Magnetic particle biosensors 3

Chapter Atomic Force Microscopy Chapter ATOMIC FORCE MICROSCOPY 3.1 INTRODUCTION Microspheres used for biological tagging are usually paramagnetic, where the bead has an induced magnetization only in the presence of an external field [1-3]. Although paramagnetic beads down to hundreds of nanometers diameter can be detected, future applications require the use of even smaller beads (a few nanometers) for the tagging of proteins [4]. The detection of such small paramagnetic particles poses a problem as the dipole field produced by the beads is small. Alternatively, the use of soft ferromagnetic beads with no remanence may provide a solution, as they are able to produce larger fields, but there is a limit to how small such particles can be made because they must be multidomain [5]. When the size of a magnetic particle shrinks towards the nanoscale, it will become a single ferromagnetic domain before reaching the superparamagnetic regime. Thus the ability to detect a single ferromagnetic domain particle would be an advantage for magnetic tagging in the 5-20 nm range [6]. In this chapter, we explore the issues of using ferromagnetic particles for biosensing by attaching ferromagnetic particles to microfabricated cantilevers and using atomic force microscope (AFM) methodology to move the bead in a controlled manner over a spin valve (SV) sensor. All experiments were done in a static external field with each ferromagnetic bead having a clearly defined direction of magnetization independent 42 Chapter Atomic Force Microscopy of the applied field. Note that the beads used are multidomain, but future applications would move toward single domain particles. Ferromagnetic beads attached to AFM cantilever tips have previously been used to scan over a serpentine GMR sensor to obtain the dependence of GMR response on bead position [5]. Similarly ring shaped anisotropic magnetoresistance (AMR) sensors have been imaged using AFM cantilevers with an attached ferromagnetic bead (a partially magnetized NiFe sphere of diameter 4.3 µm) to demonstrate the localized detection of the radial component of the dipolar fringing field [7]. The major difference in our work compared to that reported in the literature is that a SV structure was used as a sensor material instead of AMR or GMR. As discussed in Chapter 1, SV sensors are much preferred for increased sensitivity to a single magnetic particle. The chapter will first introduce the principles behind the atomic force microscope and the method of attaching magnetic particles to the tips of microfabricated AFM cantilevers. The setup for combined AFM and SV experiments will then be presented, followed by the results and an analytical model of the data. 3.2 ATOMIC FORCE MICROSCOPY (AFM) Stemming from the invention of the scanning tunneling microscope (STM) in 1981 by Gerd Binnig and Heinrich Rohrer, the atomic force microscope was introduced by Gerd Binnig, Calvin Quate and Christoph Gerber in 1986 [8, 9]. The STM and AFM, together with other variations, are collectively known as scanning probe microscopes (SPM) and all use a physical probe to scan across the surface of a specimen, allowing for the direct imaging of the surface down to the nanometer or even atomic scale [10]. A 43 Chapter Atomic Force Microscopy limitation of STM is that only conducting or semiconducting substrates can be imaged. This limitation was addressed with the invention of the AFM, allowing for the measurement of the topography of almost any kind of surface, including ceramics, glass, polymers and biological samples, on a length scale of angstroms up to 100 microns. The main components of a modern day AFM comprise of a microfabricated cantilever, a laser beam deflection system, a piezoelectric scanner head, an electronic control unit, and a computer for controlling the tip approach, scan processes, and for generating and presenting images (Fig. 3.2.1) [11-13]. Rectangular or V-shaped AFM cantilevers are typically microfabricated from silicon or silicon nitride (Si3N4). A sharp tip is fabricated at the free end of the cantilever. The two primary scanning modes in AFM are the contact (or static) and noncontact (dynamic or AC) mode, simply referring to whether or not the tip comes into physical contact with the sample surface. When a scan is done in contact mode, the cantilever tip