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Noncontact imaging of materials using evanescent microwave magnetic dipole probe and modulated scatterers

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NONCONTACT IMAGING OF MATERIALS USING EVANESCENT MICROWAVE
MAGNETIC DIPOLE PROBE AND MODULATED SCATTERERS
by
RUN WANG
Submitted in partial fulfillment o f the requirements
For the degree o f Doctor o f Philosophy
Dissertation Adviser: Dr. Massood Tabib-Azar
Department o f Electrical Engineering and Computer Science
CASE WESTERN RESERVE UNIVERSITY
May, 2006
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UMI Number: 3218693
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CASE WESTERN RESERVE UNIVERSITY
SCHOOL OF GRADUATE STUDIES
We hereby approve the thesis/dissertation o f
W anjr
& UTL
7V?. D .
candidate for the
degree.
(signed)_
(Chair o f the Committee)
a &
(Date)
16
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*Lqqy~
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To my husband, fo r his endless love and support
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TABLE OF CONTENTS
Table of contents................................................................................................................................... 1
List of Tables........................................................................................................................................ 4
List of Figures....................................................................................................................................... 5
Acknowledgements............................................................................................................................ 11
Abstract.................................................................................................................................................12
1.
Introduction............................................................................................................................. 14
1.1
1.2
Motivation....................................................................................................................... 14
1.1.1
Semiconductor industry.........................................................................................15
1.1.2
Biomedical applications........................................................................................16
1.1.3
High frequency integrated circuit detection....................................................... 17
1.1.4
Aging aircraft.......................................................................................................... 17
Current Techniques........................................................................................................IB
1.2.1
Four point resistivity measurement.....................................................................18
1.2.2
Eddy current probe................................................................................................. 19
1.2.3
Scanning near-field optical microcopy............................................................... 20
1.2.4
Electricdipole probe............................................................................................. 20
1.3
Advantagesof Evanescent Microwave Magnetic Dipole Probe........................... 21
1.4
Thesis Outline.................................................................................................................24
2.
Probe Design and Analysis................................................................................................. 26
2.1
Principle of Probe Operation.......................................................................................26
2.2
Probe D esign................................................................................................................... 28
2.2.1
Resonator probe....................................................................................................... 29
2.2.2
Transmission line p ro b e....................................................................................... 33
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2.3
Probe Analysis ...........................................................................................34
2.3.1
Detection of conductivity change....................................................................... 35
2.3.2
Detection of magnetic field density change...................................................... 44
2.3.3
Detection of dielectric constant change............................................................. 48
3.
Experimental Setup and Results.........................................................................................61
3.1
Experimental Setup........................................................................................................61
3.2
Probe Calibration............................................................................................ 64
3.2.1
Sensitivity..................................................................................................................64
3.2.2
Resolution.................................................................................................................. 65
3.2.3
Accuracy................................................................................................................... 65
3.2.4
Minimum detectable signal...................................................................................66
3.2.5
Reproducibility..........................................................................................................67
3.3
Scanned Imaging Results.............................................................................................67
3.3.1
Conducting samples................................................................................................67
3.3.2 Damascene copper on silicon.................................................................................82
3.3.3 Magnetized ferromagneticsam ples........................................................................86
4.
Near-field Electromagnetic Modulated Scatterers Imaging.............................................91
4.1
Introduction........................................................................................................................ 91
4.2
Principle of operation....................................................................................................... 94
4.3
Array of local scatterers and imaging at10 G H z .....................................................102
4.4
AFM as a local scatterer and imaging at 100 GHz ...................................................103
5............. Conclusion and Future work...........................................................................................112
5.1
Conclusion................................................................................................................ 112
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5.2
Future W ork........................................................................................................... 112
6.
Appendix.................................................................................................................................116
7.
Bibliography.........................................................................................................................132
3
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LIST OF TABLES
Table 1.1
Comparison of some common methods for material characterization
23
using the evanescent microwave microscope.
Table 3.1
Estimated parameters of probes with different diameters at different
distances between tip and sample.
4
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78
LIST OF FIGURES
Figure 1.1
Four-point resistivity measurement diagram.
19
Figure 2.1
Lumped-element model o f magnetic dipole probe.
30
Figure 2.2
Lumped-element diagram o f an electric dipole probe.
33
Figure 2.3
Relative resonant frequencies o f evanescent microwave resonator
33
probe and microstrip transmission line resonator.
Figure 2.4
(a) Microstripline resonator and probe assembly. Cl is a tuning
35
capacitor and is used to adjust the coupling between the
transmission line and the resonator part, (b) Magnetic dipole
probe configuration, (c) Electric dipole probe configuration.
Evanescent waves extend out o f the both dipole probes.
Figure 2.5
The reflection coefficient ( |S n |) of EMMP when a conducting
37
sample is placed near the probe. The change in / 0 caused by the
sample placed near the tip is about 33 MHz for d ~ 500 pm.
Figure 2.6
Corresponding shift o f | Su | curves due to the introduction o f
38
four different conductivity samples close to the probe tip.
Figure 2.7
(a) Equivalent circuit model of the resonator in presence of a
40
conducting sample, (b) equivalent lumped parameter circuit
model.
Figure 2.8
The
reflection
coefficient
( | Sn | )
of
EMMP
when
a
ferromagnetic sample is placed near the probe. The change in f 0
caused by the sample placed near the tip is about 10.5 MHz for
5
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45
d ~ 300 pm.
Figure 2.9
Equivalent circuit model for the microstripline resonator and
49
coupling to the transmission line.
Figure 2.10
Equivalent circuit representing the interaction between the
51
sample and (a) the magnetic probe, and (b) the electric probe.
Figure 2.11
Corresponding shift o f | Sn | curves due to the introduction o f
55
four different conductivity samples close to the probe tip o f (a)
magnetic probe, and (b) electric probe.
Figure 2.12
Experimental graphs depicting the output of the magnetic and
56
electric dipole probes as a function of frequency.
Figure 2.13
Calibration results for the magnetic and electric probes versus the
58
sheet resistances of the conducting samples.
Figure 2.14
Calibration results for the magnetic and electric probes versus the
59
sheet resistances o f the semiconducting samples.
Figure 2.15
Calibration results for the magnetic and electric probes versus the
60
relative dielectric constants o f the samples.
Figure 3.1
Experimental setup used in performing evanescent microwave
63
probe measurement.
Figure 3.2
Corresponding shift o f 15n | curves due to the different probe
68
coupling strengths.
Figure 3.3
Evanescent microwave probe calibration for critical and overcoupling probes.
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69
Figure 3.4
Relative reflected microwave magnitude as a function o f distance
70
(D) between the probe tip and sample for critical and over­
coupling probes.
Figure 3.5
Evanescent microwave probe calibration with the under-coupling
71
probe.
Figure 3.6
Relative reflected microwave magnitude as a function o f distance
72
(D) between the probe tip and sample for under-coupling probe.
Figure 3.7
Evanescent microwave critical coupling probe resonant
72
frequency as a function o f sheet resistance at and fixed distance
(D) between the probe tip and sample, obtained using metallic
films with different sheet resistances.
Figure 3.8
Evanescent microwave probe calibration results for critical and
73
over-coupling over a 0.91 Q/square obtained using metallic films
with different sheet resistances.
Figure 3.9
Relative resonant frequencies of evanescent microwave resonator
74
probe and microstrip transmission line resonator obtained using
metallic films with different sheet resistances.
Figure 3.10
Evanescent microwave probe calibration obtained using metallic
75
films with different sheet resistances.
Figure 3.11
Evanescent microwave probe measurement results match the
76
predicted values shown in dotted lines, for £,=().3 mm, 0.4 mm,
and 0.6 mm diameters.
Figure 3.12
Reflected microwave magnitude as a function o f distance (D)
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77
between the three different diameter (Q probes’ tips and the brass
sample.
Figure 3.13
Reproducibility measurement. Repeated measurements
79
performed over short term o f time at different spots on metallic
samples with different sheet resistances. The error bars indicated
the range o f sensor output over the repeated measurements.
Figure 3.14
Long term stability o f the sensor range. Measurements were taken
80
at two different distances o f 50 pm, and 100 pm between tip and
sample.
Figure 3.15
EMP image o f a sample with two different conducting regions at
81
d = 0.5 mm and A0 = 5° per step. The sample is covered with
aluminum and subsequently gold is added to the small region as
shown above.
Figure 3.16
EMP image of an aluminum film thickness variation at d = 0.5
mm and
82
= 5° per step. The sample is prepared by evaporation
o f around 300
aluminum onto a glass substrate.
Figure 3.17
EMP image of a copper film on silicon substrate.
83
Figure 3.18
EMP image of copper film after 5 minutes sulfidation at 150 °C.
84
Figure 3.19
EMP image of copper sulfide after 1 minute annealing in air at
85
150 °C.
Figure 3.20
Evanescent magnetic microwave probe calibration curve.
86
Figure 3.21
Relative reflected microwave magnitude as a function o f distance
87
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(D) between the probe tip and sample.
Figure 3.22
Long term stability measurement. Measurements are taken at two
different distances between tip and sample.
Figure 3.23
Images of permeability in a magnetized ferreomagnet sample
obtained using the magnetic probe sensor: (a) two magnets and
(b) three magnets in parallel.
Figure 4.1
Schematic of local scatterer array used to combine traveling
wave imaging with near-field super-resolution, (a) Transmission­
mode operation, and (b) reflection-mode operation, c) Cross
section diagram of sample-scatterer interaction in the
transmission mode.
Figure 4.2
Experimental setup.
Figure 4.3
Micromotor array (4x4) used in preliminary studies.
Figure 4.4
The change of received spectrum when a sample o f
E r=
2.2 is
placed between one o f the micromotors and the horn antenna.
Figure 4.5
Calibration curve and the simulation results.
Figure 4.6
10 GHz 4x4 image o f a composite dielectric sample. The
calibration curve of figure 5 was used to convert the reflected
w ave’s amplitudes to permittivity values of different regions.
Figure 4.7
Schematic of near-field microwave measurement with a
commercial AFM.
Figure 4.8
Photographs of (a) scanning near-field microwave microscopy
experimental setup with AFM system, and (b) microwave
9
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microscopy setup.
Figure 4.9
Simultaneous AFM and near-field millimeter wave images
109
obtained from thin layer of titatnium film covered with carbon
nanotubes. The scans were performed at 100 GHz.
Figure 4.10
A MEMS array o f local modulated scatterers.
110
Figure A .l
(a) Gap in a microstrip line , and (b) Capacitive n-nctwork model
117
for a gap in a microstrip line.
Figure A.2
(a) Symmetrically excited two-port network resulting in Ceven, (b)
119
Antisymmetrically excited two-port c network in Codd.
Figure A.3
Cross section o f a microstrip line.
120
Figure A.4
(a) Ceven and Codd per unit width o f microstrip lines of width-to-
124
height ratio of 0.5 and relative dielectric constants from 1.0 to
15.0. Gap spacing-to-width ratio ranges from 0.1 to 2.0. (b)
Same as (a) except width-to-height ratio o f 1.0. (c) same as (a)
except width-to-height ratio of 2.0.
Figure B .l
The AFM Imaging of silicon nitride (Si3 N4).
10
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132
ACKNOWLEDGEMENTS
I am forever indebted to my advisor, Dr. Massood Tabib-Azar for offering me the
opportunity to perform this research. Without his great guidance and encouragement, this
work could not go through.
I would like to thank my committee members for their valuable help and suggestion
on my thesis.
I am very grateful to all members o f Advanced Devices Optical & Electronic group
for their friendship and help. Special thanks go to Frank Li, Joe Zarycki and Liang You
for their unfailing help to give me a smooth start on the research. I also thank Yan Xie
for valuable suggestion and help.
This work is supported by Case Western Reserve University.
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Noncontact Imaging of Materials Using Evanescent Microwave Magnetic Dipole Probe
and Modulated Scatterers
Abstract
by
RUN W ANG
A near-field magnetic-dipole probe suitable for non-contact imaging of materials
was described and the effects of resonator coupling strength, operation frequency, and the
probe wire tip geometry on the conductivity resolution of the probe are experimentally
determined. Using a simplified circuit model o f the resonator, w e were able to interpret
the system ’s output and predict the magnitude of reflected wave and relate it to the
properties of the samples under investigation. Thus, the probe was calibrated to perform
quantitative conductivity measurement. It has been shown that we have detected metal
nonuniformities with 1% accuracy and 5 x 1 0 3cr and 2 x 1 0 2cr conductivity resolution at
2 GHz operation frequency for the critical and over-coupling probes, respectively. We
also discussed the calibration results of probes with different coupling strength over a
0.91 Q/square sample.
It has been shown that resonator probe has 100 times higher
conductivity resolution than that of the transmission line probe.
Furthermore, we
characterized and compared the calibration results of probes with tip wires of different
diameters. We also reported its applications in imaging high-frequency electromagnetic
properties o f magnetic metallic samples.
The probe was calibrated to perform
12
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quantitative conductivity measurements in uniformity of the electromagnetic properties
o f damascene copper on silicon, and its subsequently sulfidized and annealed surface, and
magnetized ferromagnetic materials.
Moreover, we discussed a new technique that combined aspects o f the “freespace” imaging with the super resolution o f near-field scanning probes by using an array
o f local scatterers near a sample. The local scatterers generated the near-fields waves
upon illumination with a microwave beam. These near-fields interacted with the nearby
material and affected the reflection coefficient (or more generally, scattering parameters)
o f scatterers in the array. Different scatterers were mechanically modulated at different
base frequencies.
Thus, the free-space reflected waves from the array were spatially
modulated according to the local sample properties and the corresponding scatterer’s
modulation frequency.
We discussed applications of this technique in imaging a
dielectric sample at 10 GHz using an array o f micromotors and a layer of carbon
nanotubes at 100 GHz using an atomic force microscope tip as the local scatterer.
13
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Chapter 1
INTRODUCTION
1.1 Motivation
There is a growing demand to develop non-contact and non-destructive imaging
techniques to detect corrosion, defects, and nonuniformities o f conductivity and dielectric
constant and thickness of the materials with very high resolution. Non-destructive methods
of imaging surface and subsurface structures and material properties are critical for
acceptance testing and failure detection o f countless applications: semiconductor defect
detection, thin film resistivity measurement, continuity o f embedded transmission lines in
high density interconnect multichip modules, and substrate epoxy void detection.
Microscopy o f surface and sub-surface defects and features is a very important tool
necessary for the advancement of high technology and for maintaining the critical edge
over other competing nations. Optical microscopy has been extensively used for centuries
to obtain information regarding visual defects on the order of a few micrometers or larger.
On the other hand, scanning electron microscopy with its wide range of resolution
(between a few angstroms and hundreds of microns) is a relatively new tool without which
the present state of sophistication of microelectronics would not have been possible.
Added to the arsenal of these tools in recent years is the scanning tunneling microscopy
with atomic resolution that has helped us to detect the probability amplitude o f the
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electronic cloud in atomic orbital. Therefore, with the present arsenal of tools one can
examine matter over a very large range o f length scale.
What is missing is a non-destructive and compact microscope with mid-range
resolution in the 0.1-100 micrometer range which, in addition to yielding information
regarding surface irregularities, also detecting sub-surface defects with relative ease.
1.1.1 Semiconductor industry
For example, mapping defects and thickness variation of thin conducting layers is
very desirable for the semiconductor industries [1-3]. The problem o f maintaining uniform
metal deposition is of primary importance in semiconductor device fabrication. Irregular
gas flow, dust in the deposition chamber, substrate imperfections, organic contaminants,
and a host of other phenomena can cause variation in the quality o f deposited metal films.
