Resolution of Patterned Magnetic Media

Transcription

1 Resolution of Patterned Magnetic Media by Ki Seog Song Bachelor of Science in Engineering Mechanical Design and Production Engineering Seoul National University, 1989 Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE at the Massachusetts Institute of Technology June Massachusetts Institute of Technology. All rights reserved Signature of Author... Ki Seog Song Department of Mechanical Engineering May 5, 2000 Certified by Kamal Youcef-Toumi Professor of Mechanical Engineering Thesis Supervisor A ccepted by Ain. A. Sonin Chairman, Department Committee on Graduate Students MASSACHUSETTS INSTITUTE OF TECHNOLOGY SEP LIBRARIES

2 Resolution of Patterned Magnetic Media by Ki Seog Song Submitted to the Department of Mechanical Engineering On May 5, 2000 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mechanical engineering ABSTRACT Point magnetic recording (PMR) has been proposed as a method for writing data on the Patterned Magnetic Media (PMM). In this thesis, two criteria were presented to predict the PMM resolution during the PMR process that was fabricated in the Nanostructures Laboratory of MIT and characterized in the Mechatronics Laboratory of MIT. FEM analysis was performed to determine the magnetic field concentration at the end of the probe during the PMR process. The interaction field between pillars was also estimated using the FEM model. The results from the FEM analysis along with the two criteria were used to determine the resolution of the media. A resolution of 250nm was predicted for Ni arrays with pillar diameter and height of 100nm and 180nm respectively. The two criteria showed that the optimal external field Hext from a coil is 300 Oe and the MFM probe coating(cocr) thickness is 40nm for these pillar arrays. The FEM analysis was very effective in getting writing field at the magnetic probe during the PMR process. The interaction field model with a commercial magnetostatic field simulation tool indicated that the interaction field can be a serious problem in implementing high density PMM storage device. Thesis Supervisor: Kamal Youcef-Toumi Title: Professor of Mechanical Engineering 2

3 ACKNOWLEDGEMENTS I sincerely thank my advisor, Professor Kamal Youcef-Toumi for his sincere supervision on my works and for all the opportunities he has given me. His way of thinking along with his brilliant ideas deeply affects my thoughts on this thesis. My friends in Mechatronics Laboratory deserve my special gratitude for all those pleasant talks, interesting discussions for my research. I will never forget the time with you guys- Bemardo, Osamah, Vidi, Vincent, Yong... Most of importantly, I thank my wife. Without your support and constant love to me, this work would never have been possible. May, 2000 Ki Seog Song 3

4 TABLE OF CONTENTS ABSTRACT... 2 ACKNOWLEDGEMENTS...3 TABLE OF CONTENTS...4 LIST OF FIGURES...6 LIST OF TABLES... 8 CHAPTER 1. INTRODUCTION Introduction Historical Review T hesis O utline...12 CHAPTER 2. BACKGROUND Introduction Performance Requirement C apacity A ccess T im e Data Rate Concept of the Patterned Magnetic Media Advantage of PMM Anisotropy: Easy Axis and M-H curve Magnetization Reversal of PMM pillar Point Magnetic Recording using MFM Concept of the Point Magnetic Recording PMR Experiment Setup Writing on the Patterned Magnetic Media Measurement of Writing Field Summary...27 CHAPTER 3 EFFECT OF INTERACTION FIELDS ON PMM'S AREAL DENSITY: 1 ST CRITERION Introduction Concept of Interaction Theoretical Model

5 3.4 FE M M odel Input Simulation Engine and Procedure Simulation Result Sum m ary CHAPTER 4.. EFFECT OF THE INTERACTION FIELD ON THE PMM'S AREAL DENSITY DURING THE PMR PROCESSING Introduction Definition of the 2 "d Criterion FE M M odel The Necessity for an FEM Modeling FE M Input Simulation Engine[Maxwell] Simulation Procedure FEM Simulation Result Mesh Numbers, Size and Calculation Time Field Concentration near Probe: Qualitative Analysis Field Concentration Comparison between FEM Simulation and Experiment Results: Quantitative Analysis The Application of 2 "d Criterion Sum m ary...63 CHAPTER 5 CONCLUSIONS & RECOMMENDATIONS...66 BIBLIOGRAPHY...68 APPENDIX PMR PROCESS FEM MODELING INTERACTION FIELD FEM MODELING

6 LIST OF FIGURES FIGURE 1.1 PROSPECTIVE MEDIA PERFORMANCE...10 FIGU RE 2.1 PM M PILLAR FIGURE 2.2 PROLATE SPHEROID...19 FIGURE 2.3 HYSTERESIS LOOPS FOR COHERENT ROTATION...21 FIGURE 2.4 POINT MAGNETIC RECORDING SCHEME...23 FIGURE 2.5 EXPERIMENTAL SETUP FOR PMR PROCESS...25 FIGURE 2.6 MFM IMAGE OF PMR WRITING EXPERIMENT...26 FIGURE 2.7 POINT MAGNETIC RECORDING FIELD MEASUREMENT...27 FIGURE 3.1 INTERACTION FIELD BETWEEN PILLARS...29 FIGURE 3.2 RECTANGULAR PRISM MODEL...31 FIGURE 3.3 HORIZONTAL DISTRIBUTION OF PMM PILLARS...34 FIGURE 3.4 INTERACTION FIELD FROM PRISM APPROXIMATION...35 FIGURE 3.5 M-H AND B-H DIAGRAM FOR ONE MAGNETIC DOMAIN PA R TIC LE FIGURE 3.6 B-H CURVE FOR PMM PILLAR...37 FIGURE 3.7 FIELD DISTRBUTION FROM A PMM PILLAR...38 FIGURE 3.8 INTERACTION FIELD FROM THE FEM SIMULATION...39 FIGURE 4.1 HALF PLANE GEOMETRY OF MFM PROBE...44 FIGURE 4.2 B-H CURVE FOR MFM TIP...45 FIGURE 4.3 A QUARTER SOLID MODEL-PROBE AND AIRPILLAR...46 FIGURE 4.4(A) A QUARTER SOLID MODEL-OVERALL VIEW...47 FIGURE 4.4(B) A CONDUCTOR SOLID MODEL-EXTERNAL COIL...47 FIGURE 4.5 SOLUTION PROCESS FLOWCHART...52 FIGURE 4.6 FIELD DITRIBUTION NEAR THE MAGNETIC PROBE...58 Co/Cr Coating Thickness 20nm Hext = 300 Oe AirPillar Spacing 200nm FIGURE 4.7 FIELD DITRIBUTION NEAR THE MAGNETIC PROBE...58 Co/Cr Coating Thickness 40nm Hext = 300 Oe AirPillar Spacing 200nm 6

