Evanescent microwave probes and their applications in non-destructive quantitative evaluation of materials

EVANESCENT MICROWAVE PROBES AND THEIR APPLICATIONS IN
NON-DESTRUCTIVE QUANTITATIVE EVALUATION OF MATERIALS
by
TAO ZHANG
Submitted in partial fulfillment of the requirements
For the degree of Doctor of Philosophy
Thesis Advisor: Dr. M. Tabib-Azar
Department of Electrical Engineering and Computer Science
CASE WESTERN RESERVE UNIVERSITY
May, 2003
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UMI Num ber: 3092041
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CASE WESTERN RESERVE UNIVERSITY
SCHOOL OF GRADUATE STUDIES
We hereby approve the thesis/dissertation of
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Contents
Chapter 1
Introduction
1-2. Near field microwave microscopy
1-2. Evanescent microwave microscopes (EMM) or probes (EMP)
Chapter 2
Microstrip resonator and Its model
2-1. Microstrip transmission line
2-2. Model and calibration procedure of microstrip resonator
2-3. Model of microstrip resonator system using ABCD matrix
2-4. Discussions of load impedance near the tip
Chapter 3
Model of charge distribution at the tip
3-1. Model of interaction
3-2. Charge distribution and capacitance of metal tip over dielectric samples
3-3. Sheet resistance or loss tangent of samples
Chapter 4
Designs and Implementations of EMP systems
4-1. AM modulation, FM modulation and microwave diode detector
4-2. High-speed EMP system based on true logarithmic amplifier (TLA)
4-3. Coupling of microstrip resonator
4-4. Self resonant EMP probe
Chapter 5
Microwave AFM System
5-1. Characterization of AFM tip
5-2. Microwave AFM system
5-3. Experimental results of microwave AFM system
Chapter 6
Quantitative characterization of materials using EMP
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6-1. z decay of EMP probe in Smith chart
6-2. Permittivity characterization
6-3. Sheet resistance characterization
6-4. Proposed future work
iv
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List of Tables
Table 2-2-1. The design parameters of 50 Q microstrip line at 1GHz using Duroid
substrates
Table 3-3-1. Some important parameters of a microstrip resonator with resonant
frequency near 1 GHz operating at three different coupling conditions
V
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List of Figures
Figure 1-1-1. Schematic of RCA scanning capacitance microscopes (SCM) sensor
Figure 1-1-2. Transfer functions of RCA SCM sensor
Figure 1-1-3. Experimental setup to determine the sensitivity of SCM sensor
Figure 1-2-1. Microwave resonator (a) and its SI 1 (b) in the air and close to metal ground
Figure 2-2-1. Model of gap capacitor, A/2 microstrip line and load impedance at the tip
because of tip-sample interaction
Figure 2-2-2. Teflon screw is used to mechanically change the coupling capacitance
Figure 2-2-3. Simplified model of gap capacitor, A/2 microstrip line and load impedance
at the tip because of tip-sample interaction
Figure 2-2-4. Extracted load impedance (a) at the tip from input impedance (a) was
nearly open that is expected.
Figure 2-2-5. Extracted convergent capacitance and resistance change at the tip of a
microstrip resonator versus different gap
Figure 2-2-6. Corresponding S 11s (Magnitude) near resonant frequency were not
convergent.
Figure 3-2-1. Axi-symmetric surface is the sum of curved surfaces and flat surfaces. Axisymmetric subsections are divided.
Figure 3-2-2. a) Numerically evaluated charge distribution of the 380 pm diameter sphere
projected along its z axis at two different stand-off distances of d=l pm and d=200 pm.
In (b) the sphere-sample forms a dipole while in (c), the sphere alone is polarized and
forms two back-to-back dipoles. This situation is also schematically depicted in the (a)
inset
Figure 3-2-3. Calculated capacitance of 380 pm sphere from formula (3-1-13) and (3-114) are compared with numerical results. Formula (3-1-13) and (3-1-14) used very poor
approximation.
Figure 3-2-4. Capacitance versus gap between a 380 pm diameter sphere and a metallic
base plate.
Figure 3-2-5. Measured and simulated capacitance change of the tungsten tip
Figure 3-2-6. Measured capacitances of the spherical and conical (Ti) tips as a function of
tip-sample stand-off distance at 1 GHz.