Often, these variations are not visible upon even detailed surface inspection; rather, one
examines the material destmctively to determine the location and nature o f subsurface
flaws. This often involves applying acid or corrosive gas cutting the wafer to examine the
cross section, or using an automated four-point probe. These methods are not desirable for
a variety of reasons. The first is the use of harmful chemicals, the second is slow and the
last lacks high spatial resolution. Therefore, a method to examine subsurface irregularities
in metallic films nondestructively would be of great use to the semiconductor industry.
Furthermore, the semiconductor electronics industry has driven the development of
electronic devices including ferromagnetic materials to enable ultra-fast switches and
programmable microprocessor. The development of magnetic probe has presented the new
opportunities for its use for non-destructive mapping of ferromagnetic domains.
15
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1.1.2 Biomedical applications
The evanescent microwave probe can be used to monitor electrical activities in
bone samples [4-6]. Resorption and remodeling o f bone have been attributed to steocytic
cells sensing changes in streaming potentials generated during deformation o f the tissue.
Thus, measurements of the electromagnetic properties of such tissues could prove crucial
in the development o f models to explain bone remodeling.
Evanescent microwave
magnetic dipole probe (EMMP) is sensitive to moisture and ionic mineral content such as
variations in tooth enamel. EMMP is capable o f detecting the onset o f caries- believed to
be accompanied by minute surface blemishes with increased moisture and varying
degrees of mineralization.
Having a microwave power o f less than nano-Watts, this
unique probe promises to significantly reduce the time-to-detection o f cavity formation,
enabling timely prevention.
The scanning near-field microwave microscope (SNM) also belongs to the family
o f local probes with the ability to “see” inside the sample using electromagnetic waves
over a wide range o f frequencies [7-15].
For example, the nucleus inside a breast
cancerous cell was imaged in-vitro without harming the cell using a near-field microwave
probe integrated with AFM [11].
The scanning near-field microscope can be very
valuable in performing surface and subsurface imaging o f embedded nanostructures,
leading to an in-depth understanding of interactions between microscopic objects and
their environments. Moreover, the scanning near-field microscope has the unique ability
to provide direct images of subsurface structures owing to the penetration and possible
resonant absorption of its electromagnetic signal inside materials.
16
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Measuring and monitoring the local dielectric property variations may be used to
detect voids, porosity and delamination in composite materials [16-20]. Moreover, once
the dielectric properties o f a sheet material are known, it is possible to detect its thickness
variation [20]. Dielectric properties o f mostly in vitro (excised) biological tissues at radio
and microwave frequencies have been the subject o f research for over four decades [1720]. A few studies have also been conducted on the dielectric properties of cancers in a
variety of tissue types at radio and microwave frequencies [20]. Typical differences in
the permittivity between the normal and malignant tissues are 10-20%.
Recent
experiments have shown large interest o f active microwave imaging in biomedical
applications [20].
1.1.3 High frequency integrated circuit detection
The ability of assessing delamination and the integrity of the interface between
different layers is also critically important, and early detection would substantially mitigate
production losses.
The technological evaluation in the printed circuit board (PCB)
production needs quality inspection tools to verify the traces and pads. The use o f the
evanescent microwave magnetic probe can be extended to inspect printed circuit boards for
a variety of defects in solder paste.
1.1.4 Aging aircrafts
Moreover, corrosion of aging aircrafts has recently become an expensive and
safety-critical problem nowadays [21]. The annual direct cost o f aircraft corrosion in the
U.S. alone has been estimated to be in excess of 13 billion dollars. These high costs are, in
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part, due to the current inability o f inspection techniques to detect, characterize, and
classify corrosion processes before significant damage has occurred.
This would also
require a high spatial resolution detection system, allowing for the detection of corrosion
defects at the initiation stage. Such a system would lead to minimized repair costs and a
reduced risk of damage to essential aircraft structures.
1.2 Current Techniques
Before coming to terms with the electric dipole probe and magnetic dipole probe, it
is more useful to first consider the present state of the art in nondestructive materials testing.
Different detecting methods can be used in imaging materials, such as four-point resistivity
measurement, eddy current probe and scanning near-field optical microscopy (SNOM).
1.2.1 Four-point resistivity measurement
The four probes are arranged in a linear fashion, where the two outer probes are
connected to a current supply, and the inner probes to a voltage meter, as shown in Figure
1.1. As current flows between the outer probes, the voltage drop across the inner probes is
measured. The relationship of the current and voltage values is dependent on the resistivity
of the material under investigation and the geometrical characteristic o f the probe. Fourpoint method requires electrical contact which may damage the sample.
18
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Leads may be aay teagtli.
la s tn w s e a f
I
C arres! S o u rce
I
May be AC or DC.
R su itm cs Being Measwrei
C2
Figure 1.1
Four-point resistivity measurement diagram.
1.2.2 Eddy-current probe
Eddy-current nondestructive testing is commonly carried out on metals at a single
frequency using an induction probe which senses the presence of cracks through changes in
its driving point impedance. A basic eddy-current probe consists of a primary coil carrying
an ac current and a secondary coil. In the presence of a conducting sample the mutual
inductance of these coils is changed due to eddy currents excited in the sample by the timevarying magnetic field of the primary coil. The in-phase component o f the eddy-current
signal is related to the shielding efficiency of the sample, while the quadrate component is
determined by losses. The coils may be mounted on the same or the opposite sides o f the
sample. The first arrangement is used mostly for eddy-current defectoscopy [22, 23] while
the second arrangement has been extensively used for the determination o f the
superconducting penetration depth [24],
These tests are often performed at frequencies such that the electromagnetic skin
depth is much smaller than the crack depth. The eddy-current probes currently available
have a depth resolution of 25 microns and a horizontal resolution of about 100 microns,
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and operates at frequencies in the 10 KHz-100 MHz range. It lacks the fine thickness
sensitivity o f the magnetic dipole probe [25].
1.2.3 Scanning near-field optical microscopy
Scanning near-field optical microscopy (SNOM) is a technique which can achieve
spatial resolution performance beyond the classical diffraction limit by employing a sub­
wavelength light source or detector positioned in close proximity to a specimen. Such a
sub-wavelength source usually consists o f an aperture at the end of a tapered probe, which
functions basically as a waveguide.
SNOM uses evanescent optical fields to image
variations in the refractive index or optical absorption with spatial resolution of 10-100
using light o f 6000
wavelength [26]. Currently, the optical and mechanical properties of
fiber-based probes are still rather poor and remain as the limiting performance factor for
many SNOM applications.
Although many companies commercially produce SNOM
probes, current fabrication processes are not suitable for large-scale production.
Each
probe must still be individually inspected for pinholes and other flaws. Therefore, optical
fiber-based SNOM remains relatively expensive, and the cost is likely to remain high until
more efficient probe fabrication techniques are developed. Another important advantage of
the microwave probes over near-field optical probes is that coherent imaging [27] and
polarization contrast [28] may be easily achieved.
1.2.4 Electric dipole probe
In the past, our group has extensively worked with electronic dipole probe which is
better suited for the insulator and semiconductor materials measurement [29-33].
20
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The
electric dipole experiences a short electric field line at microwave frequencies that
diminishes its use in mapping metallic samples, which can be verified in the Chapter 3.
1.3 Advantages of Evanescent Microwave Dipole Probe
It is well known that evanescent electromagnetic fields can be used to surpass the
Abbe barrier in microscopy and to resolve objects much smaller than the wavelength of
the excitation fields [34-39]. Both evanescent optical waves and microwaves have been
used in high-resolution imaging to resolve features several times smaller than the
wavelength of radiation.
Evanescent microwave (EM) complements electronic and
optical microscopes in the range of 0.01 prn-1 cm.
Since EM is a noncontact,
noninvasive, and nondestructive method, it will be very useful in the semiconductor
fabrication environment. Moreover, testing can be done in air, most liquids, or vacuum
with suitable probe structure and essentially no sample preparation.
Moreover, in contrast to other groups, our research in evanescent microwave
imaging has concentrated on using microstripline, which has the following unique
advantages.
(a) The EMMP uses coherent microwave sources that are readily and inexpensively
available over a wide range o f frequencies covering 100 MHz up to 100 GHz.
(b) The EMMP does not require conducting or optically transmitting/reflecting samples.
(c) The resolution of the EMMP can be engineered over a wide range by using different
diameters o f conducting wires between resonator and ground, and feedline-toresonator coupling strengths in addition to resonant frequency.
21
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(d) The EMMP can image sub-surface defects and non-uniformities within the
microwave skin depth inside the sample.
(e) The EMMP does not require any coupling medium and it can be used in air, vacuum,
or in a suitable liquid.
(f) Operating at very high frequencies, and using the homodyne detection technique, the
EMMP can achieve very high scan rates (up to a few cm/s) over hot and cold samples.
(g) Many different parallel EMMPs can be used simultaneously to scan over large areas.
(h) EMMP can be integrated with silicon micromachined parts to produce miniature
parallel and compact probes.
As we w ill discuss in the next chapters, the probe operates the ambient
environment and does not require any vacuum or cooling. It is extremely versatile and
can be used to study high conductivity (metallic samples with various non-uniformities
including residual stress and brazed junctions, etc.) as w ell as high resistivity
(semiconducting and dielectric) samples. It can also be used to replace optical, magnetic,
electrostatic and tunneling current schemes in detecting minute displacements with the
added benefit of being simple, nearly drift-free and easy to implement and calibrate.
Table 1.1 gives a comparison o f some commonly used characterization techniques.
It shows the versatility o f evanescent microwaves in being useful for a wide range of
conductivity. Large scale mapping o f materials with a resolution o f up to 0.01 pm is
possible with evanescent microwaves by using higher frequencies o f operation. Methods
with higher resolution than this have the disadvantage of being incompatible for detecting
large-scale inhomogeneities over large areas.
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STM uses evanescent electronic wavefunctions to image atoms at the surface o f
metals or other conducting materials.
AFM uses interactions between near-field
electronic wavefunctions and atomic cores to image atoms at the surface o f insulators.
Table 1.1
Comparison of some common methods for material characterization using
the evanescent microwave microscope.
Method
Resolution
Conductivity limits
Comments
Optical
1- lOnm
No requirements on
For high resolution the probe needs to
conductivity
be a few nm form the sample; a
microscopy
250x250 pm scan takes 30s
Scanning
100 nm
to
Vacuum sample preparation; charging
that are
on nonconductive samples can be
Limited
electron
materials
microscopy
conductive
avoided by using a thin metal layer;
expensive instruments
Scanning
Atomic
Good
electron
or
No free electrons involved so can be
tunneling
level
ionic
conductivity
conducted in air/liquid/vacuum; field
microscopy
required
of view of only a few pm2; 300x300
nm area scan takes 10 min
Atomic
Crystallized
No requirements on
Surface preparation required; both
force
hard
conductivity
contact and noncontact methods exist
microscopy
material:
atomic
biological:
23
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2nm
X ray
5 pm (subpm
Poor
No limitations
Sample
with
Order
of
to
preparation
the
surface.
required.
Expansive and huge equipment
synchrotron)
Ultrasonics
sensitivity
No requirements
Intimate coupling required due to
poor transmission over boundaries;
1mm
not useful at high temperatures
Eddy
50 pm
current
Sample should be
Cannot detect planar cracks in the
conducting
plane o f the eddy; complicated coil
designs for some applications
Evanescent
-0 .4
microwave
1cm
pm
depth
Good for large scale mapping; hot
limits bulk probing
and moving samples can be imaged;
in metals
no sample preparation; can be used in
Penetration
air/liquid/vacuum
1.4 Thesis Outline
Here, we reported a novel imaging system for metals using magnetic-dipole probe.
As w ill be discussed in the Chapter 2, the magnetic dipole probe is sensitive to the
microwave properties of the metals and it has an exponential sensitivity based upon the
tip-to-sample distance variations. We demonstrated the ability o f magnetic dipole probe
in detecting minute changes in the conductivity with 5x 10 3cr resolution at 2 GHz
operation frequency, which is comparable to the conventional noncontact technology.
24
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As they are important considerations in the electric dipole probe, the effect of the
operation frequency, the probe wire tip geometry, and the feedline-to-resonator coupling
strength on the conductivity resolution of the probe for magnetic dipole probe should also
be considered and emphasized. Furthermore, w e compared the conductivity resolution o f
a critical-coupling resonator probe with a microstrip transmission line probe.
Chapter 2 reviews the probe design principle and typical design guideline. The
attractive characteristics o f EMMP are described and compared with other methods.
Equivalent lumped circuit models for different samples are presented and analyzed with
numerical examples.
Noncontact imaging o f materials using evanescent microwave
magnetic dipole probe system architecture is also illustrated.
Chapter 3 shows the prototype system measurement setup, procedure and results
with comparison to the expected performances.
The effects o f varying dimensional
parameters such as tip diameter and tapering angle, and tip and sample distance are
explained.
Finally, the measurement procedures and specifications o f the system are
presented.
Different measurement data are presented compared with the calculated
values. Stability, reproducibility and accuracy measurement curves are also listed.
Chapter 4 presents the working principle
electromagnetic modulated scatterers imaging.
and architecture o f near-field
Experimental setup is detailed with the
measurement images obtained at 10 GHz and 100 GHz illustrated.
Chapter 5 concludes the thesis with a discussion o f the results and the potential
for future work.
25
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Chapter 2
PROBE ANALYSIS AND DESIGN
2.1 Principle of Probe Operation
The classical limit (Abbe barrier) to the spatial resolution of any instrument that is
based on the propagation of electromagnetic fields over a distance greater than a
wavelength (the “far field”) is X/2. This limit results from the fact that in order to obtain a
point-like image (a 5 function in mathematical form), one must retrieve signals that contain
all spatial frequency components from the object. However, the spatial frequencies higher
than
1/X,
known
as
evanescent
waves,
electromagnetic wave of wavelength X.
decay
exponentially
in
a propagating
Evanescent fields were first used by Bethe in
calculating the coupling coefficient of microwave waveguides connected to each other
through a hole much smaller than the microwave wavelength [40]. Nevertheless, in 1928
Synge proposed a near-field scanning optical system that exceeds the Abbe barrier by
taking images that depend on the “ near field” evanescent field [41]. The basic idea is to
closely scan a point-like field source over an object so that the evanescent field is still
strong enough to interact with the object. Early demonstrations of near-field microwave
scanning microscopes were reported by Soohoo [42] in 1962 and Ash and Nicholls [43] in
1972 (the latter has a spatial resolution of 0.5 mm=A/60). In later developments, a spatial
resolution of 0.1 mm (a/2500) was achieved [44, 45].
The extension of near-field
microscopy to visible light by Pohl and co-workers and Lewis and co-workers in 1984 [46,
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47], attracted much attention and resulted in several important improvements to the
technology. Recently, a near-field microwave microscope based on a SQUID (operating at
77 K) has been developed with a spatial resolution of 30 pm [48].
In almost all near-field microscopes the point-like source arise from a probe
configuration that has an aperture (or gap) of diameter (width) much less than A./2. Typical
stmctures include tapered optical/microwave waveguides and an aperture o f diameter d on
the wall of microwave cavity with thickness / (which can be considered also as a circular
waveguide).
A basic problem with all such probes is large loss in intensity o f the
electromagnetic probe waves radiating form the aperture. For example, the exponential
attenuation (a ) of the dominant TEn mode of an electromagnetic wave through a circular
waveguide o f length 1 and diameter d is [42]
a = exp [-3.68(/ / d)]
(2-1)
(this attenuation should not be confused with the exponential decay of evanescent fields).
Efforts to improve the spatial resolution by reducing the aperture diameter d reduce the
intensity of the probing field, which leads to diminished sensitivity.