is brought into mechanical contact with the surface. As the tip moves on the surface, varying topographic features cause a deflection in the cantilever which is measured by reflecting a laser beam off the back side of the cantilever into a quadrant photodetector. The amount of cantilever deflection is calculated from the differences in light intensity between each of the quadrants of the photodetector. If the measured deflection is kept constant by moving the z piezoelectric to compensate any movement of the tip (this is achieved by the electronic feedback controller), then a constant, defined force is maintained between the tip and the sample, preventing the tip from crashing into or lifting off the sample surface. The movement of the z piezoelectric provides a direct 44 Chapter Atomic Force Microscopy measurement of the surface topography. This is called “constant force” imaging and is the most common feedback mode used (both for contact and non contact scanning). When a cantilever moves across a sample surface in contact mode AFM, the lateral motion of the cantilever can cause damage to soft or fragile samples such as biological specimens or polymers. For such cases, noncontact AFM is preferred whereby the cantilever is oscillated (typically at the fundamental resonant frequency) and scanned over the surface without any physical contact between tip and sample. A force interaction between the tip and the sample results in a change in the resonant frequency, oscillation amplitude and phase of the vibrating cantilever, any of which can be used to control the tracking of the probe over the surface. This mode allows for higher sensitivity compared to contact mode and provides the ability to scan ‘soft’ samples without causing any physical damage [13, 14]. Controller (Data Processing and Display) Feedback Loop x, y, z control Cantilever deflection Laser z X, Y, Z Piezoelectric Scanner 4-Quadrant Photodetector x Cantilever y Tip Sample Fig. 3.2.1 Schematic of an atomic force microscope (AFM). 45 Chapter Atomic Force Microscopy In our experiments, contact mode AFM was used to scan a ferromagnetic particle “tip” attached to a Si3N4 cantilever (spring constant k = 0.10, 0.39 and 0.76 N/m) over a SV sensor to investigate the sensor response with respect to bead position. The experiments were undertaken in ambient and image sizes up to 100 x 100 µm2 could be acquired. The latter is an important necessity because the microfabricated SV structures must first be located in the AFM scan and small area scanners are not suitable for this task. The details regarding the fabrication techniques for the 12 x µm2 SV sensors used for the experiments can be found in Section 2.3(a). 3.3 AFM CANTILEVERS (a) Magnetic bead attachment to microfabricated AFM cantilevers In order to move a magnetic dipole with a fixed direction of magnetization over a SV sensor, we adopt the method of attaching a single ferromagnetic µm diameter particle (SpheroTM CFM-80-5), onto the tip of a microfabricated silicon nitride AFM cantilever (OMCL-RC series, Olympus). For attachment of magnetic particles to the tip of AFM cantilevers, two x,y,z linear stages (M460A-XYZ, Newport) were used together with an inverted optical microscope (Axiovert 25 CA, Carl Zeiss) (Fig. 3.3.1(g), (h)). Figure 3.3.1(a)-(f) shows the schematic for the bead attachment process. A cantilever was first mounted to a holder along the x axis direction, and the holder x, y, z position is adjusted to view and locate the tip. A piece of silicon wafer with a cone shaped drop of non-conducting epoxy (Ablebond 2025D, National Starch and Chemical Company) was attached to the other holder, and brought into the focus of the microscope (Fig. 3.3.1(a)). Using the CCD 46 Chapter Atomic Force Microscopy camera, the cantilever tip and the tip of the epoxy cone were brought into contact to transfer a small amount of epoxy to the tip (Fig. 3.3.1(b)). The tip and Si chip were next separated and the chip replaced with a piece of Si wafer with ferromagnetic particles distributed on its surface (Fig. 3.3.1(d)). The epoxy coated cantilever tip was then brought into contact with a single magnetic particle, and the bead detached from the wafer surface (Fig. 3.3.1(f)). The cantilever was then baked at 100ºC for 10 minutes to cure the epoxy. Figure 3.3.1(i) shows an optical microscope image of a single µm