module is used to control the amplitude o the signal. Finally, as in reality the output o requency selection network cannot be reduced to zero at requencies ar away rom, a band-pass ilter is needed, to reduce the secondary mode oscillation o the beam. Figure 4. Schematic illustration o a SAD circuit. Filter Frequency selection network Ampliier Amplitude limiting Phase compensator Suppose the gain o the requency selection network is A, and its phase-requency curve is φ a, the rest o the SAD circuit loop is considered as a eedback module, with a gain o F and phase-requency curve φ b. When the SAD circuit loop working in a close-loop mode, the Barkhausen conditions should be met [15]: A( ) F( ) 1 r ( ) ( ) a r b r r ()
5 Sensors 1, Generally, the amplitude condition in () is not a crucial one, as the non-linearity in the eedback module makes the amplitude o the signal always satisy the irst equation. Thereore, the working requency is rather determined by the second Equation o (), the phase condition. Figure 5. Simulation o phase-requency curves o the SAD circuit loop, with AB and A B the linear interval. Where = 65,67 Hz and = Hz. a b a A A B B Figure 5 illustrates the phase-requency curves or requency selection network as well as the eedback module. As seen rom the igure, the eedback module shows a good linearity in its phase-requency curves. And in a neighborhood o the mechanical resonance requency, at least in the interval o ± 1 Hz, the requency selection network also shows a good linearity. Ater mass loading, mechanical resonance requency decreases, and φ a () simply has a parallel shit o, to φ a ()... Analyte Concentration Controlling The sensing system is mounted in a glass canister, with a thin glass slide as top window. Drops o liquid ethanol were jetted by a transer pipette through this window to provide deined vapor concentrations to the canister. Suppose the volume o the canister is V vessel, and liquid ethanol with a volume V analyte is jetted into the canister. When volatilized completely, the concentration o ethanol vapor ollows Equations (3) and (4) where M is the molecular weight o the analyte, and P is the ambient atmospheric pressure: C 3 { mg / m } V analyte analyte (3) V vessel
6 Sensors 1, C 3 { mg / m } C{ ppm} M 73 P.4 73T (4) For the experiments, we calculate the saturated concentration o ethanol vapor, known the ambient temperature and pressure o atmosphere. Then, an appropriate volume V analyte is chosen, to make sure that with six liquid injections, the concentration o the ethanol vapor in the canister increases at a constant pace and is inally below the saturated level. The open-loop test and the close-loop one are perormed in the same canister, with the same ambient conditions. The transer pipette has a precision o measurement o.3%, which ensures the coherence o the two tests, and the comparability o the results..3. Open-Loop Tests An Open-loop test records the variation o mechanical resonance requency o the micro-cantilever. The micro-cantilever used in this work is a probe rom a commercial Atomic Force Microscopy (AFM) system supplied by the Veeco Company. It consists o a micro-machined silicon beam with a piezoelectric zinc oxide layer. The MRF o the AFM cantilever is 5, Hz, according to the speciicationz and is measured at 66,64 Hz. Polyethyleneoxide (PEO) was chosen as the sensitive material, or its good sensitivity and selectivity to ethanol vapor [16]. An aqueous solution o PEO was jetted on top o the cantilever. Ater the evaporation o the solvent, the tip o the cantilever was covered with a layer o sensitive material in the orm o granule (Figure 6), and the MRF o the cantilever decreases to 65,67 Hz accordingly. Figure 6. Scanning electron micrographs o the micro-cantilever: (a) Beore the deposition o PEO sensitive material. (b) Ater the deposition o PEO sensitive material. (a) (b) The open-loop test instruments system is illustrated by Figure 7. A signal generator provides an actuating signal, and the laser beam was ocused on the ree-moving end o the coated cantilever. The laser beam delection signal was captured by a photodetector, and the amplitude o the oscillation was read out rom the screen. By sweeping the actuating signal near the mechanical resonance requency, can be detected. The Q-actor o the coated probe is near 13 at ambient conditions o standard atmospheric pressure and 93 K temperature.
