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 2000
©2000 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
Accepted by............................................................
.
......................
Ain. A. Sonin
Chairman, Department Committee on Graduate Students
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
SEP 2 0 2000
LIBRARIES
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
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
TABLE OF CONTENTS
ABSTRACT .........................................................................................
2
ACKNOWLEDGEMENTS.......................................................................3
TABLE OF CONTENTS..........................................................................4
LIST OF FIGURES.................................................................................6
LIST OF TABLES ...............................................................................
8
CHAPTER 1. INTRODUCTION................................................................9
1.1 Introduction .....................................................................................
9
1.2 Historical Review..........................................................................11
1.3 Thesis Outline.................................................................................12
CHAPTER 2. BACKGROUND..............................................................14
2.1 Introduction ....................................................................................
14
2.2 Performance Requirement................................................................14
2.2.1 C apacity ...................................................................................
14
2.2.2 A ccess T im e..............................................................................15
2.2.3 Data Rate...............................................................................16
2.3 Concept of the Patterned Magnetic Media.............................................
16
2.3.1 Advantage of PMM....................................................................16
2.3.2 Anisotropy: Easy Axis and M-H curve................................................17
2.3.3 Magnetization Reversal of PMM pillar...............................................20
2.4 Point Magnetic Recording using MFM................................................22
2.4.1 Concept of the Point Magnetic Recording............................................22
2.4.2 PMR Experiment Setup..............................................................24
2.4.3 Writing on the Patterned Magnetic Media..........................................25
2.4.4 Measurement of Writing Field.........................................................26
2.5 Summary....................................................................................27
CHAPTER 3 EFFECT OF INTERACTION FIELDS ON PMM'S AREAL
DENSITY:
1
ST
CRITERION...................................................28
3.1 Introduction ....................................................................................
3.2 Concept of Interaction.....................................................................29
3.3 Theoretical Model..........................................................................30
4
28
3.4 FE M M odel...................................................................................35
3.4.1 Input....................................................................................
35
3.4.2 Simulation Engine and Procedure..................................................37
3.4.3 Simulation Result.....................................................................37
3.5 Sum m ary....................................................................................
39
CHAPTER 4.. EFFECT OF THE INTERACTION FIELD ON THE PMM'S
AREAL DENSITY DURING THE PMR PROCESSING..............40
4.1 Introduction.................................................................................40
4.2 Definition of the 2 "d Criterion.............................................................40
4.3 FEM Model....................................................................................42
4.3.1 The Necessity for an FEM Modeling.................................................42
4.3.2 FE M Input.................................................................................42
4.3.3 Simulation Engine[Maxwell].......................................................
4.3.4 Simulation Procedure..................................................................53
4.4 FEM Simulation Result....................................................................55
4.4.1 Mesh Numbers, Size and Calculation Time..........................................55
4.4.2 Field Concentration near Probe: Qualitative Analysis............................56
4.4.3 Field Concentration Comparison between FEM Simulation and Experiment
Results: Quantitative Analysis....................60
4.5 The Application of 2 "dCriterion.........................................................62
4.6 Summ ary....................................................................................63
CHAPTER 5 CONCLUSIONS & RECOMMENDATIONS............................66
BIBLIOGRAPHY................................................................................68
APPENDIX......................................................................................72
1.
PMR PROCESS FEM MODELING.....................................................72
2. INTERACTION FIELD FEM MODELING...........................................79
5
48
LIST OF FIGURES
FIGURE 1.1 PROSPECTIVE MEDIA PERFORMANCE.................................10
18
FIGURE 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 RTIC LE .........................................................................
36
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
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........................................................................
61
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).............................65
7
LIST OF TABLE
TABLE 4.1 MESH ELEMENTS AND SIZES OF EACH OBJECT....................56
8
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 2000. 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
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
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
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/in2 .
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
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
2nd
criterion for the PMM resolution.
13
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.
2.2.1 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
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.
2.2.2 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
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.
