Eur. Phys. J. Appl. Phys. (2015) 72: 10601
DOI: 10.1051/epjap/2015150214
THE EUROPEAN
PHYSICAL JOURNAL
APPLIED PHYSICS
Review Article
Linearization strategies for high sensitivity magnetoresistive
sensors
Ana V. Silva1,2 , Diana C. Leitao1,2 , João Valadeiro1 , José Amaral1 , Paulo P. Freitas1,3 , and Susana Cardoso1,2,a
1
2
3
Instituto de Engenharia de Sistemas e Computadores – Microsistemas e Nanotecnologias, 1000 Lisboa, Portugal
Instituto Superior Tecnico, Physics Department, Universidade de Lisboa, 1049 Lisboa, Portugal
International Iberian Nanotechnology Laboratory, 4715 Braga, Portugal
Received: 17 April 2015 / Received in final form: 28 July 2015 / Accepted: 31 August 2015
c EDP Sciences 2015
Published online: 5 October 2015 – Abstract. Ultrasensitive magnetic field sensors envisaged for applications on biomedical imaging require
the detection of low-intensity and low-frequency signals. Therefore linear magnetic sensors with enhanced
sensitivity low noise levels and improved field detection at low operating frequencies are necessary. Suitable devices can be designed using magnetoresistive sensors, with room temperature operation, adjustable
detected field range, CMOS compatibility and cost-effective production. The advent of spintronics set
the path to the technological revolution boosted by the storage industry, in particular by the development of read heads using magnetoresistive devices. New multilayered structures were engineered to yield
devices with linear output. We present a detailed study of the key factors influencing MR sensor performance (materials, geometries and layout strategies) with focus on different linearization strategies available.
Furthermore
√ strategies to improve sensor detection levels are also addressed with best reported values of
∼40 pT/ Hz at 30 Hz, representing a step forward the low field detection at room temperature.
1 Introduction
Currently available sensing techniques include induction,
fluxgate, SQUID (superconducting quantum interference
device), nuclear precession, Hall-effect, magnetoresistance,
magnetostrictive/piezoelectric
composite,
magnetotransistor, magneto-impedance, magneto-optics and
MEMS (microelectromechanical systems) based magnetic
sensors [1]. Their application to fields with stronger industrial penetration determines their development and maturity, thus five main technological families are dominant:
SQUID sensors applied to magneto-encephalography is
the prevalent technique for neuroimaging, NMR (nuclear
magnetic resonance) is a powerful tool for medical diagnose and chemical spectroscopy, resonance fluxgate sensors are predominant in the military industry, inductive
sensors in geomagnetic research and magnetoresistive sensors govern the data storage industry [2]. When choosing
a magnetic sensing technology different parameters need
to be considered, e.g., sensitivity, linearity, field range, frequency bandwidth, operating temperature, dimensions.
The evolution in the fabrication of thin films with
well controlled thickness (as low as few Å), driven by the
semi-conductor industry, allowed the development of
nanostructured devices. In the recent decades, the generation and manipulation of spin-polarized electrons in
magnetic multilayered thin-film structures gave birth to
a
e-mail: scardoso@inesc-mn.pt
spintronics, with the discovery of giant magnetoresistance
by Fert et al. and Grunberg et al. in 1988 (2007 physics
Nobel prize) paving the way to the digital information
revolution [3]. These spintronic materials can act as
extremely sensitive magnetic field sensors, because their
electrical resistance can change in the presence of magnetic fields at room temperature by factors much larger
than are possible with conventional magnetic materials.
Magnetoresistive (MR) sensors, with their tunable response and adjustable operation range [4], are the ideal
candidates for room temperature, small footprint and cost
effective applications at the pico to mili tesla (T) range
(10−12 to 10−3 T). Field sensing can be done in an extremely small, lithographically patterned area, reducing
size and power consumption requirements and thus being
suitable for array applications. Multiple MR sensors can
be electronically addressed and multiplexed with on-board
electronics. This thin film technology is compatible with
standard silicon integrated circuit (IC) technology [5,6],
allowing for large scale fabrication and closed packed
implementations, ideal for portable solutions. Nowadays
several commercial products using MR sensors provide
high performance at reasonable cost [7]. Steering angle,
mechanical torque and position sensors are used in
automation applications, at assembly machines and industrial robots [8]. Magnetometers used as digital compasses
to detect the earth’s magnetic field [9] are used in the
automotive industry as well as personal electronic devices.
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Magnetoresistive sensors have been successfully applied
to industrial sensing as electrical current sensors in power
systems [10,11] or spindle high-speed measurements.
Non destructive testing, either for flux leakage detection
for packaging control [12] or metal surface cracks scanning [13,14], is another relevant area where MR sensors
are used. Magnetic biosensors based on MR technology
used to detect surface binding reactions of biological molecules labelled with magnetic particles, is an emerging field
providing key advantages for both research and clinical
settings, as sensors can be arrayed and multiplexed to perform complex protein or nucleic acid analysis in a single
assay with full scalable IC integration capability, making
it appealing for point-of-care (POC) applications along
with lab-on-chip systems [15–21].
One of the most challenging MR detection areas is
brain activity sensing, where field signals are of very low
intensity and at low-frequency (pT range below 100 Hz),
requiring sensing devices with challenging detectivity limits, at room temperature. Some major breakthroughs have
already been achieved, leading the way to portable neural
activity sensing [22–24].
1.1 Magnetoresistive mechanism
A magnetoresistive device is a solid-state transducer which
directly converts an external magnetic field (Hext ) into a
resistance, given a dc bias current supply:
R = f (Hext ).
(1)
These devices are composed of a combination of magnetoresistive materials, whose magnetization will tend to
align with the external field and are optimized to maximize their resistance variation [26]. The devices will have
a minimum (Rmin ) and a maximum (Rmax ) resistance
plateau and the path from one level to other can be
engineered to be a linear one, allowing them to work as
magnetic field sensors. The magnitude of the magnetoresistance effect (MR) can be expressed as a percentage and
is defined as follows:
MR(%) =
Rmax − Rmin
× 100.
Rmin
(2)
Three main thin film magnetic sensor technologies are
based in MR: anisotropic magnetoresistance (AMR), giant
magnetoresistance (GMR) and tunnel magnetoresistance
(TMR).
1.1.1 Anisotropic magnetoresistance
The AMR effect is characteristic of transition ferromagnetic materials (and their alloys), where their electrical
resistance is a function of the angle between the material
magnetization and the direction of the electrical current
flowing trough it. This phenomenon arises from spin-orbit
coupling, reflecting the interaction between the spin
of the conduction electrons and the crystal lattice [27].
An increase in the resistance of the system occurs as the
majority s-electrons are scattered into (minority) d-orbital
states. The anisotropic scattering probability of the
d-bands depends on the orientation of the magnetization
relative to the flowing current, being higher when these orbitals are parallel to the current direction and lower when
they are perpendicular.
Typical AMR values at room temperature are ∼5% for
NiFe and CoFe bulk alloys [27] and lower for patterned
thin films (∼2%) [28], due to additional scattering (e.g.,
grain boundaries, film interfaces). These low MR values
are the main reason why these sensors have been gradually
replaced by GMR and TMR devices.
1.1.2 Giant magnetoresistance
Advances in thin film deposition techniques led to the
development of a new class of devices. Giant magnetoresistance is observed in thin film multilayered structures
composed of alternating ferromagnetic and non magnetic
layers. The observed effect is a significant change in the
electrical resistance of such structures depending on
whether the magnetization of consecutive ferromagnetic
layers are parallel or anti-parallel [29]. The origin of this
effect is the (diffusive) electron spin dependent scattering
within the ferromagnetic layers and at their interfaces.
Depending on the magnetization direction of the ferromagnetic layers, there is an electron scattering asymmetry
which results in different resistances for each spin dependent current.