7 FIGURE 4.8 FIELD DITRIBUTION NEAR THE MAGNETIC PROBE...59 Co/Cr Coating Thickness 20nm Hext = 200 Oe AirPillar Spacing 200nm FIGURE 4.9 FIELD DITRIBUTION NEAR THE MAGNETIC PROBE...59 Co/Cr Coating Thickness 20nm Hext = 300 Oe AirPillar Spacing 200nm FIGURE 4.10 FIELD AT THE TARGET PILLAR POSITION DURING THE PMR PR O C ESS FIGURE 4.11 FIELD AT THE PILLAR PROBE THICKNESS 40nm Hext = 300 Oe...64 FIGURE 4.12 FIELD AT THE PILLAR PROBE THICKNESS 20nm Hext = 300 Oe...64 FIGURE 4.13 MFM IMAGE OF PMR (SPACING: 200 nm)

8 LIST OF TABLE TABLE 4.1 MESH ELEMENTS AND SIZES OF EACH OBJECT

9 Chapter 1 Introduction 1.1 Introduction Magnetic data storage system has played a major role in data storage industry. Since its introduction by IBM, the performance of the devices has been improved rapidly. Grochowski et al [16] expected that the required data density for HDD would be 16 Gbit/cm 2 beyond year Is it possible to achieve that areal density as high as 16 Gbit/cm 2 with current HDD technology? The answer is No. HDD will face the superparamagnetic limit at which the size of the bits become too small to remain stable at room temperature in the near future. Therefore, a lot of efforts have been given to develop new technologies which are able to overcome the superparamagnetic limit in the memory storage device industry. There exist two most important parameters in data storage system. The first one is areal density and the second one is read/write speed. Both of them are required to be competitive in the data storage market. Figure 1.1 compares several candidates to replace current HDD technology in terms of these two performances. Recently, the lab demonstration of 1.7 Gbit/cm 2 recording was performed by IBM scientists and the read/write speed was as high as 150 Mbit/sec. This performance was achievable with HDD-MR technology. But mentioned as before, this technology has an intrinsic limitation of superparamagnetism. 9

10 the media surface, an external field is applied to the media from an external coil below the media. Because the MFM tip is extremely sharp, a magnetic field is concentrated very much at the end of the probe. Such field is able to magnetize a small area on the media. The resolution of the writing process is very sensitive to the performance of the MFM tip. Probe Media Coil Figure 2.4 Point Magnetic Recording Scheme The coil plays a major role in the PMR process. There are two things to notice, here. First, the coil can be used to control the intensity of the writing field by modifying the quantity of current flowing the coil. Secondly, the coil can be used to change the direction of the writing field. This can be performed when the MFM probe has a low coercivity. In writing, the MFM probe must be chosen so that the probe field alone is not strong enough to change the pillar's magnetization. Furthermore, the coil field is not increased 23

11 applications were reported. In addition, the speed of R/W is also limited because of the heavy Read/Write head used in optical system. A patterned magnetic media (PMM) having periodic arrays of magnetic pillars has been proposed to overcome the superparamagnetism limit of the current magnetic storage system. In patterned media, each single domain magnetic pillar is used to store one data bit. So PMM can offer the high areal density of 160 Gbit/cm 2 by reducing the transition and track edge noise and providing a simplified tracking method. In this thesis, we focus on the resolution of PMM. The purpose and research method are explained in section 1.3 in detail. 1.2 Historical Review Lambert et al [18][19] first recognized the advantages of the patterned media. They showed that PMM can decrease the noise problems and get higher track density. The magnetic characterization on PMM array was done by Gibson et al. [14] [15] [20] They proved that the interaction field could play an important role in the recording process. Chou et al.[5-8] fabricated the arrays of Ni pillars with the density as high as 65x10 9 pillars/in 2 and observed their magnetic states with MFM. They examined the switching and interaction properties of isolated nickel (Ni )and cobalt (Co) bars whose magnetization axis lies in the sample plane. Especially Chou et al proved that the patterned magnetic media would be promising as a high density media for next generation. 11

12 Moreland et al [22] started to use a strong MFM tip that can influence the pillar magnetization for writing on the patterned magnetic media. Gibson et al [14] performed writng on the array of bars with the recording density as high as 7.5 Gbit/in 2. The point magnetic recording was introduced by Ohkubo et al.[23-27] They could get recording density as high as 150 nm data bit. The PMR method has such a simple structure that implementation is easy and the small bit size is achievable. 1.3 Thesis Outline In this thesis, two criteria are presented to predict the PMM resolution that was fabricated in the Nanostructures Laboratory of MIT and characterized in the Mechatronics Laboratory of MIT. The media consist of Nickel pillars whose diameter is 100 nm and height is 180 nm. First, we will propose two criteria to determine the maximum areal density of PMM. Secondly, some FEM model will be developed to figure out the magnetic field concentration at the end of the probe during Point Magnetic Recording process. And interaction field between PMM pillars will be analyzed with FEM model, also. The results from the FEM analysis will be compared with the experimental results. After proving that this modeling describes the actual field behavior very well, the results from the FEM analysis along with the two criteria presented will be used to determine the media resolution. Chapter 2 is devoted to explain some basic concept about patterned magnetic media. General performance requirement for high density magnetic storage device is introduced 12

13 in section 2.2. And section 2.3 discusses the important magnetic properties of PMM such as magnetic anisotropy, switching property. In section 2.4, the point magnetic recording experiment performed by Bae [4] is presented. Chapter 3 describes the effect of interaction field between magnetic pillars on the resolution of PMM. The 1 st criterion is given and the FEM model for interaction field is developed. In chapter 4, the FEM model to explain the field behavior near the tip during the PMR process is developed and applied to the 2 nd criterion for the PMM resolution. 13

14 Chapter 2 Background 2.1 Introduction In this chapter, some basic concepts about the patterned magnetic media (PMM) are given. Section 2.2 introduces important performance parameters for a high density magnetic storage device. Magnetic anisotropy and switching field of the PMM pillars are also discussed in the following section. In section 2.4, the point magnetic recording (PMR) experiment performed by Bae[4] is presented. 2.2 Performance Requirement The performance of a recording system is usually described by several parameters such as capacity, access time, and data rate. In the following section, the definition of each parameter is given and the performance data of state of the art current HDD system is examined Capacity The capacity is the total amount of data that can be stored on a device. It is usually measured in megabytes. The capacity of a media unit is the product of its areal density and recording area. Areal density is the number of bits in a given area. That is obtained by multiplying BPI (Bits-Per-Inch) and TPI (Tracks-Per-Inch). In a magnetic recording system, BPI defines how many bit can be written onto one inch of a track on the disc 14

