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Volume 15, Special Issue
October 2012
www.sensorsportal.com ISSN 1726-5479
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Dickert, Franz L., Vienna University, Austria
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Enderle, Stefan, Univ.of Ulm and KTB Mechatronics GmbH, Germany
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Erkmen, Aydan M., Middle East Technical University, Turkey
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Faiz, Adil, INSA Lyon, France
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Li, Sihua, Agiltron, Inc., USA
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Malyshev, V.V., National Research Centre ‘Kurchatov Institute’, Russia
Marquez, Alfredo, Centro de Investigacion en Materiales Avanzados, Mexico
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Mi, Bin, Boston Scientific Corporation, USA
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Mulla, Imtiaz Sirajuddin, National Chemical Laboratory, Pune, India
Nabok, Aleksey, Sheffield Hallam University, UK
Neelamegam, Periasamy, Sastra Deemed University, India
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Oberhammer, Joachim, Royal Institute of Technology, Sweden
Ould Lahoucine, Cherif, University of Guelma, Algeria
Pamidighanta, Sayanu, Bharat Electronics Limited (BEL), India
Pan, Jisheng, Institute of Materials Research & Engineering, Singapore
Park, Joon-Shik, Korea Electronics Technology Institute, Korea South
Passaro, Vittorio M. N., Politecnico di Bari, Italy
Penza, Michele, ENEA C.R., Italy
Pereira, Jose Miguel, Instituto Politecnico de Setebal, Portugal
Petsev, Dimiter, University of New Mexico, USA
Pogacnik, Lea, University of Ljubljana, Slovenia
Post, Michael, National Research Council, Canada
Prance, Robert, University of Sussex, UK
Prasad, Ambika, Gulbarga University, India
Prateepasen, Asa, Kingmoungut's University of Technology, Thailand
Pugno, Nicola M., Politecnico di Torino, Italy
Pullini, Daniele, Centro Ricerche FIAT, Italy
Pumera, Martin, National Institute for Materials Science, Japan
Radhakrishnan, S. National Chemical Laboratory, Pune, India
Rajanna, K., Indian Institute of Science, India
Ramadan, Qasem, Institute of Microelectronics, Singapore
Rao, Basuthkar, Tata Inst. of Fundamental Research, India
Raoof, Kosai, Joseph Fourier University of Grenoble, France
Rastogi Shiva, K. University of Idaho, USA
Reig, Candid, University of Valencia, Spain
Restivo, Maria Teresa, University of Porto, Portugal
Robert, Michel, University Henri Poincare, France
Rezazadeh, Ghader, Urmia University, Iran
Royo, Santiago, Universitat Politecnica de Catalunya, Spain
Rodriguez, Angel, Universidad Politecnica de Cataluna, Spain
Rothberg, Steve, Loughborough University, UK
Sadana, Ajit, University of Mississippi, USA
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Sandacci, Serghei, Sensor Technology Ltd., UK
Saxena, Vibha, Bhbha Atomic Research Centre, Mumbai, India
Schneider, John K., Ultra-Scan Corporation, USA
Sengupta, Deepak, Advance Bio-Photonics, India
Seif, Selemani, Alabama A & M University, USA
Seifter, Achim, Los Alamos National Laboratory, USA
Shah, Kriyang, La Trobe University, Australia
Sankarraj, Anand, Detector Electronics Corp., USA
Silva Girao, Pedro, Technical University of Lisbon, Portugal
Singh, V. R., National Physical Laboratory, India
Slomovitz, Daniel, UTE, Uruguay
Smith, Martin, Open University, UK
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Somani, Prakash R., Centre for Materials for Electronics Technol., India
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Srinivas, Talabattula, Indian Institute of Science, Bangalore, India
Srivastava, Arvind K., NanoSonix Inc., USA
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Stefanescu, Dan Mihai, Romanian Measurement Society, Romania
Sumriddetchka, Sarun, National Electronics and Comp. Technol. Center, Thailand
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Sun, Junhua, Beijing University of Aeronautics and Astronautics, China
Sun, Zhiqiang, Central South University, China
Suri, C. Raman, Institute of Microbial Technology, India
Sysoev, Victor, Saratov State Technical University, Russia
Szewczyk, Roman, Industr. Research Inst. for Automation and Measurement, Poland
Tan, Ooi Kiang, Nanyang Technological University, Singapore,
Tang, Dianping, Southwest University, China
Tang, Jaw-Luen, National Chung Cheng University, Taiwan
Teker, Kasif, Frostburg State University, USA
Thirunavukkarasu, I., Manipal University Karnataka, India
Thumbavanam Pad, Kartik, Carnegie Mellon University, USA
Tian, Gui Yun, University of Newcastle, UK
Tsiantos, Vassilios, Technological Educational Institute of Kaval, Greece
Tsigara, Anna, National Hellenic Research Foundation, Greece
Twomey, Karen, University College Cork, Ireland
Valente, Antonio, University, Vila Real, - U.T.A.D., Portugal
Vanga, Raghav Rao, Summit Technology Services, Inc., USA
Vaseashta, Ashok, Marshall University, USA
Vazquez, Carmen, Carlos III University in Madrid, Spain
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Wandelt, Barbara, Technical University of Lodz, Poland
Wang, Jiangping, Xi'an Shiyou University, China
Wang, Kedong, Beihang University, China
Wang, Liang, Pacific Northwest National Laboratory, USA
Wang, Mi, University of Leeds, UK
Wang, Shinn-Fwu, Ching Yun University, Taiwan
Wang, Wei-Chih, University of Washington, USA
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Watson, Steven, Center for NanoSpace Technologies Inc., USA
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Wells, Stephen, Southern Company Services, USA
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Yang, Dongfang, National Research Council, Canada
Yang, Shuang-Hua, Loughborough University, UK
Yang, Wuqiang, The University of Manchester, UK
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Yong Zhao, Northeastern University, China
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Yufera Garcia, Alberto, Seville University, Spain
Zakaria, Zulkarnay, University Malaysia Perlis, Malaysia
Zagnoni, Michele, University of Southampton, UK
Zamani, Cyrus, Universitat de Barcelona, Spain
Zeni, Luigi, Second University of Naples, Italy
Zhang, Minglong, Shanghai University, China
Zhang, Qintao, University of California at Berkeley, USA
Zhang, Weiping, Shanghai Jiao Tong University, China
Zhang, Wenming, Shanghai Jiao Tong University, China
Zhang, Xueji, World Precision Instruments, Inc., USA
Zhong, Haoxiang, Henan Normal University, China
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Sensors & Transducers Journal (ISSN 1726-5479) is a peer review international journal published monthly online by International Frequency Sensor Association (IFSA).
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
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Sensors & Transducers Journal, Vol. 15, Special Issue, October 2012, pp. 1-13
1
SSSeeennnsssooorrrsss &&& TTTrrraaannnsssddduuuccceeerrrsss
ISSN 1726-5479
© 2012 by IFSA
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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
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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.
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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 = Il/(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)
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(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
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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.
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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.
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