2.2.3 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
2.3.1 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
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.
2.3.2 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
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 +a2a2 +a 2a)+
)+....
2
KK
2 (a)a+
(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 K1
18
or K2 in the equation above. The values of these constants at room temperature for Ni are
K1 = -0.5, K 2 = -0.2.
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
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 =
(2-3)
' +(Na -N)M
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
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_
_
_
_
(b) H perpendicular to M,
(a) H parallel 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
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
M,
(2-5)
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]
2.4.1 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
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
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.
2.4.2 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
Reading Module
Piezo Actuator
Deflection
SensorBo
User
Sampol
Writing Module
Figure 2.5 Experimental Setup for PMR process
2.4.3 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
Spacingi: 300 nm
Spacing: 1500 nm
Spacing: 250 nm
Spacing: 200 nm
Figure 2.6 MFM Images of PMR Writing Experiment
2.4.4 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
800
-
-,
600
-
a)
400
0
U
U
U
Polynomial Fit
U
Cu
-0
.
Experiment Data
200-
.U)
U0
0
I
I
U
200
400
600
I
800
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
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
3.2 Concept of Inteaction
HA-*B
1
Up
%
4
HA-+C
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
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 targetpillarfrom being
switched by the interactionfield, the interactionfield Hin must be less the
switchingfield Hs;
H < Hs
3.3 Theoretical Model
From an assumption that the magnetization in a pillar
field Hji ,between two pillars i and
j,
j
is uniform, the interaction
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
4
2
3
5
6
0S
9
8
7
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
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
fJ)2
Mf +aM+b
4r
1
_
C + Zo
C - Zo
+(y - y,) 2 +(CZ)
[(X -
+ [(
_ X2
+(y
- yo)2
+ Zo)2](3/2)
+(C
(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
f(x
M.r={cot
47c
"
cot
f(x
0
0 , yO
,yO,z9+ cot
,-z 0 ) + cot
f(-xo,yO,zO)+cotf(-xo ,-yO , z) + cot-
f(x0 ,-y
0
,zO)+
f(xO,-yO,-z
0
)+
f(-xo , yO ,-z 0 ) + cot- f(-xO,-yO,-z 0 )}
21/2
2
2
[(a -x )2 +(b-y 2 +(C-ZO) 2 (C -)
Ax09yo9z )=
(a - x0 )(b - y0 )
cot-
32
(3-3)
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
= 4+
x H2ndnearest
Hi
5 22
=5.41 x Hj
33
I
2
3
4
5
6
8
9
0S
7
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
500
Prism Approximation
Switching Field
400-----
ir"
300
4)
200
0
E
100
0
-10
A
0
100
I
I
I
200
300
400
Spacing between Ni Pillars [nm]
Figure 3.4 Interaction Field from Prism Approximation
3.4 FEM Model
3.4.1 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
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 (= 33440 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
H,
Hc
P
H
*
(b)
(a)
Figure 3.5 M-H and B-H diagram for One Magnetic Domain Particle
36
H
Figure 3.6 B-H curve for PMM Pillar
3.4.2 Simulation Engine and Procedure
The details about the simulation engine Maxwell from Ansoft are introduced in
Chapter 4.
3.4.3 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
1200 nm
Tip angli 170
Thickness t
4000 nm
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
600
500-
-
2
Approximation
FEM Analysis
Switching Field
-Prism
-4-400 -
-v 300 -
.
200
S100 0 -
-100
0
100
300
200
400
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
1 s'
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
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
presented. The
2 nd
2 nd
Criterion for determining the maximum resolution is
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
Criterion2: A targetpillaris flipped using the PMR process when thefield onto it
is higher than the switchingfield while the field onto the neighboring
pillars is lower than the switchingfield;
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
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
H upper limit = Hext + Hint
(4-1)
H lower limit = Hext
(4-2)
-
Hint
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
4.3.1 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.