15 surface (especially the innermost track) while TPI is the track density which is expressed as the number of tracks per inch. In recent laboratory demonstration of the recording density of 11 Gbit/in 2 by IBM, the linear bit density was nearly 360,000 BPI. On the other hand, the track density is about 30,000 TPI. We can notice that the track density is much lower than the linear bit density. This is due to the inherent mechanical structure of the hard disk drive. The HDD read/write head slider should maintain the very small gap of 50 nm from the surface of disk. This is achieved when the spring force of the HDD suspension is balanced with the air pressure acting on the HDD head slider. This limits the stiffness of the mechanical arm and results in the reduction of total bandwidth of the tracking servo Access Time The access time is the average time taken to move from one data point to another point and to begin reading or writing. The access time is defined as summation of various time measurements and delays such as seek time, settling time and latency. Seek time is the time required, on average, to move the read/write head to another location on the disk, usually varies from 8 msec to 16 msec. Settling time is a delay required for transient tracking errors to lie down. Latency is the average time required for the disk to rotate to a desired sector. On average, latency is the time for half of a disk revolution. The seek time can not be expressed as a function of the seek distance between the old track and the new track. This is because the head is being accelerated during most of a seek operation. In addition, the seek procedure may be more complicated than a single jump from one track to another. After single jump, the tracking system reads the actual 15

16 track address and performs a few fine seeks to reach the goal track. The delay for these fine seeks has significant effect on overall seek time. The settling time becomes a more significant component of the access time as the seek time is reduced. Current servo bandwidth for HDD ranges from 600 Hz to 750 Hz. Therefore the settling time is from 1.3 to 1.7 msec. This takes an important portion of the access time. Latency depends on the HDD spindle rotation speed. For Diamondmax 2880 drive, its rotation rate is 5,400 rpm, and the average latency time is calculated to be 5 msec. This means that the latency time is a big portion of total access time. A lot of efforts have been made in order to increase the spin speed of HDD Data Rate Data transfer rate refers to speed at which bits are sent. In a disk storage system, the communication is between the CPU and the controller, plus the controller and the disk drive. Typical units are megabits-per-second. Internal transfer rate is the rate that data is written to and read from the discs. 2.3 Concept of the Patterned Magnetic Media Advantages of PMM The concept of the patterned media is introduced to overcome the limitation of the thin film media. The patterned media consist of periodic arrays of single domain magnetic particles fabricated using the current lithography technology. The idea is 16

17 simple. Each particle is used to store one bit of data. The advantages of the single domain pillar array as a magnetic storage medium can be summarized as follows: " The writing process in the PMM is simplified and quantized, which results in much lower noise and error rate. * Crosstalk is reduced due to the nonmagnetic filler surrounding the pillars. * Tracking is simplified because there is a variation of magnetic field between pillars regardless of their magnetization direction. " PMM can be a solution to the superparamagnetic limit of the thin film media Anisotropy: Easy Axis and MH curve Figure 2.1 shows the picture of a single pillar. Each magnetic pillar is so small as below 1 p m that it becomes a single magnetic domain. A single domain is always magnetized along a preferable magnetization direction, called easy axis. Along this axis, the pillar has only two stable magnetization states, equal in magnitude but opposite in direction. Easy axis is determined by many factors. The most important one is the magnetic anisotropy of the PMM pillar. This magnetic anisotropy also affect the shape of the MH curve, or the shape of the hysteresis loop. 17

18 i Easy Axis N Figure 2.1 PMM pillar There exist two important magnetic anisotropy. The first one is crystal anisotropy and the other one is shape anisotropy. The crystal anisotropy is caused by the spin-orbit interaction. The electron orbits are linked to the crystallographic structure, and by the interaction between the lattice and the spins, the spins prefer to align along well-defined crystallographic axes. Therefore there exist directions in space in which it is easier to magnetize a given crystal than in other directions. For example, the direction of easy magnetization for nickel (Ni), cobalt (Co) are <111>, <0001>, respectively. Crystal anisotropy may be regarded as a force, which tends to turn the magnetization to directions of a certain form in the crystal. Because the applied field must do work against the ansiotropy force to turn the magnetization vector away from an easy direction, there must be energy stored in any crystal in which Ms points in a noneasy direction. This is called the crystal anisotropy energy E. In a cubic crystal, let M, make angles a, b, c, with the crystal axes, and let xl, c2, a3 be the cosines of these angles, then the crystal anisotropy energy E is expressed as following equation.[10] E = K +K 1,(alac +a 2a2 +a 2a)+ K 2 (a)a+ 2 )+... (2-1) The easy axis is along the magnetization direction at which, E, in equation (2.1) is minimum. The strength of this anisotropy force is expressed by anisotropy constants K 1 18

19 or K 2 in the equation above. The values of these constants at room temperature for Ni are K 1 = -0.5, K 2 = The shape anisotropy is created by the shape of the magnetic structure. For a polycrystalline specimen having no preferred orientation, if it is spherical in shape, the same applied field will magnetize it to the same extent in any direction. But if it is nonspherical, it will be easier to magnetize it along a long axis than along a short axis. Thus, shape can be a source of magnetic anisotropy. Stoner has treated shape anisotropy quantitatively for the case of a particle in the shape of a prolate spheroid(rod) with semimajor axis c and semi-minor axes of equal length a shown in Figure 2.2. The shape anisotropy constant Ks is as follows.[11] 1 KS =-(Na -N )M 2 2 (2-2) where Na and Nc are the magnetizing coefficients parallel to the a and c axes, and M the magnetization. The strength of shape anisotropy, as the equation (2-2) suggests, depends on the axial ratio of the structure, which determines the term (Na-Nc), and on the magnetization M. M J Figure 2.2 Prolate Spheroid 19