ferromagnetic particle attached to a Si3N4 cantilever tip. 47 Chapter (a) Atomic Force Microscopy cantilever x y tip wafer with epoxy cone (epoxy chip) (g) z Microscope objective (b) Manipulator arm Holder attached to x,y z stage (h) (c) Newport x,y,z stage (i) (d) wafer with magnetic particles (e) (f) Fig. 3.3.1 (a) The cantilever and wafer chip (with epoxy peak) are mounted along the x axis onto two x, y, z stages. (b) The cantilever tip and 48 Chapter Atomic Force Microscopy epoxy peak are brought into contact. (c) The cantilever tip and epoxy peak are separated. (d) Epoxy chip is replaced with a chip with µm magnetic particles on the surface. (e) The cantilever tip is brought into contact with a single magnetic particle. (f) A magnetic particle is detached from the wafer surface. (g) The bead attachment apparatus. (h) Image of the positioning stage, cantilever and wafer chip with respect to the microscope objective. (i) Optical micrograph of a single magnetic particle attached to a Si3N4 cantilever tip. (b) Magnetization of bead attached AFM cantilevers To magnetize the ferromagnetic particles in different magnetization directions, the cantilevers were first mounted on “half-moon” metal pieces in order to be attached to the AFM piezoelectric scanner head (Fig. 3.3.2(a)). The half moons were cut from nonmagnetic 0.3 mm thick aluminum sheets and flattened with a hammer, an essential step as commercial half-moons supplied by the AFM manufacturer (Veeco) were of magnetic material and found to interfere with experiments. Paraffin wax, melted at 95ºC on a hot plate, was used to stick each cantilever to the center of a half-moon (Fig. 3.3.2(b)). Aluminum half moon Piezoelectric scanner Cantilever chip (a) Aluminum half moon (b) U-shaped clip to hold half-moon Wax Cantilever chip Fig. 3.3.2 (a) Underside view of AFM scan head with attached half moon. (b) Optical micrograph of AFM cantilever chip mounted on an Al half moon. 49 Chapter Atomic Force Microscopy Four AFM cantilevers mounted onto half-moons (each with attached µm bead) were stuck onto a wooden holder and placed in specific orientations between the poles of a dipole magnet (Walker Scientific) (Fig. 3.3.3(a)). The beads where magnetized in a field of Tesla for 15 minutes so as to fix the required bead magnetization direction (Fig. 4.3.3(b)). The electromagnet was then turned off and the AFM cantilevers removed from the pole gap. Half moon with mounted cantilever chip Wooden holder held in place by a retort stand (b) (a) pole Power supply Magnetic dipoles Fig. 3.3.3 (a) Schematic of the setup for the magnetization of magnetic particles. (b) Dipole magnet and power supply used for the bead magnetization. Figure 3.3.4 shows a schematic of the four bead magnetization directions used in our experiments. 50 Chapter Atomic Force Microscopy Case (i) Case (ii) Usual AFM tip Bead tip Case (iii) Case (iv) . m = my m = −m y m = −m x m = mz Fig. 3.3.4 Single ferromagnetic bead attached to the tip of an AFM cantilever. Cases (i)-(iv): End view (i.e. cross section of the cantilever width) of the magnetization directions of the ferromagnetic bead for the four examples considered. 3.4 EXPERIMENTAL SETUP: Combined AFM and SV A Topometrix Explorer atomic force microscope (Veeco) was used to scan each magnetic particle “tip” in a controlled manner over a spin valve sensor (Fig. 3.4.1(a)). AFM scans of 76 x 76 µm2 and 51 x 51 µm2 were carried out in contact mode at scan rate of µm/s. Low laser power was used for all scans to avoid any laser effects on the SV response. The SV chip was mounted on a small piece of Veroboard, connected to external measurement circuits (Fig. 3.4.1(c)), and placed on a manual x, y linear translation stage (UMR-5.25A, Newport). The translation stage allowed placement of the AFM tip over the active area of the SV and sample holder. Further modifications to the AFM were the addition of permanent bar magnets next to the SV chip (Fig. 3.4.1(b)). These were used to apply a field of 17 Oe in the transverse direction (y) of the SV, to enable the SV to work in the linear response region where sensitivity is optimum (refer to Fig. 2.3.2). The movement of the magnetic bead across the SV moves the SV response by ∆R/R corresponding to the field change caused by the bead. A constant current of mA 51 Chapter Atomic Force Microscopy measurement of SV response