The maximum resistance value is achieved when the
magnetization of the ferromagnetic (FM) layers have an
antiparallel configuration, while the minimum occurs for a
parallel one. The existence of the GMR effect is independent of the current direction through the multilayer. Two
current modes are possible: current-in-plane (CIP) and
current-perpendicular-to-plane (CPP). The largest MR
values are observed in CPP mode, because all conduction
electrons must pass through all layers and all spin-filter
interfaces of the structure. The highest GMR values reported are up to ∼65% at room temperature in CPP-GMR
multilayers [30]. However, because the active length of
these structures is the multilayer thickness, usually much
smaller than the typical device lateral dimensions, these
structures exhibit very small resistances that would require either sub-micron fabrication or extremely sensitive
electrical measurements and thus are not normally used
as sensing devices.
In the beginning of the 90s, Grunberg devised a sensing system scheme based on the essential structure for the
GMR effect (two ferromagnetic layers, separated by a non
magnetic metallic layer, FM1/metallic spacer/FM2) [31]
being readily followed by IBM’s introduction of the spin
valve (SV) system [32]. In the SV one of the FM electrodes
is used as a reference direction while the other FM is free
to rotate, allowing the controlled presence of two, parallel
and anti-parallel magnetization configurations [33]. The
thickness of the non-magnetic spacer is tuned in order to
achieve high magnetoresistance while maintaining a small
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coupling between the two FM layers. State of the art specular SVs reach MR values of the order of ∼20%. In this
case the introduction of a small oxide layer next to the
FMs induces specular reflection at the interface increasing electron scattering [34].
1.1.3 Tunnel magnetoresistance
Before the discovery of the GMR effect, it was already
known that the electrical resistance of magnetic tunnel
junctions (MTJ) depends on the relative orientation of its
ferromagnetic layers, similarly to GMR [35]. This effect is
called tunnel magnetoresistance (TMR) and has a different physical origin of the GMR effect. It occurs in multilayered structures in which the electrons tunnel across a
thin (5–20 Å) insulating barrier (I) sandwiched between
two ferromagnetic layers in a FM1/I/FM2 like structure.
In these structures the electric current flows perpendicular
to the layers plane (CPP configuration). The TMR effect
is a result of the (non-diffusive) spin dependent tunneling
probability. Upon applying a voltage, the electrons at the
Fermi level of FM1, tunnel into free equivalent spin states
at the Fermi level of FM2 and vice-versa. In ferromagnetic
materials there is an imbalance at the density of states of
the spin up and spin down electrons near the Fermi level,
which orientates the magnetization of the layer to a certain direction. As a consequence, the tunneling of electrons
is different according to their spins [36]. The conductance
across the insulating barrier is dependent on the voltage at
its surfaces (bias voltage) and on the ferromagnets magnetization configuration, with the largest resistance value
achieved when the FM layers have an antiparallel orientation, while the lowest value occurs for the parallel configuration.
Overall, TMR yields a resistance variation one-two
orders of magnitude higher than GMR technology, and
thus is steadily replacing the other MR technologies in
most applications. Initially, amorphous aluminum oxide
(AlOx) tunnel barriers exhibited TMR values as high as
∼70% at room temperature [37]. Major improvements
were achieved upon the inclusion of crystalline MgO barriers and textured MTJ stacks. TMR values up to ∼600%
were reported at room temperature for simple CoFeB/
MgO/CoFeB structures [38], and optimum values decrease
to ∼250% for complex engineered stacks developed for device applications [9,39–42]. The reported high TMR values are a consequence of coherent spin polarized tunneling.
In fact, the physics of spin filtering has been extensively
addressed for single crystalline MTJs, where the electron
wave functions and its attenuation rates are symmetry
dependent, hence playing a major role in setting the tunneling probability [43–45]. As stated by Tiusan et al. this
picture can also be extended to sputtered MTJ stacks [45].
Driven by the magnetic recording industry, many other
sensing applications have benefited from its technological
developments. Figure 1 summarizes the technological evolution for this field. A wide range of other applications for
MR sensors exists, that has been breached by AMR and
SV based sensors, but where MTJ based sensors appear
Fig. 1. Magnetic recording technology evolution. From referc
ence [25], IOP Publishing. Reproduced by permission of IOP
Publishing. All rights reserved.
Fig. 2. Key properties of MR technologies (for devices with
µm2 dimensions). Adapted from reference [46], in press.
when their specifications surpass those of AMR or GMR.
These include various types of field sensors (from nT to
1 T fields) used in several electronic and industrial applications [10] along with biosensing systems [15], whose
specific requirements will define which of the technologies
to use. Key properties such as operational linear range,
thermal stability, materials cost, thermal treatments required or electrical robustness against electrostatic discharge need to be evaluated together while selecting the
best type of MR technology for a particular application
(Fig. 2).
1.2 Typical sensor structure
From a merely structural point of view, MTJs are very
similar to SVs, both consisting of two ferromagnetic electrodes separated by a non-magnetic spacer (metallic for
SVs and insulator in MTJs case). As device applications
require a stable fixed reference electrode, several strategies can be considered: one can either resort to FM layers with different coercivities (using different materials
and/or different thicknesses) or, as first introduced by
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(a)
Fig. 3. Typical device structure. Arrows refer to magnetization
orientation of layers at low fields. Sensing layer dimensions:
thickness (t), lateral dimensions: width (w) and height (h).
IBM [33], one can deposit an antiferromagnetic (AFM)
layer adjacent to one of the FM layers, fixing its magnetization direction trough exchange bias coupling at the interface. This creates a reference direction, while the other
FM layer is free to rotate in response to a low external field, acting as a sensing electrode. Commonly used
antiferromagnetic materials include FeMn [47], NiO [48],
MnIr [28] and PtMn [49]. The magnetization direction of
this fixed layer can only be reversed at fields above the
exchange bias field (μ0 Hexch ), which can be as high as
85 mT (Hexch = 850 Oe) [50], but typically is ∼30–40 mT.
The strength of the reference direction can be further enhanced by replacing the single fixed layer by a synthetic
anti-ferromagnetic (SAF) structure, which is composed of
two ferromagnets separated by a thin spacer layer (most
common Ru, thinner than 1 nm), with thickness tuned
to have anti-ferromagnetic coupling, as described by the
RKKY theory [51]. One of the ferromagnetic layers is exchange biased by an AFM. As a consequence, pinning
fields in the order of several hundreds of kOe are obtained [52]. SAF structures have a null net magnetization
at low fields, being also advantageous for patterned structures leading to a reduced magnetostatic coupling between
reference and sensing layers [53]. These types of structure
also improve thermal stability and lead to a lower distribution of blocking temperatures [54]. Figure 3 illustrates
a typical structure of such devices, comprised of /seed layers/AFM/pinned FM/Ru spacer/reference FM/spacer/
sensing FM/cap layers. The bottom films generically
represent the underlayers commonly used to enhance electrical properties (e.g., CuN, Ta as buffer layers) or to promote the correct crystallinity (e.g., Ta, Ru, NiFeCr as seed
layers).
1.3 Sensor transfer curve
The sensor behavior is characterized by its transfer curve,
which represents directly the output resistance
dependence on field signal. For an ideal magnetic sensor
this curve is linear and hysteresis-free within the intended
field operating range (Fig. 4a). The curve possesses two
stable resistance plateaus and a linear reversible path between them. Saturation fields (Hsat ) define the ideal linear
range (2Hsat ) of the device, where a dR variation
(b)
Fig. 4. MR transfer curve principle. (a) R(H) linear behavior and typical magnetization orientations correspondence.
(b) CPP configuration for magnetoresistive sensing.
corresponds to a single dH value. The key feature of a
magnetic sensor response is its field sensitivity, which represents how reactive a sensor is to a field variation, and can
be measured experimentally from the slope of the transfer
curve. Commonly the sensitivity is presented normalized
as in:
ΔR
1
MR
S=
=
.