4.3.2 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
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, 25-50 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
1200 nm
Tip angli17
Thickness t
4000 nm
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
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
Initial Magnetization Direction
AirPillar
Figure 4.3 A QuarterSolid 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
Background(air)
Conductor
MFM probe
Figure 4.4 (a) A Quarter Solid Model-Overall View
13200nm
Current Direction
7200n
180COnm
. . .. .
..-
-iv
Figure 4.4 (b) A Conductor Solid Model
47
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
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
=
at
Because of
0
-
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
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
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
Start solution process
Solve for conduction
Current(J)
Perform error
analysis
Error
criterion
satisfied?
Refine Mesh
No
Yes
Slve fr magnetic
Refine Mesh
Perform error
analysis
Error
No
criterion
< satisfied?
Yes
Solution finished
Figure 4.5 Solution Process Flowchart
52
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/CoverSheets 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
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.
*ChooseAssign.
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
eSelect the outside surface of a conductor in the conduction path.
eSelect Currentfrom the pull-down menu.
*Enter value in the Value field.
Solution Options
After material attributes,
boundaries, and sources have
been specified,
Setup
Solution/Optionsis 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
4.4.1 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 70-80
55
x 106
Bytes. The Sun
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
Probe
No. of elements in Mesh Min. Tetrahedron
Vol. [nm 3]
7955
0.150
Max. Tetrahedron
Vol.[nm 3
6135
Conductor
3046
1719.72
1.442E+6
AirPillarCenter
992
6.29
11,225
AirPillarSide
344
78.677
14,947
Background(air)
53,165
0.2689
7.65E+6
Table 4.1 Mesh Elements and Sizes of each Object
4.4.2 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
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
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
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
4.4.3 Field Concentration Comparison between FEM
Simulation and Experiment Results : Quantitative
Analysis
The result graph from the simulation was drawn in Figure 4.10. The graph shows the
field at the tip as a function of an external field from the coil during the PMR process.
This value doesn't include the effect of interaction field between pillars. This can be
directly compared with the experimental data obtained in chapter 2. The x-axis shows the
external field vertically applied by the coil. The y-axis is the writing field near the tip
which is calculated by taking the volumetric average of the magnetic field in the region of
the target air-pillar. The red dotted line means the switching value 420 Oe which was
obtained from the PMR experiment. Figure 4.10 shows two simulation curves, each with
the different magnetic coating thickness on the tip. The black filled circular data point is
for the MIFM coating thickness of 20 nm and the black diamond point is for the MIFM
coating thickness of 40 nm. The experimental data is shown with the red rectangle.
The curves obtained from he FEM simulation agree well with the experimental data.
This proves that the simulation explain the field behavior correctly. It also means that the
hysteresis curve of the PMM probe given as input for the simulation governs the
magnetic behavior of the MFM probe well during the PMR process. As expected, a
simulation curve with higher coating thickness had a higher value of writing field near
the MFM tip. The slope is decreasing generally as the applied field from the coil
increases. This result shows that the field flowing through MIFM probe is getting
60
saturated as the external field increases. In the meanwhile, there are some variances of
experimental measurement seen in the graph. We can suspect that the MFM probes used
in the PMR experiment have non-uniform coating thickness.
There is one other thing to notice from this graph. The required minimum external
field for switching is 300 Oe. To get the higher value over 420 Oe in the region of
target pillar, at least over 300 Oe external field should be applied.
800
700
600
.0
L-
500 -
0400U
300
LL 2--probe
200----
thickness 20nm
probe thickness 40nm
experimental data
Switching Field
U
100
-
0I
0
I
100
I
I
200
I
i
i
I
i
300
i
I
400
i
i
500
External Field from the Coil [Oe]
Figure 4.10 Field at the Target Pillar Position during the PMR Process
61
4.5
The Application of 2 nd Criterion
The result graph for the
2 "d
Criterion was drawn in Figure 4.11, 4.12. The graph
shows the possible field ranges calculated with Equation (4.1) and (4.2) in each region of
the target pillar and the nearest neighboring pillars. Here the interaction field Hint between
the PMM pillars is from the FEM simulation in section 3.4. Those values are shown with
symbol L (the pillar at left side to the target pillar) and R (the pillar at right side to the
target pillar) as a function of the PMM pillar spacing. As explained in section 4.2, our
goal is to flip only target pillar without flipping the adjacent pillars. In order that, the field
in the region of target pillar should be always over switching field 420 Oe which is
shown as black dotted line while keeping the field value onto the neighboring pillars
below the switching field.
