5. GMR-TYPE MAGNETIC BIOSENSOR
5.4. Detection of magnetic markers
5.4.3. Dependence of the sensor signal on the marker coverage
Chapter 5: GMR-type magnetic biosensor
should be considered as nothing more than a suitable tool to gain effective comparable data from the raw measurements. These adjustments are carried out for all measurements with a fixed protocol and could easily be integrated into an automated signal analysis for an actual product.
-40 -30 -20 -10 0 10 20 30 40
0 50 100 150 200 250
300 two reference elements - saturated + saturated 5 % Bangs 0.86 µm - reference
- saturated + saturated
output voltage diff. amplifier [V]
out-of-plane magnetic field [kA/m]
-40 -30 -20 -10 0 10 20 30 40
0 50 100 150 200 250 300
two reference elements - saturated + saturated 5 % Bangs 0.86 µm - reference
- saturated + saturated
output voltage diff. amplifier [V]
out-of-plane magnetic field [kA/m]
(a) (b)
Figure 61: Comparison of initial and compensated differential signals a) differential raw signals
b) compensated differential signals
simple model is developed that only takes into account the strength of the induced stray field and consists four straight sense lines only. According to the real system, the stripes have equal widths and spacings of 1 µm each. As sketched in Figure 62, the position of a single microsphere is varied between the centers of the two inner stripes. For each position, the average induced in-plane stray field is calculated within all four stripes. The total section area of (7 µm)2 is large enough to ensure that most of the marker’s stray field is enclosed for all of its positions. The marker’s moment m is assumed to be dipole-like with its origin at the microsphere’s center. It is oriented out-of-plane and has a magnitude according to line 8 of Table 4. Thus, the average induced in-plane magnetic field H in stripe number i is given by:
i i i 3 2 5/ 2
i
1 1 m 3
H dA H(A ) with H and
A 4 d 1
r d
= = ξ
π + ξ
∫
ξ = Equation 19Here, Ai denotes the area of sensor line number i, r resembles the horizontal distance between the microsphere’s center and an integration point in one of the sensor lines, and d is the vertical distance between the center of the microsphere and the plane of the sensor. The latter value depends on the mean diameter of the particle, which was chosen according to the values given in line 5 of Table 2 and the thickness of the passivation layer (see chapter 4.1). The integration across the sensor stripes for the different microsphere positions was carried out with the help of a MATLABTM program with a mesh size of (20 nm)2. The distance between the different microsphere positions is also set to 20 nm.
2,6 2,8 3,0 3,2 3,4 3,6 3,8 4,0 4,2 4,4 0
100 200 300 400 500 600 700 800 900 1000 1100
average induced field in stripe [A/m]
position of microsphere [µm]
stripe 1 stripe 2 stripe 3 stripe 4
Figure 63: Average induced in-plane fields in the four different stripes for a Bangs 0.86 µm particle in dependence of its position
The results for a single Bangs 0.86 µm particle are shown in Figure 63. As the microsphere is moved from the center of stripe 2 to the right, the average induced stray fields in stripes 1 and 2 decrease, while the opposite is happening for stripes 3 and 4. Due to symmetry, the signals are identical for stripe 2 and 3 at the extremal particle positions, which is also true for stripes 1 and 4. Obviously, the contribution of the outer stripes is relatively small (less than 10 % of the inner stripes), which justifies the choice of a limited integration area. The average fields across all four stripes are displayed in Figure 64. Part a) shows the absolute values, while part b) presents the same curves normalized to their respective maximum values.
Chapter 5: GMR-type magnetic biosensor
While the magnetic moments of the microspheres determine the magnitude of their induced stray fields, their size governs the dependence of the signal on their position.
For larger markers, the signal stays at a higher level when they are positioned within the gap between the sensor lines, which is related to the increased range of their magnetic stray field relative to smaller particles. From the data in Figure 64 b), one can obtain the average signal of each microsphere relative to its maximum as it is moved across the sensor area (see Table 6). Since each position of a microsphere on top of a spiral-shaped sensor element has the same probability, these values represent correction factors when comparing the surface coverage of each microsphere type.
2,6 2,8 3,0 3,2 3,4 3,6 3,8 4,0 4,2 4,4 0,0
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
normalized average induced field
position of microsphere [µm]
Spherotech 1.31 µm Chemagen 0.90 µm Bangs 0.86 µm Bangs 0.35 µm 2,6 2,8 3,0 3,2 3,4 3,6 3,8 4,0 4,2 4,4
0 40 80 120 160 200 240 280 320 360
average induced field [A/m]
position of microsphere [µm]
Bangs 0.86 µm Spherotech 1.31 µm Chemagen 0.90 µm
Bangs 0.35 µm
(a) (b)
Figure 64: Average induced stray fields of all four stripes for the four different microspheres a) absolute values
b) relative values
Bangs 0.35 µm Bangs 0.86 µm Chemagen Spherotech
average rel. signal 0.70 0.87 0.88 0.97
Table 6: Average signals of the different microspheres as their position on the sensor is varied
According to the method described in chapter 5.4.2, the response of the different types of magnetic markers is investigated in dependence of their surface coverage.