as a function of tip position. A Nanovoltmeter (Keithley 2182) reads the voltage drop across the SV at a constant current (supplied by Keithley 2400). The advantages of using AFM was that firstly, we were able to move a single ferromagnetic bead across the SV sensor while ensuring that the orientation of the bead magnetization was fixed. Secondly, the voltage drop (i.e. resistance) measured by the Nanovoltmeter could be input into the AFM controller allowing the response of the SV sensor to be recorded with respect to the bead position on the SV. 3.5 EXPERIMENTAL RESULTS (a) Spin valve sensor voltage response (12 x µm2) When a ferromagnetic bead is brought into contact with a SV, the magnetization of the free layer rotates in response to the field produced by the bead, resulting in a change in the SV resistance. During a typical AFM scan, a ferromagnetic bead was brought into contact with the surface and scanned over the SV. The SV experienced a field dependent on the position (x, y, z) and the relative magnetization direction of the bead. Since the AFM was operated in contact mode, the height (z) was fixed and the figures of Section 3.5 thus show the two dimensional (2D) images which represent the sensor voltage response with respect to the bead x, y position. Figure 3.5.1 shows that there is only a response of the SV when the ferromagnetic bead is over the active area of sensor, and that the magnitude of the sensor response depends on the magnetization of the bead and the position of the bead with respect to the sensor. The brighter pixels represent data points with higher SV voltage output. The same set of experiments was 53 Chapter Atomic Force Microscopy also repeated with a larger scan area of 76 x 76 µm2 (Fig. 3.5.2) and similar results were obtained [15]. Case (i) (a) (b) Case (ii) (c) Case (iv) Case (iii) (e) (f) (d) (g) (h) Fig. 3.5.1 Simultaneous SV voltage and AFM topography scans of a single ferromagnetic bead over a spin valve sensor for different bead magnetization cases (i)-(iv) as defined in Fig. 3.3.4. Scan size: 51 x 51 µm2. The active sensor region is shown boxed. (a) Sensor voltage response, case (i). Range: -17.5 to +63.5 µV. (b) Corresponding topography image, case (i). (c) Sensor voltage response, case (ii). Range: 16 to +19 µV. (d) Corresponding topography image, case (ii). (e) Sensor voltage response, case (iii). Range: -12.7 to +6.1 µV. (f) Corresponding topography image, case (iii). (g) Sensor voltage response, case (iv). Range: -164.5 to -109 µV. (h) Corresponding topography image, case (iv). 54 Chapter Atomic Force Microscopy Case (i) (a) (b) Case (ii) (c) Case (iii) (e) (f) (d) Case (iv) (g) (h) Fig. 3.5.2 Simultaneous SV voltage and AFM topography scans of a single ferromagnetic bead over a spin valve sensor for different bead magnetization cases (i)-(iv), as defined in Fig. 3.3.4. Scan size: 76 x 76 µm2. The active sensor region is shown boxed. (a) Sensor voltage response, case (i). Range: -54.5 to +48.5 µV. (b) Corresponding topography image, case (i). (c) Sensor voltage response, case (ii). Range: 16 to +15 µV. (d) Corresponding topography image, case (ii). (e) Sensor voltage response, case (iii). Range: -11.3 to +7.9 µV. (f) Corresponding topography image, case (iii). (g) Sensor voltage response, case (iv). Range: -138 to -103.5 µV. (h) Corresponding topography image, case (iv). (b) Spin valve sensor voltage response (12 x µm2 and 12 x 24 µm2) To show the repeatability of our experiments, we used another set of cantilevers with attached µm ferromagnetic particle magnetized in each of the four different directions (Fig. 3.5.3, with exception of Case (iii) now magnetized in +x direction) and scanned on SV sensors of different sizes (12 x µm2 and 12 x 24 µm2). Similar SV voltage response characteristics were observed for both cases, (Figures 3.5.3 and 3.5.4). 