Figure 4.11 shows the result from the simulation with probe thickness 40 nm and
HEx-r 300 Oe. This case is expected to provide the highest field in the region of the target
pillar because probe thickness ranges from 20 nm to 40 nm. The graph shows the
simulation curves for two spacing 200 and 250 nm, respectively, each having upper and
lower limit. According to these results, we can see that the PMM with diameter 100 nm
and height 180 nm which were fabricated at the Nanostructures Laboratory and used for
the PMR experiment in the MIT Mechatronics Laboratory has a resolution of 250 nm.
For 200 nm spacing, the lower limit value of target pillar shown with black-filled delta is
below the switching field so that this target pillar will not be flipped. In contrast, for 250
nm spacing, both the lower and upper limit value of the target pillar are over switching
62
field while the writing field in the region of the neighboring pillars are below the
switching field.
Figure 4.12 shows the result from the simulation whose probe thickness is 20 nm and
HEX-T
is 300 Oe. The result graph shows that either spacing of 200 or 250 nm doesn't
satisfy the
2 nd
Criterion because the lower limit value of them is below the switching field
as shown. This result can be explained as the strong effect of interaction field between
PMM pillars which determines the range of writing field from upper level to lower level.
This means that we have to reduce the size of PMM pillar in order to decrease the PMM
resolution further.
Now we are prepared to explain the reason why some unusual flipping happened to
the neighboring PMM pillar in chapter 2. Figure 4.13 shows the MFM Image of the PMR
Experiment with 200 nm Period Array again. We can see that the pillar marked with
black solid line on the left side of the target pillar was also switched. This kinds of
behavior can be understood with the discussion in this section.
4.6
Summary
In this chapter, the influence of interaction field and magnetic field concentration on
the PMM resolution was studied. The FEM analysis to get the writing field during the
PMR process was in good agreement with the experiment results. The FEM simulation
results were applied to determine the PMM resolution through
the application of
2 nd
2 nd
Criterion, especially
criterion could explain that the neighboring pillar flipped in the
experiment of chapter 2.
63
700
600
Hupper limit = Hext by coil + Hint
Hiower limit = H ext by coil - Hint
500
2
400
300
aD
200 1*me
*j) 100
4
--
0-
A--
-y---100 -
-20-%0
-
-
-200
-
-
Upper Limit, Spacing = 200nm
Lower Limit, Spacing = 200nm
Upper Limit, Spacing = 250nm
Lower Limit, Spacing = 250nm
Switching Field
-100
0
100
200
300
Distance from the Center Pillar [nm]
Figure 4.11 Field at the Pillar Probe Thickness 40 nm HEXT= 300 Oe
700600
500-
2
400-za
I-
....
300
0
4.'
200
(a
100-
U-
~
Upper Limit, Spacing = 200nm
Lower Umit, Spacing = 200nm
v
0
- A - Upper Limit, Spacing = 250nm
- Lower Limit, Spacing = 250nm
-100- Switching Field
i i i
I I I
. . . .I V I , . l 1.1.. .
300
200
100
0
-100
-200
0
I
Distance from the Center Pillar [nm]
Figure 4.12 Field at the Pillar Probe Thickness 20 nm
64
HEXT =
300 Oe
Figure 4.13 MFM Image of PMR (Spacing: 200 nm)
65
Chapter 5
Conclusions & Recommendations
By using two criteria presented in this thesis, we were able to predict the resolution
of a PMM that was fabricated in the MIT's Nanostructures Laboratory and characterized
in the Mechatronics Laboratory at MIT. The media consist of Nickel pillars whose
diameter is 100 nm and height is 180 nm. The predicted resolution about this pillar array
is 250 nm.
