http://www.sensorsportal.com/HTML/DIGEST/Journal_Subscription.htm http://www.sensorsportal.com/HTML/DIGEST/Journal_Subscription.htm SSeennssoorrss && TTrraannssdduucceerrss Volume 15, Special Issue October 2012 www.sensorsportal.com ISSN 1726-5479 Editors-in-Chief: professor Sergey Y. Yurish, tel.: +34 696067716, e-mail: editor@sensorsportal.com Editors for Western Europe Meijer, Gerard C.M., Delft University of Technology, The Netherlands Ferrari, Vittorio, Universitá di Brescia, Italy Editors for North America Datskos, Panos G., Oak Ridge National Laboratory, USA Fabien, J. 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Available in electronic and on CD. Copyright © 2012 by International Frequency Sensor Association. All rights reserved. SSeennssoorrss && TTrraannssdduucceerrss JJoouurrnnaall CCoonntteennttss Volume 15 Special Issue October 2012 www.sensorsportal.com ISSN 1726-5479 Research Articles Shock Resistance of MEMS Capacitive Accelerometers Yongkang Tao, Yunfeng Liu, and Jingxin Dong................................................................................. 1 Research on Nonlinear Vibration in Micro-machined Resonant Accelerometer Shuming Zhao, Yunfeng Liu, Fan Wang, Jingxin Dong ..................................................................... 14 Reversible and Irreversible Temperature-induced Changes in Exchange-biased Planar Hall Effect Bridge (PHEB) Magnetic Field Sensors G. Rizzi, N. C. Lundtoft, F. W. Østerberg, M. F. Hansen ................................................................... 22 Synthesis and Characterization of Nickel Ferrite (NiFe2O4) Nanoparticles with Silver Addition for H2S Gas Detection N. Domínguez-Ruiz, P. E. García-Casilla, J. F. Hernández-Paz, R. C. Ambrosio-Lázaro, M. Ramos-Murillo, H. Camacho-Montes, C. A. Rodríguez González ................................................ 35 Electron-Relay Supercapacitor Mimics Electrophorus Electricus’s Reversible Membrane Potential for a High Rate Discharge Pulse Ellen T. Chen and Christelle Ngatchou .............................................................................................. 42 Ultralow Detection of Bio-markers Using Gold Nanoshells Dhruvinkumar Patel, Xinghua Sun, Guandong Zhang, Robert S. Keynton, Andre M. Gobin ............ 49 Evaluation of Anchoring Materials for Ultra-Sensitive Biosensors Modified with Au Nanoparticles and Enzymes Solomon W. Leung, David Assan and James C. K. Lai ..................................................................... 59 Authors are encouraged to submit article in MS Word (doc) and Acrobat (pdf) formats by e-mail: editor@sensorsportal.com Please visit journal’s webpage with preparation instructions: http://www.sensorsportal.com/HTML/DIGEST/Submition.htm International Frequency Sensor Association (IFSA). http://www.sensorsportal.com http://www.sensorsportal.com/HTML/IFSA_Publishing.htm http://www.sensorsportal.com/HTML/BOOKSTORE/NDIR_Gas_Measurement.htm http://www.sensorsportal.com/HTML/BOOKSTORE/NDIR_Gas_Measurement.htm http://www.sensorsportal.com/HTML/BOOKSTORE/NDIR_Gas_Measurement.htm http://www.sensorsportal.com/HTML/BOOKSTORE/NDIR_Gas_Measurement.htm Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 1 SSSeeennnsssooorrrsss &&& TTTrrraaannnsssddduuuccceeerrrsss ISSN 1726-5479 © 2012 by IFSA http://www.sensorsportal.com Shock Resistance of MEMS Capacitive Accelerometers Yongkang Tao, Yunfeng Liu, and Jingxin Dong Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, 100084, China Tel.: +86-10-62796732, fax: +86-10-62792119, E-mail: taoyongkang@tsinghua.org.cn Received: 14 September 2012 /Accepted: 1 October 2012 /Published: 8 October 2012 Abstract: With deeper research of silicon micro accelerometer, and its wider applications in the commercial fields such as drilling, consumer electronics, automotive industry, and in special military field, the device’s shock resistance has been an urgent issue. The paper presents a theoretical approach of the micro structure's shock response, and focuses on the finite element impact dynamic simulation considering the contact effects of stoppers. A kind of MEMS capacitive accelerometers are designed and fabricated. Failure types due to different shock circumstances are investigated, and experimental estimation of the micro-structure's three-orientation shock resistibility is analyzed, using Hopkinson Pressure Bar (HPB) apparatus. Results indicate that beams' stiffness and stoppers' areas are the key factors to determine the shock resistance, and pulse duration also plays a critical role in the shock effects of micro-machined structures. Copyright © 2012 IFSA. Keywords: MEMS accelerometer, Shock resistance, Impact simulation, HPB, Failure analysis. 1. Introduction MEMS (Micro-electromechanical Systems) sensors are more robust to shock due to its small mass, high aspect ratio and good frequency response. As MEMS technology has been widely applied in various fields, including drilling, consumer electronics, automotive airbag and harsh military environments, sensors’ resistance to shock has become a crucial issue. The shock amplitude during fabrication, deployment, or operation, could be as high as 5,000 g-10,000 g [1] with tens of microseconds to several milliseconds duration time. Till now, multiple methods have been applied to address MEMS device reliability at every step of device design and development. Srikar and Stephen obtained the time-domain criteria to distinguish between the impulse, resonant and quasistatic responses of MEMS structures to shock loads [2]. Stefano investigated the effect of accidental drops on a polysilicon MEMS http://www.sensorsportal.com Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 2 accelerometer within macro-scale and meso-scale finite element approach [3]. D. M. Tanner et al. performed shock experiments on a surface micro machined engine, and studied the susceptibility of MEMS device to shock [4]. More extensive experiments on various MEMS sensors and flight tests on artillery projectiles are presented in T. G. Brown’s report [5]. The survivability of MEMS accelerometer under high-g environment mainly includes two aspects: the integrity of micro structure and the sensor’s performance change after enduring shock events. The paper analyses the shock reliability of a kind of comb-finger accelerometers’ micro structure. Through theoretical approach and finite element analysis, the accelerometer's shock response of deformation and stress concentration is investigated, considering the contact effects of stoppers. HPB shock experiments are performed to determine the typical failure modes and to obtain an experimental estimation of MEMS accelerometers’ structure due to performance change in different shock environments. Beneficial suggestions are concluded to improve the shock resistibility of MEMS sensors. 2. Design and Fabrication of MEMS Accelerometers The MEMS accelerometer investigated is a kind of gap sensing differential capacitance transducer. Considering a comb-finger silicon micro-machined accelerometer developed by our research group [6], the sensing element shown in Fig. 1, mainly consists of movable mass, multi-fingers, spring beams and overload stoppers. The proof mass is a kind of frames with comb-fingers stretched from either side as the movable pole of the differential capacitor pair. The mass is attached to the Pyrex 7740# glass substrate by one clamped–clamped beam and four folded beams. The fixed comb fingers are anchored directly on the glass in a staggered layout with the movable comb to constitute two differential capacitors. The overload stoppers are composed of several small silicon cylinders in x direction, while stoppers are also placed in y direction. Table 1 shows the typical structure parameters of the tested accelerometer. Fig. 1. Simplified sketch and micrograph of the MEMS accelerometer’s structure. Table 1. Structure parameters of the accelerometer. Items Values Items Values Sensitive mass 570 μg Stoppers’ areas of x-axis 1800 μm2 Stiffness of the x direction 158 N/m Distance between stopper and mass 2 μm Stiffness of the y direction 4478 N/m Stoppers’ areas of y-axis 600 μm2 Stiffness of the z direction 14430 N/m Distance between stopper and mass 2 μm Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 3 The accelerometer is fabricated by SOG (silicon on glass) MEMS technology including metal sputtering, RIE and ICP etching, wafer bonding and so on (Fig. 2). It’s packaged in a 10-pin LCC ceramic shell. Differential capacitance changes due to external acceleration input, and the capacitance detection circuit converts the change to DC voltage Vd linearly in a wide bandwidth. A PID conventional controller is applied to form a closed serve loop. The movable mass is driven back by the electrostatic force generator when capacitance change is detected. Fig. 3 gives an outline of the measuring and controlling system. Fig. 2. Fabrication technology and SEM photo of the structure. 1 2 3 4 Ring Quad Diodes 2 11 3 1 4 6 5 7 11 4 R2 R3R1 R5C1 C2 AGND AGND R4 Vout Vin 0 0 2 refC V d Fig. 3. Sketch of the measuring and controlling circuit. 3. Theoretical Approach of Shock Response Theoretical approach gives a brief mind of what happens due to shock. Some assumptions are made here to simplify the modeling process: (i) the package transmits the shock load to the substrate directly without damping; (ii) the acceleration is transferred to the proof mass through the spring beams [7]; (iii) the irregular shock pulse induced is approximated by a half-sine waveform which could be expressed as follow. Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 4 sin( ) 0 ( ) sin( ) ( ) sin[ ( )] ( ) 0 p p p a t t a t a t u t a t u t t                  (1) where pa is the amplitude of the shock,  is the effective pulse width of the waveform, ( )u t is the unit step signal. The accelerometer unpowered could be modeled as a second order system of mass-damp-spring. Using Laplace and inverse Laplace transform to solve the differential equation (2), the displacement response of the mass to the shock pulse [8] could be calculated as equation (3), in which k denotes the mechanical stiffness, m indicates the proof mass, / 2c mk  indicates the damping ratio of the system, and /nw k m denotes the non-damping natural frequency of the micro structure. 2 2 ( ) ( ) d x dx m c kx t ma t dt dt    (2) 2 1 0 0 2 2 ( ) 0( 2 ) [ ( )] ( ) [ ] ( ) ( )2 n n n n R t ts w x x w L t x t L R t R t ts w s w                   (3) For different damping conditions, ( )R t is given by 2 2 2 1, ( ) [ cos( ) sin( ) ( cos( 1 ) sin( 1 ))] 1 n p w t n n n n R t a t t w e w t w t w                              , (4) 1, ( ) [ cos( ) sin( ) ( ( ) )]nw t p nR t a t t e w t                    , (5) 2 2( 1) ( 1)1, ( ) [ cos( ) sin( ) ]n nw t w t pR t a t t e e                         , (6) where coefficients ,, ,, ,    are expressed as follow. 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 / , ( / ) 4 / ( / ) 4 / 2 4 / , ( / ) 4 / ( / ) 4 / ( 1) ( 1) , 2 1 2 1 n n n n n n n n n n n n n n n n n w w w w w w w w w w w w w w w w w                                                                     (7) Equations (3)-(7) express the deformation of sensor's micro structure under the acceleration shock. As shown in above Fig. 1, the accelerometer is supported by 6 parallel beams, and the stiffness of x direction could be calculated by 348 /x zk EI l . The tested accelerometer is designed to be an under Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 5 damping system with 1  . The mechanical parameters could be tested by electrometric methods referred to our previous work [9]. Fig. 4 shows that the displacement response follows the input waveform, and different damping circumstances influence the oscillation after the induced shock pulse. 0 0.5 1 1.5 2 2.5 0 200 400 600 800 1000 Input half sine waveform Time /ms A cc el er at io n/ g 0 0.5 1 1.5 2 2.5 -20 0 20 40 60 Response of the accelerometer due to half-sine shck Time /msD is pl ac em et r es po ns e of t he m as s/ μ m ζ=0 0 0.5 1 1.5 2 2.5 0 200 400 600 800 1000 Input half-sine shock waveform Time /ms A cc el er at io n/ g 0<ζ<1 0 0.5 1 1.5 2 2.5 -20 0 20 40 60 Response of the accelerometer due to half-sine shock Time /ms D is pl ac em en t re sp on se o f th e m as s /μ m 0<ζ<1 Fig. 4. Response of the accelerometer due to half-sine shock under different damping circumstances Fig. 5 shows the theoretical approach of shock response spectrum. The displacement represents the maximum deformation of the spring beams, which could indicate the maximum stress distribution of the structure to a certain extent. From the shock response spectrum, it could be concluded that damping could efficiently reduce the deformation to a short duration shock pulse less than 2 ms, as damping is a kind of energy consumption components. For long duration pulse, the sensor responses quasistatically, and the device simply tracks the applied load. Fig. 6 gives the maximum displacement respect to duration time in different damping conditions. It indicates that pulse width plays a critical role in the dynamic shock response of MEMS accelerometers’ structure. For under damping system, there is a peak point which should be avoided by adjusting the structure’s natural frequency. 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 duration time of half sine shock pulse τ/ms m ax im um d is pl ac em en t r es po ns e /μ m ap=30g,T=377μs ζ=0.31 ζ=0.51 ζ=0.81 ζ=1 ζ=1.5 ζ=2 Fig. 5. Accelerometer's shock response spectrum. Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 6 0 0.5 1 1.5 2 2.5 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 damping ratio ζ m a xi m u m d is p la ce m e n t r e sp o n se /μ m ap=30g,T=377μs τ=0.1ms τ=0.25ms τ=0.5ms τ=0.75ms τ=1ms τ=3ms τ=5ms Fig. 6. Maximum displacement respect to duration time of the accelerometer. In fact, for over range shock accelerations, the displacement of proof mass would exceed the minimum stopper gap. The stopper could limit the free motion while on the other hand, impact force on the contact surface of stoppers may bring other stress concentration problems. More approximate theory model should take contact into consideration. 4. FEA Simulation 4.1. Static Analysis By assuming the accelerometer’s structure with a gravity acceleration of 30 g (1 g=9.8 m/s2), 3D finite element simulations have been performed using ANSYS 10.0. Fig. 7 shows three conditions of constraints and loads, and Fig. 7(c) has the largest margin, which is applied in the following simulation. Fig. 7. Different simulation conditions of constraints and loads. The maximum von Mises stress is found at the connection part of the clamped-clamped beam due to the largest deformation (Fig. 8). Detailed results show that the deformation and stress are proportional to the Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 7 acceleration amplitude almost linearly in the static analysis. The proof mass would touch the stoppers in x direction within a 45 g shock acceleration input. Fig. 8. Static analysis by ANSYS (deformation magnified, unit: g, μm, s). 4.2. Dynamic Impact Analysis For shock accelerations greater than 45 g, considering the contact effects of stoppers, dynamic FEA simulation using ANSYS/LS-DYNA is applied to calculate the structure’s deformation and stress distribution under various shock amplitudes and pulse width. Fig. 9 briefly shows the stress distribution at different time under 4000 g, 200 μs shock. Both the spring beams and stoppers become fragile under the combined effects of shock inertial force and contact force. The maximum stress appears on the stoppers at t=88 μs. Fig. 9. Stress distribution of the micro structure at different time. Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 8 Fig. 10 is the simulated deformation of the mass, and it shows that x-direction stopper and the mass have collided with each other 9 times in 200 μs, as the distance between them is 2 μm. The first contact happens at 27-28 μs, with a velocity of 0.172 m/s. By setting x=2 μm, the theoretical first contact time is 28-29 μs and the velocity is 0.199 m/s solved from equation (3). The frequent contacts between the micro structure and stoppers would cause stress concentration on the contact surface. Fig. 11 gives a comparison between the maximum stress concentration elements in clamped-clamped beams and x-direction stoppers. It could be seen that the stoppers endure more harsh impact than the beams (more than 10 times larger). Fig. 10. X displacement of the movable mass within the shock pulse. Fig. 11. Time response curve of the stress distribution on stoppers (left) and beams (right). 5. Shock Experiments and Analysis 5.1. Shock Experiments Based on the above analysis, a modified Hopkinson pressure bar (HPB) is used to load MEMS accelerometers at various shock accelerations (Fig. 12). With the adjustment of gas pressure values and energy absorb cushions made of foamed aluminum, the incident pulse could generate approximate semi sinusoidal accelerations ranging from 104 to 105 m/s2, and the pulse width could be expanded to more than 300 μs. The packaged accelerometer is mounted on a designed mechanical fixture. A high-g Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 9 piezoelectric accelerometer is also attached to measure the experienced shock acceleration curve. Typical shock acceleration curve with 200 kS/s sample rates is shown in Fig. 13. The wave oscillation is due to stress relaxation of the crystal inside the piezoelectric sensor after high-frequency dynamic shock. Shock experiments of 66 MEMS accelerometers’ structures have been carried out individually in three orthogonal orientations, shown in Table 2. Micro images of the sensor structure are observed. Functionality of the accelerometers including the scale factor, zero-bias, capacitance and impedance between different poles has been measured both before and after the shock test. Fig. 12. The block diagram and photo of the HPB apparatus. Fig. 13. Typical shock acceleration curve. Table 2. Number of MEMS accelerometers tested at different shock level. Level x-direction y-direction z-direction < 1,000 g 2 1 3 1,000 g-5,000 g 9 10 9 5,000 g-7,000 g 5 4 1 7,000 g-10,000 g 2 3 2 > 10,000 g 7 6 2 Total samples 25 24 17 Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 10 5.2. Failure Analysis Failure of the micro structure after HPB shock experiments has been observed in different parts of the accelerometers, such as spring beams, stoppers, proof mass, peripheral frames and so on, while the comb fingers, bonding pads and die package shell are rather robust to shock. Several micro images of typical failure modes are shown in Fig. 14. Failure types on the spring beams appear as deformation, cracks, partial pitting, fracture of several beams and complete fracture of total beams. Failures of the stoppers are shown as cracks, pitting, collapse, partially damaged and totally damaged. Failures of the peripheral frames are classified into pitting, cracks and fractures. Pitting of the proof mass on the contact area with the stoppers has also been observed. Typically more than 2 failure types could appear under one shot, and some failure types are specific to a particular shock direction and amplitude range, while some of them always occur in company with each other. A full discussion of the results and failure analysis in three orientations respect to various amplitudes and pulse width are shown as follow. Fig. 14. Micro images of different failure modes. 