55 Chapter Atomic Force Microscopy The data are consistent with the results of Section 3.5(a) using 12 x µm2 SV area devices. Case (i) (a) (b) Case (ii) (c) Case (iii) (e) (f) (d) Case (iv) (g) (h) Fig. 3.5.3 SV voltage and AFM topography scans of a single ferromagnetic bead over a spin valve sensor for bead magnetization cases (i)-(iv) as defined in Fig. 3.3.4. Scan size: 30 x 30 µm2. The active sensor region (~12 x µm2) is boxed. (a), (c), (e), (g) are the sensor voltage responses for cases (i)-(iv) respectively, with (b), (d), (f), (h) the corresponding topography image. One problem is that the location of the SV response region for cases (ii) and (iii) in Fig. 3.5.3 is much lower than the boxed region (where the SV is physically located). We attribute this observation to the quality of the SV, as wet etching does not produce well defined SV structures in all cases. Furthermore, using the very same set of cantilevers we were able obtain the characteristic sensor voltage responses in the 12 x 24 µm2 SV (Fig. 3.5.4), leading us to believe that the anomaly in the Fig. 3.5.3 data is solely due to the quality of the SV sensor. 56 Chapter Atomic Force Microscopy Case (i) (a) (b) Case (ii) (c) Case (iii) (e) (f) (d) Case (iv) (g) (h) Fig. 3.5.4 SV voltage and AFM topography scans of a single ferromagnetic bead over a spin valve sensor for bead magnetization cases (i)-(iv), as defined in Fig. 3.3.4. Scan size: 46 x 46 µm2. The active sensor region (~ 12 x 24 µm2) is boxed. (a), (c), (e), (g) are the sensor voltage responses for cases (i)-(iv) respectively, with (b), (d), (f), (h) the corresponding topography image. (c) Spin valve sensor response in z direction (height dependence) Using our AFM setup, we measured the SV response in the z direction by approaching the magnetic bead tip to the sensor surface while keeping the x and y position fixed. An µm magnetic particle magnetized in the z direction [Case (iv)] was scanned over the SV sensor to first obtain a 2D sensor voltage response (Fig. 3.5.5(c)), after which positions were chosen for obtaining the SV z direction response (Fig. 3.5.5(a)). From figure 3.5.5(c) we would expect the SV signal to decrease as the tip approaches the surface at position (i), increase at position (ii) and remain constant at position (iii) because the bead is far from the SV active area. This is indeed what is observed in z response curves (Fig. 3.5.5(a)). Note that the distance axis shows only the relative change in the tip-sample separation, with more negative distances corresponding 57 Chapter Atomic Force Microscopy to the tip being further from the surface. However the tip certainly contacts the surface as demonstrated by the obvious snap-to-contact in the cantilever deflection signal (Fig. 3.5.5(b)). 20.0 SV Voltage output (µV) (a) (c) (ii) 18.6 (i) (iii) (ii) 17.3 (i) (iii) 15.9 (b) Deflection of cantilever (arb. units) Distance (nm) (d) (ii) (i) (iii) Distance (nm) Fig. 3.5.5 Data for a 12 x µm2 SV device taken with an µm bead magnetized in the z direction (case iv). The z dependence of the SV response was measured at the z locations (i), (ii) and (iii). (a) Height (z) dependent SV voltage response for the three positions (i), (ii) and (iii). (b) Corresponding force distance curves. (c) 2D sensor voltage response, with the z approach locations indicated on the image. (d) Corresponding topography image with the box showing the location of the SV. From the z voltage response (Fig. 3.5.5(a)) we observe that the SV is sensitive to the fields generated by the magnetic particle even when the particle is at a distance of 58 Chapter Atomic Force Microscopy µm above it the surface. The data also highlights the localized sensitivity of the SV sensor in the z as well as the x, y directions. This method of force curves is an effective way to find the z dependence of the SV response due to a single magnetic particle. However, only a limited number of points can be selected at any one time and it is thus not practical when large areas need to be investigated. In Chapter 5, an alternative method will be proposed for the investigation of SV response to the z position of a bead. 3.6 ANALYTICAL MODEL (a) Spin valve geometry In order to better understand the images obtained, we used a model similar to that of Wood et al. [16]. The magnetic bead (of defined magnetization) is placed in a fixed location, and the effect of the field from the bead on the SV resistance is found. This is repeated for different positions of the bead to obtain the expected x, y SV response and allows for comparison with the AFM experiments. The model geometry follows that of the experimental sample (Fig. 3.6.1(b)) with the pinned magnetic direction (Mpinned) along the sensor transverse direction (y-axis), and the magnetically free direction (Mfree) along the sensor longitudinal direction (x-axis). As the SV is mostly sensitive