(3)
Rmin ΔH linear
(ΔH)linear
The linear range depends on material and device geometry (shape and dimensions), while MR is intrinsic of the
FM/spacer/FM structure and interfaces. For MTJs, the
maximum resistance variation is defined as in equation (4),
valid in a first approximation [55], where W and h are the
lateral dimensions of the sensor, RA is the resistance-area
product, which is an intrinsic property of the tunnelling
barrier and cos α is the cosine average of the angle (α)
between reference and sensing layers magnetization
directions:
ΔRMTJ =
RA
1
MR
cos α.
2
W ×h
(4)
Magnetoresistive devices will have a linear response to
an external field only if the sensing layer magnetization
changes its direction trough coherent rotation. To achieve
this behavior, sensing and reference layer magnetizations
are set orthogonal (by every interplay) to each other and
the external magnetic field is applied perpendicular to the
sensing layer but parallel to the reference one (Fig. 4b).
1.4 Macrospin model for coherent rotation
The Stoner-Wohlfarth model [56] provides a good estimation of the required conditions for the linearization of MR
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sensors with micrometric dimensions, when layers can be
considered to have a magnetic single-domain like behavior
and edge effects can be neglected. Under these assumptions the magnetization of a single ferromagnetic layer
(M ) is described as a single collective vector, whose magnitude (saturation magnetization – Ms ) remains constant
and orientation may vary in space and time, being defined
by the system energy minima. The total energy associated
with the sensing layer has two types of contributions:
E sen = Eapp + Ek ,
where Eapp is the energy term associated with all magnetic
fields sources external to the ferromagnetic layer, defined
by unit of magnetic material volume (V sen ) as:
Eapp
= −μ0 H app × M sen ,
V sen
and where Ek represents the internal anisotropy energy
terms. This term has several sources, which can be divided
in two families, one that represents all sources intrinsic to
the deposition of the ferromagnetic material, namely of
magneto-crystalline and magnetostrictive natures and another family of magnetostatic nature, that represents the
anisotropy created by the self-demagnetizing field of the
ferromagnetic layer. In this work for the intrinsic
anisotropy term is only considered the uniaxial anisotropy
induced by an applied magnetic field during deposition,
defined as:
Eku
= −K u sin2 φ,
V sen
where K u is the uniaxial anisotropy constant and φ is
the angle between the ferromagnetic layer magnetization
direction and its deposition induced easy axis (e.a.), coru
responding to a field of strength Hk = μ2K
.
0 Ms
The self-demagnetizing term depends on shape anisotropy. For most geometries the exact self-demagnetizing field can only be calculated numerically. For thin films
ferromagnets of micrometric lateral dimensions where
t <<< h < W , the demagnetizing field can be maximized
by:
−Nh Mssen cos ϕ,
where Nh is the principal component of the demagnetizing
tensor N [57] along the axis parallel to h and ϕ is the angle
between the magnetization and that axis. The energy term
associated with this field is given by:
sen
Eself−demag
μ0
Nh (Mssen )2 cos2 ϕ.
=
V sen
2
To understand the conditions required for a MR device
to have a linear behavior, one can consider the energy
balance of the sensing layer composing the following structure: reference layer/spacer/sensing layer, where the system is considered to be under the influence of an external
field low enough for the reference layer to have its magnetization fixed. In this situation one can consider in addition to Ek terms three applied field contributions: (i) the
applied external field (H ext ), (ii) the Neel coupling field
Fig. 5. Scheme of studied structure configuration. (a) Reference and sensing layers with parallel induced uniaxial easy
axes. (b) Reference and sensing layers with perpendicular
induced uniaxial easy axes.
(H N ) (induced by correlated interface roughness at the
spacer interfaces with the ferromagnets) and (iii) the field
created at the sensing layer by the demagnetizing field of
the reference (H ref
d ).
Upon material deposition, two different configurations
of sensing and reference layers can be considered (Fig. 5)
one where their uniaxial induced anisotropy axes are parallel (parallel anisotropies) and one where they are perpendicular (crossed anisotropies). The MR device is
always aligned such that the external field to be sensed
is parallel to the e.a. of the reference layer.
In the first configuration (Fig. 5a), the energy of the
sensing layer (expressed relative to θ, the angle between
the sensing layer magnetization and external field) is given
by equation (5):
2
E sen
Nh Mssen
sen sin θ
sen
(H
=
μ
M
−
N
M
)
+
0
k
h
s
s
V sen
2
2
− cos θ Hext − Hdref + HN .
(5)
For a given range of Hext the minimization of equation (5)
yields a minimum corresponding to θ = π, as long as
Hext is negative enough for [Hext − Hdref + HN < −|Hk
−Nh Mssen |] and similarly a minimum corresponding to θ =
0 is always present, as long as [Hext − Hdref + HN > |Hk −
Nh Mssen |]. When Hext − Hdref + HN < |Hk − Nh Mssen | (moderate fields) two distinct situations can occur. When the
induced anisotropy term is higher than the self demagnetizing one (Hk > Nh Mssen ) a hysteretic curve is present
(Fig. 6), corresponding to two possible minima (cos θ = 1
and cos θ = −1). The point where cos θ = 0 is denominated coercive field (Hc ) and is defined by:
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Hc = Hk − Nh Mssen ,
(6)
The European Physical Journal Applied Physics
Fig. 6. Hysteretic transfer curve corresponding to parallel
induced anisotropies for condition Hk > Nh Mssen .
Fig. 8. Transfer curve corresponding to perpendicular induced
anisotropies.
layer, i.e., a linear magnetic response (Fig. 8).
2
E sen
sen cos θ
(Hk + Nh Mssen )
=
μ
M
0
s
V sen
2
− cos θ Hext − Hdref + HN . (7)
Saturation fields for this type of magnetic response are
given by:
ref
Hd − HN ± (Hk + Nh Mssen ) ,
Fig. 7. Transfer curve corresponding to parallel induced
anisotropies for condition Hk < Nh Mssen .
while Hf = Hdref − HN is the curve off-centre.
A linear magnetic response is obtained if the induced
anisotropy term is lower than the self demagnetizing one
(Hk < Nh Mssen ) (Fig. 7). In this case only one energy minimum exists corresponding to:
cos θ =
Hext − Hdref + HN
.
Nh Mssen − Hk
and its slope
1
Nh Mssen + Hk
,
meaning that the self demagnetizing field will not concur
with the uniaxial anisotropy and that sensor sensitivity
is increased by minimizing both induced anisotropy and
demagnetizing field.
Both situations yielding a linear sensor response have,
at zero external field, a perpendicular configuration of
reference and sensing layers magnetization directions
(α = π2 ) and thus the resistance output of a MTJ device
(Eq. (4)) with a linear behavior is given by:
The saturation fields which define the linear range are
defined by:
ΔRMTJ =
RA Hext − Hdref + HN
1
MR
,
2
W ×h
2Hsat
(8)
where 2Hsat = Hk ± Nh Mssen .
ref
Hd − HN ± (Hk − Nh Mssen ) .
The sensitivity of sensor will then be proportional to the
curve slope:
1
.
Nh Mssen − Hk
The highest sensitivity is reached when Nh Mssen balances
Hk .
In the configuration where reference and sensing layers
have perpendicular induced uniaxial easy axes (Fig. 5b)
the energy balance is given by equation (7). In this condition, there is only one possible behavior of the sensing
1.5 Choice of electrode material for TMR sensors
Adequate choosing of materials is the starting point to
design solid MR sensors. Figure 9 presents a summary of
coercive field for CoFe alloys used as ferromagnetic electrodes in MTJs. The values correspond to unpatterned
films, being the main source of coercivity the intrinsic
anisotropy. For the parallel anisotropy configuration, the
higher the Hk the higher the sensitivity, as long as
the demagnetizing (Hdsen ) field is strong enough to fulfill
the linear response condition: Hk < Hdsen , whereas for the
crossed configuration lower Hk yields higher sensitivity.