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Figure 3-2-7. Measured capacitances of the spherical and conical (Ti) tips as a function of
tip-sample stand-off distance at 1 GHz
Figure 3-1-1. EMP system using AM or FM modulation. In these systems phase lock-in
amplifier (PLA) is the key instrument.
Figure 4-1-2. Optimum FM modulation frequncy must be chosen to make magnitude
constant as large as possible. 90 KHz is chosen.
Figure 4-1-3. (a)Effective Q factor was 3400 which was 34 times larger than Q factor of
S 11. (b) S 11 of the resonator
Figure 4-1-4. The output of schottky diode versus RF power. The magnitude of
modulation signal was fixed at 0.4 V.
Figure 4-1-5. Biased schottky diode and Point-contact diode
Figure 4-2-1. High-speed EMP system based on TLA
Figure 4-2-2. The offset phase and magnitude of experimental system from 0.5 GHz-1
GHz were measured for calibration.
Figure 4-2-3. The full Differential measurements use two identical probes at two arms.
The third arm is reserved for calibration.
Figure 4-2-4. The measured magnitude of S ll using experimental system fits quite well
with the measured magnitude of S ll using HP8720C network analyzer.
Figure 4-2-5. The input impedance of a microstrip resonator with 380 pm sphere tip over
copper ground with 1 |Jm gap, 125 pm gap and 250 pm gap.
Figure 4-3-1. The Smith chart of less, near critical and over coupled resonator using the
system described in section 4-2.
Figure 4-3-2. The phase of less, critical and over coupled resonator with open at the end
of probe.
Figure 4-4-1. Schematic of the self-oscillating evanescent microwave probe (SO-EMP)
with an integrated RF amplifier.
Figure 4-4-2. The experimental S21 (both phase and amplitude) spectrum of the SO-EMP
resonator with the amplifier turned off.
Figure 4-4-3. The experimental S 21spectrum of the RF amplifier (VNA-25) used in the
SO-EMP.
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Figure 4-4-4. The oscillation spectra obtained using a spectrum analyzer of the SO-EMP
with and without a metallic sample.
Figure 4-4-5. The SO-EMP linescans over a 12.5 pm square wire (a) and three 4-pm
diameter carbon fibers (b)
Figure 3-4-6. The SO-EMP output (a) and the EMP output (b) versus distance (in the zdirection) using a metallic (copper) sample. The SO-EMP decay length is around 70 pm
while that of the EMP decay length is in excess of 400 pm. Both probes had similar
tapering and tip sections.
Figure 5-1-1. Fabricated coaxial shielded AFM compatible tip by Yaqiang wang in our
group.
Figure 5-1-2. The I-V characteristic of coaxial AFM compatible tips
Figure 5-1-3. Load impedance characterization using a single cable and HP8720C
network analyzer
Figure 5-1-4. Extracted resistance and capacitance of three AFM tips
Figure 5-1-5. Setup used to characterize the coaxial AFM compatible tip
Figure 5-1-6. Extracted resistance and capacitance of one AFM tip using grounded
copper foil to perpendicularly approaching the AFM tip at 10 GHz. Z was smaller, gap
was smaller. Z=0 corresponding to about 0.5mm gap between ground and AFM tip.
Figure 5-1-7. AFM compatible co-coaxial tip was mounted on the metal half washer. The
half washer was mounted on the AFM head and connected to EMP system.
Figure 5-1-8. AFM compatible co-coaxial tip was in the air or touch ground. The S ll of
AFM tip was sensitive to set-point of AFM system.
Figure 5-2-1. AFM compatible tips used as monopole antenna
Figure 5-3-1. (a) cell AFM image; (b) Cell pAFM (magnitude) image using method 1 at
1GHz; (c) Cell p.AFM (phase) image using method 1 at 1GHz.
Figure 5-3-2. pAFM image of semiconductor sample using method 2 at 10.5 GHz. The
bright line was S i3N 4.
Figure 5-3-3. (a) pAFM of sputtered 2000A Au on glass substrate using method 3 at
18GHz. (a) AFM of sputtered 2000A Au on glass substrate using method 3 at 18GHz. (c)
The spatial resolution was smaller than 20 nm at the edge of the Au layer.