7 Sensors 1, 1 75 Figure 7. Schematic drawing o the experimental setup o the open-loop tests [3]..4. Close-Loop Tests In a close-loop experiment, the system working requency r o the SAD circuit loop was detected. Schematic diagram o the test can is illustrated in Figure 4. The resolving power o the tests is approximately.5 Hz. To ensure that the SAD circuit loop works in its closed-loop mode, the ollowing two adjustments should be made. Firstly, the tunable capacitor in the requency selection network should be adjusted to compensate C, that is to say, at a requency, the output o the requency selection network is equal to. Secondly, connect the requency selection network with the eedback module, and adjust the phase compensator, to meet the phase condition in the Barkhausen conditions. 3. Results and Discussion 3.1. Initial Osets A pair o experimental datapoints can be observed in Figure 8. The liquid ethanol was jetted every 3 minutes in both o the tests. The set o triangle symbols represents the mechanical resonance requency in the open-loop test. The step-orm points record the working requency o the SAD circuit loop as a unction o time. As the volatilization takes place, the working requency o the circuit loop decreases and at the end o the volatilization, the working requency stabilizes gradually. As mentioned at the beginning, it is the coeicient α between the SWF shit r and the MRF shit what we exploit. It is easy to notice that in this result, the initial requency, which corresponds to a vapor concentration o, is dierent. Such an oset o the initial requency is caused the by the oset o the initial phase. During the adjustment o the phase compensator beore a close-loop test, an error o operation is inevitable as the signal superposition is depending on subjective judgment. Thereore, an oset o initial phase was introduced, noted as φ oset. The requency oset oset is thereby created. The requency oset is 38 Hz in this experiment.
8 Sensors 1, Figure 8. Typical raw data o the requency shit o a SAD circuit loop and the internal micro-cantilever. To improve the visibility o the data points, the data are sampled with a time step o 4 seconds. The abscissa is time and each unit represents 4 seconds. oset injection o ethanol As φ oset is the phase oset at = in an open-loop adjustment, rom () we have: When the system works in a close-loop mode, we also have: Developing (6) at =, using a Taylor development: a( ) b( ) oset (5) a( oset ) b( oset ) (6) a( ) 1 a( ) a ( ) oset... oset! b( ) 1 b( ) b ( ) oset... oset! As the linearity shown in Figure 4, in the interval o this development, the high order derivatives are ar less than the irst order derivative. Thus: ( ) ( ) ( ) a b a oset b( ) oset (7) From (5) and (7), we have: oset oset a( ) b( ) (8)
9 Sensors 1, 1 75 It is seen rom (8) how φ oset causes oset, the oset o the initial requency in experimental results. The literature expression o α later on will show that this coeicient will not be aected by the initial requency oset. 3.. Dierences between MRF Shits and SWF Shits Figure 9 shows the MRF and the SWF as a unction o gas concentration. Ater six sequential ethanol injections o equal quantity, the MRF decreases rom 65,67 Hz to 65,455 Hz, and the SWF decreases rom 65,78 Hz to 65,498 Hz. A result o simulation o SWF calculated rom the MRF measured is also presented or comparison. Figure 9. Frequency shit in response to the injection o ethanol. (a) MRF o the micro-cantilever in open-loop test [ ]. (b) SWF in close-loop test [ ]. (c) Simulation results o SWF [ ]. It is the ratio o the slope o two experimental curves that represents the coeicient α. The linear expression is obtained by interpolating the curves using the least-square principle. As the close-loop has a higher resolution power, its data shows a better correlation: : : r : r simulate y x R ,.9966 y x R ,.9999 y x R ,.9969 Both experimental result and simulation result demonstrate the existence o a coeicient α which makes r = α. The value o α is also calculated: α real =.9666, α simulate =.964.
10 Sensors 1, We are going to explore this a little bit urther. As a requency oset oset is observed, we are going to demonstrate it has no inluence to α. Suppose that the SWF o the SAD circuit loop decreases rom r to r, when the MRF decreases orm to. Transorm the deinition r r ( ) to: (1 )( ) oset oset (9) Ater mass loading, at the new resonance requency, a new phase oset From the discussion o Figure 4, there is: oset exists: a ( ) b( ) oset (1) a( ) a( ) (11) A deduction ollows the routine o (8), we have: oset oset a( ) b( ) (1) For the irst term o the denominator, use (11), we have: a ( ) a ( ) a ( ) b ( ) For the second term o the denominator, develop using Taylor development at 3 b( ) b( ) 1 b( ) 1 b( ) 3...! 3! : (13) (14) Notice the linearity o ( ), we have: b b( ) b( ) Substitute the denominator o (1) by (13) and (15), using (8), we have: oset oset oset oset a( ) b( ) (15) (16) Using (5) and (1), we have: ( ) b oset oset (17) Thus: b ( ) oset oset a( ) b( ) (18)