20 2.3.3 Magnetization Reversal of PMM pillar When the particle becomes smaller than the critical size, it becomes single-domain, and the magnetization reversal mechanisms are quite different from that of larger particles. These magnetization reversal mechanism depends on the size and geometry of the particles. At sizes below about 1 p m for materials such as cobalt or nickel, the particles becomes single-domain, but the magnetization is non-uniform throughout the particle volume, and the magnetization reverses by incoherent mechanisms such as curling or vortex propagation. For very much smaller particles, the magnetization is uniform over the entire volume, and reverses by coherent rotation. Coherent Rotation In this mode, magnetization rotates in the same angle everywhere through the particle. The moments in the particle remained parallel to one another during the rotation. This mode is called coherent rotation, or Stoner-Wohlfarth mode. Suppose that the field is applied along the easy axis, and that H and M, both point along the positive direction of this axis. Then let H be reduced to zero and then increased in the negative direction. The magnetization will flip when H reaches the value of _2K HC = ' +(Na -N)M (2-3) MS where Hcj is the intrinsic coercivity, Na and Nc are the demagnetizing coefficients parallel to the a and c axes, K is the crystal anisotropy constant, and Ms is the saturation magnetization. The first term in Equation (2-3) comes from the crystalline anisotropy, 20

21 and the second term comes from the shape anisotropy. Equation (2-3) is only for the case when the easy axes of both are parallel to the applied field. If we plot M vs. H for the case of H parallel to M,, the hysteresis loop is rectangular, as shown in Figure 2-3 (a). On the other hand, if the field is perpendicular to easy axis, the field Hci is needed to saturate the magnetization in the field direction. It is shown in Figure 2-3 (b). M 'M _ H (a) H parallel to M, (b) H perpendicular to M, Figure 2.3 Hysteresis loops for Coherent Rotation Curling The curling mode was investigated theoretically by Frei et al [13], by the methods of micromagnetics. Their calculations are too intricate to reproduce here, and only the main result will be given. The following is from "Introduction to Magnetic Materials" by Cullity. For the case of the coherent rotation, the energy barrier to a magnetization reversal is magnetostatic energy due to the free poles formed on the surface. But the energy barrier to a curling reversal is mainly from exchange energy between spins, 21

22 because the spins are not parallel to one another during the reversal. Thus, we can conclude that if highly elongated particles in an assembly reverse by curling, the coercivity should be independent of the packing fraction, because no magnetostatic energy is involved. The equation of the pillar's switching field for a curling mode is given by Hd > NCMS - 2M k /(2a /DO) 2 (2-4) where k is the constant dependent on aspect ratio given by Aharoni in [1] and a is semiminor axis. Do is the characteristic length defined in the following equation, Do 2A 2 (2-5) M, where, A is exchange constant. 2.4 Point Magnetic Recording using MFM[Bae, J.] This section is based on the research performed by Bae. [4] Concept of the Point Magnetic Recording In this section, the basic concept of the point magnetic recording is provided. Figure 2.4 shows the basic scheme of the point magnetic recording. Simply speaking, the PMR process is to use the magnetic field concentration. First, the sharp magnetic tip is brought and contacted to the media surface. A sharp probe should be able to contact the surface extremely slightly to get the really small contact area. While the probe is contacted with 22

23 the media surface, an external field is applied to the media from an external coil below the media. Because the MFM tip is extremely sharp, a magnetic field is concentrated very much at the end of the probe. Such field is able to magnetize a small area on the media. The resolution of the writing process is very sensitive to the performance of the MFM tip. Probe Media I Coil Figure 2.4 Point Magnetic Recording Scheme The coil plays a major role in the PMR process. There are two things to notice, here. First, the coil can be used to control the intensity of the writing field by modifying the quantity of current flowing the coil. Secondly, the coil can be used to change the direction of the writing field. This can be performed when the MFM probe has a low coercivity. In writing, the MFM probe must be chosen so that the probe field alone is not strong enough to change the pillar's magnetization. Furthermore, the coil field is not increased 23

24 up to a level that can switch all the pillars in the sample. Only the concentrated field near the probe is strong enough to switch the selected pillar PMR Experiment Setup For the PMR process, the experimental setup shown in Figure 2.5 was used. The setup can be largely divided into two major parts, a writing module that applies a field specified by the user and a reading module that measures the magnetic states of the pillars. In the figure, the former corresponds to the lower blue area and the latter corresponds to the upper gray area. The setup includes a coil and commercial atomic force microscope, D3500 machine. The coil was attached under the sample to apply a field perpendicular to the sample plane. To write a magnetic data onto the PMM, we bring the MFM tip to the specific magnetic pillar, then an external field is applied by the coil. This creates a very concentrated field near the tip and the target pillar flips. The basic function of MFM is used for reading the data. While the probe is placed on the target pillar, the cantilever beam of the sensor deflects according to the magnetic force applied to the tip. This deflection is monitored by the laser sensor and the signal is feedbacked to the MFM control box. 24

25 Piezo Actuator Reading Module Deflection SensorBo User Sampol Writing Module Figure 2.5 Experimental Setup for PMR process Writing on the Patterned Magnetic Media Bae [4] was successful in writing bits onto the patterned media array having as small as 200 nm period using the point magnetic recording scheme described in the previous section. The result of writing onto the pillar arrays in various spacing is shown in Figure 2.6. A pillar in the dashed square is the target pillar. As one can see by comparing the image before and after the arrow, only the target pillar flips its magnetization at a certain field. The adjacent pillars were not switched by such process. On exception is the pillar on the left-hand side of the target pillar in 200 nm period array. That is in the solid line square. Such unusual behavior of the pillar will be given an explanation later in chapter 4. 25

26 Spacing: 1500 nm Spacingi: 300 nm Spacing: 250 nm Spacing: 200 nm Figure 2.6 MFM Images of PMR Writing Experiment Measurement of the Writing Field One must know the exact amount of field applied to the pillar during point magnetic recording process for many reasons. However, the field is much difficult to measure because total flux available for the sensor is very small and limited to the small spot size. Bae [20] proposed a method of measuring the writing field during the PMR process by using the pillar arrays with known switching fields. Figure 2.7 shows the field at the tip during the PMR process as a function of external field from coil. A 2 "d order polynomial fit was performed on the data points. This is represented in black solid line that passes trough the data points. One can notice that the slope of this line is decreasing as the external filed from coil increases. This shows that the field concentration effect by the probe is reducing as the MFM probe is saturated. 26

27 , U U a) Cu -0.U) U U U Polynomial Fit. Experiment Data I I U I External Field from Coil [ Oe ] Figur e 2.7 Point Magnetic Recording Field Measurement Fieur 2.5 Summary Chapter 2 was devoted to explain basic concepts related to patterned magnetic media. In section 2.2, the definitions of the important performance parameters for a high density magnetic storage device were given. The performance data of state of the art current HDD system was examined, also. Section 2.3 discussed magnetic anisotropy and switching field of the PMM pillars. In section 2.4, the point magnetic recording experiment performed by Bae [4] was presented. 27