The FEM analysis was very effective in getting the writing field at the magnetic
probe during the PMR process. The result was in good agreement with experimental
results. This implies that our assumptions about magnetic properties of the MFM probe
describe the behavior of the probe very well in the FEM analysis.
The application of two criteria for resolution indicates that the optimal external field
HEXT
from a coil is 300 Oe and MFM probe coating(CoCr) thickness is 40 nm for our
magnetic pillar arrays. This result confirmed our prediction that the areal density is a
function of magnetic probe and external field.
The interaction field model in chapter 3 shows that the interaction can be a serious
problem in implementing high density PMM storage device. Therefore, to reduce size of
the individual pillar is absolutely required in order to increase the PMM resolution.
The
2 nd
criterion could explain the unusual flipping of the adjacent pillar in 200 nm
spacing PMM array during PMR process.
66
This research considered only one type of a PMM pillar. To guarantee that two
criteria presented here are effective in predicting the resolution of a PMM, this method
should be applied to more PMM arrays having various dimensions and switching fields.
The exact B-H curve is the most important element in our FEM Analysis. More
efforts for characterizing the magnetic state of the MFM probe should be given.
Now this FEM simulation is very much time consuming. This resulted from the big
dimension difference among each object. One needs to find some new methodology that
can reduce the problem definition region for the MFM probe. After that, the parametric
FEM analysis will be possible. Then it can become a stronger tool for designing a PMM
array.
67
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Institute of Science", J. Appl. Phys. 30, p70S(1959)
[2] Babcock, K., M. Dugas, S. Manalis, and V. Elings, Mater. Res. Soc. Symp. Proc.
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[4] Bae, J.M., "A Data Storage System based on Patterned Magnetic Media and
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[5] Chou. S.Y., M. Wie, P.R. Krauss, P.B. Fischer, "Study of Nanoscale Magnetic
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[6] Chou, S., "Patterned Magnetic Nanostructures and Quantized Magnetic Disks",
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[7] Chou, S.Y., P.R. Krauss, and L. Kong, "Nanolithographically Defined Magnetic
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[8] Chou, S.Y., P.R. Krauss, P.J. Renstrom, "Imprint Lithography with 25-Nanometer
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[9] Chui, B.W., T.W. Kenny, H.J. Mamin, G. Bnnig, M. Despont, U. Drechsler, W.
Haberle, M. Lutwyche, and P. Vettiger, "Ultrahigh-density atomic force microscopy
data storage with erase capability", Applied Physics Letters 74(9), p1329(1999)
[10] Cullity, B.D., "Introduction to Magnetic Materials", Addison-Wesley Publishing
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Company, Inc. 1972 ISBN 0-201-01218-9, p2 1 1
[11] Cullity, B.D., "Introduction to Magnetic Materials", Addison-Wesley Publishing
Company, Inc. 1972 ISBN 0-201-01218-9, p2 4 3
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Ferromagnetic Particles", Physical Review 106(3), p446 (1957)
[14] Gibson, G.A. and S. Schultz, "Magnetic Force Microscope Study of the
Micromagnetics of Submicrometer Magnetic Particles", J. Appl. Phys. 73(9), p4516
(1993)
[15] Gibson, G.A., J.F. Smyth, S. Schultz and D.P. Kern, "Observation of the Switching
Fields of Individual Permalloy Particles in nanolithographic Arrays via Magnetic
Force Microscopy", IEEE Trans. Magn. 27(6), p5 187 (1991)
[16] Grochowski, E. and Hoyt, R.F., "Future Trends in Hard Disk Drives", IEEE Trans.
Magn 32(3), p1 8 50 (1996)
[17] Joseph, R.J., E. Schlomann, " Demagnetizing Field in Nonellipsoidal Bodies", J.