to planar fields along the transverse (y-axis) direction, we calculate the expected response of the SV sensor by considering only the transverse components of the field in the sensor plane (By) generated by a single magnetic particle [17]. The particle is placed at a fixed height (z) because the SV images are obtained when the magnetic bead tip scans across the surface in contact mode. 59 Chapter Atomic Force Microscopy (a) Cr/Au SV sensor x; Mfree x (b) y Spin valve material r Mfree z y; Mpinned Cr/Au electrode Isense Mpinned Fig. 3.6.1 (a) Optical micrograph of the SV sensor which was used as the basis of the model. Top view of a 12 x µm2 SV with Cr/Au contacts. (b) Schematic of a magnetic microbead over a SV sensor showing definition of axes and magnetization directions. (b) Modeling The field created by a single magnetized bead can be described as a pure dipole given by B= μ0 ⋅ [3(m ⋅ rˆ)rˆ − m] , 4π r (3.1) with rˆ pointing from the bead center and m is the magnetic moment [18, 19]. Using Eq. 3.1 and converting to Cartesian coordinates [20], we obtain for the four different bead magnetization cases considered (see Fig. 3.3.4); Case (i): m = m y ; By = μ0 m 3my − ], [ 4π ( x + y + z ) ( x + y + z ) μ0 m 3my − Case (ii): m = −m y ; B y = − ], [ 4π ( x + y + z ) ( x + y + z ) Case (iii): m = −m x ; B y = − μ0 3mxy ], [ 4π ( x + y + z ) (3.2) (3.3) (3.4) 60 Chapter Atomic Force Microscopy Case (iv): m = m z ; By = μ0 3myz ], [ 4π ( x + y + z ) (3.5) where B y is the magnitude of the y component of the field. The magnitude of the fields ( B y ) experienced in the x, y plane of the sensor due to a bead placed above it at a fixed height z can be calculated for any x y position, and this result can be represented as a density plot (Fig. 3.6.2 shows an example for the bead at x = 0, y = 0). Case (i) Case (ii) 30 30 20 20 10 10 -10 -10 -20 -20 -30 -30 -30 -20 -10 10 20 30 -30 -20 -10 Case (iii) Case (iv) 30 30 20 20 10 10 -10 -10 -20 -20 -30 -30 -30 -20 -10 10 20 30 10 20 30 -30 -20 -10 10 20 30 Fig. 3.6.2 Density images representing the magnitude of the y-component fields ( B y ) experienced by a planar surface when a magnetic bead with four different magnetizations [Cases (i)-(iv)] is held at position (0,0,z). Bright pixels represent field positive. The axes show the length scale in micrometer, with an image size of 76 x 76 µm2. 61 Chapter Atomic Force Microscopy We next subdivide the active area of a typical SV sensor into square segments of 0.76 x 0.76 µm2. The size of the subdivided areas is chosen to make each modeled segment equivalent in area to each pixel in the AFM scans (data Fig. 3.5.2). By calculating the By fields [Eqs. 3.2 - 3.5] experienced by each segment due to a bead at a fixed position (x, y, z), summing up the fields over all individual segments, and then dividing by the total number of segments, we obtain the effective field (By) experienced by the entire sensor for a bead at a fixed position. Repeating this procedure for varying positions of the magnetic bead, we obtain a density plot representative of the effective field (By) experienced by the SV at every bead position. The resistance change of the sensor corresponding to By can then be calculated for every bead position by using the measured sensor response data (Fig. 2.3.2) and assuming a linear relationship between the sensor response ∆R/R and the applied field (By). (c) Model results In our experiments, the bead is always in contact with the sensor plane (z = ~ µm i.e. the bead radius) and the theoretical calculation of sensor output versus bead position can be shown as 2D density plots in (x, y). Comparing the data to our model, we find that the experimental images correspond to our model predictions (Fig. 3.6.3), although we observe a slight elongation of the characteristic voltage response in the vertical direction. We attribute this elongation to the SV regions underlying the Cr/Au contacts which contribute a small change to the sensor response. The Cr/Au contact lines are directly deposited over the wet-etch defined sensor strip so there may be some residual MR material. 