6. TMR-TYPE MAGNETIC BIOSENSOR
6.3. Sensor characteristics
Chapter 6: TMR-type magnetic biosensor
connected to large contact pads through holes in the insulating glass layer, so that two-point measurements of single TMR elements can be carried out between the common lower electrode and a specific upper electrode contact. The entire sensor layout is shown in Figure 76. To the right, the topography across a single sensor element is explicitly displayed along the dashed line above the SEM micrograph. In order to bring the free magnetic layer as close as possible to the fluid interface, the hole in the insulating glass layer is expanded over as much of the sensor surface as allowed by lithographic restrictions. But apart from that middle area with a diameter of 30 µm, there are also two rings with larger distances of the free magnetic layer to the fluid interface (width = 5 µm each). The subdivision of the total sensor area to the three different distances is shown in column 2 of Table 9, which leads to an area weighted average distance of 339 nm. As the strength of a marker’s stray field in the sense layer strongly depends on this distance (chapter 3.2.1), the signal produced by a marker depends on its respective position on the sensor surface. This is illustrated in column 3 of Table 9 for the maximum in-plane stray field component of a Bangs 0.86 µm particle with an out-of-plane magnetic moment of 20.6 fAm2. At the largest distance, the stray field only reaches about 2/3rd of the maximum value for a particle situated in the sensor’s center. For smaller markers, those differences get even larger. In an optimized sensor design, such topography variations should be avoided.
distance interface-sense layer
[nm] sensor area at this distance
[µm2] maximum stray field of a Bangs 0.86 µm marker [A/m]
300 707 3620 330 707 3210 400 550 2470 Table 9: Subdivision of a sensor for the different distances of the sense layer to the interface
be different from the bulk values. Also, uncorrelated roughness contributions at the interface lead to thinner barriers at some localized spots. Due to the exponential thickness dependence of the tunneling current, those thinner regions dominate the transport and lead to an effectively thinner barrier. The same reasoning holds true for metallic impurities within the barrier, which present islands for the tunneling electrons.
Concerning the barrier height, the bandgap of Al2O3 is about 8.7 eV (Ref. 234). Since the Fermi energy in undoped insulators is situated in the middle between the valence and the conduction band, the maximum barrier height is half the bandgap, i.e. 4.35 eV in this case. According to the Brinkman fit, it only reaches 72 % of this maximum value for our barriers, which can be due to a number of reasons. First of all, the cited bandgap is for crystalline Al2O3, which is certainly not the case for our barrier. Its structure is amorphous, which leads to a reduced bandgap. Also, the simplified model of Brinkman does not take into account the effect of image forces on the tunneling electrons, which round off the corners of the barrier and make it lower and narrower (Ref. 214; Ref. 216).
-0,5 -0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5 110
115 120 125 130 135 140 145 150 155
data fit
specific conductance [nA / (V µm2 )]
bias voltage [V]
(b)
-0,5 -0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5 -60
-50 -40 -30 -20 -10 0 10 20 30 40 50 60
specific current [nA / µm2 ]
bias voltage [V]
(a)
Figure 77: Electrical characterization of the tunneling barrier a) specific current curve
b) specific conductance curve
In any case, the values for the height, thickness and asymmetry of the barrier agree pretty well to the references for optimum barriers from other work on similar systems (Ref. 123; Ref. 235; Ref. 236). With respect to the resistances and TMR ratios, a group of 15 individual elements on a sensor chip is analyzed at a bias voltage of 10 mV. The area resistances range from 8.71 to 9.75 MΩµm2 in the parallel state (mean:
(9.20 ± 0.36) MΩµm2), and the TMR ratios vary between 44.2 and 48.3 % (mean:
(46.6 ± 1.4) %). The relatively large distribution of these values has its origin in spatial variations of the film properties across the sensor chip, where the TMR elements are situated within an area of 2 x 10 mm2. Still, the values agree to the expectations for this particular layer system (Ref. 123).
Exemplary magnetotransport measurements are shown in Figure 78. Part a) displays a major loop taken with the field applied parallel to the pinning direction. While the free Py layer switches its magnetization direction around zero field, the Co70Fe30
layer is pinned to the antiferromagnet Mn83Ir17 and has its hysteresis loop shifted by the exchange bias field HEB, which has a magnitude of about 64 kA/m. Due to the large exchange bias, a stable antiparallel alignment of the magnetization vectors of the two ferromagnetic layers is reached between the parallel orientations, which guarantees that the sensor resistance varies by the full magnitude of the possible TMR ratio (respective magnetization vectors indicated by arrows). According to Equation 33, an exchange bias of 64 kA/m corresponds to an area specific
Chapter 6: TMR-type magnetic biosensor
anisotropy energy constant kEB of 0.40 mJ/m2 (MSCoFe=1650 kA/m, Ref. 237), which agrees well to the respective literature (Ref. 238).
Figure 78: Magnetotransport measurements of spherical TMR sensor elements with a diameter of 50 µm
a) major loop b) minor loop
Part b) of Figure 78 shows corresponding minor loops of a sensor element. When the field is applied in the direction of the cooling field, the orange peel coupling causes a ferromagnetic pinning of the free Py layer to the exchange biased Co70Fe30 layer. In our case, the pinning field HP has a magnitude of about 1.6 kA/m. Theoretically, the strength of HP is given by Equation 36, a sketch of which is shown as a function of the free magnetic layer thickness tF in Figure 79. Here, perfectly correlated sinusoidal roughness with an amplitude h of 0.4 nm and a wavelength λ of 20 nm is assumed (values taken from the measurements on similar systems in Ref. 123). The red curve represents the total pinning field HP, which takes on a value of 1.5 kA/m at a free layer thickness of 8 nm, thus corresponding rather well to the experimental results.