A
technological
breakthrough
in
near-field
optical
microscopy
was
the
development by Betzig and co-workers in 1991 of a gradually tapered optical fiber
(waveguide) probe with light intensities four orders of magnitude greater than previous
designs [49]. This improvement made single molecule imaging (with resolution ~V 40V 120) possible. Such a probe, however, only reduces the excess losses due to reflection
and absorption over the tapered region of the optical waveguide, not the exponential decay
associated with Eq. (2-1). A very different approach reported by Wichramasinghe and co­
workers is the use of an apertureless device, in which the probing light is the light scattered
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
from an AFM tip near the sample [50]. In this technique the light intensity does not suffer
waveguide exponential decay, resulting in better spatial resolution.
We describe here a new microwave probe structure in which the probing field is
radiated from a sharpened solid metal loop tip instead of an aperture or gap. As the tip
radius decreases, the spatial resolution increases due to the localization of the interaction
between the tip and sample. Moreover, since the field intensity at the tip increases as the
tip sharpens, the total energy that is radiated from the tip and absorbed by a sample with
comparable dimensions does not decrease significantly.
The result is improved spatial
resolution without sacrificing the sensitivity.
2.2 Probe Design
Evanescent field probes have used: open resonators with an aperture in one
plane[51], rectangular waveguide with an aperture in the end plane[52, 53], the center
conductor of coaxial transmission line[54, 55], a coaxial transmission line resonator with
an aperture[56], and microstrip resonator incorporating wire probes or loops[53, 57]. For
each o f these probes, the dimensions o f the aperture or wire that is used determine the
resolution.
In this thesis, we report the results of evanescent microwave magnetic probes
(EMMPs) that use microstrip microwave transmission line resonators, which are the
source of evanescent fields and detector for perturbations to those fields. Because these
resonators are easily manufactured in linear arrays, quick characterization o f large sample
is possible.
Furthermore, by optimizing the resonator coupling and tip design, the
28
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
microwave microscope design, and data analysis, different resolution can be achieved as
demonstrated in the chapter 3.
2.2.1 Resonator Probe
Shorted-circuited transmission lines behave as parallel resonant circuits in the
frequency range where they are close to an odd multiple o f a quarter wavelength long.
The same property is true of open-circuited lines that are a multiple o f a half wavelength
long.
They behave as parallel resonant circuits, and when the transmission line is
uniform over its entire length and radiation losses are small, a resonator will result.
Using this model, it is assumed that all the probing fields are generated around the short
wire that constitutes the probe. The probe wire can either be connected to the ground
plane, or it can be open. These two configurations result in a magnetic or an electric
dipole probe configuration, respectively.
2.2.1.1 Magnetic Dipole Probe
First let’s consider the magnetic dipole probe, as shown in Figure 2.1.
In this
lumped-element model, the loop is considered as a collection o f transmission line
elements formed into the shape of the loop.
Interlaced with these are capacitors
representing the coupling between each transmission line differential element and the
sample itself.
Lastly, the sample is modeled by an inductive element and a resistive
element in series. The resistor represents the resistivity o f the sample, and the inductor
represents the self-inductance of the eddy currents induced by the microwave probe.
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
When the magnetic dipole is brought close to the metallic sample, Cair increases,
but it is important to note that Leff decreases as well. When Cajr increases, it does not
short out the whole probe tip - as is the case with the electric dipole - it merely reduces
the current passing though each differential transmission line element by shunting part o f
the current from the loop to the sample. This has the effect o f keeping the probe matched
reasonably w ell when close to the sample.
It is important to note that while the magnetic dipole probe is relatively
insensitive to changes in the probe-sample distance, it is still relatively sensitive to
changes in sample resistivity because it remains w ell matched near metallic samples.
A
7J4 resonator
probe tip
Figure 2.1
Lumped-element model o f magnetic dipole probe.
Here, the capacitors
Cair short out incremental sections of the transmission line inductance Lloop, raising the
30
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effective capacitance while decreasing the effective inductance.
Therefore, the probe
remains matched near metallic samples.
2.2.1.2 Electric Dipole Probe
The obvious question at this point is “why use a magnetic dipole probe at all?”
The use of the electric dipole probes and eddy current probes already seem quite w ell
established. However, the electric dipole experiences a short at microwave frequencies
that diminishes its use in mapping metallic samples, and the eddy current probe lacks the
exceptionally fine thickness sensitivity o f either dipole probe.
The magnetic dipole
experiences no such short, and is very sensitive to film thickness. This can be further
explained by considering the lumped element models of the magnetic and electric dipole
probes.
Consider the electric dipole probe, as shown in Figure 2.2.
In this, a series of
transmission line elements is connected in series to represent the terminal section o f the
probe. A collection of capacitors in parallel represents the capacitance between the probe
tip and the sample. The resistor R sarap represents the resistivity (fi/D ) of the sample, and
the inductor represents the self-inductance o f the eddy currents induced by the evanescent
microwaves coming off the end o f the probe.
When placed near a metallic conductor, the capacitance Cair = Ceff increases,
causing a microwave short at the end o f the probe. As a result, the probe m oves far away
from resonance - and as its effectiveness as a microwave probe depends on operating
close to this resonance, its usefulness is diminished. Consider the equation for resonance
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(2 -2)
Here, one can see that the resonant frequency is dependent upon the effective capacitance
Ceff and the effective inductance LefJ . As the electric dipole probe is brought closer to
the metallic sample, C eff increases, changing the resonant frequency as w ell as shorting
the electric field lines. The probe becomes unmatched so the Q o f the resonator drops
and the resonant frequency changes drastically as well.
This effect is useful, and has been explored by Steinhauer et al. [58], allowing
them to produce qualitative 2D images of the variation in Q by follow ing the change in
the resonant frequency as the probe moved over the sample. When the probe was close
to the sample, Q dropped.
When the probe was far from the sample, Q rose.
variation was significant enough for them to produce images of metal surfaces.
probe tip
*
A
XU resonator
32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
This
Figure 2.2
Lumped-element diagram of an electric dipole probe. The capacitors Cair
short out the end of the transmission line, while allowing the series inductances to remain
unaffected. Therefore, the probe becomes unmatched near metallic samples.
2.2.2 Transmission Line Probe
As shown in Figure 2.3, we compare the calibration results o f a probe with the
resonator and a microstrip transmission line probe with 100 pm over the sample. We
adjust the coupling capacitance to get the critical coupling and compare the resonant
frequency. It has been shown that the conductivity resolution o f the resonator probe is
100 times higher than that of the transmission line. The resonator probe improves the
signal-to-noise ratio by a factor related to the quality factor ( Q ) o f the resonator.
1.002
o 0.998
Transmission line
gf 0.996
S 0.994
« 0.992
£
Resonator
0.99
0.988
0.986
0
1.5
0.5
2
2.5
Sheet resistance (Q/square)
Figure 2.3
Relative resonant frequencies o f evanescent microwave resonator probe
and microstrip transmission line resonator.
33
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2.3 Probe Analysis
The probe consists of a feedline and a X/4 resonator fabricated on Duroid
substrates, as shown in Figure 2.4, in contrast to the X/2 resonator used in electric dipole
probe. One end of the stripline is connected to ground by a conducting wire at the probe
tip, and the other end is coupled to a short feed line by a coupling screw, which can be
used to change the coupling capacitance value and tune the coupling strength between the
feedline and the resonator. This arrangement takes advantage o f the resonator structure
in order to improve the signal-to-noise ratio by a factor related to the quality factor ( Q )
of the resonator, which is verified later. The probe tip is usually tapered to confine the
electromagnetic fields to improve the probe’s resolution. The sample is placed under the
probe tip and point measurement is performed to map its properties.
Bsufator (DurouU
(a)
Figure 2.4
(a) Microstripline resonator and probe assembly. Cj is a tuning capacitor
and is used to adjust the coupling between the transmission line and the resonator part.
34
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\
____
yim K trin lm
(b)
Mierostrmline
c.
Ground plane
(c)
Figure 2.4
(b) Magnetic dipole probe configuration, (c) Electric dipole probe
configuration. Evanescent waves extend out of the both dipole probes.
2.3.1 Detection of conductivity change
When a conducting object is placed in the vicinity of the tip o f the resonator, the
resonator’s reflection coefficient changes as shown in Figure 2.5, due to a part of
electromagnetic field existing outside the waveguide [59]. Both the resonance frequency
( / r) and the reflection coefficient amplitude ( |S n |) are affected by the presence o f the
sample. The amount o f changes in the resonance ( f r and | .S'n |) depends primarily on the
microwave properties o f the sample as well as on the distance between the resonator’s tip
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and the sample ( d s ), and the tip’s effective area ( Aeff) [60], Many characteristics o f the
sample can affect the resonance of the evanescent microwave probe, including
permittivity, permeability, conductivity and the topography o f the sample. Keeping d s
and Aeff fixed, the tip can be scanned over the sample and variations in the sample’s
microwave properties can be mapped. Different signal detection methods can be used to
monitor the microwave properties o f a sample using an EMMP.
One can fix the
operation frequency at f r and monitor the change in the reflection amplitude.
f r is
usually chosen to yield maximum change in the probe’s reflection coefficient for a given
range of parameters in a sample.
0
Conducting
sam ple
1.90
1.92
1.94
1,96
IAS
2.00
Frequency iCi! I/)
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 2.5
The reflection coefficient (| Sn |) of EMMP when a conducting sample is
placed near the probe.
The change in / 0 caused by the sample placed near the tip is
about 33 MHz for d, ~ 500 pm.
Figure 2.6 shows the shift in the reflected signal with four different conductivities
samples placed near the probe tip for the magnetic and electric probe, respectively. A s
can be seen, both the reflection coefficient amplitude and bandwidth depend on the
conductivities o f the samples located near the tip.
Defects and stresses can locally
change the conductivity, and hence can de detected by the microwave probe. W e use
these dependencies to characterize different conducting samples.
.14
-15
-
Hi 'ViJjw
-16
M<
1?
•
*18
*
-19
•
-20
•
-
2 .2 8 * 1 0 '-12 rt!---
6* 10 ’-ills:
*21
—
2 . 0101 )
2,0 550
2 021KI
Ffteti’.sc)*.c%>t >11/)
2.0250
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.0300
Figure 2.6
Corresponding shift o f |S n | curves due to the introduction o f four
different conductivity samples close to the probe tip.
We modeled the stripline resonator by a series LCR circuit near its resonance
frequency as shown in Figure 2.7a. The resonator and coupling circuit shown in Figure
2.7a can be represented by the equivalent lumped-parameter circuit shown in Figure 2.7b.
When a conducting sample is placed near the probe tip, its electromagnetic properties are
coupled to the LCR circuit by a coupling capacitor Cc . For simplicity, conductors can be
modeled as an inductor Ls in series with a resistor Rs . Conducting wire at the probe tip
can also be modeled as an inductor Ll in series with a resistor R, . L(l, C0 and R0 are
the intrinsic circuit parameters of the stripline resonator.
The capacitance C0 and
inductance L0 are given by [61]:
C0 = - C l , and L, = - C l ,
0
2
(2-4)
2
where C and L are the distributed capacitance and inductance per meter for the
microstrip line and I is the length o f the resonator.
The input admittance at the location o f C3 is given by:
(2-5)
coL l -
jRL
in which transmission line o f length I is with an inductor L l and a resistor R, at the
short-circuit end and a capacitive network o f C j, C2 and C3 representing the coupling
region as shown in Figure 2.4. Yc is the characteristic admittance o f the transmission line,
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
which is equal to y j c ' / L . G0 is the equivalent parallel admittance that accounts for
conductor and dielectric losses in the microstrip line.
Sample
(a)
Resonator
Sample
C
re
<
j L l.
Co £ R o
5
L o:
3
!
<**
^Rt
(b)
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
:> R ,
Figure 2.7
(a) Equivalent circuit model o f the resonator in presence o f a conducting
sample, (b) equivalent lumped parameter circuit model.
The input admittance seen across Q is given by:
Y = > C ,+
'
{2 . 6)
jcoC,+Y„
jo C ,+ Y „
In a gap coupled microstrip resonator Cl » C2 , so it is operated as a series resonant
circuit.
As we know, series resonance occurs when the imaginary part o f the
denominator vanishes. The condition for resonance is thus
Y „ -G „ = -ja C t.
(2-7)
Using this relationship and approximating G0 - jcoCl by - jcoC, for all values o f co in
the vicinity of the resonant frequency, we can get
( 2 -8 )
(jr
When Yin = Yc at resonance, all of the incident power will be coupled into the resonator,
Y =
.
(2-9)
o C ,= jY fit .
(2 - 1 0 )
^0
It may be seen as
When the dispersion of the microstrip line can be neglected, the Q, is given as
QL =% C„Ra.
The parameter becomes
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(2-11)
m
”
t
j
k
= \ Yc = I '
j
=
(
2
_
1
2
)
Therefore,
« o = 2 Q ,./Y t .
(2-13)
Our probes are designed to have 50 Q characteristic impedance at resonance, therefore
using
= 0 .0 2 0 '’ ,
« 1 0 0 , and tu0 = 2;r ■2 x 109rad / .v, we can calculate the value o f
Q around 0.11 pF , which is quite close to the calculated value listed in Appendix A.
In the presence o f the sample, L l and G0will change accordingly with the sheet
resistance of the sample and the distance between the probe tip and the sample. U sing
these relationships, we can critically couple the resonator without the presence o f the
sample, and then bring the resonator down to different sheet resistance samples, keeping
the constant distance between the probe tip and samples. The presence of the samples
w ill change the coupling of the resonator, which would result in the different reflected
microwave magnitudes.
Using this relationship, we can characterize the microwave
properties o f the sample. Furthermore, w e could keep the distance constant and change
Cj to get critical coupling for different samples, which results in the different resonant
frequencies. As can be seen in chapter 3, this relationship is linear.
Given a change in the reflection coefficient o f ASn per a small perturbation in
conductivity of A c t of a sample placed in the vicinity o f the probe, we can only detect
ASn only if it is equal to or larger than the noise level in the system. The detected signal
ASn can be related to the slope of the resonator at f x (where f x is the operation
frequency, kept fixed throughout the measurement) using the following relationship [62]:
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
xA/.
ASn
A/
1
The slope
(2-14)
f,
AS,-’li '
is the sensitivity o f the resonator at f x and can be denoted as
A/
S r . Therefore, ^ LL can be written as:
A
ct
^ il = ^ i l x ^ L = S -S
A
A /
ct
A
(2-15)
ct
where Sx is the frequency sensitivity o f the resonator (=
), and S f is the shift in the
A -P
resonator frequency per unit change in the conductivity (=
) o f a sample placed near
A
ct
the tip.
The minimum detectable signal (MDS) is defined as the smallest change in the
input that produces an output (AVaut = A S uVin) equal to the root-mean-square (RMS)
value of the noise (Vnrms) [30, 63]. Thus, for MDS we can write [6 6 ]:
MDS
It clearly shows
related to
AS
= A c t = ------- =
sx-sf
V IV
nrms! m .
Sx -Sf
(2-16)
that to improve MDS, Sx and S f should be maximized. Sx is
thequalityfactor
of the resonator, while S f is determined by the physical
interaction between the evanescent fields and the sample. It can be shown that S f for the
conducting samples is given by:
1
5
f
=
A ct
(2-17)
AR
A ct
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where Rs is the resistance of the conducting sample and it is equal to
for the
infinite thick samples. Therefore,
AR
A ct
=
2
= -^~ R s.
(2-18)
2cr
Simplifying the equivalent circuit, we can express S f as [66]:
s
- V
'
AR , _
- V
Act
AS,
1
Act
)ct
Assuming that the resonator is matched to the characteristic impedance o f the feed
line at the resonance frequency, Sx is given by [64]:
Sx * s ^ - ( \ - — ) ,
Cl)q
COq
where co = co0 + Aco, Aa> / ru0 «: 1, and
5
= - 1 if co<o)Q and
(2 -2 0 )
5
= +1 if co > co0. From the
above equation, sensitivity is proportional to the quality factor o f the resonator, as
expected.