Figure 6-0-1. Gap between probe tip and ‘flat’ GaAs wafer. The step size was 0.017 pm.
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Figure 6-1-1. z decay of metal (red), GaAs (green) and Duroid substrate (black).
Figure 6-2-1. Measured permittivity versus the value using IPC-TM-550
Figure 6-2-2. Calibration curve of permittivity with air gap about 50 pm using true log
amplifier (TLA) based EMP.
Figure 6-2-3. Calibration curve of permittivity with air gap about 50 pm using phase
lock-in amplifier (PLA) based EMP.
Figure 6-3-1. Capacitive part of the load impedance at the tip as a function of stand-off
distance obtained using a network analyzer. Negative stand-off distance refers to tipsample contact that also results in tip bending and application of contact force.
Figure 6-3-2. Resonant frequency (fo) as a function of the stand-off distance is three
different samples.
Figure 6-3-3. Probe’s output voltage at the resonant frequency (V0) as a function of
stand-off distance for different samples. The sheet resistance of sample is shown in inset.
Figure 6-3-4. V0 as a function of sheet resistance at three different stand-off distances.
Figure 6-3-5. V0 as a function of sheet resistance and stand-off distance.
Figure 6-3-6. Sheet resistance map using non-contact EMP and contact CoReMa
technique.
Figure 6-3-7. Sheet resistance map of conductive SiC
Figure 6-3-8. Sheet resistance calibration curve of TLA based EMP system. 200 mV DC
bias and 100 times amplification have been used.
Figure 6-3-9. Sheet resistance calibration curve of PLA based EMP system. RF power
was -10 dBm. 5000 times amplification has been used.
Figure 6-3-10. Sheet resistance calibration curve of TLA based EMP system. 100 mV DC
bias and 100 times amplification have been used. The samples were sputtered gold layers.
Figure 6-3-11. Sheet resistance calibration curve of TLA based EMP system. RF power
was -10 dBm. A M m odulation index was 5 %. 10000 tim es am plification was used.
ix
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Evanescent Microwave Probes and Their Applications in
Non-destructive Quantitative Evaluation of Materials
Abstract
by
TAO ZHANG
This thesis discusses the models, measurement systems, and calibration procedures of
Evanescent Microwave Probes (EMP). The applications in evaluation of semiconductor
and dielectric materials are also discussed. The extraction of load impedance near the
probe tip and TLA (True Logarithmic Amplifier) based EMP systems are the original
ideas of this research. Full differential probes that have largest dynamic range and good
sensitivity are proposed in this thesis. Sheet resistance as small as 0.2 £>cm has been
detected using TLA based EMP system with 200 pm diameter tungsten tip at 50 pm
stand off. We estimate the sheet resistance sensitivity of the probe (Apa/p0) to be 3xl0'2
at 210 pm stand-off, 1.5xl0'2 at 50 pm stand-off and 5xlO'3 at 5 pm stand-off for the
80<2/square sheet resistance at 1 GHz. Less than 7% error of non-contact permittivity
measurement has been achieved using numerical method to estimate the stand-off
distance. M icrowave A tom ic Force M icroscopes (pAFM ) and m icrow ave
characterization of AFM tips are also exploited in this thesis. The details of 200 nm thick
Au edge had spatial resolution about 20nm in pAFM images.
x
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Chapter 1
Introduction
1-1. Near field microwave microscopy
Evanescent microwave microscopy is used to nondestructive image and map
nonuniformities and defects in metals, semiconductors and dielectrics with sub-micron
spatial resolution. Permittivity, sheet resistance and carrier profile can be quantitatively
determined by carefully calibration.
Various local probes, including optical probes in near field scanning optical microscopes
(NSOM), and capacitive probes in scanning capacitance microscopes (SCM) and
evanescent microwave microscopes (EMM) or probes (EMP) are developed and reported.
NSOM provide resolution on the order of 1-10 nm using light of 600 nm wavelength.