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A.V. Silva et al.: Linearization strategies for high sensitivity MR sensors
Fig. 9. Coercive field values for different CoFe alloys as
function of film thickness. (Co70 Fe30 )80 B20 data for unpatterned samples of Ta/CoFeB/Ta thin films, annealed for
15 min at 250 ◦ C under a 1 T field; (Co80 Fe20 )80 B20 and
(Co80 Fe20 )90 B10 values for AlOx/CoFeB multilayer structures
annealed at 330 ◦ C under 0.5 T, from reference [58]; #
point of (Co50 Fe50 )80 B20 from reference [59] and £ value
from reference [60]; Co80 Fe20 data for AlOx/CoFe structures,
∗ value for glass/Al2 O3 (3 nm)/[CoFe (t) /Al2 O3 (3 nm)]n
multilayers and value & for Si/Al2 O3 /CoFe (3 nm)/
AlOx (1.5 nm)/CoFe (4 nm)/AlOx (1.5 nm) stacks annealed
for 45 min at 330 ◦ C under 70 mT.
AlOx barriers are relatively simple to fabricate, typically grown by depositing elemental aluminum and subsequent oxidation [63–70]. For sensing applications
AlOx-MTJs present TMR values up to ∼50% [8,71,72],
being five times lower than values obtained for state of the
art MgO-MTJ stacks engineered for devices (Sect. 1.1.3).
In this type of junctions the only condition required
for a good quality barrier is that it be sufficiently nonconductive. In contrast, MgO-based junctions rely on coherent tunnelling processes to achieve high TMR values
and therefore a particular crystallographic orientation is
necessary, requiring tight control of deposition and annealing parameters and a more restrict choice of electrode
materials. Consequently in applications that can cope with
TMR ∼50%, AlOx MTJs become advantageous for sensor
engineering since the use of several electrodes such as Fe,
CoFe, CoFeB, NiFe and their combinations already have
been successfully demonstrated. Since no crystallization
is required, annealing temperatures as low as 200–250 ◦ C
are employed only to set Hexch .
Adding a soft magnetic NiFe layer after CoFeB (ferromagnetically coupled) results in a sensing performance
improvement by presenting lower ferromagnetic coupling
trough the barrier (Hf ) and reducing coercivity, thus
having a better reversibility and linearity around zero magnetic field, while maintaining the large TMR characteristic of thick CoFeB within CoFeB/MgO/CoFeB stacks,
as exemplified for patterned structures in Figure 10. The
inclusion of NiFe directly after CoFeB strongly reduces
TMR due to the texture propagation from NiFe (fcc 1 1 1)
Fig. 10. MR loops of two MTJ patterned structures with the
same SAF reference electrodes and different sensing electrodes.
Red line represents pillar with 4 nm thick (Co25 Fe75 )80 B20
as sensing layer. Black line represents behavior of a structure with (Co25 Fe75 )80 B20 (4 nm)/Ni80 Fe20 (3.3 nm) sensing electrode. NiFe deposited after ion milling removal of
c
Ru(7 nm)/Ta(10 nm). [2011] IEEE. Reprinted with permission from reference [61].
to CoFeB (bcc 1 0 0) [61]. Correct crystallography can be
assured introducing a thin Ta dusting layer (∼0.21 nm)
between these layers. This inclusion does not destroy the
ferromagnetic coupling between CoFeB and NiFe, but
causes a strong reduction of Hc and Hf (Fig. 11) while
enhancing the sensing layer magnetic moment (Fig. 11 inset) and while maintaining the characteristic large MR
values [9,62]. In contrast AlOx MTJs do not require dusting layers when including soft magnetic layers to the sensing electrodes to reduce coercivity [73], thus simplifying
the composition of material stacks. Instead if MR ratio is
crucial for the detection level MgO-MTJ should be considered. State-of-the-art complex MgO-MTJs stacks proper
for robust sensing applications show TMR ∼250%
(Sect. 1.1.3). Such large values result from the strong spin
polarization induced by the crystalline structure of the
ferromagnetic CoFeB electrodes together with the MgO
barrier, translating into coherent tunneling through the
barrier [74]. These large values are obtained only when
both electrodes in contact with the MgO barrier show bcc
crystalline structure with (1 0 0) out-of-plane texture, promoted in as-deposited amorphous-CoFeB upon annealing
at 270–350 ◦ C [75].
2 Linearization strategies
Usually and as deposited MTJs display a squared output
signal, due to the parallel configuration of reference and
sensing electrodes and thus cannot be straightforwardly
used as magnetic field sensors. The reference electrode
magnetization direction is defined by setting the exchange
coupling direction trough annealing in a uniformly
strong magnetic field (> few hundred mT) and several
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ii. external magnetic field biasing created on-chip
(e.g., using integrated permanent magnets or current
line) [77,78] (Fig. 12c, Sect. 2.2);
iii. reduction of the sensing layer thickness until the superparamagnetic limit (e.g., CoFeB thicknesses below
1.5 nm) [79–81] (Fig. 12d, Sect. 2.3) or
iv. use of exchange biasing on the sensing layer, which
upon annealing can be set orthogonal to the reference
layer [62,82,83] (Fig. 12e, Sect. 2.4).
The effects of these strategies in terms of sensitivity,
linearity, noise and magnetic field detection limit need to
be considered in detail in order to choose the best approach for the envisaged application.
2.1 Tailoring the self-demagnetizing field: shape
anisotropy and layer thickness engineering
Fig. 11. Easy axis direction, small field VSM loops for MTJ
unpatterned stacks, showing the sensing layers magnetic response for samples with and without NiFe in the sensing electrode structure. Inset: full range VSM loops for the same two
samples. Current in plane tunneling (CIPT) measurements indicate that TMR remains unaffected at 200% in both types of
c
stacks. [2012] IEEE. Reprinted with permission from reference [62].
strategies can be used to set the magnetization of sensing
layer orthogonal, yielding a linear response (Fig. 12). Some
deposition systems allow a crossed configuration to be set
during deposition (Sect. 1.4 and Fig. 12a). Alternatively
one can either resort to:
i. use of the self-demagnetizing field of the sensing
layer [76] (Fig. 12b, Sect. 2.1);
The self-demagnetizing field of the sensing layer is a key
factor in the linearization of a magnetoresistive sensor,
being therefore important to understand which are the
best sensor geometries. The demagnetizing field (Hd ) of
a magnetic layer is given by the following expression:
∇ · M (r) (r − r )
Hd (r) ≡ d3 r |r − r |3
V
n · M (r) (r − r )
+ d2 r .
(9)
|r − r |3
S
The first integral is over the entire volume (V ) of the magnetic layer while the second integral is over its boundary surface (S) where the magnetic poles distribute, with
(n) the unitary vector normal to each surface. In the
Fig. 12. Summary of linearization strategies for MR sensors.
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A.V. Silva et al.: Linearization strategies for high sensitivity MR sensors
macrospin case: ∇ · M (r) = 0. Assuming that the layer’s
magnetization is always in the sensor plane, its demagnetizing field is also in-plane and magnetic poles are distributed only along its lateral dimensions (width and height).
This self-demagnetizing field, at mid-thickness, can be decomposed in components along those two directions Hd =
Hdh ex + Hdw ey , which can be expressed along the layer’s
half-width and half-height respectively as follows:
⎧
t
w
⎪
2 2
h
⎪
⎪ h
2M
s
⎪
2
⎪
H
≡
−
cos
θ
dzdy,
⎪
d
⎪
h 2
⎪
4π
2 + z2
⎪
+
y
⎨
t −w
2
−
2
2
t
h
⎪
⎪
2 2
w
⎪
⎪
2M
s
⎪
w
2
⎪
H
≡
−
sin
θ
dzdx.