Using the above relationships, it can be shown that the MDS is given by:
V
IV.
V IV
MDS = Act = mms------- in = ----------nrms m------- .
S ,S ,
____
j
72Q
(2-21)
$X2slh (C o + Cc)oFrom the typical probe parameters in our work, we can get L0 = 1.2AnH ,
C 0 = 3 p F , C c = 2.7p F , Vnrms IVin « 1 x 1 0 3 and Q * 2000 at f 0 = 2GHz .
Using those
numbers, we can get the conductivity resolution of this probe as:
MDS = Act * HT4 a .
43
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(2-22)
2.3.2 Detection of magnetic field density change
When the tip of probe is placed in the vicinity of a sample, the resonator’s
reflection coefficient changes as shown in Figure 2.8, due to magnetic flux </>B change in
the area o f the loop probe.
Both the resonance frequency ( f r ) and the reflection
coefficient amplitude ( |S U |) are affected by the presence of the sample. The amount of
changes in the resonance ( f r and |5 n |) depends primarily on the magnetic field density
as w ell as on the distance between the resonator’s tip and the sample ( d s ), and the tip’s
effective area ( AejJ) [64, 65]. Keeping d s and Aeff fixed, the tip can be scanned over the
sample and variations in the magnetic field density can be mapped. As opposed to the
electric dipole probes where the resonance frequency becomes smaller in the presence of
the sample, the resonance frequency o f the magnetic dipole increases if the sample is
metallic or is conductive. The main reason for this is that in addition to inductive
coupling with the sample, the loop also couples to the sample capacitively. This
capacitive coupling can reduce the tip’s inductance by shunting the probe tip to the
ground. Thus, the resonant frequency increased as can be seen in Figure 2.8.
44
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ferrom agnetic
-30
Sample
-35
-40
-4> I —
!,%
Figure 2.8
JL
—
........................... I........................... I...........................
1.975
1.99
2.WI5
2.02
1 )
IUV
I
1n
The reflection coefficient (| 5 U |) o f EMMP when a ferromagnetic sample
is placed near the probe. The change in
/0
caused by the sample placed near the tip is
about 10.5 MHz for d ~ 300 pm.
Different signal detection methods can be used to monitor the microwave
properties of a sample using an EMMP. When dealing with conducting samples, the
resonance frequency is predominantly affected by the probe-sample distance. Thus, one
can use the resonance frequency as a control signal to regulate the probe-sample distance.
Operating the probe at a constant resonance frequency necessitates adjusting the probesample distance as the probe is scanned over the sample.
This process enables
controlling the probe-sample distance quite well. The reflected signals amplitude at the
resonance frequency, however, changes even when the probe-sample distance is kept
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
constant by fixing the resonance frequency.
Thus, w e monitored the change in the
reflected signal at constant resonance frequency (i.e., constant probe-sample distance) to
image the permeability variations in the sample. Under these conditions, the inductive
coupling between the probe and the sample in addition to the dissipation determines the
probe’s output signal.
In the high-frequency regime, the dimensions o f circuits are very small. In order
to accurately measure the amplitude and phase o f the fields at a point inside a circuit, a
field probe must be as small as possible, so that the perturbation o f the operating circuits
by the probe can be ignored approximately.
The design o f the evanescent magnetic
microwave probes started using a conducting loop. We have evaluated the energy of
interaction between the probe and the magnetic field emanating from the sample surface.
Consider a one-turn loop of conducting wire C which is placed in a magnetic field B .
The magnetic flux <f>B linking loop C can be written
f(„= 5X M .
(2-23)
where AA is some sub-area o f the loop and B± is the component o f the magnetic field
which is perpendicular to this sub-area. The summation is over all o f the different subareas required to make up the total area o f the loop. The sub-areas are assumed to be
sufficiently small that the magnetic field is approximately uniform over each sub-area. It
was assumed that the loop is immersed into a plane linearly polarized electromagnetic
wave in free space and is placed in the x - z or y - z
plane, perpendicular to the
magnetic field H y - or H z - components, which are considered to be constant over the
area o f the loop. Because the dimensions of the loop probe are much smaller than the
wavelength and the form of the loop is circular, the induced electrical field is
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
compensated in the loop. Under these conditions, the current I induced in the loop is
only proportional to the magnetic field radiated from the sample.
Measuring the
magnetic field distributions on a sample, the probe signal S has the form [73]:
S=CI(l ),
(2-24)
where C is the coupling coefficient, which is associated with the properties o f the probes
and can be obtained by calibration, and I is the relative distance between the sample and
the probe plane. Because of the small size, the probe can be placed very near to the
sample with a small influence on the sample and an increased sensitivity o f the
measurement.
We model the coupling between the loop probe and a sample with the equivalent
circuit shown in the inset of Figure 2.8. The loop probe is represented as an inductor L l ,
the test material as a series combination o f its effective inductance Ls and complex
impedance Z s = Rs +1/ jcoCs , and the coupling as a mutual inductance M . Since the
materials o f concern are good conductors with a microwave skin depth much smaller than
the sample thickness, we model the sample inductance by an identical image of the loop
probe, so that Ls = L l . The self-inductance of the loop probe is roughly estimated as
L l = 1 .2 5ju0a , assuming a circular loop with inner diameter a .
In the high-frequency
limit, the surface impedance of the sample can be written as Zs = ^ jju0jurcop , where p r
is the complex relative permeability of the material, a is the microwave frequency, and
p is the resistivity of the material, which is considered to be independent o f p r . Since
the loop and its image are roughly circular inductors, we can calculate M as the mutual
inductance between two circular loops in the same plane. However, because this two-
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
circular-loop model only approximately describes the geometry, w e w ill ultimately need
to treat the value of M as a fitting parameter. In the high-frequency limit, w e can take
coLs to be much greater than \ Z S \. From the equivalent circuit shown in Figure 2.8, we
find
that
the
load
impedance
presented
by
the
probe
and
sample
is
Z had = jco0( l - k 2) + k 2(Rs + j X s ) , where the coupling coefficient k = M I ^ L s Ll is a
purely geometrical factor. The frequency shift is produced by the imaginary part o f Z load,
while the real part of Z load determines the Q o f the microscope.
Because of the tolerances in fabrication, it is very difficult to produce probes with
equal properties, for example equal electrical impedances. It means that it is improper to
compare measurements form different probes without calibrating the probes. Using a thin
film technology, the production costs for the magnetic field probe are very small and a
very stable field probe can be fabricated, i.e., it is suitable for industrial applications.
For the measurements the distance between the probe and the circuit is an
important factor. If the probe is too near to the circuit, it may obtain a larger signal, but it
then disturbs the operation of the circuit.
For the measurement shown later, it was
designed to hold the probes in a constant plane from the sample during the measurements,
so that the results finally can be compared with each other. The probe is placed 100 pm
above the sample.
2.3.3 Detection of dielectric constant change
We modeled the microstripline resonator near its resonance frequency as shown
in Figure 2.9.
In the presence of the sample, Z load will change accordingly with the
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
microwave properties of the sample and the distance between the probe tip and the
sample, as w ill shown later. The change o f Z load will be detected through the resonator
section, taking advantage of the resonator structure in order to improve the signal-tonoise ratio by a factor related to the quality factor ( Q ) o f the resonator. Using the w ell
known microwave circuit analysis, we can relate the reflection coefficient o f the quarter
wavelength resonator to the impedance o f the magnetic and electric dipole probes.
Therefore, the amplitude and the phase o f the reflected wave can be shown as functions
o f the microwave properties of the sample under study.
R esonator
Figure 2.9
Equivalent circuit model for the microstripline resonator and coupling to
the transmission line.
A. Magnetic dipole probe
The geometry of the current loop probe is shown in Figure 2.4(b). The method o f
images can be applied to calculate the loop’s impedance placed in front o f a dissipative
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
medium like a real conductor or a semiconductor.
The electric field produced by the
image loop modifies the electric field at the surface o f the sample. Using the method of
images we replace the conducting plane by an image loop carrying a current I i :
l i = - J ] I 0e
where
tj
is real and 0 < 77 < 1,
£ is
if
(2-25)
the phase difference between I 0 and I . , and I0 is the
driving current o f the magnetic dipole antenna.
7
and £ are chosen to produce the
appropriate changes in the field of the magnetic dipole antenna due to the presence o f the
conducting plane.
Sample
_
Resonator
11
Cc r
i
Mi
'L
)
t
f
e
Ri <
<> R t
o-
(a)
Figure 2.10
Equivalent circuit representing the interaction between the sample o f (a)
the magnetic probe.
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sample
Resonator
o
M
LS
1
:c
R l <!
j
$
"1
o — *-
(b)
Figure 2.10
Equivalent circuit representing the interaction between the sample o f (b)
the electric probe.
As shown in Figure 2.10(a), the loop probe is represented as an inductor Ll , the
sample as a series combination o f its effective inductance Ls and complex impedance
ZS = R S + 1/ ja)Cs + 1 / jo)C( ;
(2-26)
the coupling asa mutual inductance M , and Cc is the coupling capacitor between the
probe tip and the sample. The self-inductance o f the loop probe is roughly estimated as
Ll = 1.25ju0a ,
(2-27)
where a is inner diameter o f the circular loop. In the high-frequency limit, the surface
resistance o f the sample can be written as
I o s + 1 1 jcoCc ,
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(2-28)
where jurs is the complex relative permeability o f the sample, /
is the microwave
frequency, and crs is the conductivity o f the material, which is considered to be
independent o f jurs. For the high-frequency range, we can take coLl to be much greater
than \ Z S \. From the equivalent circuit shown in Figure 2.10(a), we find that the load
resistance represented by the probe and sample is
Zioad = M A (! - k2) + k 2
+ 1/
),
(2-29)
where the coupling coefficient k = M ! ^ L L is a purely geometrical factor. The phase
and amplitude o f the electric and magnetic fields, produced by the image loop, can be
calculated from the reflection coefficients of the corresponding fields.
B. Electric dipole probe
The change in the load resistance when a material object is placed near the probe
is calculated by treating the probe as an electrically short and insulated antenna (i.e. the
length of the dipole is much shorter than the microwave wavelength), where the
insulation is provided by the air gap between the probe and the sample as shown in
Figure 2.10(b). When the probe length T is larger than the radius of the insulation b ,
the input admittance of this electrically short and insulated antenna is approximately
given by:
7 = [Z, ]-1 = G + jcoC =
a *nT— (— r -^
T T) + jco £'l^~ ( P\ + j;1 + ^ ) ,
L 1 Li
ln( r / ^ ) - ! + ( ! + r )
H b / c ) p s + (1 + y)
(2-30)
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where
<
7
S
is the conductivity of the sample,
ej
is the permittivity o f the insulator
( s i = £rie0), c is the radius o f the wire, b is the distance between the probe and the
sample and
g , ln(T / b) - 1
£s
(2-31)
In( b/ c )
and
(2-32)
where s s is the permittivity o f the sample ( s s = £sr£0) and / is the frequency o f the
microwave signal. In the present work, £i r- l , f = 2 GHz, 7 = 2 mm, c = 400 pm and
b « 1 5 0 pm.
In our case, load impedance change is detected by the change in reflection
coefficient through a quarter wavelength resonator section. As can be seen, the coupling
between the resonator and the transmission line will also result in Figure 2.11(a) and
2 . 1 1 (b)
show | FT | as a function o f the microwave frequency for four different
conductivities samples placed in front of the probe tip for magnetic and electric probes,
respectively. The conductivities varies from
6
xlO 6 /Q m t o 6 xlOfi/Q m . The distances
between the probe tip and the sample are changed to keep the resonant frequency fixed.
There is a change o f 1.5 dB and 1.1 dB in the reflection coefficients at the resonant
frequency for magnetic and electric dipole probes, respectively.
53
R eprod u ced with permission o f the copyright owner. Further reproduction prohibited without permission.
6 *ld -VOm
frequency ((iHz)
(a)
54
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-iff
-31
-32
m
3
§£t
-34
-35
-36
-37
1.971
U 73
1.97?
1,975
1.979
1.981
Frequency (<JHz)
(b)
Figure 2.11
Corresponding shift o f |5 U | curves due to the introduction o f four
different conductivity samples close to the probe tip of (a) magnetic probe, and (b)
electric probe.
The following experiments were carried out to characterize the probes.
2 .1 2
Figure
shows the amplitude of the reflected wave for two cases of the magnetic and electric
dipole probes. The resonance frequency o f the magnetic probe configuration is higher
than that of the electric probe configuration.
55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0
-1 0
*20
-
1(1
M agnetic
Probe in air
Electric
•40 . p rob e in air
r
-50
1 .9 6
<r
]m
: om
?.<K)
? oj
** o
t-r e q u e u e y ( ( i l l / )
Figure 2.12
Experimental graphs depicting the output o f the magnetic and electric
dipole probes as a function of frequency.
As shown in Figure 2.13, w e compared the calibration results o f the magnetic
probe with the electric probe over the different sheet resistance conducting samples. We
adjust the coupling capacitance to get the critical coupling for both probes. It has been
shown that the conductivity resolution of the magnetic probe is more than
2
times higher
than that of the electric probe because the magnetic probe is better matched to the
conducting samples than the electric one.
Comparison o f magnetic probe with the electric probe over the different sheet
resistance semiconducting samples is also carried out. It has been clearly demonstrated
56
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
in Figure 2.14 that conductivity resolution o f the electric probe is better than that o f the
magnetic probe this time. Moreover, more experiments were carried out to testify the
theory by comparing the resolution of the two probes o f the dielectric samples. As shown
in Figure 2.15, the dielectric resolution o f the electric probe is almost 10 times higher
than that of the magnetic probe.
57
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Relative reflected microwave magnitude
1.2
Electric probe
\
1
0.8
0.6
Magnetic probe
0.4
«t4ft-1 )<twv
0.2
0
0.01
0.1
1
10
Sheet resistance UE'square)
Figure 2.13
Calibration results for the magnetic and electric probes versus the sheet
resistances of the conducting samples.
58
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S.!
o
_
3
1, 0 2Tj
2
p
0.9
<
1.8
o
T5
0
*p
0 .8
,l
I k aric probe
u
>
0.5
fi£
<M
100
10
UVi
Sheet resistance (f 1/sqtiare)
Figure 2.14
Calibration results for the magnetic and electric probes versus the sheet
resistances of the semiconducting samples.
59
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Rotative reflected microwave magnitude
Magnetic probe
X
nicenie proK
I t
2
4
a
*
10
i:
14
16
18
Relative d ie le c tr i c c o n s t a n t
Figure 2.15
Calibration results for the magnetic and electric probes versus the relative
dielectric constants o f the samples.
60
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Chapter 3
EXPERIMENTAL SETUP AND RESULTS
3.1 Experimental Setup
In this paper, two different kinds o f probes were characterized and compared.
The first one is the microwave resonator probe with a feedline. The other is a microwave
microstripline probe.
Both o f the probes are fabricated on a 0.85 mm thick Duroid
( er = 2.2 ) substrate with the center conductor width o f 3.0 mm to have 50 Q.
characteristic impedance at the operating frequency o f 2GHz.
The imaging system
operates at a relatively low frequency range so that the penetration depth o f the probe is
greater. Therefore it is suitable for characterizing the bulk properties of relatively thick
films. Probe tip is approximately tapered by 60° angle to confine the electromagnetic
fields to improve the probe’s resolution.
A wire is attached to the tapered end o f the
probe and forms a loop by terminating at the ground plane of the resonator.