Both SCM and EMP operate at microwave frequency range and have nano-meter spatial
resolution.
sample
Vout
Vin
probe
UHF oscillator
Figure 1-1-1. Schematic of RCA scanning capacitance microscopes (SCM) sensor
SCM was invented in IBM [1] and was used to image the dopant profile within
transistors. The SCM signal is determined by oxide thickness, dielectric constant of
oxide, dielectric constant of semiconductor sample and carrier concentration of
1
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2
semiconductor. In 2001 5 nm spatial resolution and ±5% accuracy is required [2]. The
capacitance sensor in the RCA videodisc player is used in the SCM extensively. The
small RCA sensor is composed of a 915 MHz UHF oscillator, LCR circuits and peak
detection circuits (figure 1-1-1). The capacitance of LCR circuit includes the tip-sample
interaction capacitance, stray capacitance of wire and variable capacitance of voltage-
Vout (V)
controlled varactor diode.
4
•
3
■
2
-
10000
1
0
15000
i - 50000
—
0.00
10.78
Vin (V)
Figure 1-1-2. Transfer functions of RCA SCM sensor
The tip-sample capacitance change shifts the resonant spectrum of LCR circuits witch
produces a DC output voltage of peak detection circuits in proportion to the tip-sample
capacitance change. Figure 1-1-2 shows the measured transfer functions of a RCA sensor
at different air gap between tip and metallic ground. The sensor is mounted to a
computer-controlled z-stage with 0.017 |Jm per step resolution. The origin of z-axis is at
metallic surface. If Vin is fixed at an optimized value, Vout is a good measure of
capacitance change as shown from figure 1-1-2. Because the response time of the
varactor diode and the peak detection circuits are very fast (<200 ns), the transfer
functions can be monitored using x-y mode in oscilloscope. The frequency of sweeping
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3
signal can be 1 MHz to get stable output. This is the best way to find the optimized Vin
during SCM imaging and determine the optimum probe length.
DC bias
Ad
d=4mm-6mm
Vibration
source
PLA
Function
generator
Figure 1-1-3. Experimental setup to determine the sensitivity of SCM sensor
In the setup shown in the figure 1-1-3 a vibration source (microphone) near the tip was
used to excite resonant vibration of the small metallic beam. Phase lock-in amplifier was
used to detect small output signal of SCM sensor with tune signal (Vin) fixed. Same
sinusoidal source with frequency less than 100 KHz was used as input signal of the
microphone and reference signal of phase lock-in amplifier. Laser was used to amplify
the small gap change of the beam and the corresponding capacitance change can be
estimated. The sensitivity of this sensor was estimated to be 5.04xl0'13 F/V.
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The SCM sensor has the following characteristics.
1) SCM is a scalar system with only one output. The tip-sample interaction is assumed
capacitance dominated. Real part of impedance change because of sheet resistance or
loss tangent difference can not be determined and will affect the accuracy of SCM
measurement.
2) The SCM sensor is very compact. The resonant spectrum is electrically tuned. The
LCR circuit can be lumped devices or distributed band pass microstrip filter [3].
3) The small DC output needs phase lock-in amplifier to improve signal to noise ratio
and boost the dynamic range of the system. Phase lock-in amplifier is bulky and
expensive. The time constant of phase lock-in amplifier is set to be larger than 10 ms
to get stable signal. The SCM system using phase lock-in amplifier may have speed
problem.
1-2. Evanescent microwave microscopes (EMM) or probes (EMP)
EMP was first used by Sohoo [4] and later by Ash [5] to show super-resolution imaging
capabilities of evanescent or decaying electromagnetic fields. The near field tip-sample
interaction changes the load impedance near the tip and reflection coefficient of the
resonator. This tip-sample interaction and S 11 of a microstrip resonator are shown in
figure 1-2-1. The resonant frequency of the microstrip resonator shifts about 3 MHz
lower when the tip is near the metallic ground.
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5
Ground
Prob
Insulator (Duroid)
Ground plane
-35
-
40
-
meta
copper
45
1.864
1.869
1.874
1.879
1.884
Frequency (GHz)
(a)_
(b)
Figure 1-2-1. Microwave resonator (a) [6] and its S l l (b) in the air and close to
metal ground
Experimentally a spatial resolution of 20 nm [6], conductivity resolution of 10'1 crs in
AP
metals, — - = 5 x 10 3 in semiconductors and 10" es in dielectrics have been obtained
around 1 GHz [7]. The EMP is used to map nonuniformities in metal, semiconductor
(sheet resistance and recombination life time), dielectrics, biological and botanical
material [7-10].