⎪
d
⎪
w 2
4π
⎪
2
⎩
x +
+ z2
t
h
−2 − 2
2
An analytical solution for these integrals, as a function
of sensor’s dimensions was introduced by [84] assuming a
macrospin behavior and W, h >> t:
⎧
t
w
8Ms
h
⎪
⎪
cos θ,
⎨ Hd ≡ − 4π √ 2
2
w +h h
(10)
t
h
8Ms
⎪
w
⎪
⎩ Hd ≡ −
√
sin θ.
4π
w 2 + h2 w
Sensor designing typically takes advantage of shape
anisotropy as the sensing layer is patterned in a rectangular shape, with its longest dimension (width) orthogonal to the reference fixed direction. The higher the
aspect ratio of the sensing layer dimensions (width to
height: w/h ) the more dominant is Hdh , with larger w/h
enhancing the sensor’s linear operating range and lowering its field sensitivity (Fig. 13). The macrospin model
becomes advantageous for the estimation of the best device dimensions afore microfabrication. Figure 14 presents
an example of such estimation, where a systematic size
analysis allows the determination of the aspect ratio value
at which the demagnetizing field surpasses Hk , linearizing the magnetic response (w/h ≤ 50/3) from 2μ0 Hsat =
0.66 mT to 3.33 mT for h = 3 μm to 1 μm, respectively.
The self-demagnetizing field is also proportional to the
saturation magnetization Ms and thickness of the sensing
layer (t) (Eq. (10)). For aspect ratios above 10/1 the de8Ms t
magnetizing field is maximized by − 4πH
and the conk h
dition of no coercivity (Eq. (6)) yields:
h < hthreshold =
8Ms
t.
4πHk
(11)
Figure 15 presents the evolution of Ms and Hk for CoFeB
((Co70 Fe30 )80 B20 ) thin films as a function of layer
thickness (t) from where, using the macrospin model, the
threshold height (hthreshold ) at which a sensor curve
changes from square to linear, was estimated (Eq. (11)).
For example, sensors using 5 nm thick (Co70 Fe30 )80 B20
sensing layers can only have linear curves upon patterning with h values below 1.2 μm, while 10 nm thick are
linear even with h = 2.8 μm heights.
Fig. 13. Transfer curves for patterned MTJ structures with
dimensions w = 20 µm and varying heights. CIPT revealed
average TMR = 200% and RA = 7.6 Ω µm2 . With kind permission from Springer + Business Media: from reference [85].
Fig. 14. Example of macrospin simulation for sensor linearization using shape anisotropy. Same axes definition as in Section 1.4, offset fields values of µ0 HN = −µ0 Hdref = 0.5 mT.
2.2 External biasing
Manipulating the self-demagnetizing field can be insufficient to promote a linear sensor behavior, in particular
when the microfabrication process is not suitable for small
dimensions (h ∼ 1 μm). Moreover, if sensor area is considerably large (requirement of some low noise
applications) [41], the transfer curve often presents
discontinuities. On the other hand, if the sensor area is
significantly small, edge roughness and other local defects
act as low anisotropy sites favoring the creation of localized inverted magnetization volumes which can lead to
jumps in the transfer curve. Applying an external field bias
(Hbias ), transversal to the sensing direction can suppress
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The European Physical Journal Applied Physics
Fig. 15. Ms and Hk experimental values for unpatterned samples of Ta/CoFeB/Ta thin films, annealed for 15 min at 250 ◦ C
under a 1 T field, as a function of layer thickness and corresponding calculated htreshold from the macrospin model. Value
marked with * taken from a MgO-MTJ full stack annealed for
1 h at 280 ◦ C under 1 T.
these effects [87–89] and promote a hysteresis-free curve.
This can either be achieved with an external field or a local
field (on-chip integrated) and can be implemented with a
permanent magnet (PM) or a current line loop. External
field creation is a bulky solution regularly used for experiments optimization toward a final monolithic solution.
For example, on-chip permanent magnet biasing is widely
used in MR read heads. Thin film permanent magnet integration allows for strict control of its dimensions and
hence the magnitude of the created bias field. In contrast
line loops present the disadvantage of needing electrical
feeding and could require extra powering electronics and
thus being scarcely employed.
Figure 16 exemplifies MTJ based sensors with on-chip
PM biasing strategy, where a reduction in Hc from 0.4 mT
to 0.05 mT is visible for an isolated sensor (Fig. 16a). Magnet efficiency depends on the gap spacing, therefore is not
unexpected to see a smaller impact (still, important) in
larger sensors, or when arrays of sensors are used instead
of single elements. Figure 16b shows the impact of PM biasing in arrays of 82 sensors connected in series, through
reducing the (Hc ) from 0.63 mT to 0.19 mT.
For current-perpendicular-to-plane configurations, the
PM elements can be placed above the top electrode, after top metallization deposition (Fig. 17a), avoiding an
extra lithography step. This strategy was successfully validated in reference [78]. To ensure the best field uniformity,
dimensions should be considerably larger than the sensing layer size. Alternatively a pair of PMs can be defined
side by side the top metallization (Fig. 17b). While this
last method requires extra lithography and liftoff steps,
Fig. 16. Transfer curves for patterned MTJ structures with
and without 120 nm thin film Co66 Cr16 Pt18 integrated permanent magnets to create a constant field for device biasing.
Unpatterned films present an average Ms ∼ 100 kA/m and
µ0 Hc ∼ 60 mT. (a) Single MTJ pillar behavior using a PM
pair with 460 × 40 µm2 of lateral dimensions and a gap of
24 µm, producing an average field at mid-sensor of 1 mT.
(b) Array of in series 82 pillars with dimensions of 5 × 20 µm2
enclosed by PM with 1 × 1.2 mm2 lateral dimensions and gap
of 78 µm yielding an average field at mid-array of 1.8 mT.
c
[2012] IEEE. Reprinted with permission from reference [86].
it provides a far better field uniformity (created at gap)
than the single PM or a loop line. The field created by the
PM at the sensing layer can be calculated by equation (9),
dependent on the PM magnetization, dimensions and gap.
Although somehow difficult to achieve precise values for
the PM field strength at sensors with large area, Figure 18
illustrates the clear impact of PM in the sensor coercivity.
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A.V. Silva et al.: Linearization strategies for high sensitivity MR sensors
Fig. 18. Statistical analysis on the coercivity values (µ0 Hc ) of
MTJ patterned structures as a function of sensor area. With
kind permission from Springer + Business Media: from reference [85].
Fig. 17. Common on-chip PM biasing configuration.
(a) One PM at top electrode (b) PM pair side by side with
top lead.
The linearization effect of (Hbias ) can be studied by energy minimization analysis, adding an extra energy term:
sen
Ebias
= μ0 Mssen Hbias sin θ,
V sen
to equations (5) and (7) of the macrospin model
(Sect. 1.4). Figure 19b presents a systematic study on
sensor curve coercivity with increasing external field bias,
transversal to sensing direction, where above μ0 Hbias =
0.9 mT a linear curve is achieved. Chaves et al. have
also showed that a further increase in the bias strength
can in particular cases lead to lower noise density at lowfrequencies [90]. However this noise reduction happens at
the cost of sensitivity (Figs. 16 and 19a) and the net effect
will be an increase in the sensors detection limit. When
the MR sensor application targets low field detection the
best compromise is the lowest bias field possible, strong
enough to linearize the MTJ and stabilize the sensing layer
magnetic configuration.
2.3 Ultrathin sensing layer
On-chip biasing enlarges the final device dimensions, so
if small footprint is a requirement other strategies should
be considered. A different approach uses a CoFeB sensing layer thin enough to have granular film structures
that in the limit present a superparamagnetic (SPM) like
Fig. 19. Example of macrospin simulation for sensor engineering using a external field bias. Same axes definition as in
Section 1.4, sensor dimensions w = 50 µm and h = 50 µm,
offset fields values of µ0 HN = −µ0 Hdref = 0.5 mT. (a) Normalized sensitivity evolution of linearized curves with Hbias .