For the
microwave resonator probe, three different probes are characterized, with the wire
diameters o f 300 pm, 400 pm and 600 pm, respectively. All the probes are mounted in
an aluminum fixture to eliminate coupling and decrease the background noise that would
decrease the probe sensitivity. The tip o f the resonator protrudes through a hole in the
box.
The experimental setup used in the present work is shown in Figure 3.1.
It
consists of a microwave resonator coupled to a feedline, which is connected to a three-
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
port circulator circulating the signal from the FM-modulated radio frequency source to
the resonator, and detects the reflected wave to a phase detector.
The phase detector
compares the reflected signal with the reference signal from the radio frequency signal
generator. Its amplitude output is then fed to a lock-in amplifier to maintain phase lock
and to a digital multimeter to measure the reflected wave magnitude. The output voltage
o f the digital multimeter is proportional to the reflected wave from the stripline resonator
and attained a minimum value when the frequency was tuned to the resonance frequency.
62
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PC and
DAQ control
ek-in Amplifier
-*{
Digital Multimeter
( ienerator
_SM A
Connector
m
Probe
Sample Holder
Phi Positioner
X positioner
Motor
Motor 2
Base
Figure 3.1
Experimental setup used in performing evanescent microwave probe
measurement.
The circulator, the phase detector, and the stripline are connected to a vertical
support that is connected to a table top base and can be positioned in the vertical direction
with one micrometer. The sample is mounted on an X-Phi stage and scanned underneath
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the probe tip. The outputs of lock-in amplifier and digital multimeter are connected to
the input of the DAQ card in the computer, which can as well as position the sample
platform.
The whole imaging system is automated by the PC which also keeps the
constant distance between the probe tip and the sample.
We have used both open and closed loop wire probes at the end of the quarter and
half wavelength sections, respectively. The open loop probe is a piece o f wire that is
connected to the ground through a capacitor (formed by the end of wires) o f the order o f
tenth of a picoFarad.
In the case o f the open loop probe the effective length o f the
resonator is somewhat larger because of the fact that the probe is not at the voltage node.
In the case of the open loop, it should be noted that the voltage node is not at the probe
position.
However, due to the presence of capacitive coupling to the ground, the
amplitude o f the voltage there is reduced and a resonator with an effective length larger
than the physical length o f the microstrip line section results.
3.2 Probe Calibration
To perform quantitive mapping o f conductivity and dielectric constant, we
calibrate the probes over a wide range o f samples. Different parameters are measured
and compared with the theoretical values.
3.2.1 Sensitivity
Sensitivity is defined as incremental ratio of the output ( y ) to the input ( x )
S = Ay / Ax.
64
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In the above equation, x denotes the desired measurand.
3.2.2 Resolution
The smallest increment in the value o f the measurand that results in a detectable
increment in the output.
It is expressed as a percentage o f the measurand range.
For
example, if a temperature sensor yields an increment of AV output voltage in respect to a
AT change in the temperature of an object, then the maximum resolution (f?max) is the
smallest AT (denoted by ATmin) that yields a detectable AV and it is expressed as
ATr, .
*m,(%)=ioo-
max
min
The average resolution (Rav) is then given by the average of R(T) over the range
o f measurand (temperature):
Z A J;
«„(%
)=
'
CIV
'
100
---------m
\
max min/
/ ’T '
where n is the number of AT in the measurand range that are considered.
3.2.3 Accuracy
A measure of how closely the result of the experiment (sensor output) approximates
the tme value. Since the true value of the unknown (measurand) is not known a priori, a
comparative measurement is needed in specifying the accuracy o f a transducer. Inaccuracy
is usually described as follows:
e a{%) = W X m ~ X t) I X t
65
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where X t is the true value of the unknown X , and X m is its measured value. In practice,
inaccuracy is expressed as a percentage o f full-scale output (FSO):
e f (%) = 100(Xm- X l) / X FSO.
Clearly, | e f |<| s a \. X t can be obtained either from other measurements or from
the National Bureau of Standards (NBS). Since for a repeated number o f measurements at
a value of X t different values of X m might be obtained, it is useful to define an error
denoting the maximum range of X m. Error bars can be generalized to introduce a band in
the case of an experimental curve. Error band, then, denotes the maximum and minimum
values o f X m throughout the range o f X t . Error bars and error bands can be obtained
statically or dynamically.
In dynamic error measurements, the system is subjected to
various real-life disturbances such as shock, vibration, or acceleration.
In static error
measurement, the error is measured under ideal conditions.
3.2.4 Minimum detectable signal (MDS)
Assuming that the signal or the measurand does not contain any noise, the
minimum signal level that yields a readable transducer output is determined by the noise
performance o f the transducer. To account for the noise level generated by the transducer,
all the internal noise sources of the transducer can be bunched together to form a single
noise source. This single noise source, which is called the equivalent input noise source,
when connected to the input of the ideal (noiseless) transducer yields the output noise level
the transducer under study. The minimum signal level that yields a reliable transducer
66
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output signal, the MDS, is usually taken as the root-mean-square (RMS) equivalent input
noise (signal-to-noise ratio of 0 dB).
3.2.5 Reproducibility
The difference in the output readings at a given value o f the measurand X , where
X is consecutively reached from X~ (or X ").
3.3 Scanned Imaging Results
3.3.1 Conducting Samples
Figure 3.2 shows the shift in the reflected signal with different feedline-toresonator coupling strength. As can be seen, both the quality factor ( Q ) of the probe and
the resonant frequency depend on the coupling strength.
To perform quantitative
mapping o f conductivity, we calibrated the probe over a range o f sheet resistance, from
0.059 Q/square to 2.24 Q/square.
In our experiment, w e used a Signatone four-point
probe, together with Keithley 182 sensitive digital multimeter and 202 programmable
current source, to measure the sheet resistance o f different samples. With this highly
sensitive setup, a change of
deviation was below
2
1 0 “4 a
in surface resistance could be detected, and the
%.
67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
>5,0
-100
15,0
-
/
3
-
mder ( eiipMftj
fiver C.oiionwi;
25.0
tA
\
Critical
w &
m
-45,0
1.92
1.93
1.94
1 5
1,96
1 97
1.98
1 99
2.00
2 01
2.02
2 03
Fieqneney t l i l l z ’l
Figure 3.2
Corresponding shift of | Sn | curves due to the different probe coupling
strengths.
Figure 3.3 shows the calibration results at 100 pm distance from the probe tip to
the sample for the critical and over-coupling probes. The accuracy o f our measurement is
better than 1%.
5 x 1 0 3 cr and
2
The conductivity resolutions o f the EMMP are shown to be around
x10
2 cr
at the operation frequency of 2 GHz for the critical and over­
coupling probes, respectively.
Over-coupled resonators have poor Q , this being the
reason for their lower resolution.
68
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1,2
Over «»pJirt§
Critical awpling
0 .0 i
o.i
i
Sheet resistance (fi/square)
io
Figure 3.3 Evanescent microwave magnetic dipole probe calibration for critical and over­
coupling probes.
Figure 3.4 shows the decay characteristics for resonator probe with different
coupling strengths. As expected and shown in Figure 3.4, we could notice that decay
characteristic for critical and over-coupling probes vary.
Critical-coupling probe
provides a larger dynamic range for changes in probe-to-sample distance. For resonators
with equal Q , the larger the shift in reflected signal magnitude when a sample is brought
in from infinity the larger the dynamic range. The dependence of the output signal on the
distance is not exponential. However, approximating them with the exponential decay,
they have the characteristic decay length of 360 pm, and 410 pm, respectively. As can be
seen, even without changing the operation frequency, it is possible to vary the distance
sensitivity o f the probe over a wide range.
69
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1,115
Over coupling
0,7 «—----------->
------11
*---------------------------*------ --------- ----------1— .—
500
1OO0
I 500
------------ » _
2000
Distance (urn)
Figure 3.4
Relative reflected microwave magnitude as a function o f distance (D)
between the probe tip and sample for critical and over-coupling probes.
As shown in Figure 3.5, there exists a bump for the under-coupling probe o f the
sample sheet resistance versus the relative reflected microwave magnitude, due to the
critical-coupling of the probe above certain sheet resistance sample, which would result
in the inconsistency relationship between sample sheet resistance and the reflected
microwave magnitude. In the decay characteristic of the under-coupling probe as shown
in Figure 3.6, w e could see that at certain distance, the probe reaches the critical-coupling,
resulting in the minimum relative reflected microwave magnitude. As can be seen, for
the different coupling probes, critically-coupled probe is better for achieving bigger
resolution and consistency.
70
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0,95 r
H.K5 -
0.73 L
tl.65 i
0,55 r
Ii
1
\ coupling
0.45 *
V
> ft ts n
w
CeJ ft
0,15
Figure 3.5
10
ft I
Sheet resistance if!square)
Ml
Evanescent microwave probe calibration with the under-coupling probe.
1.05
-g
0.95
I
0.85
<u
& 0.75
£
M
0.65
T3
<D
o 0.55
<D
<L>
0 0.45
1
Under coupling
0.35
0.25
500
1000
1500
Distance (pm)
71
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2000
Figure 3.6
Relative reflected microwave magnitude as a function o f distance (D)
between the probe tip and sample for under-coupling probe.
Taking advantage of the characteristic that different probe coupling strengths
would result in different resonant frequencies, w e could keep the distance between the
probe tip and the sample constant, and adjust the coupling strength between the feedline
and the resonator to achieve critical coupling, which results in the different resonant
frequency, as shown in Figure 3.7. For this calibration, the conductivity resolution o f the
EMMP is shown to be around 10_1cr at 2 GHz.
S- 2 0 1 S
\
2000
0
J
*
Sheet resistance ( f t j
Figure 3.7
a
Evanescent microwave critical coupling probe resonant frequency as a
function o f sheet resistance at and fixed distance (D) between the probe tip and sample,
obtained using metallic films with different sheet resistances.
72
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Furthermore, w e adjust the coupling at 100 pm between the probe tip and a
sample of 0.91 Q/square, then fix the coupling strength and calibrate other samples at the
same distance. For the critical coupling probes, we could see the conductivity resolution
differs at the point of 0.91 Q/square, as shown in Figure 3.8. For the samples o f sheet
resistances smaller than 0.91 Q/square, the conductivity resolution is shown to be around
6x10 3er.
On the other hand, the conductivity resolution is shown to be 10 ”2 o for
samples with sheet resistances larger than 0.91 Q/square. This variation is caused by
different probe coupling in presence o f different sheet resistance samples. Over-coupling
is achieved with the presence o f larger sheet resistance samples and under-coupling with
smaller sheet resistance samples.
■awe
5,
Ov«rrtmipling
Over
(i i—
0.01
0.1
'slve: resist# iu' i£). ^a.jrej
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.8
Evanescent microwave probe calibration results for critical and over­
coupling over a 0.91 Q/square obtained using metallic films with different sheet
resistances.
As shown in Figure 3.9, we compare the calibration results o f a probe with the
resonator and a microstrip transmission line probe with 100 pm over the sample. We
adjust the coupling capacitance to get the critical coupling and compare the resonant
frequency. It has been shown that the conductivity resolution o f the resonator probe is
100 times higher than that of the transmission line. The resonator probe improves the
signal-to-noise ratio by a factor related to the quality factor ( Q ) o f the resonator.
I ,<*12
Ti.tmttr.sM or. :itt
RCKMWtW
0.4% L —
0
0,5
-
- ...... - ..—
I
*......... .......
1.5
?
2.5
Sheet resistance (Q /square)
Figure 3.9
Relative resonant frequencies of evanescent microwave resonator probe
and microstrip transmission line resonator obtained using metallic films with different
sheet resistances.
74
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It is also essential to examine how the probe’s resolution is affected by the
geometry o f its resonator.
For our probes, over coupling is achieved for the isolated
probe or when no sample is present. Figure 3.10 shows the calibration results at 100 pm
distance between the probe tip and the samples. The accuracy o f our measurement is
better than 1%. A s can be seen, the probe with smaller diameter tip has better resolution.
1.05
a
8
.a
twin
o.9
tC '.H
tz 0.85
8
* mm
>
*f
0.8
0.75
0.01
Figure 3.10
0.1
5*he«t feMSU'tce
1
10
Evanescent microwave probe calibration obtained using metallic films
with different sheet resistances.
To verify the feasibility of our probe model, the four-point probe conductivity of
different samples was measured and the evanescent microwave probe output at
200
pm
and / = 2.01 GHz, corresponding to these points, is plotted versus the conductivities, as
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
shown in Figure 3.11. Figure 3.11 also presents the predicted system responses o f three
different probes, respectively, shown by the solid-line curves based on the estimation of
wire tip values. The predicted responses closely match the experimental curves. In the
simulation, we estimated the inductance and resistance o f the probe tips o f 1.3 nH and
0.31 Q for 0.3 mm tip, 1.24 nH and 0.29 Q for 0.4 mm tip, and 1.165 nH and 0.26 Q for
0 .6
mm tip, respectively.
1.02
I£
P
0.98
I
1
1
U
t*
£ -0 .4 tiift!
0.94
*§
06
0.92
4>
Conductivity ( 1 0 ‘ t l m i
Figure 3.11
Evanescent microwave probe measurement results match the predicted
values shown in dotted lines, for £=0.3 mm, 0.4 mm, and 0.6 mm diameters.
Figure 3.12 shows the decay characteristic for magnetic probes that have different
diameter conducting wires. Thinner diameter probe provide a larger dynamic range for
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
changes in probe-to-sample distance.
The dependence o f the output signal on the
distance is not exponential. However, approximating them with the exponential decay,
they have the characteristic decay length o f 700 pm, 640 pm, and 450 pm, respectively.
Thinner wire tip has more concentrated and confined fields near the apex. The lateral
confinement of the fields also reduces their extension in the z direction, which results in
smaller decay length. As can be seen, even without changing the operation frequency, it
is possible to vary the distance sensitivity o f the probe over a wide range.
Predicted
system responses are also presented in Figure 3.16 with the dotted lines, which are quite
close to the experimental values. In the simulation, the air gap capacitance changes from
5 pF at 100 pm to 0.01 pF at 1000 pm. The inductance and resistance of the probe tips
are listed in Table 3.1.
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.02
Theorv
0 .8 8
I—
0
— .I—
20#
400
ftJHI
—
K00
*—
;
1000
Distance pmvt
Figure 3.12
Reflected microwave magnitude as a function o f distance (D) between the
three different diameter ( 4 ) probes’ tips and the brass sample.
Table 3.1
Estimated parameters o f probes with different diameters at different
distances between tip and sample.
Distance=100 pm Distance=1000 pm
R(Q)
L(nH)
R(Q)
L(nH)
1.435
0.125
2.72
0.3 mm
0.82
1.39
2.7
0.12
0.4 mm
0.8
1.305
2.65
0.107
0.75
0.6 mm
Probe tip
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The above measurements were repeated ten times for reproducibility test. Figure
3.13 shows the variation of each measurement to be as small as 0.1 %. In addition to
short term reproducibility test, we also investigated the long term stability o f the EMMP.
Before each measurement, we make sure the probe-sample distance constant by keeping
the lock-in amplifier output constant. Figure 3.14 shows the variation to be around 0.5 %.
4200
>
Average value
41(10
s
I 3700
3*00
3500
3400
0
1.5
0.5
Sheet
Figure 3.13
re s is ta n c e
2
HI
3
sq u a re)
Reproducibility measurement. Repeated measurements performed over
short term o f time at different spots on metallic samples with different sheet resistances.
The error bars indicated the range o f sensor output over the repeated measurements.
79
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ym
3550
0
Figure 3.14
Hi
20
Ml
40
lo w fniintste!
511
60
70
Long term stability o f the sensor range. Measurements were taken at two
different distances of 50 pm, and 100 (am between tip and sample.