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 8,5
9,0 9,5 10,0 10,5 11,0 11,5 12,0 12,5 13,0
0 5 10 15 20 25 30 35 40 parallel 45
perpendicular to pinning direction
area x resistance [MΩ µm2]
in-plane magnetic field [kA/m]
HP
TMR [%]
-100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 8,5
9,0 9,5 10,0 10,5 11,0 11,5 12,0 12,5
0 5 10 15 20 25 30 35 40 45 50
area x resistance [MΩ µm2 ]
in-plane magnetic field [kA/m]
HEB
TMR [%]
(a) (b)
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
total pinning field HP only 1/tF contribution
magnetic field [kA/m]
free layer thickness [nm]
factor 1-exp(-2π sqrt(2) tF / λ)
factor from free layer exp. contr.
Figure 79: Dependence of the pinning field HP on the thickness tF of the free magnetic layer
In order to point out the different contributions in Equation 36 to the total pinning field, the blue curve in Figure 79 shows the 1/tF prefactor and the black one the 1-exp contribution. Even though the 1-exp expression alone would cause an increase of HP
with increasing tF, this effect is counterbalanced by the 1/tF term, resulting in a monotonous decrease of HP with increasing tF. This dependence has also been observed experimentally by fabricating TMR sensors with different free layer
97
thicknesses. Although HP can be compensated by an in-plane bias field, from an application point of view it is preferential that the sensitive region of the TMR characteristic is as close to zero field as possible. In this case, it might be possible to do without such an additional bias field when using those sensor systems for the detection of magnetic markers. Thus, the thickness of the free magnetic layer was chosen to be comparably large for our sensors (8 nm, see chapter 6.2).
Returning to part b) of Figure 78, the red curve shows the dependence of the sensor resistance on an in-plane field which is applied perpendicular to the pinning direction.
In this case, half the maximum TMR value is expected if the magnetization of the free layer would follow the field while the magnetization of the hard layer would stay pinned to the antiferromagnet (see Equation 31 for θ = 90°). However, due to the anisotropy induced by the antiferromagnet, this field direction is the hard axis for both magnetic layers, so ideally, both magnetization components increase linearly with the magnitude of the perpendicular field. The only difference is the strength of the anisotropy (direct exchange coupling for the pinned layer and orange peel coupling for the free layer), which causes the magnetization of the free layer to rotate more quickly. Therefore, no perpendicular configuration is achieved, and the TMR ratio reaches a maximum below TMRmax / 2. For higher fields, the angle between the two magnetization vectors decreases again, and with it the TMR ratio.
In order to quantify this effect, a simple Stoner-Wohlfarth model (Ref. 239) of the free (index F) and the pinned (index P) layers with magnetic moments mF/P is applied. It only includes the Zeemann and the anisotropy energy terms:
F/ P 0 F/ P F/ P 0 F/ P F/ P
E (H)= −µ m H cosθ −K cosφ = −µ m H cosθ −K sinθ Equation 37 Here, H is the magnitude of the applied in-plane field (the respective directions and
angles are sketched in the inlet of
Figure 80 a). According to chapter 6.1.4, the area specific anisotropy energies kF/P = KF/P / A can be expressed by:
F 0 F F P
P 0 P P E
k M t H
k M t H
= µ
= µ B
B
Equation 38
For both ferromagnetic layers, the orientation of the magnetization vectors MF/P is obtained by minimizing the total energies EF/P. As a result, the angles ΘF/P between MF/P and H are given by:
( )
( )
F P
P E
θ arctan H / H θ arctan H / H
=
= Equation 39
As sketched in part a) of
Figure 80, ΘF decreases much faster than ΘP (values of HP and HEB chosen according to the data described above). The maximum difference between the two angles is obtained at a field around 10 kA/m, but reaches only a value of 72°.
Therefore, according to Equation 31, the best TMR ratio achievable in this configuration is limited to 35 % of the maximum value. The simulated dependence of the TMR ratio on the strength of the field perpendicular to the pinning direction is compared to the measured values in part b) of
Chapter 6: TMR-type magnetic biosensor
Figure 80. Within the scope of this simple model, the two curves agree well to each other. The hysteresis in the measured curve is most probably caused by a slight misalignment of the applied field from the hard direction.
0 5 10 15 20 25 30 35 40
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35
data simulation
normalized TMR
in-plane field H [kA/m]
0 20 40 60 80 100 120 140 160 180 200 0
10 20 30 40 50 60 70 80 90
free layer pinned layer
angle between H and M [°]
in-plane field H [kA/m]
H M
K Θ
Φ
(a) (b)
Figure 80: Stoner-Wohlfarth model for a TMR characteristic with the field applied perpendicular to the pinning direction
a) angles
b) comparison of the normalized TMR to the data
Since the in-plane stray fields of the magnetic markers are radially symmetric when magnetized perpendicular to the plane, the actual response of our TMR sensor can be regarded as the average between its characteristics parallel and perpendicular to the pinning direction. Thus, a signal is expected even without a bias field that compensates for HP.