The most important characteristic of the EMP technique include
1) Microwave source are readily available in the range of 100Hz-100 GHz. Low cost
dielectric oscillator or phase locked Gunn oscillator are very stable (<60ppm/°C).
2) Microstripline or other waveguide technologies enable design and fabrication of a
variety of EMP structures with different capability. Microstrip line has moderate
Q and can integrate with other chips very easily. The rectangular waveguide can
operate up to 300 GHz and have larger Q factor.
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3) The EMP resolution can be adjusted over a wide range not only by its operation
frequency but also by changing its tip geometry, i.e., different tip taper angles,
substrate thickness and waveguide length. The micro-sphere or nano-sphere
technology makes quantitative calibration much easier.
4) The EMP can image nonconductive as well as conductive samples in both
conduct and non-contact modes. It can acquire both magnitude information and
phase information. Sheet resistance or loss tangent map can be obtained.
5) Operating at very high frequencies, the EMP can speed faster thanlOO ns/pixel.
The detection circuits with dynamic range more than 60 dB are accurate, small
and low cost.
6) Various methods including micro wave-based method can be used to correct for
EMP stand-off distance.
7) Using microwave techniques a single EMP can be designed to operate at multiple
frequencies.
EMP system is targeted to detect both real and imaginary part of load impedance near the
tip. Its application includes but is not limited to dopant profile imaging. There are four
kinds of conventional EMP systems and measurement schemes for electrical probe
(without coil loop or other impedance matching network near the tip).
(a) Systems use AM or FM modulation and demodulation near resonant frequency [7-9].
It is simple and straightforward and used to explore the applications of EMP systems.
The bulky and slow phase lock-in amplifier is the key instrument for such systems.
(b) D.E.Stemhauer et al. used FM modulate the source with a deviation about 3MHz and
used a phase locked loop to keep the microwave source frequency locked to resonant
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7
frequency of the resonator [10]. The lock-in amplifier was used to time-integrate the
diode detector output. The demodulated signal at 2fFM of FM modulation was used to
represent Q factor and this needs an additional calibration step. There was no feed
back control in z axis in that system.
(c) X.D Xiang et al. used microwave phase shifter and phase detector in the phase locked
loop [11], In this configuration, the resonant frequency shift and Q factor were
determined by measuring the error signal of the phase locked loop and the diode
detector output. The dynamic range of the measurement may be very poor if lock-in
amplifier is not used to amplify the diode output. Most of their work also required
‘soft contact’.
(d) A.F.Lan, M. Golosovisky et al, used reflectivity to achieve non-contact quantitative
characterization of conducting layer at 82 GHz [12], The reflectivity in their paper is
r (z,R) = SI l(z ,/?)/S I 1(0, AZ) - f ( z ) T ( R ) . Where S ll (0,A1) is the S ll of the probe
which contacts with bulk Aluminum sample at 0 distance and V(R) is solely
depended on sheet resistance. A low frequency mode was used as distance control.
Network analyzer 8510C is the key instrument in their setup.
These systems are not fast because time constant of phase lock in amplifier (a-c) is
normally set to larger than 10ms to get acceptable signal to noise ratio or use commercial
expensive network analyzer (d). Method b and c use frequency shift and Q factor during
imaging process. The Q factor measured in these methods may not be accurate and
require an additional painful calibration step. In (d) because of reference chosen no
quantitative load impedance can be extracted. In this thesis we demonstrate a high-speed
and large dynamic range near field microwave system setup using true logarithmic
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amplifier (TLA) and combine this EMP sensor with AFM system. We also show that the
sharp probe tip can be used as transmitting or receiving electrically small antenna. These
systems use electromagnetic wave to transfer near field information. A compact self
resonant EMP (SO-EMP) system which integrates oscillator with microwave resonator is
also discussed.
Extensive research efforts have given to understanding of MOS capacitance of tip-oxidesemiconductor structure [13-15]. In this thesis a semi-close form capacitance calculation
method for axis-symmetric structures over stratified dielectrics or metal is developed and
compared with experimental results. This fast calculation method can be used to build
capacitance database for calibration, estimate stand-off distance during imaging process
and estimate the electromagnetic field or charge distribution at sample surface or in the
sample.