(b) Coercivity of sensor response as function of Hbias . Inset:
sensor curve evolution from hysteretic to linear.
behavior. These structures can be used to achieve linear hysteresis-free responses, with simple designs and low
power consumption (no external biasing element), without
the requirement of large aspect ratios.
In ultra-thin sensing layers at CoFeB/MgO/CoFeB
stacks the perpendicular anisotropy at the sensing layer/
tunnel barrier interface leads to an out-of-plane anisotropy
component which will compete with the existent in-plane
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anisotropies [79]. The latter can result in a linear response
to in-plane magnetic fields [80,81]. Figure 20a shows the
progress of patterned MTJ transfer curves with decreasing sensing layer thickness. The latter presents simultaneously both types of responses, sharp hysteretic ones with
TMR values up to ∼200% (t > tcritical ) and linear responses with TMR values down to 40%, translating the
thin CoFeB evolution from the ferromagnetic to the SPMlike regime (t ≤ tcritical ). This transition is also illustrated
in the inset of Figure 20a with the abrupt drop in coercive field at tcritical ∼ 1.45 nm which is in accordance with
other reported values [79–81,92–94]. Tsai et al. estimated
∼23 nm as the average lateral size of the ferromagnetic
particles at the sensing layer [94] while Shen et al. obtained 40–120 nm [95] which for the given tcritical implies
that the clusters have a pancake-like shape. For t ≤ tcritical
a linear response is always present, independent of junction area (Fig. 20b) [92]. The dramatic decrease in TMR
is attributed to weakening of ferromagnetic order in the
sensing layer, as the barrier conductance is proportional
to the magnetization component along the applied field,
being the magnetic moment of the clusters and the layer
thickness highly correlated [95].
When sensitivity is a key factor for the sensing application at hands the best thickness choice is the closer to
tcritical possible (t ∼ 1.5 nm), since it combines a linear
hysteresis free response with the best sensitivity attainable: 103%/mT and linear range of μ0 ΔHlinear = 0.4 mT
(Fig. 20a). On the other hand, when the sensor key factor is a large linear range, a smaller thickness is required
(t < tcritical ), e.g., for t = 1.4 nm a μ0 ΔHlinear = 6 mT
with 4%/mT is obtained (Fig. 20a). Zeng et al. reports
wider ranges obtained with nano MTJs, with optimum
values of μ0 ΔHlinear = 60 mT and 0.2%/mT [80].
In this ultra thin CoFeB layers, even for temperatures
below the blocking temperature the thermal ambient energy is sufficient to change the magnetization direction
of the grains [94]. The resulting relaxation of magnetization orientation causes the magnetic moment of the entire grain to align with any applied magnetic field. This
strategy is therefore advantageous when both in-plane and
out-of-plane field sensing is required. Teixeira et al. showed
35%/mT of sensitivity and linear range of μ0 ΔHlinear =
0.75 mT for in-plane detection and μ0 ΔHlinear = 1.6 mT
and 4%/mT for out-of-plane fields, employing micrometric
MTJs.
Moreover noise measurements showed negligible magnetic noise in the sensitive region for SPM-like thicknesses
which partially compensates the associated sensitivity loss
for lower frequency signals. However at higher frequency
ones, the sensitivity decrease causes significant reduction
in the signal-to-noise ratio of the devices [92], and thus distinct strategies to recover the sensitivity are necessary
(Sect. 3.1).
2.4 Soft exchange biasing of the sensing layer
MTJ with stack incorporated sensing layer biasing,
usually consisting of a soft pinned sensing layer, have the
Fig. 20. Magneto-transport characterization for 100×100 µm2
patterned MTJ circles with varying sensing layer thickness
(t). (a) Transfer curves. Inset: Corresponding coercive fields
as function of t. (b) TMR as function of t. Reprinted with
c
permission from reference [91]. [2008], AIP Publishing LLC.
advantage of providing linear MR devices, without resorting to shape anisotropy or external biasing. This strategy
is capable of yielding competitive sensitivity values, allowing a device footprint controlled only by the area of the
MTJ (no additional structures), which can also be crucial for low detectivity applications (large area sensors;
Sect. 3.2).
These multilayer stacks include two AFM films: one
next to the pinned layer and another adjacent to the
sensing layer. Both AFM layers set the magnetization of
the FM layers in a fixed direction by exchange bias
(Fig. 21). However the exchange field (Hexch ) of the sensing layer must be small as it will define the sensor saturation field and consequently its sensitivity. The exchange
10601-p12
A.V. Silva et al.: Linearization strategies for high sensitivity MR sensors
Fig. 21. Typical double exchange-pinned electrodes device
structure. Arrows refer to magnetization orientation of layers
at low fields.
Fig. 22. Schematic view of SAF reference and soft-pinned
sensing electrodes magnetization after the consecutive annealing steps. Arrows refer to magnetization orientation of layers
at low fields.
coupling strength is set by an adequate choice of antiferromagnet and adjacent ferromagnetic layer [96].
In order to set the sensing and reference electrodes
magnetization orthogonally it is required that both exchange coupled interfaces have different temperature stabilities. The exchange bias vanishes above the blocking
temperature (Tb ), being close to the Neel temperature
(TN ) for thick AFM films with large grain sizes, while for
thin films Tb << TN due to finite size effects [97]. Therefore, the Tb value is not characteristic of the material but
depends on the AFM thickness [62,97]. To have different
Tb values for bottom reference (TbRL ) and sensing electrode (TbSL ), such that TbRL > TbSL , one can either resort
to different AFM materials or use the same material with
different thickness.
Through consecutive annealing steps under orthogonal in-plane magnetic fields at different temperatures, the
crossed configuration between the magnetization of reference and sensing layers is then defined [62,82,83,98].
The first annealing, performed at higher temperature, sets
both AFM fixed layers magnetizations in the same direction, while the second annealing step at a lower temperature sets the soft pinned sensing layer magnetization at a
perpendicular direction to the bottom one (Fig. 22).
Since the linear operation range (defined by saturaSL
tion fields) is dominated by Hexch
, for applications requirSL
can be achieved
ing high sensitivity a reduction in Hexch
by increasing the distance between the coupled layers,
by inserting a thin non magnetic metallic layer between
the FM and AFM. As its thickness increases, the linear
Fig. 23. (a) Sensitivity of double exchange MTJ circular pillars as function of sensor radius, with average values of TMR
(∼190%) and RA (∼17 Ω µm2 ). (b) Transfer curves for two
different radius.
operating range decreases [62,83], allowing a sensitivity
improvement. The sensing layer is thereby weakly pinned
when compared with the reference one.
Figure 23 shows data for a stack with 2 Å thick Ru
layer between sensing layer and AFM where an average
of μ0 ΔHlinear ∼ 0.6 mT and a sensitivity of 28%/mT is
obtained, being mostly independent of sensor area. The
difference in exchange bias strength between reference and
sensing electrodes was achieved by employing different adjacent ferromagnetic layers, IrMn/CoFe for the bottom
pinned layer and NiFe/Ru/IrMn for the sensing layer. Orthogonality between electrodes was created with consecutive annealings, the first at 330 ◦ C under 1 T during 2 h
and a second at 150 ◦ C, 20 mT for 1 h. All patterned MTJs
had circular symmetry and areas as high as 4072 μm2 fabricated without loss of linearity nor sensitivity, which is
advantageous for low field detection applications (Sect. 3).
This double exchange stacks have also been demonstrated as a successfully approach for nanosensors, where
the effect of the stray fields dramatically increases. Nanometric circular MTJs with μ0 ΔHlinear ∼ 40 mT and sensitivities of (∼3%/mT) were obtained with the use of a
CoFe/CoFeB/Ta/NiFe/MnIr sensing layer. Their sensitivity is almost size independent consistent with a linear
operation range dominated by the exchange field
strength [42].
3 Towards pTesla detection with MTJ sensors
3.1 Sensitivity control using magnetic flux
concentrators
Particular applications require enhanced sensitivity alongside low field detection at low operating frequencies.