Figure 3.2-3.14 clearly demonstrate the capability o f EMMP in performing
detection o f corrosion, defects, conductivity and thickness nonuniformities. Figure 3.15
shows an EMMP image around 1 cm in both directions. The image shows a sample with
two different conducting regions scanned at d - 0.5 mm and A0 = 5° per step.
The
sample is covered with aluminum and subsequently gold was added to one small region.
The image not only shows the ability o f the probe to scan large areas (even larger area
scans can be obtained), but also reveals the ability o f EMMP to detect minute change in
conductivities.
As mentioned before, the EMMP can also detect the thickness
80
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nonuniformities in the conducting materials. Figure 3.16 shows the EMMP image o f an
aluminum film thickness variation at d = 0.5 mm and A</> = 5° per step. The image also
implies the application o f the EMP in detecting the nonuniformities and defects o f the
conducting materials.
Vil tj UNM1IK.V
iii‘S.<p«res
0 .0 '
X axis (mm)
Figure 3.15
EMMP image of a sample with two different conducting regions with
Ad = 0.5 mm and A(f> = 5° per step.
The sample was covered with aluminum and
subsequently gold was added to the small region as shown above.
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.16
EMP image of an aluminum film thickness variation at Ad = 0.5 mm and
A<j>- 5 ° per step. The sample was prepared by evaporation o f around 300
aluminum
onto a glass substrate.
3.3.2 Damascene Copper on Silicon
The following experiments were carried out to characterize the probes.
We also used the copper film on silicon, copper sulfide film after copper film is
sulfidized for 5 minutes at 150 °C, and the same copper sulfide film after 1 minute
annealing in the air at 150 °C as our three imaging samples Copper film on silicon was
rather uniform according to the scanning image shown in Figure 3.17. Due to the large
sample area, nonuniform sulfidation temperature would result in different Cu and S ratio
82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
in the compounds. Different sulfidation temperatures due can lead to varying degrees o f
conductivity, thus leading to unusual patterns in the images, as shown in Figure 3.18.
Annealing in the air for 1 minute further changes the composition and structures o f the
film, which result in the larger sheet resistance changes o f the image shown in Figure
3.19.
Figure 3.17-3.19 clearly demonstrate the capability o f EMMP in performing
detection of sheet resistance nonuniformities for various kinds o f materials.
10
0
80 -
■
Sheet resistance
(Q/square)
0.317
0.312
0.307
0.302
?<39bI u 2 ^ 7
0 . 2“ 2
0 .28?
0.282
0,275
-80 -
-100
-80
-m
-40
-20
0
20
40
60
80
lb
0
X axis (mm)
Figure 3.17
EMP image of a copper film on silicon substrate.
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sheet resistance
(Q /sq u u ie )
0,346
0.330
0,314
0.298
0.282
0,266
>
-40
0.250
0.234
0.218
-100
-80
-60
-40
-20
0
20
40
60
80
100
X axis (mm)
Figure 3.18
EMP image of copper film after 5 minutes sulfidation at 150 °C.
84
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sheet rest stance
(£1'square)
1,254
0.953
0,723
0.549
0,41?
0,317
0,240
0.183
0.139
■WWWWfc
m sm sm
wWiXfmwism^z
n B i■
1-------- 1------- t ------- r
-100 -80 -60 -40 *20
0
20
40
60
80
100
X axis (mm)
Figure 3.19
EMP image of copper sulfide after 1 minute annealing in air at 150 °C.
3.3.3 Magnetized Ferromagnetic Samples
To perform quantitative mapping o f conductivity, we calibrated the probe over a
range o f magnetic field density, from -4565 to 4498 Gauss. In our experiment, w e used a
DC magnetometer to measure the magnetic field. With this setup, a change o f 0.1 Gauss
could be detected, and the deviation was below 5%.
Figure 3.20 shows the calibration results for different magnetic field.
The
accuracy o f our measurement is better than 1%. The magnetic field resolutions o f the
EMMP are shown to be around 6 x l 0 45 at the operation frequency o f 2 GHz. Figure
3.21 shows the decay characteristics for magnetic probe. The dependence o f the output
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
signal on the distance is not exponential. However, approximating it with an exponential
decay, it has the characteristic decay length o f 360 pm. The spatial resolution o f our
microscope is expected to be on the order of the loop diameter when the probe is within
one loop diameter o f the surface.
R elative re fle cte d m icrow ave m agnitude
0.6
•
0 .4
-
(3,2
—4-------- --------- ------------------- --------- ,—
-5000 -4000 -5000 -2000 -IO0O
-6000
Figure 3.20
HK>
0
4000
5000
Evanescent magnetic microwave probe calibration curve for the magnetic
fields.
86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1,05
0
S f®
? m »; i
I 5 fl0
2W Q 0
Distance (urn)
Figure 3.21
Relative reflected microwave magnitude as a function o f distance (D)
between the probe tip and sample.
The above measurements were repeated ten times for reproducibility test, which
shows the variation of each measurement to be as small as 0.8 % . In addition to short
term reproducibility test, we also investigated the long term stability of the EMEP.
Before each measurement, we make sure the probe-sample distance constant by keeping
the lock-in amplifier output constant. Figure 3.22 shows the variation to be no larger
than 0.7 %.
87
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2 im i
W~Z
1900
~v
5..... *... i ------ ♦----- ♦
t
4
1 1700
a
1
SI 500
'I I W i
1
IS
i
c:$* 11CIO
*)«)
0 .6 :
f
700
20
0
30
40
50
00
70
1 tine >;m inute I
Figure 3.22
Long term stability o f the sensor range. Measurements are taken at two
different distances between tip and sample.
The imaging measurement are done using the ECCOSORB M F-190 rigid
magnetically loaded epoxide slab-shaped sample, whose relative permeability is 9.0 at
100 Hz and 7.0 at 1.0 GHz. The thickness o f the magnetic stock is 6.35 mm and a thin
copper sheet with the thickness of 30 pm is attached to the backside o f the magnetic
stock to get fixed boundary conditions and isolate the other effects from the backside o f
the magnetic stock.
Since the magnetic slab-shaped sample can not be permanently
magnetized so the circular permanent magnet are put under the stock. In that way, we
could test the magnetic regions above the magnetic stock. Different arrangements o f the
permanent magnets would result in different scanning images. Figure 3.23 shows the
88
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
scanned magnetic regions resulting from two and three permanent magnets in parallel at a
distance o f 100 pm from the magnetic probe.
Multimeter
readout (mV)
118.0
127.9
137.8
147.6
I
'57.5
67.4
.77.3
187.)
197.0
X axis
(a)
M ultim eter
readout (m V )
1
337.3
342.5
347.8
383.0
358.3
363.5
368.8
374.0
o
X axis
(b)
89
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.23
Images of permeability in a magnetized ferromagnetic sample obtained
using the magnetic probe sensor: (a) two magnets and (b) three magnets in series.
In conclusion, we demonstrated the application o f a evanescent microwave
magnetic dipole probe in mapping ferromagnetic materials permeability and remnant
magnetization field o f
6 x l 0 “45 at the operation frequency o f 2 GHz. The probe is a
relatively simple device that may find used in circuit design and optimization,
troubleshooting, and production testing.
It should also be possible to extend the
technique to image ferromagnetic antiresonance, and antiferromagnetic resonance using
the microscope.
90
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Chapter 4
ELECTROMANGETIC MODULATED
SCATTERERS IMAGING
4.1 Introduction
Scanning local probe microscopy techniques have advanced our knowledge o f
surfaces and materials at atomic scales [66-70]. Local probe microscopy that includes
tools such as scanning tunneling microscope (STM) [66], scanning near-field optical
microscopy (SNOM) [67], atomic force microscopes (AFM) [68], magnetic force
microscope (MFM) [69], and magnetic resonance force microscopy (MRFM) [70] have
revealed detailed information regarding atoms at and near material surfaces, mechanical
properties at nanometer scale and local coulombic and spin interactions.
The scanning near-field microwave microscope (SNM ) also belongs to the family
of local probes with the ability to “see” inside the sample using electromagnetic waves
over a wide range of frequencies [69-77].
For example, the nucleus inside a breast
cancerous cell was imaged in-vitro without harming the cell using a near-field microwave
probe integrated with AFM [73].
The scanning near-field microscope can be very
valuable in performing surface and subsurface imaging of embedded nanostructures,
leading to an in-depth understanding o f interactions between microscopic objects and
their environments. Moreover, the scanning near-field microscope has the unique ability
to provide direct images of subsurface structures owing to the penetration and possible
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resonant absorption o f its electromagnetic signal inside materials.
Our group has integrated the near-field microwave probe on an atomic force
microscope probe to simultaneously perform AFM topography and microwave imaging
at nanometer scale [69-77]. The results are quite interesting since AFM enables
identifying objects by essentially following their contour the way we may identify objects
in a dark room where w e cannot see and the microwave is analogous to the light switch
that enables seeing inside the sample.
The added benefit of the integrated scanning
system is that one can obtain simultaneous AFM and scanning near-field microwave
images, and take advantage of the familiar AFM and its knowledge base to validate and
reference microwave images.
The microwave waveguides that were integrated with the AFM probe [73] are
usually lossy and quite dispersive limiting the ability o f the SNM to image over wide
frequency range and leading to complications in quantitative measurements.
Thus, to
enable the AFM probe to perform SNM over a wide frequency range, it is necessary to
develop a different method to generate and measure near-fields at the AFM tip. Here w e
develop a technique that uses a conducting AFM tip as a local modulated scatterer [78] to
image electromagnetic properties of objects with near atomic resolution. The microwave
passing through the sample is reflected back by the AFM tip (the tip may be vibrated in
the non-contact mode), which is kept near the sample at a constant distance. Provided
that the AFM probe is conducting and that the sample is at least partially transmitting, the
reflected microwave will be affected by the interaction between the AFM tip and the
sample. In this method, the conducting AFM tip acts as a small antenna that receives and
reflects the microwave as schematically shown in Figure 4.1. The coupling between the
92
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AFM tip and the sample determines the reflected wave. Provided that the distance
between the tip and the sample is kept constant, the coupling between the tip and the
sample is primarily affected by the electromagnetic properties of the sample. Thus, the
main contributor to the reflected signal is the electromagnetic property o f the sample
under test.
Parallel AFM probe tips, vibrated at different frequencies can be used to
acquire the near-field image over large surface areas.
The transmission-mode “local scatterer” approach w ill work best for dielectrics
and resistive samples and the technique will fail for the conducting samples and it should
be operated in the reflection mode.
Measuring and monitoring the local dielectric property variations may be used to
detect voids, porosity and delamination in composite materials [76-83]. Moreover, once
the dielectric properties o f a sheet material are known, it is possible to detect its thickness
variation [83], Dielectric properties o f mostly in vitro (excised) biological tissues at radio
and microwave frequencies have been the subject o f research for over four decades [8083]. A few studies have also been conducted on the dielectric properties o f cancers in a
variety of tissue types at radio and microwave frequencies [83]. Typical differences in
the permittivity between the normal and malignant tissues are 10-20%. Recent
experiments have shown large interest o f active microwave imaging in biomedical
applications [83].
Before implementing with the AFM system, we devised a larger scale setup using
micromotors for proof o f concept demonstration. Fast data collection and imaging was
achieved by exciting different micromotors at different radial frequencies and using a set
o f band-pass filters to separate different frequency components. This approach enabled
93
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
using a single microwave horn antenna to collect spatial information from different
micromotors in the array. The array design, a simple theory to quantify the images, and
the calibration procedure using multiple measurement points corresponding to different
dielectric permittivities were also implemented as discussed next.
Near-field microwave probes are used to image electromagnetic properties o f
materials with spatial resolutions only limited by the probe aperture size and signal-tonoise ratio and not by the Abbe barrier. The price of this “super” resolution is point-bypoint scanning of the sample that makes it slow and requires additional mechanisms to
control the probe-to-sample distance during the scan. Here we discuss a new technique
that combines aspects of the “free-space” imaging with the super resolution o f near-field
scanning probes by using an array o f local scatterers near a sample. The local scatterers
generate near-fields upon illumination with a microwave beam.
These near-fields
interact with the nearby material and affect the reflection coefficient (or more generally,
scattering parameters) of scatterers in the array. Different scatterers are mechanically
modulated at different base frequencies. Thus, the free-space reflected waves from the
array are spatially modulated according to the local sample properties and the
corresponding scatterer’s modulation frequency.
We discuss applications o f this
technique in imaging a dielectric sample at 10 GHz using an array o f micromotors and a
layer o f carbon nanotubes at 100 GHz using an atomic force microscope tip as the local
scatterer.
4.2 Principle of Operation
Figure 4.1 shows simplified reflection- and transmission-mode techniques using
94
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
local scatterers to achieve super-resolution afforded by near-field interaction. It is also
possible to have embedded scatterers. In the transmission-mode (Figure 4.1a), the near
field waves are generated at the backside o f the sample and the surface of the scatterers.
Linearly polarized microwaves are transmitted by a horn antenna and propagate through
the
sample under investigation
as
schematically
shown
in
Figure 4.2.
The
electromagnetic wave is reflected and partially transmitted at the incident plane o f the
sample. The transmitted partial waves finally reach the backside o f the sample where an
array o f local scatterers is located. The electromagnetic wave interacts with the metallic
sections of the local scatterers generating current densities on them. The local scatterers
are located very near the sample.
Thus, their current densities induce charges and
secondary current densities in the sample and affect their scattering parameter in general.
The reflection coefficient can be viewed as a special case of a more general scattering
matrix.
In the reflection mode (Figure 4.1b), the local scatterer array is located in front of
the sample and the rest is identical to the transmission-mode setup.
The embedded
scatterer case is the combination o f transmission mode and the reflection mode.
The
embedded scatterer technique may be ideal for structural health monitoring and can be
used along with techniques that are being developed for RF-ID [xxx] to design very small
and self-contained scatterers that can be embedded in various structures and read using an
appropriate microwave ray.
95
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Local scatterer
(c)
Sample
<KA
Figure 4.1
Schematic o f local scatterer array used to combine traveling wave imaging
with near-field super-resolution, (a) Transmission-mode operation, and (b) reflection­
mode operation, c) Cross section diagram o f sample-scatterer interaction in the
transmission mode.
96
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sample
Circulator
1 lorn antenna
sstiK
I F sou rce
Array of
Jenifers
i,mm® ♦
’*SSPFr
w a iM g ir
-x,
V
w «TV
- i-ujjiiiuiui
at».... j \
generator
O O l
?OZO
° o ® o
° " ° e
Crystal
detector
Spectrum
analyser
Figure 4.2
Experimental setup. <y( is the rotation or oscillation frequency o f the ith ,
jth element.
It should be emphasized that the local scatterers are smaller than the wavelength
o f the illuminating microwave. Thus, their scattering cross section is relatively small.
By introducing sharp edges and discontinuities, one can increase the efficiency o f local
scatterers considerably.
The interaction between local scatterers and the sample is capacitive when electric
dipoles are used and it is determined by the stand-off distance as w ell as the property of
the sample. The locally modulated electromagnetic wave is reflected and received by the
same horn antenna that also transmits it.
detector or in some
A circulator directs the received wave to a
cases to an interferometer arm for homodyne
detection
(interferometry). The local scatterers are vibrated or rotated at a base frequency (100Hz1MHz) to modulate the reflected wave. The array of local scatterers can be assembled
97
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using discrete components as shown in Figure 4.3 or they can be fabricated using
micromachining techniques with integrated excitation and control electronics as
discussed later.
In the case of the micromotor array shown in Figure 4.3, each dc
micromotor was excited with different dc current values or with an ac signal that vibrated
their rotor back-and-forth at a frequency determined by the excitation signal frequency.