Single transmission line or microwave resonator is very sensitive to the impedance
change near the tip. In order to get the quantitative value and differentiate the real part
and imaginary part of load impedance accurate model of resonator is very important. The
models in the past used discrete components to model the transmission line. Few these
models were able to extract impedance near the probe tip. In this thesis an accurate model
of microstrip line resonator and corresponding calibration procedures have been
developed. The extracted impedance change near resonant frequency is convergent at 5
MHz bandwidth near resonant frequency and fits the calculated impedance quite well.
This method uses load impedance near the tip instead of frequency shift and Q factor
during imaging process.
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9
References
[1] C. C. Williams, W. P. Hough, and S. A. Rishton, ‘Scanning capacitance microscopy
on a 25 nm scale’, Volume 55, Issue 2, pp. 203-205(1989).
[2] Joeseph J. Kopanski, “Scanning Capacitance Mciroscopy” IMG003.
[3] R. F. Soohoo, J. Appl. Phys. 33, 1276 (1962).
[4] E. A. Ash and G. Nicholls, Nature (London) 237, 510 (1972).
[5] T. Tran, D. R. Oliver, D. J. Thomson, and G. E. Bridges, ‘"Zeptofarad" (10-21 F)
resolution capacitance sensor for scanning capacitance microscopy’, Rev. Sci. Instrum.
Vol 72 (6), 2618 (2001).
[6] M. Tabib-Azar and Y. Wang, "Design and Microfabriation of Atomic Force
Microscope Compatible Scanning Near-Field Electromagnetic Probes." To be Presented
in 2002 ASME Conference, 17-22 New Orleans, Louisiana.
[7] M. Tabib-Azar and D. Akinwande, ‘Real-time imaging of semiconductor spacecharge regions using high-spatial resolution evanescent microwave microscope’, Rev.
Sci. Instrum., Vol 71(3), pp. 1460-1465(2000).
[8] M. Tabib-Azar, D.-P. Su, A. Pohar, S. R. LeClair, and G. Ponchak, ‘0.4 ^um spatial
resolution with 1 GHz (A= 30 cm) evanescent microwave probe’, Rev. Sci. Instrum. Vol
70, 1725 (1999).
[9] M. Tabib-Azar, J.L.Katz , and S.R.Leclair,” Evanescent microwaves: A novel super­
resolution noncontactive imaging technique for biological applications”, IEEE Trans.
Instrum. And Meas., Vol. 48 pp. 1111-1116 (1999).
[10] C. Gao and X.-D. Xiangl, ‘Quantitative microwave near-field microscopy of
dielectric properties’, Rev. Sci. Instrum. Volume 69, Issue 11, pp. 3846-3851, (1998).
[11] D. E. Steinhauer, C. P. Vlahacos, S. K. Dutta, B. J. Feenstra, F. C. Wellstood, and
Steven M. Anlage, ‘Quantitative imaging of sheet resistance with a scanning near-field
microwave microscope’, Appl. Phys. Lett. Vol 72, Issue 7, pp. 861-863 (1998).
[12] A. F. Lann, M. Golosovsky, D. Davidov and A. Frenkel, ‘Combined millimeterwave near-field m icroscope and capacitance distance control for the quantitative mapping
of sheet resistance of conducting layers’, Appl. Phys. Lett. Vol 73, Issue 19, pp. 28322834(1998).
[13] Y. Huang, C. C. Williams, J. Slinkman, ‘Quantitative two-dimensional dopant
profile measurement and inverse modeling by scanning capacitance microscopy’, Appl.
Phys. Lett. Vol 66, Issue 3, pp. 344-346 (1995).
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[14] J. J. Kopanski, J. F. Marchiando, and J.R. Lowney, J. Vac. Sci. Technol. B12, pp.
242-247(1996).
[15] J.F,Marchiando, J. J. Kopanski, and J. R. Lowney, J. Vac. Sci. Technol. B16, pp.
463-470(1998).
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Chapter 2
Microstrip resonator and Its model
Microstrip line resonators have moderate Q factor and can operate up to 100 GHz. They
are compatible with MMIC and MIC circuits making them quite attractive candidates for
multilayer and low cost application. The substrates can be low cost soft substrates or hard
substrates (quartz, sapphire, alumina and GaAs...) with better reliability and higher
thermal conductivity. The soft substrates (Duroid series) are processed using milling
machine or H N 03 etching at the opening of protection mask.
