5. GMR-TYPE MAGNETIC BIOSENSOR
5.2. Sensor layout and characteristics
Chapter 5: GMR-type magnetic biosensor
Even though a good degree of agreement to the data is reached by the resistor network model, there are some discrepancies due to its simplicity. For example, it is observed experimentally that the GMR ratio decreases exponentially with increasing spacer thickness (Ref. 192). Within the model, this decay should be proportional to 1/tN2. The difference can be attributed to the assumption of a long free path of the electrons compared to the layer thickness, which is no longer valid in the limit of large spacer thicknesses. Furthermore, measurements of the mean free path in Py multilayer systems revealed length scales comparable to the layer thickness (Ref.
193), so that this assumption seems to be questionable even in the limit of thin spacers. Also, the resistor network model produces the same GMR ratio no matter in which geometry the current is passed through the multilayer stack, but experimentally, the current perpendicular to plane (CPP) geometry shows substantially higher GMR ratios than the current in plane geometry (CIP). This is related to the different critical length scales: in the CPP geometry, every electron is forced to pass every single layer of the stack, so it is sufficient if the spin diffusion length is larger than the layer separation. On the other hand, the critical length scale in the CIP geometry is the much shorter mean free path, which is due to the fact that the electrons have to sample both magnetic layers before being scattered in order to display a magnetoresistance (Ref. 194). This differentiation is neglected in the resistor network model.
Due to these shortcomings, it is obvious that the resistor network model is oversimplified and has to be extended or supplemented by other approaches to correctly predict all aspects of the GMR effect. There are many different methods to treat this problem, and a comprehensive review can be found for example in Ref.
195. Basically, the various approaches can be classified according to the effort they put into the electronic structure of the multilayer system and, secondly, the electron transport mechanism through the superlattice. Concerning the electronic structure of the multilayers, the most basic approaches employ a free electron model (Ref. 196) or assume a single tight binding band (Ref. 197). Though oversimplified, these methods successfully reproduce some of the main features like the dependence of the GMR ratio on the thickness of the spacer and the magnetic layers or its enhancement with increasing multilayer number. However, these results are only qualitative, and a quantitative agreement requires the incorporation of the actual band structure of the superlattice, which is either calculated from first principles within the local density approximation (Ref. 198) or derived with the help of parameterized multiple tight binding bands (Ref. 199).
With respect to electron transport, the most common model uses the widely accepted versatile semiclassical Boltzmann theory (Ref. 200). In most multilayer systems, however, its applicability is limited, and a full scale quantum mechanical transport theory like the Kubo-Landauer formalism (Ref. 201) has to be used. Combined with realistic multiband structures, this is the best way to describe the GMR effect quantitatively.
Figure 38 shows the magnetoresistance response of a continuous unpatterned layer stack to an in-plane magnetic field. Its resistance decreases by 8 % at a saturation field of 4.6 kA/m, resulting in an overall sensitivity of about 1.7 % per kA/m. The response is linear almost up to saturation and shows no hysteresis. Thus, this magnetoresistive system is quite suitable for the detection of small magnetic fields.
-10 -8 -6 -4 -2 0 2 4 6 8 1
0 1 2 3 4 5 6 7 8
∆R/R0 [%]
magnetic field [kA/m]
0
Figure 38: Magnetoresistance response of an unpatterned multilayer system
The strength of the bilinear and biquadratic coupling are determined from the magnetoresistance response of the continuous layer stack according to the fitting routine described in the diploma thesis of Sonja Heitmann (Ref. 202). It takes into account the Zeeman energy and the coupling energies (see Equation 10) and determines the respective coupling strengths by minimizing the energy sum. The resulting fitting function has the following form:
Q Q
0 Py S
H(x) 4 x 4J x 2J J
t M
=µ − + L Equation 16
Here, x represents the alternative definition of the GMR-ratio which is normalized to the high resistive state and is also normalized to its full amplitude A. The Py-thickness tPy is set to 1.6 nm, and its saturation magnetization is given by MS=860 kA/m. For one branch of a typical magnetoresistance measurement, the corresponding fit is compared to the data in Figure 39.