Thus, the reflected microwave signal from different parts o f the sample located over
different array micromotors (local scatterer), were modulated at different frequencies
given by the rotation or vibration frequency o f the corresponding local scatterer. A bank
o f band-pass filters were used (very much like a spectrum analyzer) to separate different
frequency components and construct two-dimensional images o f the spatial variations o f
the conductivity and permittivity in the sample. Figure 4.4 shows the signal from one of
the scatterers that was oscillating at 218 Hz. The scatterer was around 3.85 mm (shown
in Figure 4.3) and the wavelength of the illuminating electromagnetic wave was 3 cm
(f~10 GHz) with 1 dBm power. It is interesting to note that even for a scatterer ten times
smaller than the wavelength, the strength of the reflected signal (Figure 4.4) is acceptable
(-75 dBm). Figure 4.4 also shows the reflected signal with a dielectric sample over the
scatterer. The 1 mm thick s -2 .2 dielectric reduced the reflected w ave’s magnitude by
r
around 3 dBm.
98
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4.3
Micromotor array (4x4) used in preliminary studies.
99
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. 110
‘ 140
---- —
160
180
200
?2«
40
260
l
—
280
—
300
Frequency (H /l
Figure 4.4
The change o f received spectrum when a sample o f s r =2.2 is placed
between one of the micromotors and the horn antenna.
The spatial resolution of the final image depends upon both on the size o f the
local scatterer, its distance from the sample, and the distance between the horn antenna
and the sample.
The problem of reconstruction of distribution o f the dielectric
permittivity s of an object was considered under the following assumptions: 1)
propagation of electromagnetic radiation is considered in two-dimensional scalar case
under a plane wave illumination and 2) the object scatters radiation on small angles. In
this case the initial problem reduces into a simplified wave reflection and transmission
problem, as shown in Figure 4.1(b). A linearly polarized uniform plane wave is assumed
100
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normally incident on the dielectric.
/, is the thickness o f the dielectric and l2 is the
distance from the dielectric and the local scatterer surface which is facing the horn
antenna.
Z s is the characteristic impedance for the dielectric which is defined as:
2
Zs = —~=r , where Z0 is the characteristic impedance for free-space given by
Z0 =
— « 3 7 7 Q . Complex phase constant for the dielectric and free-space are defined
V e0
2 71 I—
2 7t
as: Ps = — tJ s s and /?0 = — . Therefore, by using the transmission line theory, it can
A)
\
be shown that the input impedance Z, for the dielectric and the motor plane is given by
Zj =j ( X f °
X 0 =tan(/?0/2) .
? where
Xs
and
X Q are
defined
as
X s = tan(/?v/j) and
7 -7 o
The reflection coefficient T is given by: T = —i
Z i+ Z 0
The reflected
power is proportional to | T f . The simulation results based on the above results along
with the experimental results obtained using the scatterer array o f Figure 4.3 at 10 GHz,
are shown in Figure 4.5. The samples were RT duroids with the known permittivities.
The thickness o f each sample was around 640 pm and the distance between the samples
and the horn antenna and the scatterer array was 0.5 mm. Larger distances between the
sample and the horn antenna were also examined with similar results but required larger
detection sensitivities.
A good agreement exists between the experimental data and
simulation results.
101
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■74
1.002
X
-76
mm •
0.996 •
X X
X
♦X X
*
Therotieal
♦
I'X p e r ic m r a l
X
\ *
\
u
SJ 0.994
-go
X
X X
0.992
c
a.
o
-82 eu
X
X
0.99
50
o
a
-78 o°
H
a.
X
\
HB
X
0.988
x*
X
♦ \ l
0.986
0.984
-84
-86
0
4
6
8
10
Relative permittivity
Figure 4.5
Calibration curve and the simulation results.
Duroid samples o f same
thickness with different relative permittivities were used.
The above measurements were repeated ten times for reproducibility test, which
showed the variation of each measurement to be as small as 1 %. In addition to short
term reproducibility test, we also investigated the long term stability o f the system. The
variation is around 2 % for a 30 minute measurement.
4.3 Array o f Local Scatterers and Imaging at 10 GHz
Figure 4.6 shows a dielectric map o f a 2.3 cm X 2.3 cm composite sample with
different dielectric regions. The image shows a sample with 16 different permittivity
102
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
regions addressed with a 4x4 array o f micromotors (Figure 4.3). The permittivity map
shows the ability o f the local scatterer array technique to provide im ages over large areas
with spatial resolution much better than the wavelength.
However, there are several
sources of errors in this type of measurements. First, it should be noted that errors in
calibration will result in erroneous dielectric constant assignments to the detected signals.
Therefore, calibration must be checked prior to each measurement cycle.
1.0
e=9.2
+ 10.2
e- .5.0
-
R eflected A m plitude
(dB m )
8=9.2
-31.78
-33.57
-33.96
-34.72
-36.56
-36.79
-38.01
-38.39
-39.00
-39.09
-40.16
-40.42
-40.64
-40.66
-40.88
-41.12
8= 10.2
1 0.2
8= 6.0
8=3.0
-0.5
0.0
0.5
1.0
X axis (mm)
Figure 4.6
10 GHz 4x4 image o f a composite dielectric sample. The calibration curve
o f Figure 4.5 was used to convert the reflected w ave’s amplitudes to permittivity values
of different regions.
4.4 AFM as a Local Scatterer and Imaging at 100 GHz
The ability to combine electromagnetic measurements with the near atomic
103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
resolution o f AFM w ill be instrumental in understanding the electromagnetic properties
of nano-scale materials and embedded nanoparticles. Such a technique with sufficient
bandwidth (lG H z-300G H z) will also enable microwave spectroscopy with very high
spatial resolution to identify nanoscale materials.
In the past w e have successfully
demonstrated near-field microwave imaging using AFM with specially designed probes
integrated with microwave waveguides. These probes were designed to operate up to 20
GHz but were found to be quite lossy above 5 GHz. The only requirement of the local
scatterer technique is that the AFM probe to be sufficiently conducting and it does not
require integrated waveguide.
Figure 4.7 schematically shows the 100 GHz-AFM system. The millimeter wave
is directed at the AFM probe (conducting) and the reflected wave is detected and
amplified and fed back to the electronic control unit o f the AFM system for simultaneous
display along with the topography image.
The AFM probe follow s the sam ple’s
topography and an image is constructed by monitoring tip displacement across the sample.
Many different AFM imaging modes are developed, including noncontact, contact,
tapping, and shear-force imaging. The millimeter wave signal that is scattered back by
the conducting AFM probe scanning over the sample, is affected by the local properties
o f the sample.
In most cases, the electromagnetic wave also penetrates the sample
enabling imaging interior of the sample and detecting embedded objects. The coupling
section o f the AFM tip and the sample is modeled as shown in Figure 4.1(a). The tipsample interaction is modeled by the coupling capacitance Cc in the noncontact mode.
Semiconductor and insulating samples are modeled by a resistance ( Rs ) and a
capacitance ( C s ).
104
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Mirror
Photodiode
Laser
diode
I
system
Sam ple
mwave
meas.
etectoi
Gunn diode
oscillator
Figure 4.7
Schematic of near-field microwave measurement with a commercial AFM.
The experimental setup used for the scanning near-field microwave microscopy is
shown in Figure 4.8. The measurement were performed using a 100 GHz mechanically
tuned Gunn diode oscillator. Directional coupler circulating the signal from the oscillator
to the sample under test, and detects the reflected wave from the AFM tip to a waveguide
detector. The output signal from the detector is then fed to the AFM imaging system and
images are generated in real time.
105
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(a)
106
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Figure 4.8
Photographs
of
(a)
scanning
near-field
microwave
microscopy
experimental setup with AFM system, and (b) microwave microscopy setup.
The images shown in Figure 4.9 were simultaneously obtained with the scanning
near-field microwave microscopy/AFM system in our group. The sample consisted o f
carbon nanotubes grown in our group using chemical vapor deposition technique on
titanium. The range in these scans was 20 pm x 20 pm. The AFM topography images
show two categories of objects.
The larger objects (1-5 pm) are bundles o f carbon
nanotubes with additional graphitic carbon on them. The finer objects are multi-walled
carbon nanotubes with around 100 nm (0.1 pm) diameter and are much better resolved in
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the near-field millimeter wave images. The near field millimeter waves generated at the
tip o f the conducting AFM probe strongly interact with CNTs and change its reflection
coefficient.
#*/
: -0.062 ¥
i
^
H
*
1
; -0.063 V
20 |tm
jfif
1
20 p tti'
*
*
a*
10 um
i / ®
•
H) um
o pm
108
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-0,061V
-0.063 V
20 um
10 pm
0
u m
101.28 nm
: 0 nra
20 um
20 jinn
10 um
0 pin
(b)
Figure 4.9
Simultaneous AFM and near-field millimeter wave images obtained from
thin layer of titatnium film covered with carbon nanotubes. The scans were performed at
100 GHz.
To reduce AFM scanning time, an array of conducting probes can be
109
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microfabricated as schematically shown in Figure 4.10. Each probe in the array can be
excited electrostatically at different frequencies.
This approach is scalable and cost
effective. However, it requires that each array member to be dynamically adjustable to
regulate their stand-off distances with samples with large topographical variations.
Metal cutting
ir
At
C o n d iietin ti s tn
Figure 4.10
A MEMS array of local modulated scatterers.
In conclusion, we demonstrated the feasibility of using the local scatterer
approach in achieving very high spatial resolution comparable to that of AFM. A 4x4
micromotor array was also used to map dielectric constant of a composite dielectric
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sample without point-by-point scanning required in near-field scanning methods.
I ll
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Chapter 5
CONCLUSION AND FUTURE WORK
5.1 Conclusion
In this research, the unique techniques using evanescent microwave magnetic
dipole probe and modulated scatterers are proposed to satisfy the noncontact imaging of
materials properties applications. The research is motivated by the growing demand for
noncontact imaging o f materials applications in semiconductor industry, biomedical
applications, high density interconnect multichip modules, substrate epoxy void detection,
and aging aircrafts.
Compared to conventional detecting systems, the noncontact
architecture is attractive for high resolution, high scan rate, and low operation cost.
A near-field magnetic-dipole probe suitable for non-contact and non-destructive
imaging of metals is described and the effects of resonator coupling strength, operation
frequency, and the probe wire tip geometry on the conductivity resolution o f the probe
are experimentally determined.
Using a simplified circuit model o f the resonator, we
were able to interpret the system’s output and predict the magnitude of reflected wave
and relate it to the properties of the samples under investigation. Thus, the probe was
calibrated to perform quantitative conductivity measurement. It has been shown that we
have detected metal nonuniformities with 1% accuracy and 5 x l 0 ”3cr and 2 x 1 0 2<r
conductivity resolution at 2 GHz operation frequency for the critical and over-coupling
probes, respectively. We also discussed the calibration results of probes with different
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coupling strength over a 0.91 Q/square sample.
The calibration results o f a critical-
coupling resonator probe were also compared with a microstrip transmission line probe.
It has been shown that resonator probe has 100 times higher conductivity resolution than
that of the transmission line probe, using the same calibration method. Furthermore, w e
characterized and compared the calibration results of probes with tip wires of different
diameters. Images obtained by evanescent microwave probe are presented. The w hole
imaging system is automated by a PC using the probe-sample distance control method.
Its applications is also reported in imaging high-frequency electromagnetic properties of
magnetic metallic samples. The probe’s output was calibrated with a Hall probe that was
also scanned over the sample. It is shown that the magnetic dipole probe detected the
magnetic field above the magnetized ferromagnetic sample with 1% accuracy and
6 x 1 0 4B resolution at 2 GHz.
Furthermore, it is used to image uniformity o f the
electromagnetic properties o f damascene copper on silicon, and its subsequently
sulfidized and annealed surface. The magnetic dipole probe has low internal impedance
and is better matched with the low impedance metallic films.
To demonstrate the
importance o f impedance matching, the calibration curve o f the magnetic probe was
compared with that of the electric dipole probe. The magnetic dipole has a conductivity
sensitivity of 7 x 1 0 4cr compared to 3.4 x 1 0 3cr of the electric dipole probe in metallic
samples.
However, the electric dipole’s sensitivity of 2 .5 xl0~2s is better than the
magnetic dipole’s sensitivity of 0.25s in dielectric samples. Owing to its pointed apex,
the electric dipole probe generally has better spatial resolution as well.
Near-field microwave probes are used to image electromagnetic properties of
materials with spatial resolutions only limited by the probe aperture size and signal-to-
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noise ratio and not by the Abbe barrier. The price of this “super” resolution is point-bypoint scanning o f the sample that makes it slow and requires additional mechanisms to
control the probe-to-sample distance during the scan. Here w e discuss a new technique
that combines aspects of the “free-space” imaging with the super resolution o f near-field
scanning probes by using an array o f local scatterers near a sample. The local scatterers
generate near-fields upon illumination with a microwave beam.
These near-fields
interact with the nearby material and affect the reflection coefficient (or more generally,
scattering parameters) of scatterers in the array.
Different scatterers are mechanically
modulated at different base frequencies. Thus, the free-space reflected waves from the
array are spatially modulated according to the local sample properties and the
corresponding scatterer’s modulation frequency.
We discuss applications o f this
technique in imaging a dielectric sample at 10 GHz using an array of micromotors and a
layer of carbon nanotubes at 100 GHz using an atomic force microscope tip as the local
scatterer.
5.2 Future work
The following aspects o f the evanescent microwave sensing system should be
optimized in future work.
The EMMP can be combined with the Atomic Force microscopy (AFM) to detect
even smaller features on the sample. Unlike the current EMMP tip, The AFM tip size is
in nanometer level, therefore, the space is more confined and the resolution can be
improved greatly with the small size of the probe Other advanced control such as Active
Q control, fuzzy logic control can be utilized for the precise control o f the AFM tip
locations.
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To reduce AFM-based modulated scatterers system scanning time, an array of
conducting probes can be microfabricated as schematically shown in Figure 4.10. Each
probe in the array can be excited electrostatically at different frequencies. This approach
is scalable and cost effective.
However, it requires that each array member to be
dynamically adjustable to regulate their stand-off distances with samples with large
topographical variations.
115
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Appendix A
Equivalent Capacitances for Microstrip Gaps
The model proposed here for the microstrip gaps is a n network, as shown in
Figure A .I.
The mathematical approach taken here is based on the integral equation
method used in [84], to calculate the excess capacitance of a microstrip open circuit. The
n model in Figure A. 1(b) is a symmetric two-port network, so that at least two
measurements are required to determine the parameters C x and C12.
(a).
C 12
-o
Cl
En
; e2
(b)
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Figure A .l
(a) Gap in a microstrip line , and (b) Capacitive n-network model for a gap
in a microstrip line.
Let ® (P ) be the potential corresponding to a charge distribution cr(P'), so that
® (P ) = j a ( P r) G (P ;P r)d P ',
where G (P ;P ')
is some
P ' are spacepoints
(A -l)
Green’s function appropriate to the particularproblem.
P and
for potential and charge, respectively. Let O x(P ) be thepotential
(constant on the strip) due to an infinitely extending microstrip line, with corresponding
charge density distribution cra0(P '). Then
® J P ) = j a J P )G J P ;P ')d P \
where Gm(P \P ') is the Green’s function for the infinite microstrip.
(A-2)
Let O^(P) be the
potential associated with a charge distribution crao(P') for z > ^ and -cr, ( P ') for z < g .
The z -coordinate axis corresponds to the axis o f the microstrip, as indicated in Fig. A .I.
Then
=
J(Tx ( n G , ( P ; P y P ' ,
(A-3)
where Gf ( P ; P ) is the Green’s function for the charge distribution with polarity reversal
at z = £ .
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Figure A .2
(a) Symmetrically excited two-port network resulting in Ceven ,. (b)
Antisymmetrically excited two-port c network in Codd .