5.2.1. X-direction Results All tested accelerometers have exhibited no damage at shock levels less than 1,000 g in x direction. Micro cracks and fractures of the peripheral frames appear under 1469 g, 360 μs; 2964 g, 390 μs and 4489 g, 360 μs shock levels. At 2106 g, 330 μs shock action, cracks have been found on the buffer structure of the clamped-clamped beams which doesn’t affect the practical function of the beams. Long duration shock pulse could lead to deformation of the spring beams, observed at the load of 2330 g, 875 μs. Severe failure types have occurred in the 14 tested specimens at shock levels more than 6000 g, such as fractures of 3-4 spring beams (7145 g, 300 μs; 7244 g, 335 μs; 7754 g, 269 μs) and large deformation of the beams (6179 g, 300 μs) in z direction. As the proof mass would twist under continued shock impact after it has touched the x-direction stoppers, both the stoppers in x and y direction have been found damaged. Fractures of partial beams reduce the support force of the proof mass, which could result in large deformation in z-direction. Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 11 5.2.2. Y-direction Results No failures happen at shock levels less than 5,000 g in y-direction. Failures only occur at the y-direction stoppers including micro cracks, pitting and collapse, when the shock amplitude is ranged from 5,000 g to 7,000 g. Two folded beams have fractured on the tested micro structure at 7244 g, 335μs shock. Experiment results show that the tested accelerometer could resist larger shock impact in y direction. It’s mainly determined by the mechanical stiffness. The stiffer the beams are, the less deformation would occur under high-g shock. 5.2.3. Z-direction Results The micro structure is weakest in z-direction as it has no stopper to limit the motion. Spring beams begin to fracture at the shock level of 3000g, and shock amplitudes more than 4,000g would lead to complete fractures of total beams. In fact, kz is much bigger than kx as shown in Table 1, but overload stoppers are designed in x-direction. Comparison of the experimental results between x and z direction indicates that the stopper is a critical factor in the shock reliability of MEMS sensors. Stoppers could limit the deformation of the micro structure and transmit the induced shock energy partially, which could reduce and share responsibility for the stress concentration in the micro structures. 5.3. Experimental Estimation Sensors are supposed to function normally with little performance change after enduring shock events. On the basis of the influence on the open-loop performance of the accelerometer, failure types could be classified into three levels: 1. almost normal, the accelerometer could practically work as usual; 2. partially available, the performance has changed but the device could still operate; 3. totally damaged, the device could not be used any more. Level 1 consists of failures of the stoppers and frames. Level 2 includes the small deformation and fractures of several spring beams, which would affect the accelerometer’s scale factor and zero bias. Level 3 happens as the proof mass falls off from the glass substrate due to the complete fractures of total beams. According to the above classification, experimental estimation of the three-orientation shock resistibility of the MEMS accelerometers’ micro structure is shown in Fig. 15 in detail. The area surrounded by the green line, the longitudinal and horizontal axis gives a safe range of shock amplitudes and pulse width. Long duration pulse would allow low shock amplitudes as the fracture stress criteria is concerned with the energy induced to a certain extent. The image at the bottom right corner gives an experimental evaluation of the shock reliability in three directions. Results show that the accelerometer could resist about 4,000-5,000 g shock in x direction, 6,000-7,000 g shock in y direction, and 3000 g in z direction. The three orientation shock resistibility is about 3,000 g, 300-400 μs with little performance change. 6. Conclusions Comparison of the results of different directions indicates that micro structure’s spring stiffness and stoppers’ areas are the key factors to determine the shock resistance. Both the pulse duration and damping ratio play critical roles in the shock effects of micro-machined structures. Research also shows that MEMS sensors have advantages of better shock resistance. Prospective research should pay attention to the contact effects between micro structures due to shock. The paper provides meaningful guides to improve the shock reliability of MEMS accelerometers. The research methods mentioned may also be applied to estimate the shock reliability of other MEMS device. Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 12 Fig. 15. Experiment estimation of the three-orientation shock resistibility. Acknowledgements The authors would like to acknowledge the help of Wang Bo and Prof. Ge Dongyun at the School of Aerospace in Tsinghua University for their experience in HPB apparatus. This work is partly supported by the 12th Five-Year National foundation of China. References [1]. Rob O’Reilly, Huy Tang, Wei Chen, High-g Testing of MEMS Devices, and Why, in Proceedings of IEEE Sensors, Lecce, Italy, 26-29 October 2008, pp. 148-151. [2]. V. T. Srikar, Stephen D. Senturia, The reliability of microelectromechanical systems (MEMS) in shock environments. Journal of Microelectromechanical Systems, Vol. 11, Issue 3, 2002, pp. 206-213. [3]. Stefano Mariani, Aldo Ghisi, et al., Multi-scale Analysis of MEMS Sensors Subject to Drop Impacts, Microelectronics Reliability, Vol. 49, Issue 3, 2009, pp. 340-349. [4]. Tanner, D. M., Walraven, J. A, et al., MEMS Reliability in Shock Environments. in Proceedings of the 38th IEEE International Reliability Physics Symposium, San Jose, USA, 10-13 April 2000, pp. 129-138. [5]. T. G. Brown and B. Davis, Dynamic High-G Loading of MEMS Sensors: Ground and Flight Testing, in Proceedings of SPIE - The International Society for Optical Engineering, Bellingham, USA, 21-22 September 1998, pp. 228-235. [6]. Dong Jingxin, et al., Micro inertial instruments—micro machined accelerometer, Tsinghua University, Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13 13 Beijing, 2002. [7]. Yee Jeffrey K, Yang Henry H, Judy Jack W., Shock resistance of ferromagnetic micromechanical magnetometers, Sensors and Actuators, A: Physical, Vol. 103, Issue 2, 2003, pp. 242-252. [8]. Subramanian Sundaram, Maurizio Tormen, et. al., Vibration and shock reliability of MEMS: modeling and experimental validation, Journal of Micromechanical and Microengineering, Vol. 21, Issue 4, 2011, pp. 1-13. [9]. Li Jiang, Gao Zhongyu, Dong Jingxin, An electrometric method to measure the mechanical parameters of MEMS devices, In Proceedings of the IEEE Conference on Optoelectronic and Microelectronic Materials and Devices, 11-13 December 2002, pp. 221-224. ___________________ 2012 Copyright ©, International Frequency Sensor Association (IFSA). All rights reserved. (http://www.sensorsportal.com) http://www.sensorsportal.com/HTML/E-SHOP/PRODUCTS_4/Evaluation_board.htm http://www.sensorsportal.com/HTML/E-SHOP/PRODUCTS_4/Evaluation_board.htm http://www.sensorsportal.com/HTML/E-SHOP/PRODUCTS_4/Evaluation_board.htm http://www.sensorsportal.com/HTML/E-SHOP/PRODUCTS_4/Evaluation_board.htm http://www.sensorsportal.com/HTML/E-SHOP/PRODUCTS_4/Evaluation_board.htm Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 14-21 14 SSSeeennnsssooorrrsss &&& TTTrrraaannnsssddduuuccceeerrrsss ISSN 1726-5479 © 2012 by IFSA http://www.sensorsportal.com Research on Nonlinear Vibration in Micro-Machined Resonant Accelerometer Shuming ZHAO, Yunfeng LIU, Fan WANG, Jingxin DONG Department of Precision Instruments and Mechanology, Tsinghua University, 100084, Beijing, China, Tel.: +86-15116987074, fax: +86-10-62792119 E-mail: Shuming.Zhao.CN@gmail.com Received: 14 September 2012 /Accepted: 1 October 2012 /Published: 8 October 2012 Abstract: This paper analyzes the nonlinear vibration of the Micro-machined Resonant Accelerometer (MRA) by system modeling and simulation. The optimization designs to weaken the influence of the nonlinear vibration are proposed. With decreasing the mechanism dimension of the MRA, the effects of the nonlinear vibration become more obviously. The nonlinear vibration affects the precision and system stability of the micro-machined resonant accelerometer. The simulation results of the nonlinear system are well consistent with the experiments, and predict that the optimizing structure will effectively weaken the nonlinear effect. Copyright © 2012 IFSA. Keywords: Micro-machined resonant accelerometer, Nonlinear vibration, Duffing equation, Optimizing structure. 1. Introduction Micro-machined Resonant Accelerometer is a novel micro-machined accelerometer based on force-frequency characteristics of resonant beams. As the Schematic of MRA shown in Fig. 1(a), when input acceleration act on the proof mass, the inertia force along the sensitive axis causes the nature frequency of resonant beams on both sides of proof mass shifting in the opposite directions. Sensing the nature frequency of the resonant beams and outputting the differential frequency make it possible to have high precision and strong anti-jamming capability. Previous works have proved the feasibility of the system [1] and some system optimizations have done to achieve a higher sensitivity. The SEM picture of MRA is shown in Fig. 1(b). In section 2 of this paper, http://www.sensorsportal.com Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 14-21 15 we build the model of the nonlinear vibration in two ways: one is the dynamic-static method based on the Newton's second Law, and the other is based on expressions of energy and variation, called the method of Lagrange equation. We analyses the influence of the nonlinear vibration in section 3 and propose the methods to reduce the bad influence of nonlinear vibration in section 4, and the new structure is being implemented. Input axial Suspended component Anchored component Resonant beam Sensing & actuating Anchor point Proof m ass Fig. 1. Schematic and SEM picture of MRA. 2. Modeling of the Nonlinear Vibration With the decreasing of the mechanism dimensions of the Micro-machined Resonant Accelerometer, the axial tension caused by the relatively large displacement of the resonant beam cannot be neglected. [2] The resonant beam can be simplified as an axially loaded elastic slender beam with a cross section A, momentum of inertia I and length L. Denoting the density of the material with ρ, the Young’s Modulus with E, the initial constant axial load N and the transversal displacement of the resonant beam with ( , )y x t , x being the axial coordinate and t the time. There are several hypotheses for the resonant beam as follows: (1) the beam is a Euler-Bernoulli beam without regard to the effects of the shearing deformation and the momentum of inertia; (2) variation of the cross section during vibration is neglected; (3) the stretching of the beam during vibration is small but finite that the linear stress-strain relationship is still applicable. [4]. 