The resonators can be built using discrete components or distributed transmission lines.
The discrete components based resonators have smaller size and lower Q factor because
of higher loss. These small resonators can be synthesized based on ABCD matrix of
distributed microstrip resonator. Distributed microstrip resonator is very easy to fabricate
and have a larger Q factor.
The model of the resonator is used to extract the complex impedance change at the tip
because of near field tip-sample interaction. The parameters of this model are
experimentally determined. The extracted complex impedance change at the tip can be
done at fixed frequency or obtained self-corrected value using mean value using multiple
frequencies. The extracted impedance change is localized and convergent value
compared to AS 11 (both magnitude and phase) which is not localized and has large swing
in frequency spectrum. Af and Q factor which are affected also by specific resonator at
specific frequency. The m odel developed in this chapter is easy to expand to m odeling of
coaxial resonators.
2-1. Microstrip transmission line
11
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12
Because the typical dimension of tip-sample interaction is much smaller than wavelength,
the interaction can be solved using quasi-static assumption. To measure the tiny
impedance change of tip-sample interaction, single transmission line or resonator can be
used. Small load impedance change at the tip can be amplified to a big input impedance
change of microwave resonator near resonant frequency.
The output signal of reflection microwave system is determined by the refection
coefficient r.
r - Z 'n ~ Z°+z0
(2-1-1)
where Z in is input impedance and Z0 is characteristic impedance. The input impedance is
determined by both load impedance Z; , gap capacitor and the transmission line between
load and reference plane.
The microstrip line supports quasi-TEM mode. Full wave analysis need solve potential
equation
V2</>+ £ 20 = 0
(2-1-2)
Characteristic impedance Z0 and effective dielectric constant £eff is frequency depended
(dispersion effects). The frequency, substrate thickness and dielectric constant are larger.
The dispersion effects are larger. It has been verified the change of eeff and Z0 in 20 MHz
bandwidth change the extracted impedance less than 1% in our model.
The effective permittivity, attenuation constant and wavelength in the transmission line
are important for modeling (both analysis and synthesis) and designing optimized
microwave sensing system.
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13
For microstrip line, the effective permittivity by quasi-TEM analysis is
M °) =
/
\2
12h ^ 1'2
1
—
+ 0.04
1 + ----w J
v +
V
'
■+
(2-1-3)
where h is thickness of the microstrip, w is the width and er is relative permittivity of
substrate. Using full wave analysis
£eff (/)_
where F =
1+ 4 F - 3 / 2
+
(2-1-4)
V £ eff ( 0 )
0.5 + 1 + 21og' l + ^
The wavelength in the microstrip line can be determined by effective permittivity.
kn
(2-1-5)
K =
where A0 is the free space wavelength.
The radiation loss is very small for microstrip line. The attenuation constant is sum of
dielectric loss and conductive loss. The conductor loss is given by
V7
a = 0 .0 7 2 -^ - X d B / m
0)Zn g
( 2 - 1- 6 )
The dielectric loss is determined by loss tangent of substrate that can be larger than
conductive loss for Duroid substrate.
£ r (£ eff
ccd —27.3-
-l)tan<5
, ■ , ■dB/m
£ eff \ r
(2-1-7)
1)
The attenuation constant a used in the resonator model uses SI units
a = l_ 1 0 (+ +cU
(2-1-8)
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14
From full wave analysis the characteristic impedance is
8h 0.25 h £eff i f ) 1
— + ------vw
w j £eff(0) l y £ejZr(f)
z a(f)= 60
(2-1-9)
This equation is used to determine the width of 50 Q microstrip line.
The quality factor defined as the ratio of stored energy to the loss. The design parameters
of 50 Q microstrip lines at 1GHz using Duroid substrates are summarized in table 2-2-1.
These substrates are used extensively in our EMP systems. The foil cladding thickness of
these substrates is 0.034mm.