To obtain Ceven, as defined by Fig. A.2(a), an infinitely extending microstrip line
is considered, as given by (A-2).
Two other lines with charge density distribution
1
—<JCC( P ') , each having a polarity reversal at z = s / 2 and z = - s / 2 , respectively, are
governed, according to (A-3), by
= | \o„(P"V,n(P-*ndP'
(A'4)
and
\<S>-,n(P) = \ \ v S P " f i - sn ( r - , n d P '
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■(A-5)
The superposition of these lines is accomplished by adding (A-2) and (A-4), and
subtracting (A-5), thereby resulting in
1
J
2
(A-6)
The quantity on the left o f (A-6) represents the potential corresponding to a microstrip
charge distribution for | z \ > s / 2 and zero charge elsewhere. Note that on the strips this
1
potential is not <PX but ratherOM+ —{<bs/2( P ) - 0 _ s/2(P )}.
Now it may be observed that a certain amount of extra charge <jteven = c r - c r aD
must be added tothe two strips in Fig. A .l (a) to raise the potential on them to <6^ . The
potential
corresponding
to
the
extra
charge
is
<reeven
is
® . - ( ® . + \ [®„2 (P ) ~ ®-./2<P M) • S° that
\ l t „ 2( P ) - 0 _ 1/2( P ) ] = f a - r " ( P ') G ‘- ( P ; P V P ' .
(A -7)
Solving (A-7) for cr/v“ (P ') gives
C even =
2 [ ( j; ven(P )d P '
J
^
(A-8)
V
/
00
where due to symmetry the integration is performed only over one o f the strips.
To evaluate Codd, as defined by Fig. A.2(b), it can be shown by an analogous
procedure that to raise (lower) the potential on the semi-infinite strip at z > s / 2
( z < s / 2 ), to <E>x (-<!><») an extra charge crfdd (~creodd) is required. The corresponding
integral equation is
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®.
) + ®-s/2(*”)} = [
(p
(P; P y p '
(A-9)
and Codd is evaluated by
\(Teodd( P ) d P '
r
o dd
(A -10)
=
<1>
where the integration is done over the strip located at z > s / 2 .
The details of the method used to obtain crco{P '), the charge distribution o f an
infinitely extending microstip transmission line, are shown in [85]. Briefly, referring to
Figure A.3 and using (A-2), the charge distribution is governed by [85]
®=o(>0 =
(A -11)
where the Green’s function, obtained by the method of partial images, is found to be [85]
'
,\2 1
An2 + y - y
l
Vh J
S ^ ’-'lo g
GSr,y') =
f
'V
27r (£-0 +£-,) n=
4(72 + l) 2 +
y h )
with K = (e0 - £{) /( f 0 + £ j ) . The potential ^ ( y ) is constant on the strip.
liiP
Figure
A.3 Cross section of a microstrip line
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(A -12)
The unknown charge distribution crx (y') is even in y ' and is expanded in an
even set of functions { T J defined by
L(y)
(A -13)
■y'
where
o|(A
-y
,n > 1
(A -14)
l,n =1
Then the charge density distribution on the strip may be written as
(A -15)
Note that the function space
contains the expended edge singularity
(1 - y ' 2y m [86],
When equation (A-15) is substituted in (A -l 1), it may be solved by projecting
both sides on a set of even-order Legendre polynomials.
The singularities in the
integrand at y = y 1 and | y ’|= 1 require special treatment as given in [85].
The Green’s function G£( P ; P r) in (A-3), obtained by using a line charge with
polarity reversal together with partial image theory [4], is
(A -16)
G£(h ,y ,z ;y ') =
where
f ( ti ) = log
V(2 - ^ )2 + 4n2h2 + ( y - y ' ) 2 + ( z ~ 4 )
4 ( z - Z ) 2 + 4 n 2h2 + ( y - y f - ( z - f )
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(A -17)
The charge distribution crxi( y ' ) , obtained from (A -ll), is used in (A-3) with the
Green’s function given in (A-16), to calculate ®_S/2(P ) , ® s 2(P ) , ® 0(1)(P ) , and
® 0(2)(P ) and, hence, the exciting potential on the left sides of (A-7), and (A-9).
The Green’s functions G even( P ; P r) , and G odd( P ; P r) are obtained, using partial
image theory, as described by the authors in [87]. Taking full advantage o f the inherent
symmetries in Figure A .l(a ) and (b) the Green’s functions are found to be
G J h , y , z ; y ’,z') =
1
27r(s(j + ex)h
where
even
2
z-z
y-y
+
(2
n
f
+
in) =
h
h /
V n
M2
^ f Z-Z^2
+
(2 n f +
-
1/2
rd
r*
odd .
+ (2 n f + y - y
V
± (2n f +
h
1/2
-
1/ 2
(A -19)
+
/
"y + y
I
-
+
h
Ceven and Codd normalized to strip width are plotted in Figure A .4 against s / w
for substrate relative dielectric constants ranging from 1.0 to 15, and width-to-height
ratios of 0.5, 1.0, and 2.0. C1 and Cn to be used in the n model for the gap may be
easily calculated using
C1 = -2C
even
C a = \ l C M - C ,)
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(A-20)
(A-21)
A l ( a ) atvd(b>
teadiVy
£ q u a tio n s
(A-20)
>*
U-
123
nVieoo(.vn9w o'"n
100-
odd
as.
s rw
fcl
Figure A.4
(a) Ceven and Codd per unit width of microstrip lines o f width-to-height
ratio o f 0.5 and relative dielectric constants from 1.0 to 15.0.
Gap spacing-to-width
ratio ranges from 0.1 to 2.0. (b) Same as (a) except width-to-height ratio of 1.0. (c)
same as (a) except width-to-height ratio of 2.0.
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Appendix B
Atomic Force Microscopy (AFM)
In the fall o f 1985 Gerd Binnig and Christoph Gerber [88, 89] used the cantilever
to examine insulating surfaces and discovered the force between tip and sample could be
measured by tracking the deflection of the cantilever. After the measurement o f atomic
structure of boron nitride by using a silicon micro-cantilever, the AFM became the most
important tools for the world of surface science.
The atomic force microscope is one o f
about two dozen types o f scanned-proximity probe microscopes. All o f these microscopes
work by measuring a local property - such as height, optical absorption, or magnetism with a probe or "tip" placed very close to the sample. The small probe-sample separation
(on the order o f the instrument's resolution) makes it possible to take measurements over
a small area. To acquire an image the microscope raster-scans the probe over the sample
while measuring the local property in question. The resulting image resembles an image
on a television screen in that both consist o f many rows or lines o f information placed
one above the other.
The principles on how the AFM works are very simple. An atomically sharp tip is
scanned over a surface with feedback mechanisms that enable the piezo-electric scanners
to maintain the tip at a constant force (to obtain height information), or height (to obtain
force information) above the sample surface. Tips are typically made from SisN 4 or Si,
and extended down from the end of a cantilever. The nanoscope AFM head employs an
optical detection system in which the tip is attached to the underside o f a reflective
cantilever. A diode laser is focused onto the back of a reflective cantilever. As the tip
scans the surface of the sample, moving up and down with the contour of the surface, the
laser beam is deflected off the attached cantilever into a dual element photodiode. The
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photodetector measures the difference in light intensities between the upper and lower
photodetectors, and then converts to voltage. Feedback from the photodiode difference
signal, through software control from the computer, enables the tip to maintain either a
constant force or constant height above the sample. In the constant force mode the piezo­
electric transducer monitors real time height deviation. In the constant height mode the
deflection force on the sample is recorded. The latter mode o f operation requires
calibration parameters of the scanning tip to be inserted in the sensitivity of the AFM
head during force calibration of the microscope.
The most common modes for the AFM are the non-contact, tapping mode [90]
and the contact mode [91] where the tip scans the sample in close contact with the surface.
The force on the tip is kept as a constant during the scanning o f the surface. Therefore,
the deflection on the cantilever can be detected and recorded for the surface topography
[92, 93]. In its repulsive "contact" mode, the instrument lightly touches a tip at the end of
a leaf spring or "cantilever" to the sample. As a faster-scan drags the tip over the sample,
some sort of detection apparatus measures the vertical deflection o f the cantilever, which
indicates the local sample height. Thus, in contact mode the AFM measures hard-sphere
repulsion forces between the tip and sample.
In noncontact mode, the AFM derives
topographic images from measurements o f attractive forces; the tip does not touch the
sample.
A. Contact mode:
The contact mode where the tip scans the sample in close contact with the surface
is the common mode used in the force microscope. The force on the tip is repulsive with
a mean value of 10‘9 N. This force is set by pushing the cantilever against the sample
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surface with a piezoelectric positioning element. In contact mode AFM the deflection o f
the cantilever is sensed and compared in a DC feedback amplifier to some desired value
o f deflection. If the measured deflection is different from the desired value the feedback
amplifier applies a voltage to the piezo to raise or lower the sample relative to the
cantilever to restore the desired value o f deflection. The voltage that the feedback
amplifier applies to the piezo is a measure o f the height o f features on the sample surface.
It is displayed as a function of the lateral position o f the sample. A few instruments
operate in UHV but the majority operate in ambient atmosphere, or in liquids. Problems
with contact mode are caused by excessive tracking forces applied by the probe to the
sample. The effects can be reduced by minimizing tracking force o f the probe on the
sample, but there are practical limits to the magnitude o f the force that can be controlled
by the user during operation in ambient environments. Under ambient conditions, sample
surfaces are covered by a layer o f adsorbed gases consisting primarily o f water vapor and
nitrogen which is 10-30 monolayers thick . When the probe touches this contaminant
layer, a meniscus forms and the cantilever is pulled by surface tension toward the sample
surface. The magnitude of the force depends on the details o f the probe geometry, but is
typically on the order of 100 nanoNewtons. This meniscus force and other attractive
forces may be neutralized by operating with the probe and part or all o f the sample totally
immersed in liquid. There are many advantages to operate AFM with the sample and
cantilever immersed in a fluid. These advantages include the elimination of capillary
forces, the reduction o f Van der Waals' forces and the ability to study technologically or
biologically important processes at liquid solid interfaces. However there are also some
disadvantages involved in working in liquids. These range from nuisances such as leaks
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to more fundamental problems such as sample damage on hydrated and vulnerable
biological samples.
In addition, a large class of samples, including semiconductors and insulators, can
trap electrostatic charge(partially dissipated and screened in liquid). This charge can
contribute to additional substantial attractive forces between the probe and sample. A ll o f
these forces combine to define a minimum normal force that can be controllably applied
by the probe to the sample. This normal force creates a substantial frictional force as the
probe scans over the sample. In practice, it appears that these frictional forces are far
more destructive than the normal force and can damage the sample, dull the cantilever
probe and distort the resulting data. A lso many samples such as semiconductor wafers
can not practically be immersed in liquid. An attempt to avoid these problem is the Noncontact Mode.
B. Noncontact mode:
A new era in imaging was opened when microscopists introduced a system for
implementing the non-contact mode which is used in situations where tip contact might
alter the sample in subtle ways. In this mode the tip hovers 50-150 Angstrom above the
sample surface. Attractive Van der Waals forces acting between the tip and the sample
are detected, and topographic images are constructed by scanning the tip above the
surface. Unfortunately the attractive forces from the sample are substantially weaker than
the forces used by contact mode. Therefore the tip must be given a small oscillation so
that AC detection methods can be used to detect the small forces between the tip and the
sample by measuring the change in amplitude, phase, or frequency o f the oscillating
cantilever in response to force gradients from the sample. For highest resolution, it is
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necessary to measure force gradients from Van der Waals forces which may extend only
a nanometer from the sample surface. In general, the fluid contaminant layer is
substantially thicker than the range o f the Van der Waals force gradient and therefore,
attempts to image the true surface with non-contact AFM fail as the oscillating probe
becomes trapped in the fluid layer or hovers beyond the effective range o f the forces it
attempts to measure.
C. Tapping mode:
Tapping mode is a key advance in AFM. This potent technique allows high
resolution topographic imaging of sample surfaces that are easily damaged, loosely hold
to their substrate, or difficult to image by other AFM techniques. Tapping mode
overcomes problems associated with friction, adhesion, electrostatic forces, and other
difficulties that an plague conventional AFM scanning methods by alternately placing the
tip in contact with the surface to provide high resolution and then lifting the tip off the
surface to avoid dragging the tip across the surface. Tapping mode imaging is
implemented in ambient air by oscillating the cantilever assembly at or near the
cantilever's resonant frequency using a piezoelectric crystal. The piezo motion causes the
cantilever to oscillate with a high amplitude( typically greater than 20nm) when the tip is
not in contact with the surface. The oscillating tip is then moved toward the surface until
it begins to lightly touch, or tap the surface. During scanning, the vertically oscillating tip
alternately contacts the surface and lifts off, generally at a frequency o f 50,000 to
500,000 cycles per second. As the oscillating cantilever begins to intermittently contact
the surface, the cantilever oscillation is necessarily reduced due to energy loss caused by
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the tip contacting the surface. The reduction in oscillation amplitude is used to identify
and measure surface features.
During tapping mode operation, the cantilever oscillation amplitude is maintained
constant by a feedback loop. Selection o f the optimal oscillation frequency is softwareassisted and the force on the sample is automatically set and maintained at the lowest
possible level. When the tip passes over a bump in the surface, the cantilever has less
room to oscillate and the amplitude o f oscillation decreases. Conversely, when the tip
passes over a depression, the cantilever has more room to oscillate and the amplitude
increases (approaching the maximum free air amplitude). The oscillation amplitude o f the
tip is measured by the detector and input to the NanoScope III controller electronics. The
digital feedback loop then adjusts the tip-sample separation to maintain a constant
amplitude and force on the sample.
When the tip contacts the surface, the high frequency (50k - 500k Hz) makes the
surfaces stiff (viscoelastic), and the tip-sample adhesion forces is greatly reduced.
TappingMode inherently prevents the tip from sticking to the surface and causing damage
during scanning. Unlike contact and non-contact modes, when the tip contacts the surface,
it has sufficient oscillation amplitude to overcome the tip-sample adhesion forces. Also,
the surface material is not pulled sideways by shear forces since the applied force is
always vertical. Another advantage o f the TappingMode technique is its large, linear
operating range. This makes the vertical feedback system highly stable, allowing routine
reproducible sample measurements.
Tapping mode operation in fluid has the same advantages as in the air or vacuum.
H owever imaging in a fluid medium tends to damp the cantilever's normal resonant
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frequency. In this case, the entire fluid cell can be oscillated to drive the cantilever into
oscillation. This is different from the tapping or non-contact operation in air or vacuum
where the cantilever itself is oscillating. When an appropriate frequency is selected
(usually in the range o f 5,000 to 40,000 cycles per second), the amplitude o f the
cantilever w ill decrease when the tip begins to tap the sample, similar to TappingMode
operation in air. Alternatively, the very soft cantilevers can be used to get the good results
in fluid. The spring constant is typically 0.1 N/m compared to the tapping mode in air
where the cantilever may be in the range o f 1-100 N/m.
In principle, AFM resembles the record player as well as the stylus profilometer.
However, AFM incorporates a number o f refinements that enable it to achieve atomicscale resolution:
•
Sensitive detection
•
Flexible cantilevers
•
Sharp tips
•
High-resolution tip-sample positioning
•
Force feedback
When using contact mode, Fig. B .l is obtained by scanning a 10 mm x 10 mm
sample using the Thermomicroscope Explorer ™ AFM system.
131
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SO^tm
394.00 run
0.00 nm
2S|im
25 nm
Figure B .l
50jwt
The AFM Imaging of silicon nitride (Si3N 4 ) grids with width o f 10 pm and
depth of about 400 nm.
132
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