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 0
500 1000 1500 2000 2500 3000 3500 4000 4500
in-plane field H [A/m]
x = [Rmax- R(H)] / (A Rmax) data
fit
Figure 39: Data and corresponding fit for determining the coupling strengths
Chapter 5: GMR-type magnetic biosensor
The fitting procedure gives the following results for the coupling coefficients from one magnetic layer to another (the fact that the coupling in infinite multilayers is given by twice that value is already included in the derivation of the fitting function):
JL = 0.97 µJ/m2 JQ = 0.46 µJ/m2
effective af-coupling: Jeff = JL + 2 JQ = 1.89 µJ/m2
The quadratic term agrees well to the data given in Heitmann’s diploma thesis (Ref.
202), whereas the linear coupling strength only reaches about 2/3rd of the value given in this reference. However, the samples analyzed in Heitmann’s diploma thesis consisted of four times as many multilayers, and it is known that the coupling strength increases with increasing multilayer number due to enhanced growth (Ref. 202).
Furthermore, the fitting procedure in Heitmann’s diploma thesis has been carried out for samples which were prepared on thin glass slides. Samples on Si-wafer substrates, which have also been investigated in this reference, only show about half the saturation field, which leads to a decreased linear coupling strength. Thus, the origin of the discrepancy can be attributed to a combination of those two factors.
0°
20 µm 90°
2 mm 1 mm
Figure 40: Layout of the GMR biosensor prototype
Individual sensor elements are patterned from the continuous stack by positive electron beam lithography and argon ion etching. A 17 nm thick tantalum layer is applied as a hard mask for the etching process to prevent resist remnants that could cause leaking sites in the subsequent protection layer (see chapter 4.1). The resulting sensor elements consist of lines with a thickness of 1 µm and a total length of about 1.8 mm which are wound into spirals with a total diameter of 70 µm and an electrical in-plane resistance at zero magnetic field of about 12 kΩ (see Figure 40). In order to prevent shortcuts between individual spiral windings, the etching process is continued into the underlying SiO2. Additionally, about 3 nm of the Ta hard mask is left over to ensure that the GMR multilayer stack remains in its original state (no intermixing, oxidation, etc.). The section analysis of the AFM image shown in Figure 41 reveals a total height of the spiral windings of about 82 nm, which implies an etching depth into the substrate of approximately 40 nm.
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An individual sensor element covers the entire area of a single probe DNA spot, which has a typical diameter of around 100 µm for standard piezo spotters. Thus, one sensor element measures the average signal of all the magnetic markers which are bound at one specific probe DNA spot. However, markers which are situated in the 1 µm wide spacing between the spiral windings only contribute a reduced signal.
This effect is analyzed quantitatively in chapter 5.4.3. By putting a number of smaller sensors underneath each probe DNA spot, it would be easily possible to resolve the internal spatial marker distribution, but for typical microarray hybridization experiments only the average signal is relevant. Therefore, our sensor is optimized for such macroscopic molecular recognition reactions.
Figure 41: AFM analysis of the inner part of a spiral-shaped GMR sensor element
A total number of 206 separate sensor elements are integrated into a prototype magnetoresistive biosensor on a total area of 5 x 12 mm2. The contact pads and interconnect lines are made of a Ta10nmAu50nmTa10nm sandwich structure and are patterned using positive photo lithography and lift-off. Keeping some elements uncovered for reference purposes, as many as 200 different probe DNA spots can be tested at the same time with this prototype.
The magnetoresistance response of a single spiral-shaped sensor element is displayed in Figure 42. Due to the isotropic design, the characteristic is the same no matter in which direction the external in-plane field is applied (the two displayed directions are oriented perpendicular to each other and are specified in Figure 40).
However, there is still shape anisotropy along the individual windings of the spiral, which causes the magnetization to lie tangential to those windings. Furthermore, contour imperfections at the edges present an additional source of domain wall pinning, which gives rise to the observed hysteresis of about 270 A/m. Such a hysteresis is not observed in the case of an unpatterned layer stack.
Chapter 5: GMR-type magnetic biosensor
-15 -10 -5 0 5 10 15
0 1 2 3 4 5 6 7
0°
90°
GMR-amplitude [%]
magnetic field [kA/m]
Figure 42: Isotropic magnetoresistance response of a spiral-shaped sensor element