11 Sensors 1, From (18) can be written as: a ( ) a( ) b( ) (19) The literature expression shows that is independent with φ oset. It is the phase-requency curve o requency selection network and o eedback module that determine the coeicient. As shown in Figure 5, at the point o, the slope o the phase-requency curve φ a () is much larger than that o φ b (), thereby the coeicient α has a value close to 1. Figure 1. Experimental phase-requency curves in compare with simulation results at MRF = 65,67 Hz and SWF r = 65,78 Hz. (a) Simulation results or SAD[ ], eedback module[ ] and requency selection network[ ]. (b) Experimental measurements o SAD[ ], eedback module[ ] and requency selection network[ ]. b a a b To calculate the coeicient α rom Equation (19), we draw the phase-requency curves in Figure 1, where the experimental data is presented together with the simulation one. For the requency selection network, both the results rom experiment and simulation show a good linearity at the neighborhood o, whereas at the point ar away rom, the slopes o the two curves deviate. The deviation is likely to be a result o non-ideal properties o the micro-cantilever. As or the eedback module, both two curves show a good linearity, and an approximate slope. Based on literature result in (19), the coeicient α can be determined rom the slopes o the phase-requency curves: α real =.9659, α simulate =.964. These results conirm our indings in gas experiments. Furthermore, as the coeicient α is related to the phase-requency curves o the
12 Sensors 1, requency selection network and o the eedback module, it is a typical value or each realization o a SAD circuit loop. 4. Conclusions Gas experiments have been perormed on a MEMS gas sensing system. The system is based on a silicon beam with a piezoelectric zinc oxide layer, and a SAD circuit loop is built to actuate the cantilever and detect its requency shits. The experimental results conirm, as predicted by another paper, the existence o a coeicient α, relating the mechanical resonance requency shit and system working requency shit. It was also discussed the relation between this coeicient and the phase-requency curves o the SAD circuit loop. As analyzed in this paper, the mass loading o the micro-cantilever modiies its MRF as well as the phase-requency curves o the SAD circuit loop, and thereore the SWF shits to meet the phase condition o Formula () so that the SAD circuit loop could continue its close-loop working. This paper shows that the SWF shit observed in operations is not an appropriate indicator o the gas concentration. To characterize the concentration o analyte, the SWF shit should be revised with a coeicient, to trace the MRF shit. And as such a coeicient is derived rom the Barkhausen conditions, it should be taken into account in all kinds o sensing system working with an actuating-detecting circuit loop. Acknowledgements The authors would like to acknowledge the support by National 863 Project o China and Science Fund o China Post Doctoral Scientists. Reerences 1. Zougagh, M.; Rios, A.; Micro-electromechanical sensors in the analytical ield. Analyst 9, 134, Lange, D.; Hagleitner, C. Complementary metal oxide Semiconductor cantilever arrays on a single chip: mass-sensitive detection o volatile organic compounds. Anal. Chem, 74, Zhou, Q. Study on MEMS chemical gas sensor based on resonating microcantilever. M.S. thesis, Tsinghua University, Beijing, China, Li, P; Zhao, J. Resonating requency o a SAD circuit loop and inner micro-cantilever in a gas sensor. IEEE Sens. J. (In press). 5. Datar, R.; Kim, S.; Jeon, S.; Hesketh, P.; Manalis, S.; Boisen, A.; Thundat, T. Cantilever sensors: Nanomechanical tools or diagnostics. MRS Bull. 9, 34, Finot, E.; Passian, A.; Thundat, T. Measurement o mechanical properties o cantilever shaped materials. Sensors 8, 8, Fadel, L.; Lochon, F. Chemical sensing: millimeter size resonant microcantilever perormance. J. Micromech. Microeng. 4, 14, S3-S3.
13 Sensors 1, Bedair, S.; Fedder, G. CMOS MEMS oscillator or gas chemical detection. Proc. IEEE 4,, Vancura, C.; Ruegg, M. Magnetically actuated complementary metal oxide semiconductor resonant cantilever gas sensor systems. Anal. Chem. 5, 77, Li, Y.; Vancura, C. Monolithic CMOS multi-tranducer gas sensor microsystem or organic and inorganic analytes. Sens. Actuat. 7, B16, Lu, J.; Ikehara, T. Characterization and improvement on quality actor o microcantilevers with sel-actuation and sel-sensing capability. Microelectron. Eng. 9, 86, Mutyala, M.S.K.; Bandhanadham, D. Mechanical and electronic approaches to improve the sensitivity o microcantilever sensors. Acta Mech. Sin. 9, 5, Yu, H.; Li, X. Resonant-cantilever bio/chemical sensors with an integrated heater or both resonance exciting optimization and sensing repeatability enhancement. J. Micromech. Microeng. 9, 19, Rogers, B.; Manning, L.; Jones, M.; Sulchek, T.; Murray, K.; Beneschott, B.; Adames, J.D.; Hu, Z.; Thundat, T.; Cavazos, H.; Minne, S.C. Mercury vapor detection with a sel-sensing, resonating piezoelectric cantilever. Rev. Sci. Instr. 3, 74, Feng, G. Resonant sensing theory and devices; Tsinghua University Publishing House: Beijing, China, 8; pp Gao, W. Study on resonant MEMS gas sensor based on thermally excited micro cantilever. M.S. Thesis, Tsinghua University: Beijing, China, 8. 1 by the authors; licensee MDPI, Basel, Switzerland. This article is an Open Access article distributed under the terms and conditions o the Creative Commons Attribution license (
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