2.1. Dynamic-static Method With the above hypotheses, we build a simplified model of the resonant beam as showed in Fig. 2(a) and analyze the differential segment as showed in Fig. 2(b). The differential equation for the transverse displacement is obtained as equation (1):    '' '' ''Ay EIy Ny q y    , (1) where 2 2 2 2 , , , y y y y y y y y t xt x              . The equation (1) is a normal vibration equation of the resonant beam and several solutions are approached. The frequency solution of the first mode as showed in Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 14-21 16 equation (2) indicates that, resonant frequency increases when N is a tensile load while decreases when N is a compressive load. ( , )y x t (a) Single-degree-of-freedom model of MRA oscillator. M M dx x    Q Q dx x     dx x     (b) Force analysis of the resonant beam. Fig. 2. The simplified modal and force analysis of the MRA oscillator. 2 0 0 1 N L f f EI   , 2 0 22 c EI f AL   (2) 0f is the first mode frequency of the resonant beam without axial load N. The coefficient c and  depend on the boundary condition. These three equations are always available when discuss the macro resonant beams. While in the micro-machined resonant accelerometer, the high Q makes it easy to get relatively large amplitude of the vibration. Thus the axial tension caused by the relatively large displacement of the resonant beams cannot be neglected.[3] Denoting the axial tension caused by the vibration displacement with T, and then equation (1) should be changed into (3):    '' '' '' ''Ay EIy Ny Ty q y     , (3) With the linear stress-strain hypothesis, the additional axial load T can be obtained as equation (4): 2 02 LL EA T EA y dx L L     , (4) Denote 2 EA L by xk and substitute the expression of T in equation (3), then the nonlinear vibration equation for the resonant beam is obtained: Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 14-21 17      2 0 1 '' '' '' '' ' 2 L xAy EIy Ny k y y dx q y     , (5) Equation (5) is a forth order partial differential equation which could not acquire an accurate analytic solution. Next part we introduce the method of Lagrange equation to obtain the approximate solution of the equation. 2.2. Method of Lagrange Equation Known that the system has certain mode of vibration which is time-independent, we introduce the normal form of solution as equation (6), where ( )x is the first order mode shape and f is the natural frequency of the harmonic vibration ( )Y t [3]:  max( , ) ( ) ( ) ( ) sin 2y x t x Y t x Y ft      , (6) Then the Lagrange Function expressed with kinetic energy T and potential energy U is:       22 2 22 2 2 2 4 0 0 0 0 1 1 1 1 L T U= [ ] 2 2 2 4 L L L L xY A dx Y EI dx NY dx k Y dx              , (7) With the Lagrange Function (7), we got the Lagrange Equation of the nonlinear system (8): L L 0 d dt YY       , (8)       22 2 22 3 0 0 0 0 0 L L L L xY A dx Y EI dx NY dx k Y dx             , (9) Equation (9) can be simplified as (10) which is a typical nonlinear Duffing Equation: 3 1 3 0MY k Y k Y   , (10) 3k is called the third order nonlinear coefficient of the system. Different from the linear solution, the frequency of the resonant beam depend upon the vibration amplitude [4]: 23 0 max 1 3 1 8 k f f Y k        , (11) 3. Properties of the Nonlinear Vibration Beam From the Duffing Equation we can obtain the relationship between the resonant frequency f , harmonic driving force 0 cosF F t , and amplitude maxY is: 22 30 3 max max 1 0 1 3 2 1 4 F kf Y Y k f k                 , (12) Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 14-21 18 For 3 0k  , the resonance curve shows a hard spring effect as show in Fig. 3. The figure also shows that the bistable and non-steady state of the nonlinear system. 0.95 1 1.05 1.1 0 0.5 1 1.5 x 10 -5 w/w0 Y m ax Fig. 3. Vibration amplitude vs. Driving frequency. There are two important effect of this nonlinear system while open-loop frequency sweeping: amplitude jumping and frequency-amplitude hysteresis.[5] As show in Fig. 4, when ordinal frequency sweeping, the amplitude increases gradually but jumps to a relatively low value from 1Y when at the frequency 1f ; while reversal frequency sweeping, the amplitude jumps to a relatively high value 2Y at the frequency 2f and then decreases gradually. Since 1 2f f , 1 2Y Y , the frequency-amplitude hysteresis loop is formed. We simulated the nonlinear by Matlab Simulink, as showed in Fig. 4(a), and the open loop experiment result of the real resonant accelerometer beam showed in Fig. 4(b) proves the validity of the nonlinear system model. 0.9 1 1.1 1.2 1.3 1.4 -2 -1 0 1 2 3 normalized frequency w/w0 am pl ifi ed a m pl itu de ordinal frequency sweep reversal frequency sweep 12.4 12.6 12.8 13 13.2 13.4 13.6 0 100 200 300 400 Frequensy/Hz A m pl itu de /m V ordinal frequency sweep reversal frequency sweep (a) The result of the nonlinear system simulation. (b) The result of the nonlinear system experiment. Fig. 4. The results of simulation and experiment show the frequency characteristics of the nonlinear system. Since we have known that the frequency of the resonant beam depend upon the vibration amplitude in the nonlinear system, the driving force and system damping all make an effect on the resonant frequency, as showed in Fig. 5. The experiment results show that, frequency increases while the driving amplitude Bistable Non-steady Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 14-21 19 increases, and decreases while the pressure of the experiment environment increases, which are well consistent with the model analyses. Also we can see the figure of merit Q becomes slightly lower while the driving amplitude increase, which may indicate the instability of the nonlinear vibration. 1.28 1.285 1.29 1.295 1.3 1.305 1.31 1.315 1.32 x 10 4 -25 -20 -15 -10 -5 率频 /Hz 幅 频 /d B 1.28 1.285 1.29 1.295 1.3 1.305 1.31 1.315 1.32 x 10 4 -150 -100 -50 0 50 率频 /Hz 相 频 /° 50mV 100mV 50mV 100mV (a) Resonant frequency varied with driving amplitude. 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 x 10 -3 1.29 1.295 1.3 1.305 1.31 1.315 1.32 1.325 1.33 x 10 4 气压/Pa 振 率 谐 频 /H z (b) Resonant frequency varied with environment pressure. Fig. 5. Resonant frequency is susceptible to driving amplitude and environment pressure. 4. Methods to Weaken the Nonlinear Vibration As we know, the nonlinear vibration is produced by the axial tension, caused by the relatively large displacement of the resonant beam. When the amplitude of the resonant beam is much smaller than the beam dimension, the axial tension caused by the displacement can be neglected. So one way to weaken A m pl it ud e/ dB Ph as e/ dB Frequency/Hz Frequency/Hz F re qu en cy /H z Pressure/pa Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 14-21 20 the nonlinear vibration is to decrease the amplitude of the resonant beam, which means to decrease the driving force and make the force stable [6]. In order to weaken the axial tension caused by the displacement, we could add a spring in series as showed in Fig. 6(a). For single beam, the physical structure could be designed as shown in Fig. 6(b). The elastic coefficient of the spring in series is 2 = 12a EA w k l l       , where A is the cross- section area of the spring, w is the width and l is the length of the spring. The third order nonlinear coefficient   2 2 3 0 = L a x a x k k k dx k k    will be decreased remarkably while the slender proportion w l decreased. The Simulink result showed in Fig. 7 indicates that, when the nonlinear coefficient 3k becomes 1/10 of the original value, the influence of the amplitude to the frequency become much smaller than before.[7] ( , )y x t ak  (a) The model of resonant beam with spring in series. (b) Physical structure of the single beam with spring in series. Fig. 6. The model and structure of resonant beam with spring in series 0.95 1 1.05 1.1 0 0.5 1 1.5 x 10 -5 w/w0 Y m ax k3 0.1*k3 Fig. 7. The optimizing structure reduces the nonlinearity of the Vibration amplitude VS Driving frequency. 