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Fig. 24. (a) Finite element method representation of magnetic
flux lines concentration using MFCs, (b) schematic representation of the MFC geometry and respective integration in the
MR device with patterned pillar, bottom contact and passivation oxide.
Placing MR sensors within the gap of magnetic flux concentrators (MFC) leads to a strong sensitivity enhancement, yielding field gains of manifold. MFCs are usually
made of soft ferromagnetic layers, e.g., NiFe [99], amorphous Co-based alloys [100,101]. These structures are patterned with particular shapes which lead to concentration
of the magnetic flux density within the gap where the sensor is placed (Fig. 24a).
The effective MFC gain (G) in magnetic field corresponds to the ratio of the magnetic field measured at the
gap (Bgap ) and the external applied field (Bext ):
G=
Bgap
.
Bext
(12)
G depends on the intrinsic magnetic properties of the
MFCs (e.g., permeability), and also on its geometric parameters. It increases linearly with the longitudinal length
(L) of concentrators, depends on the yoke and pole crosssection ratio and is inversely proportional to the gap (g).
Therefore an optimization of geometry and material characteristics is required to control the final full device footprint yielding optimized detectivity.
Figure 25 presents data for Co93 Zr3 Nb4 (CZN)
∼ 8600 Å thick films, patterned with a funnel shape separated by a gap where the MTJ is placed (Fig. 24b).
The sensor – MFC pole separation is fixed at 1.5 μm
and pole dimension is equal to pillar diameter. The CZN
films are deposited under 10 mT to set the magnetic
easy axis perpendicular to the measurement direction,
leading to a linear B(H) dependence (μ0 Hc ∼ 0.1 mT)
with linear range of (±2 mT) and μr = 841 (hard axis).
MFC with four different dimensions were adopted (inset
of Fig. 25a).
The effect of MFC1 in the magnetotransport curve of
a 15 μm radius MgO-MTJ pillar, with soft-pinned sensing
layer is presented in Figure 25a, where the reduction of
2μ0 Hsat from 7.2 mT to 1.3 mT is clear, causing a sensitivity enhancement with a gain factor of 5.1, reaching
the maximum value of 155.2%/mT. Upon MFC inclusion
an evident sensitivity decrease was continuously observed
when the sensor area increases, with MFC gain decreasing from 6.7 (radius = 10 μm, sensitivity of 180.4%/mT)
to 3.0 (radius = 36 μm, sensitivity of 84.5%/mT), corresponding to a reduction of ∼54%. The gain reduction can
be mainly explained by the increasing gap distance with
sensor dimensions, leading to an accentuated dispersion of
the field lines hence less efficient concentration.
Figure 25b compares the sensitivity evolution of fabricated sensors upon integration in the four different sizes of
MFC. For all MFC dimensions a decrease in gain with increasing gap dimension is observed, yielding the expected
reduction in sensor sensitivity. For all the characterized
sensors the MFCs do not increase sensor coercivity. The
integration of MFC with larger dimensions yields larger
sensitivities: 84.5%/mT (G = 3.0) for MFC1, 102.1%/mT
(G = 3.7) for MFC2, 122.3%/mT (G = 4.4) for MFC3 and
(G = 5.3) 147.4%/mT for MFC4 when compared with the
value obtained for the same sensor (radius = 36 μm) with
no MFC (27.8%/mT).
On the other hand, a distinct strategy using thick
MFCs with tapered profiles led to a noticeable flux increase at the sensor level [102], further strengthening the
possibility of reaching sub-nT/Hz limit in field detectivity.
Nevertheless, thicker than few nm MFCs, are more prone
to local fluctuations in composition [103] and stress [104],
and may lead to an additional out-of-plane anisotropy contributions to the system. This effect is enhanced when
microfabricated structures are considered, thus potentiating the appearance of complex magnetic domain structures at the MFCs poles, originating discontinuities and
hysteresis in the sensor response [105]. To overcome these
drawbacks synthetic-antiferromagnet (SAF) structures
consisting of multilayers alternating a ferromagnetic
material with a non-magnetic spacer, can be used as
MFCs [102]. In SAF-MFCs, the antiferromagnetic coupling between layers helps stabilizing the monodomain
state and leads to an almost zero net magnetic
moment [102,105,106]. Such configuration promotes an
improved linear response and potentiates lower magnetic
contributions to the noise level of the MR sensor, with
the drawback of smaller magnetic permeability and hence
lower gains.
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A.V. Silva et al.: Linearization strategies for high sensitivity MR sensors
the magnetization state is changing) [108,109]. For low
frequencies, D can be expressed by [76]:
ΔH
αH
αH
1
=
(13)
D=
S A×f
TMR A × f
Fig. 25. Double exchange MgO-MTJ sensors sensitivity enhancement using MFCs. (a) Comparison of transfer curves for
15 µm radius with and without MFCs. Inset table: dimensions
of MFCs types. (b) Comparison of sensitivity for diferent MFCs
as a function of sensor area and MFC gap.
3.2 pTesla detectivity levels
The total noise of a MTJ sensor has distinct contributions
from thermal, shot, random telegraph and 1/f electric and
magnetic components, being the overall equation given by
reference [107]. The minimum detectable field (D) of a
sensor corresponds to the minimum value of applied field
which causes a voltage output equal to the sensor intrinsic
noise level (SV ). Therefore, to detect magnetic fields in
the pTesla range a sensor with large signal-to-noise-ratio
(SNR) is required, combining high sensitivity values with
low noise levels. However, in the low frequency range the
sensor SV is dominated by the 1/f component. The latter
limits the field detection level and is considered to enclose
an electric and magnetic component [108]. The magnetic
part arises mainly from oscillations in the magnetization
of the sensing layer, resulting from domain-wall pinning
and depinning at defect sites (i.e., being maximum when
being S the sensor sensitivity at the operating point, A the
magnetic area of the sensor, f the operating frequency and
αH the phenomenological Hooge’s parameter. Thereby,
the detection level improvement implies: (i) a higher sensitivity steeper magnetotransport curves, (ii) large
sensing area and (iii) low αH value. Figure 26 shows the reported αH values dependence on the resistance-area product (RA) comparing obtained data for sensors at operating
point for simple and soft pinned sensing layer stacks (textured CoFeB/MgO/CoFeB structures including a pinned
reference layer). Overall, and for similar RA values, lower
αH values are obtained for stacks with simple sensing layers when compared with soft pinned sensing layer stacks.
This difference translates into lower noise levels. These
data are framed with reported values for AlOx (squares)
whose noise was measured in the saturation state (i.e.,
in the absence of local magnetization fluctuations), giving a baseline for electric noise in MTJs. For additional
reference, αH values for devices optimized for memory
applications, employing different strategies for noise level
reduction, are addressed. In all cases only saturated states
of hysteretic curves are studied. For micron sized MgO
memories, Stearret et al. reported αH = 1.3 × 10−6 μm2
higher then our typical values of ∼10−8 μm2 for RA ∼
tens of kΩ μm2 [110]. For nanometric memories, Herranz
et al. obtained a αH ∼ 6 × 10−10 μm2 [111], increasing
to αH = 3 × 10−8 μm2 [112] when a soft pinned sensing
layer was used, in line with our presented results [113].
Interestingly, Yu et al. showed that a double barrier of
CoFeB-MgO MTJ presents slightly lower hooge values
(αH = 1.2 × 10−10 μm2 with RA = 150 kΩ μm2 ) than
single barrier MgO-MTJs, resembling two single MTJ in
series, hence providing improved signal to noise ratio
under lower bias voltage [114]. Overall, lower αH
∼ 10−10 μm2 (∼40 kΩ μm2 ) values are achieved with single crystalline Fe/MgO/Fe MTJs [115], although for 12
monolayers of MgO a similar increase of αH to 10−5 μm2
was reported [116]. In the latter case, where MgO thickness reaches or overcomes the critical value of Fe lattice matching, C-doping is effective in decreasing αH to
109 −10−10 μm2 , hence decreasing the low frequency noise.