28 Chapter 3 Effect of Interaction Fields on PMM's Areal Density: 1 st Criterion 3.1 Introduction The PMM resolution depends on several parameters. These include the magnetic properties and geometry of both the individual magnetic pillar and the MFM probe, the external field intensity applied during the PMR process, and PMM spacing itself. We will see the effect of these parameters on the resolution of PMM which was fabricated and used for the PMR process. These are Nickel pillar with a 100 nm in diameter and 180 nm in height. In this chapter we study the interaction field between PMM pillars because it is an important element which limits the PMM density. The interaction field between PMM pillars is a magnetostatic field which results from the magnetization of each pillar and therefore it is a function of the magnetization states of neighboring pillars. The analysis will be at the macromagnetic level. This interaction field can be stronger than the switching field and flip the magnetization state of one pillar as the PMM is fabricated more densely. This motivated the 1 st criterion for PMM resolution. Section 3.2 provides a basic concept overview of the interaction field and the 1 st criterion to determine the PMM resolution. In section 3.3, a theoretical model based on the magnetostatic field theory will be described. In the last section of this chapter, we will develop an FEM model for examining the interaction field between PMM Pillars. The results from the 1 st criterion will be compared to that of previous theoretical model. 28

29 3.2 Concept of Inteaction HA-*B Up HA-+C 1 4 % J/ M Pillar B Pillar A Pillar C Down Figure 3-1 Interaction Field between Pillars Figure 3-1 shows the basic configuration for the interaction field between the PMM pillars. HAB means the interaction field applied onto pillar B by pillar A. HAB is determined by the spacing between pillars A and B and the magnetization state of pillar A. In Figure 3-1, the effect of pillar A on other two pillars B and C are shown. Here, there is an assumption about the direction of magnetization of a pillar--- every pillar is magnetized along the vertical axis. This assumption simplifies our analysis because we can consider just the vertical magnetic field. In the figure, the magnetization of pillar A is directed vertically upward. So the interaction field onto pillar B and C by pillar A is shown to point vertically downward. Even though the PMM pillars are regularly spaced in a grid format, the magnetization states of each pillar are so random that there exists probabilistic interaction 29

30 field distribution. But what we are simply interested in some limiting cases where the interaction field reaches a maximum value. This happens when the pillars around the target pillar are all magnetized in the same direction. This is the worst case because the interaction field can be higher than the switching field of the target pillar. Thus we can state the first Criterion for determining the maximum PMM resolution. Criterion 1: In order to prevent the magnetization of the target pillar from being switched by the interaction field, the interaction field Hin must be less the switching field Hs; H < Hs 3.3 Theoretical Model From an assumption that the magnetization in a pillar j is uniform, the interaction field Hji,between two pillars i and j, is expressed as the gradient of the magnetic potential. Hj.. =~ ( * (3-1) where Hjj is defined as the interaction field due to pillar j and rji is the distance between the two pillars. Mj is the magnetization of pillar j. Equation (3-1) can be represented in matrix form using the product of the vector Mj and the demagnetizing tensor matrix, Dij, 30

31 S I.4S Figure 3.3 Horizontal Distribution of PMM Pillars 1 t Criterion application to Rectangular Prism Pillars Let us consider our sample which exhibits nickel pillars with 1 00nm in diameter and 180nm in height. The interaction field Hji for such a sample is shown in Figure 3.4 as a function of the distance between the two pillars. This result is based on the Rectangular Prism Approximation Equation (3-3). Note that simulating Equation (3-3) results in an field that seems to increase exponentially as the spacing decreases. This shows that a serious interaction effect is expected for smaller spacing. From this graph, the PMM resolution is about 200nm at which the net interaction field Hint(= 5.41 x Hij) is almost approaching to switching field of 420 Oe. 34

32 In the case of a prism whose length is x = 2a, y = 2b, and z = 2c, where a,b and c are constants, equation (3-1) becomes; H 4 fj)2 Mf +am+b C - Zo C + Zo 1 r _ 2 [(X - +(y - y,) +(CZ) + [( _ X2 +(y - yo)2 +(C + Zo)2 ](3/2) (3-2) where Hjj is the interaction field in the z direction, and Msurf is the magnetization on the top and bottom surface of the rectangular prism. The parameters xo, yo and zo represents the geometric center of the ith pillar. Note that the integration in Equation (3-2) is performed over the surface of the jth pillar. Since the magnetization Mj is assumed to be in the z direction, then 0 M = 0 The solution of Equation (3-2) is converted into Equation (3-3) by using trigonometry function. H M.r= {cot f(x 0,yO,z9+ cot f(-xo,yo,zo)+cot- f(x 0,-y 0,zO)+ (3-3) 47c " cot f(x 0, yo,-z 0 ) + cot f(-xo,-yo, z) + cot- f(xo,-yo,-z 0 )+ cot- f(-xo, yo,-z 0 ) + cot- f(-xo,-yo,-z 0 )} /2 [(a -x )2 +(b-y 2 +(C-ZO) 2 (C -) Ax09yo9z )= (a - x 0 )(b - y 0 ) 32

33 where cot~' is the inverse of the cotangent function. The above model of a rectangular prism approximates a cylindrical model of a pillar when a = b = base radius of the cylinder and 2c = height. In order to use the 1 s' criterion, one needs to know the interaction field Hint. Hint can be obtained from Hji as follows. From the pillar array diagram, shown in Figure 3.3, the distance between the 2 nearest pillars is -5 times the distance S between the nearest pillars. The interaction field between the second nearest pillars is expressed by the following equation according to Pardavi et al.[28] 1 H2nnearest = 2I x2 nearest, where Hnearest = Hi Pardavi et al [28] also showed that the interaction field effect of the 3 rd nearest, 4t nearest pillars on the target pillar can be neglected when compared to the nearest and 2"n nearest pillars. Therefore the net interaction field is Hint =4 x Hnearest +4 x H2ndnearest = 4+ Hi =5.41 x Hj 33

34 I S Figure 3.3 Horizontal Distribution of PMM Pillars 1" Criterion application to Rectangular Prism Pillars Let us consider our sample which exhibits nickel pillars with 1 00nm in diameter and 180nm in height. The interaction field Hji for such a sample is shown in Figure 3.4 as a function of the distance between the two pillars. This result is based on the Rectangular Prism Approximation Equation (3-3). Note that simulating Equation (3-3) results in an field that seems to increase exponentially as the spacing decreases. This shows that a serious interaction effect is expected for smaller spacing. From this graph, the PMM resolution is about 200nm at which the net interaction field Hint(= 5.41 x Hij) is almost approaching to switching field of 420 Oe. 34