Appl. Phys. 36(5), p1579(1965)
[18] Lambert, S.E., I.L. Sanders, A.M. Patlach, M.T. Krounbi, IEEE Trans. Mag.
MAG-23, p3 6 9 0 (1987)
[19] Lambert, S.E., I.L. Sanders, A.M. Patlach, M.T. Krounbi, S.R. Hetzler, J. Appl.
Phys., 69, p4 7 24 (1991)
[20] Lederman, M., G.A. Gibson and S. Schultz, "Observation of Thermal Switching of a
Single Ferromagnetic Particle", J. Appl. Phys. 73(10), p6 9 6 1 (1993)
[21] Maxwell Electromagnetic Field Analysis Software, Ansoft Corporation
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[22] Moreland, J. and P. Rice, "High-resolution, Tunneling-Stabilized Magnetic Imaging
and Recording", Appl. Phys. Lett. 57(3), p310 (1990)
[23] Ohkubo, T., J. Kishigami, K. Yanagisawa and R. Kaneko, "Submicron Magnetizing
and Its Detection Based on the Point Magnetic Recording Concept", IEEE Trans.
Magn. 27(6), p5 2 8 6 (1991)
[24] Ohkubo, T., J. Kishigami, K. Yanagisawa, and R. Kaneko, "Submicron Magnetizing
and Its Detection Based on the Point Magnetic Recording Concept", IEEE
Translation Journal on Magnetics in Japan, 8(4), p2 4 5 (1993)
[25] Ohkubo, T., K. Yanagisawa, R. Kaneko, and J. Kishigami, "Magnetic Force
Microscopy for High-Density Point Magnetic Recording", Electronics and
Communication in Japn, Part2, Vol. 76, No. 5, p9 4 (1993)
[26] Ohkubo, T., J. Kishigami, K. Yanigisawa and R. Kaneko, "Reduced-area Magnetic
Bit Recording and Detection Using Magnetic Force Microscopy Based on
Application of Bidirectional Magnetomotive Force", IEEE Trans. Magn. 29(6)
(1993)
[27] Ohkubo, T., Y. Maeda and Y. Korhimoto, "Point Magnetic Recording Using a Force
Microscope Tip on Co-Cr Perpendicular Media with Compositionally Separated
Microstructures", IEEE Trans. Electron. Vol. E78-C, No. 11, p1523 (1995)
[28] Pardavi-Horvath, M., G. Jheng, G. Vertesy, and A. Magni, "Interaction Effects in
Switching of a Two Dimensional Array of Small Particles", IEEE Trans. Magn
32(5), p4469 (1996)
[29] Proksch, R.B., T.E. Schaffer, B.M. Moskowitz, E.D. Dahlberg, D.A. Bazylinski,
R.B. Frankel, "Magnetic Force Microscopy of the submicron magnetic assembly in
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a magnetotactic bacterium", Appl. Phys. Lett. 66(19), p2582(1995)
[30] Rugar, D., H.J. Mamin, P. Guethner, S. E. Lambert, J. E. Stem, I. McFadyen, and T.
Yogi, J. Appl. Phys. 68, p1169(1990)
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p1618(1994)
71
APPENDIX
1. PMR PROCESS FEM MODELING
<3D Modeler>
-MFM Probe
Choose Draw from the Executive Commander menu to access the 3D Modeler.
-Select Units: [nm]
-Select Absolute Coordinate.
-Select Lines/Polyline
Enter the values as follows:
Radius = 50nm, Coating Thickness = 20nm
Radius = 50nm, Coating Thickness = 20nm
X
Y
z
X
Y
z
0
0
-2000
0
0
-2000
0
29.7
-1990.2
0
29.7
-1990.2
0
47.8
-1964.6
0
47.8
-1964.6
0
1248.7
2041.2
0
1249.6
2047.1
0
1228.7
2041.2
0
1209.6
2047.1
0
28.7
1958.8
0
9.6
-1952.9
0
17.8
-1974.1
0
6.0
-1958.0
0
0
-1980
0
0
-1960
0
0
-2000
0
0
-2000
- Use the Surface/CoverSheets to cover this open polyline object.