62 Chapter Atomic Force Microscopy Case (i) 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 Case (iii) 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 Case (ii) 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 Case (iv) 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 Fig. 3.6.3 Comparison of experiment voltage change (left) and model voltage change (right) on a 12 x µm2 SV due to a µm ferromagnetic bead scanning the surface, with bead center at height z = µm. The axes show the length scale in micrometer. A better quantitative comparison between theory and experiment can be made by studying profiles of the line scans taken across the y direction of the images (Fig. 3.6.4). Several experimental line scans were extracted near the maximum in the output response and the most representative data is shown (we ignore the small contributions from the regions underlying the contacts). A reasonable correspondence between the modeled and experimental line profiles is observed. The error in the magnitude of the maximum sensor output between the modeled and experimental data was less than 24% in 75% of the samples. In several samples the error could be as high as 51%. We believe that the major error arises in the exact orientation of the bead dipole with respect to the sensor (e.g. Fig. 63 Chapter Atomic Force Microscopy 3.6.4 Case(ii)), as well as the uncertainty in the exact concentration of magnetic material in each individual ferromagnetic bead. Case (ii) 0.08 0.04 0.06 0.02 0.04 dR/R (%) dR/R (%) Case (i) 0.02 -0.02 -0.04 -0.02 -0.06 -0.04 -0.08 20 40 µm 60 80 100 20 µm 60 80 100 80 100 Case (iv) Case (iii) 0.02 0.1 0.01 0.05 dR/R (%) dR/R (%) 40 -0.01 -0.05 20 40 µm 60 80 100 20 40 µm 60 Fig. 3.6.4 Line scan profiles showing the normalized sensor output as a function of bead position for the four magnetization cases. Representative line scans have been chosen near the center of the SV structure, except for Case (iii) which is chosen at the region of highest voltage change. Solid and dotted lines represent the calculated and experimental voltage changes respectively. 3.7 CONCLUSION AND FURTHER WORK We have constructed a simple model to predict the response of a SV sensor to the localized fields produced by a single ferromagnetic particle. The model results were compared to that obtained from the experimental data found using AFM with a magnetic particle tip, and agree to within 24% for most of the samples. We have also used the SV 64 Chapter Atomic Force Microscopy sensor to measure the interaction of paramagnetic beads, although the sensitivity is necessarily lower [6] [Appendix A]. There are two clear implications of the above results for biosensing, both relating to the size of the magnetic bead. Firstly, although the maximum possible SV sensor response is about 3.7% (Fig. 2.3.2), the best detection value obtained from our sensor for an µm magnetic bead is 104 ferromagnetic particles to obtain the angle of rotation of the entire array of particles. A suitably calibrated SV sensor may instead be used to measure the angle of rotation of a single particle, provided that the particle position relative to the sensor is known, i.e. by observing through an optical microscope. Following the procedure used in MTC, the ferromagnetic particle can be magnetized in the z direction, and a uniform magnetic field applied in the y direction (axes are as defined as in Fig. 3.6.1(b)). The resulting torque will try to twist the particle magnetization towards the y axis, which will be mechanically opposed by the local compliance of the cell material around the particle. Any change in magnetization will cause a change in the voltage output of the SV sensor, which can be modeled to obtain the corresponding angle of particle rotation, providing information on the equivalent Young modulus of a single cell [22]. A demonstration of the feasibility of this new MTC method is given in Chapter 5. 66 Chapter Atomic Force Microscopy REFERENCES [1] D. L. Graham, H. Ferreira, J. Bernardo, P. P. Freitas and J.M.S. Cabral, J. Appl. Phys. 91, 7786 (2002) [2] M. M Miller, P. E. Sheehan, R. L. Edelstein, C. R. Tamanaha, L. Zhong, S. Bounnak, L. J. Whitman, and R. J. Colton, J. Magn. Magn. Mater. 225, 138 (2001) [3] L. Lagae, R. Wirix-Speetjens, J. Das, D. Graham, H. Ferreira, P. P. F. Freitas, G. Borghs, J. De Boeck, J. Appl. Phys. 91, 7445 (2002) [4] A. 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ASME, 124, 408 (2002) 68 [...]... position, and this result can be represented as a density plot (Fig 3. 