35 Prism Approximation Switching Field ir" 4) E A I I I Spacing between Ni Pillars [nm] Figure 3.4 Interaction Field from Prism Approximation 3.4 FEM Model Input Magnetic Properties of a Pillar As already mentioned in Chapter 2, if the PMM pillar is smaller than the critical size, it becomes single-domain. Especially at sizes below about 1 ptm for the materials such as cobalt or nickel, the particles become single-domain. For much smaller particles, the magnetization is uniform over the entire volume, and reverses by coherent rotation. There are two significant assumptions about magnetic properties of the PMM pillar in the FEM Simulation. The 1 St one is that a pillar has a magnetization curve of one magnetic domain along the easy axis. This hysteresis curve coincides with hysteresis 35

36 loops for coherent rotation when the external field H is applied parallel to the magnetization M of the pillar. The M-H graph is of a rectangular shape and is shown in Figure 3.5 (a) below. Note that in cgs system of units B = H + 47CM where B is the magnetic flus density. The B-H curve is this case is shown in Figure 3.5 (b). The 2 "d quadrant BH curve input of Ni pillar for FEM Maxwell software [21] is shown in Figure 3.6. The Residual Magnetic Flux density Br is 0.61 Tesla and the coercive Magnetic field H, is 420 Oe (= A/m). The magnetic pillar is assumed as pure Nickel. Therefore the residual induction Br is obtained from the magnetic property table. In contrast, H, is the value from the previous PMR experiment in Chapter 2. The 2 "d assumption is that the MFM pillar has an isotropic magnetic property. As mentioned in Chapter 2, a pillar has a crystal and shape anisotropy. This means the magnetic properties depend on the direction in which they are measured. Here, our interest is just about the magnetostatic field from individual PMM pillars. Considering that a magnetic pillar is the only magnetic field source and there is no external field applied to the individual pillars, our assumption is thought to be reasonable. An isotropic magnetic property is required in order to run Maxwell FEM Analysis Engine for our research. M B Hc H, P H * H (a) (b) Figure 3.5 M-H and B-H diagram for One Magnetic Domain Particle 36

37 Figure 3.6 B-H curve for PMM Pillar Simulation Engine and Procedure The details about the simulation engine Maxwell from Ansoft are introduced in Chapter Simulation Result Figure 3.7 shows the magnetic field distribution from the center magnetic pillar which is the only field source in this simulation. The other pillars(2 on the left and 2 on the right), except for the center one, are assigned air as materials in order to calculate the volumetric average of the magnetic field in the region of each pillar. The magnetization direction of the center pillar is assigned to be vertically downward. We can see that the 37

38 1200 nm Tip angli nm Thickness t Silicon R CoCr Figure 4.1 Half plane geometry of MFM probe Secondly, the magnetic properties of the MFM probe should be given to the Maxwell software. To get the exact magnetic properties of the MFM probe is difficult because the total flux available for the sensor is very small and limited to the small spot size. Several technologies for characterizing the magnetic state of the MFM probe as a function of uniform external magnetic field H applied to the MFM probe have been published before.[2,3,30] Especially Babcock etc. [3] showed that the switching behavior of MFM probe is indicative of a single-domain structure. In our simulation, there are two basic assumptions about the magnetic property of the MFM probe. The first one is that the MFM probe has magnetically single domain structure. The second assumption is that the MFM probe is magnetized along the vertical direction which is identical to the axis of pyramidal. In Figure 4.2, the BH curve used in the FEM simulation is shown. The basic form of the hysteresis curve is drawn similar to 44

39 Prism Approximation -4-- FEM Analysis Switching Field v S Spacing between Ni Pillars [nm] Figure 3.8 Interaction Field from FEM Simulation 3.5 Summary In this chapter, the influence of the interaction field on the PMM resolution was studied. Some basic concepts about the interaction field and the 1s' criterion for determining the PMM resolution were provided in section 3.2. In section 3.3, the prism approximation model based on the field theory was described. The FEM model for analyzing the interaction field between the PMM pillars was developed. The results from both FEM analysis and prism approximation model were applied to the 1 " criterion and compared each other. 39

40 Chapter 4 Effect of the Interaction Fields on the PMM's Areal Density during the PMR Processing : 2ndCriterion 4.1 Introduction In this chapter, the effect of the interaction field on the PMM's Areal Density while doing the Point Magnetic Recording is discussed. The first part of this chapter is devoted to the definition of the 2 nd Criterion for determining Maximum PMM Areal Density. And the need for an FEM model is explained. In section 4.3, some inputs and assumptions for FEM modeling are provided. Section 4.3 also includes the simulation procedures and the information about simulation engine Maxwell. In section 4.4, the results from the FEM model are analyzed and compared with the experimental measurements reported in chapter 2. Finally the results from Chapters 3 and 4 are along with the 2 nd Criterion to determine the maximum areal density of the PMM. 4.2 Definition of the 2 nd Criterion In chapter 3, we discussed the effect of the interaction field between the PMM pillars on the PMM resolution. Here the 2 nd Criterion for determining the maximum resolution is presented. The 2 nd Criterion is about the exact amount of the field applied to the target pillar and the adjacent pillars surrounding the target pillar during the PMR process. Our goal is to flip the target pillar without switching the peripheral pillars. We can state the second criterion for determining the maximum PMM resolution as follows. 40

41 Criterion 2: A target pillar is flipped using the PMR process when the field onto it is higher than the switching field while the field onto the neighboring pillars is lower than the switching field; Honto the target pillar > Hsw Honto the nearest pillar < Hsw How can we assure such distributions of the magnetic field Honto the target pillar and Honto the nearest pillar during the PMR process? One may consider two kinds of fields. The first one is the interaction field between magnetic pillars introduced in Chapter 3. And the second one is the field applied by the external coil and concentrated by an MFM probe during the PMR Process. The total magnetic field H onto the PMM pillars during the PMR process is expressed as the vector summation of Hext applied by external coil and Hint applied by the neighboring magnetic pillars. The target pillar is flipped when the magnitude of the component of H in vertical direction is greater than the switching field value Hsw. Considering only field contributions in the vertical direction, one can write a scalar summation instead of a vector summation, Hext = Hext * k H = Hint k where k =(O 0 1)T. Note that Hxt is the value obtained when only target pillar exists without neighboring pillars. The total range of the magnetic field over the PMM pillars is expressed as follows, 41