5. Conclusions We build a model with the consideration of axial tension caused by the large displacement of the resonant beams, and then simulate and analyze the influence of the nonlinear effects. The simulation results of the system characteristics are well consistent with the experiments, which verify the existence Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 14-21 21 of nonlinear vibration and the validity of the nonlinear system model. With the simulation and analyses, we propose an optimization designation to weaken the influence of the nonlinear vibration, and the new structure is being implemented. By optimizing the structure and experiment condition, the nonlinear vibration could be reduced effectively. References [1]. Hu Hao, Research on Key Technologies of Micromechanical Silicon Resonant Accelerometer, Tsinghua University, 2010 [2]. Kevin A. Gibbons, A Micromechanical Dilicon Oscillating Accelerometer, MIT, 1997. [3]. Claudia Comi, On geometrical effects in micro-resonators, Latin American Journal of Solids and Structures, Vol. 6, 2009, pp. 73-87. [4]. Song Zhenyu, Yu Hong, Dynamic analyses of nonlinear vibration of nanobeam, Journal of Micronanoelectronic Technology, Vol. 3, 2006, pp. 145-149. [5]. Liu Yanzhu, Chen Liqun, Nonlinear Vibration, Beijing: China Higher Education Press, 2001. [6]. Ville Kaajakari, Tomi Mattila, Nonlinear Limits for Single-Crystal Silicon Microresonators, Journal of Microelectromechnical Systems, Vol. 13, No. 5, 2004. [7]. Claudia Comi, Resonant Microaccelerometer With High Sensitivity Operating in an Oscillating Circuit, Journal of Microelectromechnical Systems, Vol. 19, No. 5, 2010. ___________________ 2012 Copyright ©, International Frequency Sensor Association (IFSA). All rights reserved. (http://www.sensorsportal.com) http://www.sensorsportal.com/HTML/BOOKSTORE/Smart_Sensors_and_MEMS.htm Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 22 SSSeeennnsssooorrrsss &&& TTTrrraaannnsssddduuuccceeerrrsss ISSN 1726-5479 © 2012 by IFSA http://www.sensorsportal.com Reversible and Irreversible Temperature-induced Changes in Exchange-biased Planar Hall Effect Bridge (PHEB) Magnetic Field Sensors G. Rizzi, N. C. Lundtoft, F. W. Østerberg, * M. F. Hansen Department of Micro- and Nanotechnology, Technical University of Denmark DTU Nanotech, Building 345B, DK-2800 Kongens Lyngby, Denmark * E-mail: Mikkel.Hansen@nanotech.dtu.dk Received: 14 September 2012 /Accepted: 1 October 2012 /Published: 8 October 2012 Abstract: We investigate the changes of planar Hall effect bridge magnetic field sensors prepared without field annealing and with field annealing at 240 °C, 280 °C and 320 °C when these are exposed to temperatures between 25 °C and 90 °C. From analyses of the sensor response vs. magnetic field we extract the exchange bias field Hex, the uniaxial anisotropy field HK and the anisotropic magnetoresistance (AMR) of the exchange biased thin films at a given temperature. By comparing measurements carried out at elevated temperatures T with measurements carried out at 25 °C after exposure to T, we separate the reversible from the irreversible changes of the sensors. The un-annealed sample shows a significant irreversible change of Hex and HK upon exposure to temperatures above room temperature. The irreversible changes are significantly reduced but not eliminated by the low- temperature field annealing. The reversible changes with temperature are essentially the same for all samples. The results are not only relevant for sensor applications but also demonstrate the method as a useful tool for characterizing exchange-biased thin films. Copyright © 2012 IFSA. Keywords: Magnetic biosensors, Planar Hall effect, Exchange bias, Anisotropic magnetoresistance. 1. Introduction For applications of any sensor, it is important to know and correct for the effect of varying temperatures of the sensor environment. Moreover, it is important to be aware of irreversible changes of the sensor parameters induced by varying temperatures of the environment. Planar Hall effect magnetic field sensors have proven attractive for magnetic field sensing due to their low intrinsic noise http://www.sensorsportal.com Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 23 and potentially high signal-to-noise ratio [1]. We are investigating exchange-biased planar Hall effect sensors for magnetic biodetection [2, 3]. Here, we systematically study the changes of the response of planar Hall effect bridge sensors [4] upon exposure of these to temperatures between 25 °C and 90 °C. These temperatures correspond to the range typically employed in DNA based assays with amplification by polymerase chain reaction (PCR). From analyses of magnetic field sweeps of the sensor response we extract the parameters of thin film sensor stacks at all investigated temperatures and by performing measurements at 25 °C performed after all measurements at elevated temperatures we quantify and distinguish reversible and irreversible changes of each of the sensor parameters. These studies are carried out for a stack which is not exposed to any magnetic field annealing and for stacks that are field annealed at 240 °C, 280 °C and 320 °C. The results are generally relevant for applications of exchange-biased thin film sensors and demonstrate the method as a general tool for studying thin film magnetic properties vs. temperature. 2. Sensor Model Below, we consider a material showing anisotropic magnetoresistance (AMR) with resistivities ρ|| and ρ parallel and perpendicular to the magnetization vector M, respectively. The AMR ratio, defined as Δρ/av, where   ρ||ρ and av  ρ||/3+2ρ/3, assumes a value of 2-3 % for permalloy (Ni80Fe20). Fig. 1 shows a Wheatstone bridge consisting of four pairwise identical elements of the material of width w and length l. The resistance of a single element forming an angle  to the x-axis and with a homogeneous magnetization forming an angle  to the x-axis is [4]     ,)2(cos Δρρρ),( 2 1 ||2 1   wt lR (1) where t is the thickness of the element. A current I injected in the x-direction results in the bridge output  ,),(),(2 1    RRIVy (2) where the orientation of magnetization of the elements forming angles α+ and α to the x-axis are denoted θ+ and θ. The maximum bridge output, obtained when α+ = α = π/4, is given by    , )sin(2)2(sin )sin(2)2(sin ρ pp4 1 4 1    VIV wt l y (3) where we have introduced the nominal peak-to-peak sensor output voltage Vpp = Il/(wt) [4]. Equation (3) is identical to the output voltage from a cross-geometry planar Hall effect sensor multiplied by the geometrical amplification factor l/w. Therefore, we have termed the above sensors planar Hall effect bridge (PHEB) sensors [4]. Theoretically, the angles θ+ and θ can be found by minimizing the single domain energy density for α+ and α, respectively. We divide the volume energy density by the saturation flux density to form the normalized energy density u ),(cos cos cos sin 2 s2 12 K2 1 ex   HHHHu y (4) which expresses the energy density in units of the H-field. In Eq. (4), Hy is the external magnetic field applied in the y-direction, Hex is the exchange field due to a unidirectional anisotropy along θ = 0, Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 24 HK is the anisotropy field due to a uniaxial anisotropy along θ = 0 and Hs is the shape anisotropy field of the element (preferring a magnetization orientation with  = ). Defining the demagnetization factors along and perpendicular to an element as N|| and N, respectively, the shape anisotropy field is Hs = (N  N||)Ms [5]. Our previous work [4] considered only the case of negligible shape anisotropy where θ+ = θ = θ. We write the low-field sensor output voltage as ,0 yy IHSV  (5) where we have defined the low-field sensitivity S0. For negligible shape anisotropy, minimization of Eq. (4) for Hs = 0 and small values of  yields . 1ρ exK 0 HHtw l S    (6) If the shape anisotropy is significant but still small, the sensor response curve will be modified such that it flattens near zero applied field, resulting in a decrease of S0 compared to Eq. (6), while still maintaining a peak-to-peak signal Vpp given by Eq. (3) (unpublished results). 3. Experimental A batch of four wafers with top-pinned PHEB sensors was prepared on 4” silicon substrates with a 1 m thick thermally grown oxide as follows: First, the stack Ta(3 nm)/Ni80Fe20(30 nm)/Mn80Ir20 (20 nm)/Ta(3 nm) was grown in a K. J. Lesker company CMS 18 multitarget sputter system in an Argon pressure of 3 mTorr with an RF substrate bias of 3W. The easy magnetization direction and axis of the permalloy layer were defined by applying a uniform magnetic field of µ0Hx = 20 mT along the x-axis during the deposition. Subsequently, contacts of Ti(10 nm)/Pt(100 nm)/Au(100 nm)/Ti(10 nm) were deposited by e-beam evaporation and defined by lift-off. The negative lithography process employed a reversal baking step at 120 °C for 120 s on a hot plate in zero magnetic field. One of the nominally identical four wafers was not given any further treatment and was labeled ‘not annealed’/’un-annealed’. The other three wafers were annealed in vacuum in the sputter deposition chamber at temperatures of 240 °C, 280 °C and 320 °C for 1 hour in the presence of a saturating magnetic field µ0Hx = 20 mT applied along the x-axis. The dimensions of the elements of all investigated sensors were w=20 µm and l = 280 µm (Fig. 1). All sensors were surrounded by magnetic stack with a 3 µm gap to reduce the shape anisotropy of the elements. The simple theory presented in section 2 accounts for the elements but not the corners connecting the elements. The effect of corners was therefore investigated by finite element analysis of the sensor output for a single domain sensor structure. The calculations showed a sensor response that can be described by an effective sensor aspect ratio l/w = 14.87, which is 6% higher than the nominal one of l/w=14. The magnetic properties of continuous thin films with dimensions 3×3 mm2 were characterized for all four wafers using a LakeShore model 7407 vibrating sample magnetometer (VSM) and values of Hex and HK were extracted from easy axis hysteresis loop measurements. Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 25 Fig. 1. Image of planar Hall effect magnetic bridge sensor with definition of geometric variables and symbols. Values of the stack sheet resistances ρ||/t and ρ/t for the four wafers were obtained from electrical measurements of the resistance on transmission line test structures placed near the investigated sensor chips on the wafers in saturating magnetic fields applied parallel and perpendicular to the current, respectively. Measurements of the sensor response vs. applied field were carried out as follows: the sensors were biased with an alternating current of root-mean-square (RMS) amplitude IRMS = 1/√2 mA and frequency f = 65 Hz provided by a Keithley 6221 precision current source. A Stanford Research Systems model SR830 lock-in amplifier was used to record the first harmonic in-phase root-mean- square (RMS) signal Vy,RMS. Note, that Eq. (3) also holds for the RMS values IRMS and Vy,RMS. To simplify the notation below, we will therefore refer to the RMS values as Vy and I. The applied magnetic field 0Hy was generated by a custom built electromagnet and monitored using commercially available Hall probes. Field sweeps were carried out by sweeping the field in both directions between 0Hy = ±40 mT. The sensor temperature was regulated to stability better than 0.1°C by use of a Peltier element, platinum RTD and a precision temperature controller. Sensor characteristics of all sensors were measured at temperatures from 25°C to 90°C in steps of 10°C. Each measurement performed at an elevated temperature was followed by a reference measurement performed at 25°C. In addition, we also studied the effect of repeated exposure to 90 °C for an un-annealed sensor and a sensor from the wafer that was field annealed at 280 °C. These temperature cycling experiments were carried out as follows: first, the temperature was set to 25 °C and left for 10 min before a field sweep was carried out. The field sweep took about 8 min to complete. Then, the temperature was set to 90 °C and the measurement procedure was repeated. Finally, this cycle between 25 °C and 90 °C was repeated for about 7 hours. 4. Results 4.1. As Deposited Samples In this section, we present results obtained for the samples at 25 ºC in their as-deposited state (i.e. prior to sensor characterization at elevated temperatures). We establish the model used for analyzing the field sweeps and compare to electrical and magnetic reference measurements. Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 26 The sensor signal Vy normalized with the bias current I, was measured vs. the sweeping field Hy for all four wafers. Fig. 2 shows the initial field sweeps measured for the samples with no annealing and with annealing at 280 °C. The annealing is observed to shift the peak of the sensor response towards lower field values and to increase the low-field sensitivity. The peak-to-peak value of the sensor response is found to be essentially unchanged by the annealing. -40 -30 -20 -10 0 10 20 30 40 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 No Annealing 280°C Full Curve Fit V yI - 1 [ V A -1 ]  0 H y [mT] -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -1.0 -0.5 0.0 0.5 1.0 Fig. 2. Normalized sensor output (Vy/I) vs. external field (Hy) for sensors from the wafers with no annealing and with field annealing at 280°C in their initial condition. The inset shows the low-field region of the sensor response. The lines are fits to the single domain model for the sensor response described in the text. The solid lines in Fig. 2 are least-squares fits to Eq. (3) with values of + and  obtained by minimizing Eq. (4). The investigated free parameters in the fitting were Vpp/I , Hex and HK. The value of Hs was found to vary only marginally between the different temperature and annealing conditions and was fixed to the average value µ0Hs = 0.789 mT obtained from fitting data for all sensors and temperatures with this parameter set free. In the fitting we also allowed for offsets in the sensor output and the applied field. The quality of all fits was comparable to those shown in Fig. 2. Table 1 shows the values of 0Hex and 0HK obtained from the VSM measurements, the values of /t and the AMR ratio obtained from reference electrical measurements on the transmission line structure as well as the values of 0Hex, 0HK, S0 and Vpp/I obtained from fits to field sweeps of the sensor response. Values reported for the low-field sensitivities S0 were taken as the slope of the fits between ±0.15 mT. Table 1. Parameters of the magnetic stack obtained from VSM measurements, electrical measurements on a transmission line structure and from fits to sensor field sweeps. All measurements were carried out at 25ºC on as-deposited samples (i.e. prior to any experiments at elevated temperatures). Numbers in parentheses indicate the uncertainties reported by the least squares fitting routine. VSM Electrical ref. Sensor field sweeps Annealing conditions µ0Hex [mT] µ0HK [mT] Δρ/t [Ω] AMR [%] µ0Hex [mT] µ0HK [mT] S0 [V/(AT)] Vpp/I [V/A] No annealing 2.89(5) 0.39(5) 0.1296(1) 1.88 2.66(1) 0.90(3) 465 1.779(2) 240 °C 2.02(5) 0.41(5) 0.1318(1) 2.03 1.91(1) 0.52(2) 637 1.785(3) 280 °C 1.90(5) 0.50(5) 0.1319(3) 1.95 1.60(1) 0.50(2) 699 1.764(4) 320 °C 1.39(5) 0.46(5) 0.1317(1) 2.03 1.32(1) 0.34(3) 807 1.768(7) Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 27 The values of Hex obtained from VSM measurements and fits to the sensor field sweeps correspond well to each other although the values from the field sweeps are slightly lower than those obtained from the VSM measurements. The values of HK obtained by VSM and from the sensor field sweeps are comparable for the annealed samples, but they differ about a factor of two for the un-annealed sample. The main effect of the low-temperature annealing is that Hex is found to decrease monotonously with increasing annealing temperature. A decrease of about a factor of two is observed for annealing at 320 °C. The values of HK extracted from the sensor field sweeps are found to decrease with increased annealing temperature, whereas no systematic change is found from the VSM studies. The value of /t remains essentially unchanged by the annealing. The low-field sensitivity is found to increase with annealing and increases almost by a factor of two for the highest annealing temperature. 4.2. Temperature Dependence of Parameters In this section, we first present results of the experiments carried out at elevated temperatures for the un-annealed sample and show that our measurement procedure enables us to clearly distinguish reversible and irreversible changes of the sensor parameters upon exposure to a given elevated temperature. Then, we report the results of the corresponding experiments carried out on sensors from the low-temperature field annealed wafers. All parameters shown below have been obtained from fits to sensor field sweeps as described in section 4.1. Fig. 3 shows the values of S0, Hex and HK obtained from analysis of sensor field sweeps in a series of experiments carried out on a sensor from the wafer with no annealing at sequentially increasing temperatures T. First, the sensor response was measured at 25 °C. Then, the temperature was increased to 30 °C and the sensor response was measured after a waiting time of 2 min and finally, the temperature was reduced to 25 °C to carry out a reference measurement after a waiting time of 2 min. This procedure was repeated for temperatures increasing up to 90 °C in steps of 10 °C. The sensor parameters measured at the elevated temperature T result from the sum of reversible and irreversible changes, whereas the series of reference measurements carried out at 25 °C show only the irreversible changes. This enables us to clearly distinguish the reversible and irreversible changes of the sensor parameters as indicated by the colored areas in Fig. 3. In Fig. 3, the value of S0 is found to increase about 20% when the temperature is increased from 25 °C to 90 °C. Slightly more than half of this increase is irreversible. The values of Hex and HK are found to decrease approximately linearly with increasing temperature with temperature coefficients of 0.42%/°C (27% total decrease) and 0.68%/°C (44% total decrease), respectively, in good agreement with a previous study [6]. For Hex about 20% of the change is irreversible and for HK about 50 % of the change is irreversible. Thus, the irreversible changes are significant for this sample. Corresponding series of experiments were carried out for the wafers exposed to the low-temperature field annealing. Fig. 4(a) shows the values of Vpp/I for the measurements carried out on all samples. These values are proportional to /t. The values obtained at 25 °C are close to identical and show no systematic variation with annealing conditions. Upon exposure to elevated temperatures, the values are found to decrease linearly with temperature with a temperature coefficient of 0.22 %/°C. The change is found to be fully reversible, i.e. no irreversible changes result from the increased temperature. This shows that the low-temperature field annealing and the experiments performed at elevated temperatures do not result in any detectable changes of the AMR properties of the sensor stack. Fig. 4(b) shows the values of the low-field sensitivities S0 normalized to the initial values obtained at 25 °C (given in Table 1) for the four investigated wafers as function of the measuring temperature T. Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 28 The data for the sample with no field annealing from Fig. 3 are shown for comparison. The field annealed samples show a much smaller temperature variation than the sample with no annealing. For the sample annealed at 240 °C the relative change of S0 is about 7 % when the temperature is increased to 80 °C, but more than half of this change is irreversible. For the sample annealed at 280 °C, the points measured at T coincide with the reference points measured at 25 °C, indicating that the entire change of S0 of about 3 % is irreversible. For the sample annealed at 320 °C, there is a net decrease of S0 with T of about 2 % resulting from an irreversible increase of S0 of about 3 % and a reversible decrease of S0 of about 5 %. 