4 Select YZ window.
4 Click the polyline object. (The Polyline changes from the default color to red.)
- Create 3D solid by sweeping the polyline object with commands Solids/Sweep/Around
Axis
72
+Select YZ window.
4Click the polyline.(The Polyline changes from the default color to red.)
4 Choose Solids/Sweep/Around Axis.
+Select Z as the Sweep Axis.
4 Enter 90 for the Angle of the Sweep.
4 Enter 5 for the number of steps.
4 Enter 0 for the Draft Angle.
4 Choose Enter.
-AirPillarCenter
-Select Lines/Polyline.
Enter the values as follows:
Point (0, 0, -2040)
Point (0, 50, -2040)
Center (0, 0, -2040)
Radius: 50
Starting Point (0, 50, -2040)
Ending Point (-50, 0, -2040)
Angle: 90
Point (-50, 0, -2040)
Point (0, 0, -2040)
-Use the Surface/Cover Sheets to cover this open polyline object.
4 Select XY widow.
4 Click the polyline. (The Polyline changes from the default color to red.)
4 Choose OK.
-Create 3D solid by sweeping the polyline object with command Solids/Sweep/Through
Vector.
4 Select XY window.
4 Click the Polyline.(The Polyline changes from the default color to red.)
73
+ Choose Solids/Sweep/Through Vector.
* Select Vector.
4 Enter (0, 0, -2040)
+ Enter (0, 0, -2220)
4 Select OK.
-AirPillarSide
-Select Lines/Polyline.
Enter the values as follows:
Point (0, 200, -2040)
Point (0, 250, -2040)
ARC
Center (0, 200, -2040)
Radius: 50
Starting Point (0, 250, -2040)
Ending Point (0, 150, -2040)
Angle: 90
Point (0, 150, -2040)
Point (0, 200, -2040)
- Use the Surface/Cover Sheets to cover this open polyline object.
4 Select XY widow.
4 Click the polyline. (The Polyline changes from the default color to red.)
4 Choose OK.
- Create 3D solid by sweeping the polyline object with command Solids/Sweep/Through
Vector.
4 Select XY window.
4 Click the Polyline.(The Polyline changes from the default color to red.)
4 Choose Solids/Sweep/Through Vector.
4 Select Vector.
74
4 Enter (0, 200, -2040)
4 Enter (0, 200, -2220)
4 Select OK.
-Conductor
-Select Lines/Polyline.
Enter the values as follows.
Conductor I
Conductor 2
(X, Y, Z)
(X,Y, Z)
(0,3600, 9000)
(-3600, 0, 9000)
(0,6600,9000)
(-3600,3600,9000)
(-6600,6600, 9000)
(-6600,6600,9000)
(-3600,3600,9000)
(-6600,0, 9000)
(0,3600,9000)
(-3600, 0, 9000)
-Use the Surface/Cover Sheets to cover this open polyline object.
4 Select XY widow.
4 Click the polyline. (The Polyline changes from the default color to red.)
+ Choose OK.
-Create 3D solid by sweeping the polyline object with command Solids/Sweep/Through
Vector.
4 Select XY window.
4 Click the Polyline.(The Polyline changes from the default color to red.)
4 Choose Solids/Sweep/Through Vector
4 Select Vector.
4 Enter (0, 3600, 9000)
4 Enter (0, 3600, -9000)
4 Select OK.
75
<Material Manager>
-Select Setup Materials.
-Choose Material/Add.
-Adding Material to the Database.
- Choose NonlinearMaterial.
- Choose BH Curve.
-Enter the values as follows:
H [Ampere/Meter]
B [Tesla]
-27,070
0
-21,497
0.866
0
0.904
-Enter "Probe" in a name field.