For each single measurement, the described compensation of drift and asymmetry is carried out. Afterwards, the maximum difference in the output signal is taken and plotted versus the marker coverage of the specific sensor element (Figure 65 a).
Error bars in the y-direction are given by the standard deviation of 6-8 independent measurements of the same element, while the error bars in the x-direction represent 10 % of the corresponding surface coverage, which is a typical error for the image analysis method described in chapter 5.4.2 (it is obtained from the range of the resulting coverage values when the threshold grayscale value is varied). The shaded area represents the maximum signal obtained from reference elements with zero marker coverage, which is always less than 40 mV. At coverages not too close to saturation, a linear increase of the sensor signal on the marker coverage is observed, as more and more of the sensor area gets affected by the induced stray fields. The corresponding slopes of the linear regressions to the data are shown in line 1 of Table 8. The fit is carried out with the boundary condition that the signal at zero coverage is equivalent to the average reference signal level of 30 mV. Deviations from the linear regression can be attributed to conglomerations of markers in specific regions of a sensor element, which effectively decreases the signal as the areas of influence of different markers overlap. Furthermore, there is also a certain degree of piling especially for the smallest markers at high coverages, which is an additional 79
source of error for these types of measurements as the markers are being spotted directly onto the sensor surface (compare to chapter 8.2).
0 5 10 15 20 25 30 35 40
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
1400 Spherotech Bangs 0.35 µm Chemagen Bangs 0.86 µm
max. output voltage difference [mV]
microsphere surface coverage [%]
reference signal
0 5 10 15 20 25 30 35 40
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
1400 Spherotech Bangs 0.35 µm Chemagen Bangs 0.86 µm
max. output voltage difference [mV]
microsphere surface coverage [%]
reference signal
(b) (a)
Figure 65: Dependence of the maximum output voltage difference of the differential amplifier on the surface coverage of magnetic markers
a) original data
b) data adjusted according to the range of influence of each marker type
An estimate of the minimum detectable number of markers on the surface of a sensor element is obtained by assuming a limiting output voltage of the differential amplifier of 80 mV, which is twice the maximum reference signal. From the linear regressions to the data, the corresponding surface coverage is shown in line 1 of Table 7. Line 2 displays the respective part of the total sensor area (3850 µm2) which is covered by markers, while line 3 represents the corresponding number of particles, which is calculated based on the average size of each marker type (Table 2). Due to the small size of the Bangs 0.35 µm particles, their minimum detectable number is comparably large.
Spherotech Bangs
0.35 µm Chemagen Bangs 0.86 µm
surface coverage [%] 18.0 4.1 1.8 1.0
surface area [µm2] 692.7 157.8 69.3 38.5
number of markers 514 1640 109 66
Table 7: Estimate of the minimum detectable number of markers
In part b) of Figure 65, the coverage of the markers on the sensor surface has been modified according to the correction factors presented in Table 6, which take into account the limited effectivity of markers situated within the gaps between individual spiral windings. This leads to an increased slope of the linear regression to the data (see line 2 in Table 8), which is especially true for the smallest markers. Even though the real applicable signals for this type of sensor is represented by the uncorrected diagram, the modified characteristic can be used to compare the electrical response of the system to the corresponding magnetic data of the markers. Since the origin of the sensor signals lies in the number and magnitude of local magnetic stray fields on its surface, the slopes in line 2 of Table 8 should be correlated to the specific field strengths of the markers as calculated in Table 5. Ignoring the data of the Spherotech markers for the moment, the magnetoresistive and the magnetic data relative to the respective values of the Bangs 0.35 µm microspheres agree within an error of 20 %. Due to the uncertainties in the characteristics of the various particle
Chapter 5: GMR-type magnetic biosensor
types (average size for Chemagen particles and magnetic behavior for Spherotech markers, see chapter 3.2.2.2), deviations should be expected as those values enter the calculation of the specific field strength. In particular, the Spherotech particles do not show a consistent behavior. Most probably, this is due to their abnormal magnetic characteristic, since a closed shell of ferromagnetic material effectively prevents the creation of a significant stray field.
Spherotech Bangs
0.35 µm Chemagen Bangs 0.86 µm
original [mV / %] 2.79 11.71 28.41 47.45
adjusted [mV / %] 2.91 17.03 32.28 54.55
slope of Vout(A)
relative - 1.0 1.9 3.2
absolute [A/m] 303 204 470 531
specific field
strength relative - 1.0 2.3 2.6
Table 8: Slopes of the linear regression to the data of sensor signal on marker coverage and comparison to AGM data of moment density