20 30 40 50 60 70 80 90 100 0.4 0.6 0.8 1.8 2.0 2.2 2.4 2.6 2.8 460 480 500 520 540 560   H K @T   H K @ 25oC T [°C] Slope=–0.42% / °C Slope=–0.68% / °C Reversible Irr.  0 H ex [ m T ]   H K [ m T ]   H ex @T   H ex @ 25oC Reversible Irr. S 0 @ T S 0 @ 25oC Reversible Irre versibleS 0 [ V /( T A )] Fig. 3. Values of S0 (top), Hex (middle) and HK (bottom) extracted from fits of the field sweeps on the un- annealed sample. Filled points are measured at temperature T, empty points are measured at the reference temperature 25°C after exposure to T. The full lines are linear fits corresponding to the indicated temperature coefficients. 20 30 40 50 60 70 80 90 1.50 1.55 1.60 1.65 1.70 1.75 1.80 V pp / I [ ] T [°C] @T @25°C No Annealing 240°C 280°C 320°C (a) Slope=0.22%/°C 20 30 40 50 60 70 80 90 1.00 1.05 1.10 1.15 1.20 1.25 (b) S 0 (T )/ S 0 (2 5° C ) T [°C] @T @25°C No Annealing 240°C 280°C 320°C R e v er s ib le Ir re v er s ib le Fig. 4. Values of (a) the peak-to-peak sensor response Vpp/I and (b) the low-field sensitivity S0 normalized to its initial value at 25°C obtained from field sweep fits. Different data sets are for sensors from wafers with the indicated annealing conditions. Filled points are measured at T, open points are measured at 25 °C after exposure to temperature T. The arrows to the right indicate the reversible and irreversible change for the un- annealed sample at T=90 °C. Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 29 Figs. 5(a) and (b) show the values of Hex (normalized to their initial values given in Table 1) and HK obtained for the four investigated wafers as function of the measuring temperature T, respectively. For all annealing conditions, the reversible change of Hex with temperature is linear and can be described by the temperature coefficient 0.37%/°C. For the un-annealed sample the irreversible change of Hex is about 8 % when the temperature is increased from 25 °C to 90 °C. The field annealed samples show a smaller, but not negligible irreversible change of Hex, which appears to be independent of the annealing temperature. 20 30 40 50 60 70 80 90 0.7 0.8 0.9 1.0 (a) H ex (T )/ H ex (2 5 °C ) T [°C] @T @25°C No Annealing 240°C 280°C 320°C Slope=0.37%/"C @T @25°C No Annealing 240°C 280°C 320°C 20 30 40 50 60 70 80 90 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (b)   H k [ m T ] T [°C] (a) (b) Fig. 5. Values of (a) the normalized exchange bias field Hex(T)/Hex(25°C) and (b) the anisotropy field HK. Different data sets are for sensors from wafers with the indicated annealing conditions. Filled points are measured at T, open points are measured at 25 °C after exposure to temperature T. The dashed lines indicate the initial values of the parameters. The initial values of HK are found to decrease monotonically with annealing conditions. For the sample with no field annealing, the value of HK changes almost 50 % when the temperature is increased from 25 °C to 90 °C and approximately half of this change is irreversible. The field annealed samples show a much smaller change and the irreversible change is smaller than the error on the individual points (and smallest for the sample annealed at 320 °C). The reversible decrease of HK with temperature for these samples is about 20 %. 4.3. Temperature Cycling Fig. 6 shows the effect of prolonged exposure at 90 °C on S0, Hex and HK vs. the time of the temperature cycling experiment. Note, that only half of this time was spent at 90°C. Field sweeps were measured on the sensor annealed at 280 °C and on the un-annealed sensor while cycling the temperature between 25 °C and 90 °C with each temperature step taking 18 min. The lines in Fig. 6 connect points measured at the same temperature. The extracted values for the different parameters are normalized by the value reached at 90 °C after about 7 h of temperature cycling. Fig. 6(a) shows the normalized value of S0 vs. the time of the temperature cycling experiment. As for the results discussed above, the sensitivity of the sensor annealed at 280 °C changes little upon heating compared to the un-annealed sensor. The parameters obtained at 25 °C for the un-annealed wafer show a big change (>7 %) after first exposure at 90 °C and then slowly approach their asymptotic values. Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 30 For this sample, the sensitivity at 25 °C still changes after 7h of cycling with a total irreversible change of about 20 %. The values measured during the cycle steps at 90 °C show a similar settling over a period of hours. The chip from the wafer annealed at 280 °C shows a significant initial change in the first cycle after which the parameters slowly settle near their asymptotic values. Thus, for this sample, the irreversible change of S0 is less than 5 % during the whole cycling experiment, and the value at 25 °C reaches 98.4 % of its final value after the first exposure to 90 °C. 0 1 2 3 4 5 6 7 0.80 0.85 0.90 0.95 1.00 1.05 S 0 /S 0 (7 h) Time [h] No annealing annealing 280°C @25°C @25°C @90°C @90°C (a) 1.0 1.1 1.2 1.3 1.4 1.5 1.6 0 1 2 3 4 5 6 7 1.0 1.5 2.0 2.5 H ex /H ex (7 h) No annealing annealing 280°C @25°C @25°C @90°C @90°C (b) H K /H K (7 h ) Time [h] No annealing annealing 280°C @25°C @25°C @90°C @90°C (a) (b) Fig. 6. Values of (a) low-field sensitivity S0 and (b) Hex and HK normalized by their value measured at 90 °C after 7 h temperature cycling between 25 °C and 90 °C. Different data sets are for sensors from wafers with the indicated annealing conditions. Filled points are measured at 90 °C open points are measured at 25 °C. The temperature was cycled between 25 °C and 90 °C, each temperature was held constant for 18 min. Fig. 6(b) shows the corresponding normalized values of Hex and HK. The value of Hex measured at 25 °C decreases for both sensors but the relative change for the annealed sensor is seven times smaller than for the un-annealed sensor. Again, the values measured at 90 °C show a similar behavior. The relative change in HK is bigger than for Hex for both sensors, although the change for the un-annealed sensor is twice as big as that for the sample annealed at 280 °C. We also notice for both Hex and HK and independent of low-temperature field annealing that the ratio between the values obtained at 90 °C and 25 °C approach the same value. 5. Discussion 5.1. Analysis Method The presented single domain model for the sensor response provides excellent fits of all measured field sweeps. The parameters obtained from the fits are generally found to agree well with corresponding parameters obtained by VSM and on electrical reference samples although some differences appear. In section 4.1 in Table 1 that the value of HK from the fits of the sensor measurements was about twice that obtained from the VSM measurements. This difference is in agreement with previous studies [6] and is attributed to effects of the sensor structuring. Assuming negligible shape anisotropy, the low-field sensitivity is given by S0 = (l/w)(/t)(Hex+HK)-1 (cf. Eq. (6)) and the peak-to-peak sensor output is given by Vpp/I = (/t)(l/w) = 14.87(/t) Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 31 (cf. Eq. (3)). Inserting the values for the reference samples, we find that the measured low-field sensitivities are generally about 20 % lower than the calculated values and the measured values of Vpp/I are about 9 % smaller than the calculated values. This is attributed to demagnetization effects due to the sensor geometry, which cause the magnetization of the sensor elements to deviate from the nominal single domain state near their edges [7]. From fits we found the shape anisotropy field 0Hs = 0.789 mT, which is comparable to the values of 0Hex and 0HK reported in Table 1 and hence is significant. These results indicate that the even though the results are influenced to some degree by demagnetization effects, the analysis method is robust and the parameters obtained from the fits to the single domain model reflect the variation of the physical parameters of the thin film stack. This means that field sweeps of the sensor response can be used to quantify the exchange and anisotropy fields as well as the magnetoresistive properties of the thin film stack. 5.2. Temperature Dependence of Parameters and Effect of Low-temperature Field Annealing The studies on the as-deposited samples show that the effect of the low-temperature annealing is to decrease Hex and HK while /t remains essentially unchanged. The latter indicates that the microstructure of the stack is not significantly changed by the field annealing. The changes of Hex and HK indicate that the interaction between the ferromagnetic and antiferromagnetic layers is sensitive to the low-temperature field annealing. Considering the exchange bias as an interface phenomenon, the exchange bias field and the coupling energy per area J are related by J = 0MstFMHex, where 0Ms  1.0 T is the saturation flux density of permalloy and tFM = 30 nm is the thickness of the permalloy layer. Inserting the values of Hex from the VSM measurements in Table 1, we obtain Jeb = 0.07 mJ/m2, which is comparable to values reported in the literature for similar stacks [8, 9]. The low-temperature annealing at 280 °C and 320 °C resulted in reductions of Hex of 34 % and 52 %, respectively. Similar observations have been made in studies of similar structures with a top-pinned ferromagnet [8-11]. Previous studies have generally used measurements of the magnetic hysteresis by magnetometry [9-11], magnetooptical measurements [9] or Lorentz microscopy [8] to characterize the variation of Hex and HK with temperature, but they have not systematically studied the reversible and irreversible changes induced by exposure to elevated