42 H upper limit = Hext + Hint (4-1) H lower limit = Hext - Hint (4-2) where H upper limit in Equation (4-1) means the result of field summation when the direction of Hint coincides with that of Hext. When the direction of Hint is opposite to that of Hext, the field onto the magnetic pillar is equivalent to the difference between Hext and Hint. Thus these H upper limit and H lower limit define all ranges of H applied to the individual PMM pillars. 4.3 FEM Model The Necessity for an FEM Modeling For the application of the 2 nd Criterion, Hext applied by the external coil and concentrated by the MFM tip should be determined first. The magnetic field concentration behavior by the MFM probe can be understood with Maxwell's electromagnetic field theory, but an analytical solution is not easily obtained due to the nonlinearity of the magnetic properties and the geometrical complexity of the MFM probe. So we use an FEM simulation to find the field distribution around the MFM tip FEM Input MFM Probe The MFM probe is composed of silicon tip coated with a magnetic thin film Cobalt Chromium (CoCr) to measure the magnetic field from a sample surface. The MFM probe 42

43 used in the experiments in chapter 2 was a Low Moment Magnetic Force Etched Silicon Probe. It is coated with a magnetically hard material with lower magnetic moment and therefore the pillars are less affected by the tip field in the PMR experiment. This section discusses the two important inputs of MFM probe that are required by the software. First, the geometry of the magnetic component of the MFM probe in the interested area should be provided to the software. Although the 3-Dimensional simulation was performed and a quarter solid model was used for this simulation, a half plane model is given in Figure 4.1 to illustrate the geometry of the MFM probe. The geometry is approximated with the data given by the supplier Digital Instruments (DI). The data sheet indicates a tip of 170 ± 2* for the standard MFM tip used in the D3500 machine. For the tip radius R, a relatively large range, nm, is given. The tip angle, defined in Figure 4.1, is 17. The typical coating thickness ranges from 20 nm to 40 nm. In the simulation, the results for both magnetic coating thicknesses of 20 nm and 40 nm are obtained. The result shows that the effect of the coating thickness on the magnetic field concentration is serious. The silicon inside the MFM probe is not included in this simulation model because this is a nonmagnetic material whose magnetic property is similar to that of air. 43

44 1200 nm Tip angli nm Thickness t Silicon R CoCr Figure 4.1 Half plane geometry of MFM probe Secondly, the magnetic properties of the MFM probe should be given to the Maxwell software. To get the exact magnetic properties of the MFM probe is difficult because the total flux available for the sensor is very small and limited to the small spot size. Several technologies for characterizing the magnetic state of the MFM probe as a function of uniform external magnetic field H applied to the MFM probe have been published before.[2,3,30] Especially Babcock etc. [3] showed that the switching behavior of MFM probe is indicative of a single-domain structure. In our simulation, there are two basic assumptions about the magnetic property of the MFM probe. The first one is that the MFM probe has magnetically single domain structure. The second assumption is that the MFM probe is magnetized along the vertical direction which is identical to the axis of pyramidal. In Figure 4.2, the BH curve used in the FEM simulation is shown. The basic form of the hysteresis curve is drawn similar to 44

45 the one measured by Babcock et al [3]. In their work, the coercivity is given as 365 Oe for CoCr pyramidal tip. For the saturation magnetization, M, in the hysteresis curve, the data obtained by Proksch et al [29] were used. It was 720 [emu/cm 3 ]. This value is converted into 0.91 Tesla in MKS unit for the BH curve input. Figure 4.2 BH curve for MFM tip Probe and AirCoil Figure 4.3 shows the end part of the MFM tip. The MFM probe is initially magnetized vertically upward. All pillars near the MFM tip is assigned air as material. Let's call this air..pillar from now on. This air_.pillar modeling is for computing of the volumetric average of Hext in the region of each pillar position. 45

46 Initial Magnetization Direction AirPillar Figure 4.3 A Quarter Solid Model- Probe and AirPillar External Coil To apply external field vertically, external coil is modeled as a Conductor in Figure 4.4 (a). Figure 4.4 (b) shows the conduction path and the dimension of the conductor. This object generates conduction path so that it creates external field vertically upward. To get a uniform external field, the dimension of the conductor is required to be much bigger than that of the MFM probe (1O,OOOxlO,000x24,000 nm, thickness 4000nm). In order to save computer memory and to reduce the total computation time, a quarter of 3 Dimension geometry model is used. 46

47 Background(air) Conductor MFM probe Figure 4.4 (a) A Quarter Solid Model-Overall View 13200nm 7200n Current Direction 180COnm iv Figure 4.4 (b) A Conductor Solid Model 47

48 4.3.3 Simulation Engine[Maxwell] The Maxwell simulator from AnSoft Corporation performs static magnetic field analysis. The source of the static field can be the current density in conductor, an external magnetic field represented through boundary conditions or a permanent magnet. In the simulation of the PMR process, total current in a current path was put to create the external field from the coil. The simulator solves for the magnetic field, H and the magnetic flux density, B, is automatically computed from H. <Theory> The system computes the static magnetic field in two steps: 1. The system performs a conduction current solution. To simulate the model's current flow, it computes the current density, J, arising from DC currents inside conductors. 2. The system performs a static magnetic field solution. It computes the model's H field using the current density as a source. Conduction Current Solution Before the field simulator attempts to compute magnetic fields, it computes the current density in all conductors whose current is defined by specifying the current flowing through a conductor. 48

49 Current Density The current density, J, is proportional to the electric field that is established due to a potential difference. J = oe = -ov p Where: " E is the electric field. " o is the conductivity of the material. " qp is the electric potential. Under steady state conditions, the amount of charge leaving any infinitesimally small region must be the charge flowing into that region. That is, the charge density, p (x,y,z), in any region does not change with time: V 0j = 0 at Because of - ov p = J, the equation expressed in terms of the electric potential, ;Y V * (ov ;V)= 0 This is the equation that is solved in the first step of the simulation. Static Magnetic Field Solution After computing the current density, the magnetostatic field solver computes the magnetic field using Ampere's Law and Maxwell's equation describing the continuity of flux: 49

50 The equations for those laws are given by VxH=J (4.3) V-B = 0 (4.4) respectively, where H(x,y) is the magnetic field and J(x,y) is the current density field. B(x,y) is the magnetic flux density. The magnetic flux density is computed using the relationship: B= rpoh Where p, is the relative permeability and uo is the permeability of free space which is equal to 4n x10 7 [H/m]. In computing (4.3) and (4.4), the simulator uses the current density and external magnetic field defined through boundary condition. Solution Process The magnetostatic solver first simulates the conduction current, J, in all conductors. To do this, it solves for J, computes the solution error, and compares it to the conduction percentage error. If the error is greater, it refines the mesh in the tetrahedron with the highest error, and starts another conduction solution using the refined mesh. It then computes the magnetic field H at the vertices and midpoint of the edges of each tetrahedron in the finite element mesh, using the conduction current as input. If nonlinear materials are present, it computes the field using the Newton-Raphson method, which uses the slope of BH curve to compute a linear approximation of the nonlinear solution. This approximation is then substituted into the nonlinear solution for H. 50