This can give an alternative tool to tune MgO junctions
for low frequency applications [116,117].
Figure 27 compares the detection levels as function
of the sensing area obtained with different sensor layouts
(single isolated sensors, arrays of sensors in series, or including MFCs) and also considering distinct types of MTJ
stacks namely enclosing simple, SPM-like and soft-pinned
sensing layers. Although the use of a soft-pinned sensing
layer is an effective strategy to linearize sensors without
increasing device footprint, detectivity values two orders
of magnitude higher than those achieved using single sensors with simple sensing layers (∼ tens of pTesla) [85,90]
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Fig. 26. Hooge parameter for MTJ sensors as a function of RA. Comparison between MgO and AlOx barrier
structures. AlOx-MTJ data obtained with devices at saturation from references [119–122]. CoFeB/MgO/CoFeB-MTJ data
obtained at operation point. Data marked with i from references [119, 123, 124] and ii is unpublished data from INESCMN; * from reference [90]; + from reference [85]; & from reference [42]; α from reference [118]; β from reference [125];
δ is unpublished data from INESC-MN; σ from reference [41];
γ from reference [83].
Fig. 27. Detectivity levels for soft-pinned sensing layer MTJ
sensors as function of sensing area (at 30 Hz) framed with reported values for simple and SPM-like sensing layer structures.
Comparison between single sensors (solid shapes) and sensors with integrated MFCs (half-right shapes). Square shapes
represent data for micrometric structures from reference [41],
either individual circular sensors (radius of 10, 28 and 36 µm)
or series of 952 square sensors (50 × 50 µm2 each); pentagonal shape from reference [83] measured at 10 Hz; left-triangle
shape from reference [125]; right triangle shape from reference [118] whereas star shape represents data for nanometric circular MTJ pillars (radius 200 nm) from reference [42].
Simple sensing layer data from reference [90] (upward triangle) and [85] (downward triangle), and SPM-like sensing layer
results from reference [92].
were systematically obtained by different authors. The
limitations in decreasing further the minimum detected
field of soft-pinned stacks is most probably a consequence
of higher intrinsic noise present in these stacks, resulting
from magnetic fluctuations at the sensing layer, due to
the adjacent antiferromagnet [113]. In fact, a consistently
higher noise level was also measured at the pinned layer inversion point when compared to the sensing layer in MTJ
stacks [83,113].
To effectively decrease the detection level of sensors,
one can also work on increasing the sensor sensitivity.
In this case, when MFCs are incorporated at the sides
of single sensors, a detection level enhancement is observed, resulting from the linear operating range reduction (Sect. 3.1). Alternatively, using sensors connected in
series, the detection level improves (compared to √
a single
sensor), since the noise level increases by a factor N and
the sensitivity improves by a factor N,
√ resulting in a final total improvement proportional to N [61][118]. Both
strategies have the drawback of increasing the final device
footprint, but can be very effective in the detection level
enhancement.
4 Conclusions
This paper reviews the different linearization strategies
available for TMR sensing applications discussing in detail
their implications on the final sensor performance with
particular emphasis on sensitivity and detection levels.
The linear behavior of MTJs can be engineered with
shape anisotropy providing high aspect ratios can be employed and yielding coercive fields lower than 0.1 mT (e.g.,
for a 20 × 2 μm sensor). In specific applications an external bias field transverse to the sensing direction can
promote an hysteresis free curve. Alternatively, ultrathin
CoFeB sensing layers close to a SPM-like magnetic behavior can also result in a linear response to in-plane magnetic
fields. In this case, sensitivity values of ∼100%/mT were
achieved combined with linear ranges of 0.4 mT but at
the cost of considerable TMR loss. On the other hand,
MTJs with a soft pinned sensing layer have the advantage of providing linear devices without resorting to shape
anisotropy nor external permanent magnets biasing. This
route allows a small device footprint or large sensing areas still displaying a linear behavior. An average sensitivity value of 30%/mT was obtained for MTJ pillars with a
wide range of dimensions (radius from 10 μm to 36 μm)
without TMR loss.
To further strengthen the advantages of TMR sensors
we focus on their applications to pTesla detection where
linear behaviors with enhanced sensitivity and low noise
levels at low frequencies are necessary. To achieve these
challenging performances, additional structures such as
soft ferromagnetic flux concentrators are included in the
chip design. For very large area sensors (1530 μm2 ) 5 times
amplified√sensitivities with the lowest detection levels of
∼40 pT/ Hz at 30 Hz were reported for CoFeB/NiFe free
10601-p16
A.V. Silva et al.: Linearization strategies for high sensitivity MR sensors
layer MTJs. These results outlook MTJ sensors application to biomedical imaging at room temperature and
reinforce the position and versability of magnetoresistive
sensors.
The authors would like to thank R.M. Pinto for his contribution in the graphical editing of the document. A.V. Silva and
D.C. Leitao thank FCT for grants SFRH/BD/1719751/2010
and SFRH/BPD/72359/2010. Work partially supported by
projects MAGNETRODES (EU-FP7-ICT-600730), EXCL/
CTM-NAN/0441/2012 and PTDC/EEI-PRO/3219/2012.
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10601-p19
The European Physical Journal Applied Physics
Ana V. Silva (born 1980) received her M.Sc. degree in Engineering Physics from Instituto
Superior Técnico (IST) of Universidade de Lisboa in 2010, with topic “Analytical modeling of the stress-strain distribution in a multilayer structure with applied bending”, in
collaboration with ECTM (TuDelft – Netherlands). She is currently a PhD student at
INESC-MN and IST. Her work focus on Nano Magnetic Oscillators, based on low resistance
MgO tunnel junctions. Main research areas include magnetoresistive devices for sensing and
high frequency applications, device modelling, micro and nanofabrication in IC technology.
Dr. Diana C. Leitao (born 1983) graduated in Applied Physics from Universidade do
Porto in 2005, and received her Ph.D. in Physics by the same institution in 2010, on the
topic of “Fabrication and characterization of magnetic nanowires and antidots grown using
nanoporous alumina templates”. Currently she is a post-doctoral fellow at INESC-MN and
an Invited assistant professor at the Physics Department of IST, being the co-author of more
than 40 papers (researcher ID: C-5125-2009). Her research interests include the development
and optimization of nanofabrication processes, electron beam lithography, the fabrication of
nanoscale magnetoresistive sensors, and magnetic and magnetotransport characterization of
nanostructures and nanodevices.
Prof. Paulo P. Freitas (born 1958) received his Ph.D. in Solid State Physics from Carnegie
Mellon University in 1986, followed a postdoctoral stay at IBM Watson Research Labs. He
has been a Full Professor at the Physics Department of IST, the leader of the Magnetics &
Spintronics group and Director of INESC-MN. Since 2009 he joined the International Iberian
Nanotechnology Laboratory (INL – Braga) where he is a deputy director. He received several
awards and distinctions related to his work on magnetoresistive biochips and bioelectronics,
magnetoresistive sensors, MRAMS, and read heads for ultra high density recording. He is
author of more than 350 scientific articles, two patents and inventor of a bioelectronic device. Prof. Freitas supervised 17 Ph.D. students, more than 20 post-doctoral fellows, and
develops an intense educational mission to train and coach new scientists and engineers.
Prof. Susana Cardoso de Freitas (born 1973) is a senior researcher at INESC-MN and the coleader of the Magnetics & Spintronics group at INESC-MN and also an Associated professor
at the Physics Department of IST. She is co-author of over 200 publications (researcher ID:
B-6199-2013). Since her PhD defence in 2002, she has coordinated several national projects
and participated in several EU projects. She is responsible for student training and for services provided by INESC-MN to external partners. Her research interests include advanced
thin films in large area wafers and optimization of magnetoresistive sensors for challenging
applications.
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