temperatures. In this work we were able to separate reversible and irreversible changes of the parameters for the magnetic stack vs. temperature for samples exposed to different low-temperature field annealing conditions. We find that the temperature variation of /t is fully reversible. For the exchange bias field Hex we find that the relative reversible change with temperature is the same for all samples (Fig. 5(a)). The irreversible change of Hex, however, is sensitive to the field annealing and is significantly reduced compared to a sample without field annealing. For all field annealed samples, Hex still shows irreversible change upon heating above 25 °C with a relative change that seems to be insensitive to the annealing conditions (Fig. 5(a)). For the anisotropy field HK we find from Fig. 5(b) that both the reversible and irreversible changes upon exposure to elevated measuring temperatures are significant for the sample that was not field annealed, whereas the samples that were field annealed show significantly smaller changes with temperature. Only the sample annealed at 320 °C shows a negligible irreversible change of HK upon exposure to 90 °C. The observed increase of the low-field sensitivity S0 with field annealing and with exposure to elevated temperatures results from the combined effect of the reversible decrease of /t and the decrease of HK+Hex (cf. Eq. (6)), where the latter term dominates the temperature dependence. To further investigate the effect of repeated exposure to elevated temperatures, we studied in Section 4.3 the samples with no annealing and with field annealing at 280 °C for repeated cycles between Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 32 90 °C and 25 °C. In Fig. 6(a), we found that for both the annealed and the un-annealed sample that the irreversible changes in the sensitivity as measured at 25 °C take place upon repeated exposure to 90 °C on a time scale of hours. Moreover, the relative change in sensitivity for the un-annealed sample is several times bigger than for the annealed sample. This change in sensitivity has to be attributed to the change in HK and Hex. Indeed, these two parameters show decay upon long exposure to 90 °C. Also, they show reduced irreversible changes in the annealed sensor compared to the un-annealed one. For all samples, we find that even after field annealing at temperatures up to 320 °C, the values of Hex and HK still show irreversible changes upon exposure to temperatures above room temperature. These changes have to be taken into account when these stacks and sensors are used for sensing purposes in environments at elevated temperatures. The largest changes are found for the sample that was not field annealed and we have found that the field annealing significantly reduces the irreversible changes. 5.3. Possible Mechanisms Several reports in the literature have studied the effect of annealing at low temperatures on the microstructure. King et al. [8] studied the magnetization reversal of NiFe/IrMn exchange bias couples by Lorentz transmission electron microscopy. For an un-annealed sample, they found that the magnetic domain structure in the ferromagnetic layer was highly complex on a microscopic scale near room temperature with no clear overall orientation. After field annealing of the sample at 300 °C, they found significantly larger magnetic domains that were essentially oriented along the cooling field. They could not detect any changes of the microstructure and therefore attributed the change of behavior to a reduction of the local pinning strength of the IrMn grains upon annealing. Thus, the IrMn grains strongly pinned the ferromagnetic layer before annealing resulting in the highly complex domain structure, but after annealing the pinning strength decreased due to relaxation in the spin structure of the IrMn grains such that the local pinning was insufficient to force the ferromagnet to orient along the local pinning field. Geshev et al. [10] carefully studied the interface between Co and IrMn by high resolution cross- sectional TEM and X-ray reflectivity measurements and found no effect of annealing at 215 °C on the microstructure at the interface. Upon annealing in a magnetic field applied along the initial exchange bias direction they observed a clear reduction of Hex that they attributed to relaxation of frustrated spins in the top IrMn layer. They hypothesized that the first few atomic layers of the IrMn layer show paramagnetic behavior and align themselves with the moments from the ferromagnet. When enough atomic layers of the IrMn film to sustain antiferromagnetic order are deposited, the competition between the alignment of the interface spins with those of the ferromagnetic layer and the antiferromagnetic ordering will result in high frustration of the spin structure of the IrMn layer near the interface and a high number of uncompensated spins at the interface, where the latter gives rise to the high initial exchange bias. The annealing enables relaxation of the spin structure resulting in a reduction of the pinning strength and hence of Hex. Our findings that irreversible changes of Hex appear slightly above room temperature even for a sample annealed at 320 °C for one hour and that repeated exposure to elevated temperatures result in gradually decreasing values of Hex indicate that a slow, thermally activated process is involved in the change of Hex vs. time and temperature and that the number of uncompensated interfacial spins of the IrMn layer decreases as a result of the relaxation process. Thus, our observations are consistent with the above interpretation in terms of thermal relaxation of frustrated spins in the IrMn layer near the interface to the ferromagnet. We hope that our studies will provide further inspiration to further theoretical work on this interesting topic. Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 22-34 33 5. Conclusion We have shown that measurements of the response vs. magnetic field of planar Hall effect Wheatstone bridges can be used to extract the exchange field Hex, the anisotropy field HK and the magnetoresistive properties of the exchange-biased stack of the sensors. We have studied the temperature variation of these parameters for a top-pinned NiFe/IrMn stack in the interval between 25 °C and 90 °C for samples that were not annealed and samples that were low-temperature field annealed at 240 °C, 280 °C and 320 °C for one hour. In our experiments we separated reversible and irreversible parameter changes. We found that the magnetoresistive effect is not significantly affected by the low-temperature field annealing and only shows reversible changes upon exposure to elevated temperatures. Both Hex and HK are sensitive to annealing as well as the exposure to elevated temperatures and the relative reversible decrease of Hex with temperature can be described by a single temperature coefficient. Field annealing significantly reduces but does not eliminate the irreversible changes of both Hex and HK upon exposure to temperatures even slightly above room temperature. In experiments where both field annealed and un-annealed sensors were repeatedly exposed to 90 °C, we found a large initial change and a gradual reduction of the change upon further exposure. We take these observations as indicative of a slow thermally activated process that reduces the local pinning strength of the IrMn at the interface. The observations are consistent with previous interpretations in the literature in terms of thermal relaxation of frustrated spins in the antiferromagnet near the interface to the ferromagnet, but further work is required to firmly establish this hypothesis. The present results have important consequences for the use of permalloy-IrMn exchange-bias couples in magnetic field sensors operating at variable temperatures. Stacks with no annealing are strongly influenced by exposure to temperatures above room temperature and these should thus be used with care in applications where the sensor is exposed to elevated temperatures and high accuracy is required. Examples of such applications could be magnetic biosensors operating at variable temperatures (e.g. for studies of biological interactions vs. temperature) and magnetic field sensors operating in variable temperature conditions. The presented method provides an attractive approach to quantitative characterization of the temperature-induced changes by exposure to given temperature conditions. We have shown that low-temperature field annealing and prolonged exposure to the highest operating temperature substantially reduces subsequent irreversible changes with increasing temperatures but also that it is difficult to completely eliminate irreversible changes of the sensor parameters. These therefore have to be considered for the use of the structures in sensing applications. Acknowledgements F.W. Østerberg acknowledges support by the Copenhagen Graduate School for Nanoscience and Nanotechnology (C:O:N:T) and the Knut and Alice Wallenberg (KAW) Foundation. References [1]. A. Persson et al., Low-frequency noise in planar Hall effect bridge sensors, Sensors and Actuators A: Physical, 171, 2011, pp. 212-218. [2]. C. Damsgaard et al., Temperature effects in exchange-biased planar hall sensors for bioapplications, Sensors and Actuators A: Physical, 156, 2009, pp. 103-108. [3]. B. Dalslet et al., Bead magnetorelaxometry with an on-chip magnetoresistive sensor, Lab Chip, 11, 2011, pp. 296-302. [4]. A. Henriksen et al., Planar Hall effect bridge magnetic field sensors, Appl. Phys. Lett., 97, 2010, 013507. [5]. S. Blundell, Magnetism in condensed matter, Oxford master, Oxford University Press, 2001. [6]. C. Damsgaard et al., Exchange-biased planar Hall effect sensor optimized for biosensor applications, Sensors & Transducers Journal, Vol. 15, Sp