51 The solver writes the completed solution to a file and performs an error analysis. In an adaptive analysis, it refines the mesh with the highest error, and continues solving until the stopping criterion is met. Next flow chart Figure 4.5 shows the above mechanism. 51

52 Start solution process Solve for conduction Current(J) Perform error analysis Refine Mesh Error criterion satisfied? No Yes Slve fr magnetic Perform error analysis Refine Mesh Error criterion No < Yes satisfied? Solution finished Figure 4.5 Solution Process Flowchart 52

53 4.3.4 Simulation Procedure In this section, several major commands used for the PMR Process Modeling are introduced. 3D Modeling To use advantages of symmetry, a quarter model was produced. The main steps for building 3D model of MFM probe are as follows: *Create the polyline object showing the section of MFM tip with Lines/Polyline. *Use the Surfaces/Cover Sheets to cover an open polyline object. ecreate 3D solid by sweeping the polyline object with command Solids/Sweep/Around Axis When making the volumes of pillar and conductor, the same procedure as the previous MFM probe model is used except that Solids/Sweep/Around Axis is replaced with Solids/Sweep/Through Vector Material Manager Setup Materials is selected to assign the material attributes for objects created in the 3D modeling. There are two basic methods for assigning magnetic property to each object. The first one is to specify the material attributes for objects by assigning materials from database to them. This method was used in assigning Copper (Cu) to conductor and air to background. The second one is to create new materials and add them to the local database. New BH curves were defined for MFM probe and pillar. 53

54 The step to add new material is as follows: *Choose Material/Add. eselect material type. eenter the material's properties in the Material Attributes fields. For nonlinear materials such as the MFM probe or the PMM pillars, a BH curve should be defined. For vector properties such as magnetization, the vector direction should be defined, also. *Choose Assign. eselect the option Align relative to object's orientation. *Enter Roll, Pitch, and Yaw of the vector in global orientation to align magnetization properly. Boundary/Source Manager In this simulation model, there are two section surfaces because we use a quarter of overall model. The magnetic field should flow tangential to the both surface. This properties is defined as follows: echoose Boundary. eselect Symmetry from the pull-down menu. eselect the type of symmetry as Odd Symmetry(flux tangential). To create external field by coil in the simulation model, current source of magnetic field is used. To specify the total current in a conduction path is as follows: echoose Source. 54

55 eselect the outside surface of a conductor in the conduction path. eselect Current from the pull-down menu. *Enter value in the Value field. Solution Options After material attributes, boundaries, and sources have been specified, Setup Solution/Options is chosen. The required procedures are as follows: eselect which kinds of finite element mesh is used during the solution process. eif necessary, manually seed, create, and refine the finite element mesh. eset the stopping criteria for adaptive field solution. Percent refinement per pass, Number of requested pass, and Percent error should be set here. 4.4 FEM Simulation Result Mesh Numbers, Size and Calculation Time There are several reasons that make this simulation very much time consuming. First, there exists a very big difference in the size among each object included in this simulation such as air_ pillar and MFM tip. Secondly, MFM probe has nonlinear magnetic properties. Third, the region where magnetic field should be calculated is very small when compared to overall problem region. It usually takes over five hours for the solution to this problem to converge to a percent error of 0.05% even at the fastest WorkStation model supported from MIT Athena Cluster. The result data size is usually over x 106 Bytes. The Sun 55

56 MicroSystem (Sparc Station 10) model was used for running this software. Table 4.1 shows the typical number of mesh elements and tetrahedron volume sizes for each object. Object Name No. of elements in Mesh Min. Tetrahedron Max. Tetrahedron Vol. [nm 3 ] Vol.[nm 3 Probe Conductor E+6 AirPillarCenter ,225 AirPillarSide ,947 Background(air) 53, E+6 Table 4.1 Mesh Elements and Sizes of each Object Field Concentration near Probe : Qualitative Analysis Figure 4.6 shows the effect of field concentration near the probe. The external field tends to flow through the MFM probe with much lower magnetic resistance than air. Red color means the highest field, here, the switching field 420 Oe. In contrast, blue color represents relatively low field. We can see that the field is concentrated mainly near the end part of the MFM probe. This field distribution explains how well the PMR process works even for the high density PMM array. The PMR process is possible because the 56

57 influence of field concentration by MFM tip can be confined to the region of the target air-pillar just below the MFM probe, as shown. Meanwhile, the field concentration during the PMR process depends on some parameters such as the geometry and magnetic property of the MFM probe and the strength of the external field HEXT from a coil. Figures 4.6 and 4.7 show the effect of probe coating thickness. They have the same external field HEXT 300 Oe from a coil and air-pillar spacing 200 nm. Figure 4.6 is in the case of 20 nm coating thickness and Figure 4.7 represents the field distribution in the case of 40 nm coating thickness. As shown in Figures 4.6, 4.7, the field is more concentrated at the end of the MFM probe with 40 nm coating thickness than with 20 nm coating thickness. The magnetic field can flow into MIFM probe until the field is saturated inside the tip. The saturation value per unit volume at which magnetic field can flow is the same for these two simulation. Therefore the higher volume MFM tip in Figure 4.7 can comprise more field than that in Figure 4.6. Figures 4.8 and 4.9 show the effect of the different external field. They have the same probe coating thickness 20 nm and air-pillar spacing 200 nm for these two simulations. But the applied external field HEXT is 200 Oe for Figure 4.8 and 300 Oe for Figure 4.9. We can see that the higher external field, the higher magnetic field flows through MFM probe. 57

58 Figure 4.6 Field Distribution near the Magnetic Probe Co/Cr Coating Thickness 20nm HEXT = 300 Oe AirPillar Spacing 200nm Figure 4.7 Field Distribution near the Magnetic Probe Co/Cr Coating Thickness 40nm HEXT = 300 Oe AirPillar Spacing 200nm 58

59 Figure 4.8 Field Distribution near the Magnetic Probe Co/Cr Coating Thickness 20nm HEXT = 200 Oe AirPillar Spacing 200nm Figure 4.9 Field Distribution near the Magnetic Probe Co/Cr Coating Thickness 20nm HEXT = 300 Oe AirPillar Spacing 200nm 59