-Assigning Materials to Object
- Highlight the name of an object from the objects list box displayed on the left side of the
screen
- Click the left mouse button on the object in the display window. The object and its name
are both highlighted.
Choose Assign.
Select Materials as follows.
Object Name
Assigned Material
Background
Air
Conductor
Cu
Probe
Probe
AirPillar
Air
The Magnetization orientation of the Probe should be defined as follows.
- Choose Assign.
Select the Option Align relative to Object's Orientation.
76
- Enter the value as follows.
Roll
0
Pitch
-90
Yaw
0
<Boundary/Source Manager>
-Symmetry Surface
-Choose Boundary.
-Select the Boundary Surface.
-Select Symmetry from the pull-down menu.
- Select the type of symmetry as Odd Symmetry(Flux Tangential).
-Source
- Choose Source.
- Select the outside surface of a conductor being in the same plane of Boundary Surface.
- Choose Units: Ampere.
-Enter the current o the surface in the value field:
Value
Hext
4.8279 E10
200 Oe
7.2418 E10
300 Oe
9.6558 ElO
400 Oe
-Choose Assign.
<Solution Option>
Choose Setup/Options.
Select New in a starting mesh field.
77
- Enter the value as Follows.
Residual
1E -06
Nonlinear
0.01
Percent refinement per Pass
30
Stopping Criteria
Number of requested passes
25
Percent Error
0.05%
78
2. INTERACTION FIELD FEM MODELING
<3D Modeler>
-Ni_ PillarCenter
-Select Lines/Circle.
Enter the values as follows:
Radius: 50
Center Point: (0, 0, 90)
-Use the Surface/CoverSheets to cover this open circle object.
4 Select XY widow.
4 Click the circle. (The circle changes from the default color to red.)
4 Choose OK.
- Create 3D solid by sweeping the circle object with command Solids/Sweep/Through
Vector.
4 Select XY window.
4 Click the circle.(The circle changes from the default color to red.)
4 Choose Solids/Sweep/Through Vector.
4 Select Vector.
4 Enter (0, 0, 90)
4 Enter (0, 0, -90)
4 Select OK.
-Air_ PillarSide
Select Lines/Circle.
Enter the values as follows:
Radius: 50
79
Center Point: (0, 200, 90)
-Use the Surface/Cover Sheets to cover this open circle object.
4 Select XY widow.
4 Click the circle. (The circle changes from the default color to red.)
4 Choose OK.
-Create 3D solid by sweeping the circle object with command Solids/Sweep/Through
Vector.
4 Select XY window.
4 Click the circle.(The circle changes from the default color to red.)
4 Choose Solids/Sweep/Through Vector.
4 Select Vector.
4 Enter (0, 200, 90)
4 Enter (0, 200, -90)
4 Select OK.
<Material Manager>
Select Setup Materials.
Choose Material/Add.
-Adding Material to the Database.
Choose NonlinearMaterial.
Choose BH Curve.
Enter the values as follows:
H [Ampere/Meter]
B [Tesla]
-33,440
0
-33,430
0.566
0
0.608
-Enter "NiPillar" in a name field.
80
-Assigning Materials to Object
- Highlight the name of an object from the objects list box displayed on the left side of the
screen
- Click the left mouse button on the object in the display window. The object and its name
are both highlighted.
- Choose Assign.
Select materials as follows.
Object Name
Assigned Material
Background
Air
NiPillarCenter
NiPillar
AirPillar-side
Air
The Magnetization orientation of the NiPillarCenter should be defined as follows.
-Choose Assign.
-Select the Option Align relative to Object's Orientation.
-Enter the values as follows.
Roll
0
Pitch
-90
Yaw
0
<Solution Option>
-Choose Setup/Options.
Select New in a starting mesh field.
81
-Enter the values as Follows.
Residual
1E -06
Nonlinear
0.01
Percent refinement per Pass
30
Stopping Criteria
Number of requested passes
25
Percent Error
0.05%
82