6.2 shows an example for the bead at x = 0, y = 0) Case (i) Case (ii) 30 30 20 20 10 10 0 0 -10 -10 -20 -20 -30 -30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 Case (iii) 10 20 30 Case (iv) 30 30 20 20 10 10 0 0 -10 -10 -20 -20 -30 -30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 Fig 3. 6.2 Density images representing the magnitude of the y-component... 40 30 20 10 0 0 10 20 30 40 50 60 70 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 Case (iii) 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 Case (ii) 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 Case (iv) 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 Fig 3. 6 .3 Comparison... given by B= μ0 1 ˆ ˆ ⋅ [3( m ⋅ r )r − m] , 4π r 3 (3. 1) ˆ with r pointing from the bead center and m is the magnetic moment [18, 19] Using Eq 3. 1 and converting to Cartesian coordinates [20], we obtain for the four different bead magnetization cases considered (see Fig 3. 3.4); Case (i): m = m y ; By = μ0 m 3my 2 − ], [ 5 4π ( x 2 + y 2 + z 2 ) 2 ( x 2 + y 2 + z 2 ) 3 2 μ0 m 3my 2 − Case (ii): m = −m... 2 ) 3 2 μ0 m 3my 2 − Case (ii): m = −m y ; B y = − ], [ 5 4π ( x 2 + y 2 + z 2 ) 2 ( x 2 + y 2 + z 2 ) 3 2 Case (iii): m = −m x ; B y = − μ0 3mxy ], [ 4π ( x 2 + y 2 + z 2 ) 5 2 (3. 2) (3. 3) (3. 4) 60 Chapter 3 Atomic Force Microscopy Case (iv): m = m z ; By = μ0 3myz ], [ 4π ( x 2 + y 2 + z 2 ) 5 2 (3. 5) where B y is the magnitude of the y component of the field The magnitude of the fields ( B y ) experienced... Magn Magn Mater 225, 138 (2001) [3] L Lagae, R Wirix-Speetjens, J Das, D Graham, H Ferreira, P P F Freitas, G Borghs, J De Boeck, J Appl Phys 91, 7445 (2002) [4] A Hoffman, Magnetics Business and Technology, 24 (Spring 2005) [5] J C Rife, M M Miller, P E Sheehan, C R Tamanaha, M Tondra, L J Whitman, Sens Actuators, A 107, 209 (20 03) [6] G Li, S X Wang, IEEE Trans Magn 39 (5), 33 13 (20 03) [7] M M Miller,... curves (c) 2D sensor voltage response, with the 3 z approach locations indicated on the image (d) Corresponding topography image with the box showing the location of the SV From the z voltage response (Fig 3. 5.5(a)) we observe that the SV is sensitive to the fields generated by the magnetic particle even when the particle is at a distance of 3 58 Chapter 3 Atomic Force Microscopy µm above it the surface... was 53 Chapter 3 Atomic Force Microscopy also repeated with a larger scan area of 76 x 76 µm2 (Fig 3. 5.2) and similar results were obtained [15] Case (i) (a) (b) Case (ii) (c) Case (iv) Case (iii) (e) (f) (d) (g) (h) Fig 3. 5.1 Simultaneous SV voltage and AFM topography scans of a single ferromagnetic bead over a spin valve sensor for different bead magnetization cases (i)-(iv) as defined in Fig 3. 3.4... the four different directions (Fig 3. 5 .3, with exception of Case (iii) now magnetized in +x direction) and scanned on SV sensors of different sizes (12 x 6 µm2 and 12 x 24 µm2) Similar SV voltage response characteristics were observed for both cases, (Figures 3. 5 .3 and 3. 5.4) 55 Chapter 3 Atomic Force Microscopy The data are consistent with the results of Section 3. 5(a) using 12 x 8 µm2 SV area devices... 3. 5(a) using 12 x 8 µm2 SV area devices Case (i) (a) (b) Case (ii) (c) Case (iii) (e) (f) (d) Case (iv) (g) (h) Fig 3. 5 .3 SV voltage and AFM topography scans of a single ferromagnetic bead over a spin valve sensor for bead magnetization cases (i)-(iv) as defined in Fig 3. 3.4 Scan size: 30 x 30 µm2 The active sensor region (~12 x 6 µm2) is boxed (a), (c), (e), (g) are the sensor voltage responses for cases... to believe that the anomaly in the Fig 3. 5 .3 data is solely due to the quality of the SV sensor 56 Chapter 3 Atomic Force Microscopy Case (i) (a) (b) Case (ii) (c) Case (iii) (e) (f) (d) Case (iv) (g) (h) Fig 3. 5.4 SV voltage and AFM topography scans of a single ferromagnetic bead over a spin valve sensor for bead magnetization cases (i)-(iv), as defined in Fig 3. 3.4 Scan size: 46 x 46 µm2 The active . )( y B -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 Case. cases considered (see Fig. 3. 3.4); Case (i): ymm = ; ] )()( 3 [ 4 2 3 222 2 5 222 2 0 zyx m zyx my B y ++ − ++ = π μ , (3. 2) Case (ii): ymm −= ; ] )()( 3 [ 4 2 3 222 2 5 222 2 0 zyx m zyx my B y ++ − ++ −= π μ ,. cases, (Figures 3. 5 .3 and 3. 5.4). 55 Chapter 3 Atomic Force Microscopy The data are consistent with the results of Section 3. 5(a) using 12 x 8 µm 2 SV area devices. Fig. 3. 5 .3 SV voltage