RT/Duroid
h (mm)
w (mm)
£r
tan 8
£ eff
Q
name
5880
0.875
2.654
2.2
1.872
0.0009
266.5
5870
0.875
2.558
2.33
1.961
0.0012
247.7
6002
0.875
2.191
2.94
2.367
0.00119
241
6006
0.875
1.256
6.15
4.342
0.00182
189.2
6010/10.2
0.875
0.788
10.2
6.626
0.00207
161
Table 2-2-1. The design parameters of 50 Q microstrip line at 1GHz using Duroid
substrates
The microstrip lines are enclosed in a metallic box with width wl and height h i to reduce
radiation loss and noise. The effects of enclosure are very small when
w\
— >5
w
and
hi
— >5
h
(2-1-10)
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15
2-2. Model and calibration procedure of microstrip resonator
This section will develop the model of microstrip resonator based EMP system and
corresponding calibration procedures for load impedance at the tip extraction. The
reference plane from measurement without calibration is at the beginning of feed line.
This model with reference plane at the tip will be used in chapter 6 for quantitative
characterization and imaging dielectric and semiconductor samples.
Micostrip resonator based EMP system (figure 1-2-1) is widely used in our group for
EMP imaging. It is fabricated on Duroid dielectric substrate using 50 ohm microstrip line
or stripline. The resonator is integrated with low cost surface mount VCOs, I-Q mixers,
amplifiers and other signal processing integrated circuits. Microstrip line based
directional couplers, power splitters, and filters are widely used and commercially
available. These microstrip lines are also easily fabricated on semiconductor substrate.
The EMP system based on microstrip line is the most compact system compared with
rectangular waveguide and coaxial based systems.
The microstrip A/2 resonator, the gap capacitor, and the load impedance at the probe tip
can be modeled as in figure 2-2-1. The load impedance includes interaction between
probe and underneath material and the surface impedance of the underneath sample.
The open end of the microstrip line in the air is modeled as a capacitance C0. An
additional effective length A/ is attached to the original microstrip to take into account
the open end effect.
v„ZnC.
( 2 - 2 - 1)
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16
where v0 is speed of light in vacuum, £re is effective dielectric constant of substrate. The
additional length will introduce a corresponding additional electrical length and change
the detected phase. Similarly the short-ended resonator which is called magnetic probe
can be modeled as an additional inductance witch will shift the resonance circle in Smith
chart opposite direction. In this thesis only electrical probe with open at the end is
discussed.
M l micro strip
Tip-sample
interaction
Figure 2-2-1. Model of gap capacitor, M2 microstrip line and load impedance at the
tip because of tip-sample interaction
Using curve fitting of a full wave analysis M.Kirchning etc [1]. have obtained a closed
form expression for A l .
A / = abc!d
a = 0.434907
(g°e81 + 0.26 f(wM)08544 +0.236
(e°f - 0.189
8544
/ h)0' ^ +0.87
g =l + ( w / h f 311 /(2.358er +1)
( 2- 2- 2)
,0.9236
b =1 + 0.5274atg [o.084(w/ h)xmn'g ]/ e
c = l-0.21Se~15w/h
d = 1 + 0.0377atg[0.067(w//i)1456Js - 5eom6(1~er) ]
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17
where w is microstrip width, h is substrate thickness, er is relative dielectric constant of
substrate. In our model we take account into the open effects by adding this additional
A/ to the physical length of the probe when we calibrate the microwave resonator. This
additional length is about 10 mm at 1 GHz for 5880 substrate that is about 8% of half
wave length.
We model the tip-sample interaction using load impedance at the tip Z; . The imaginary
part of Z( is the gap capacitor of the tip which is determined by the gap, size of the tip
and the electrical property (permittivity, thickness, etc.) of the underneath sample. The
real part of theZ; is determined by the gap, dimension of the tip and electrical property
(conductivity and thickness) of the underneath sample.
For transmission line we have the input impedance that does not include the gap
capacitor.
Z, + j Z 0 tan ft' I
Zinm= Z 0 J / J .
...
Z 0+ j Z t tan /37
where jS '=
2n
(2-2-3)
j a is determined by wavelength A„ in microstrip and attenuation
K
constant a , and I is the sum of physical length and effective length of the resonator as
mentioned before.
A series capacitor and two shunt capacitors are used to model the gap. The computation
using typical microstrip dimension and experiment show the shunt capacitance are at
least an order of magnitude smaller than the series capacitance and therefore, are always
neglected.
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In our experiments instead of using a simple microwave gap, we use Teflon screw to
change the coupling capacitance by varying angle between brass which is soldered at one
end of microstrip line and microstrip line. The tunable capacitor is shown in figure 2-2-2.
Experimental determination of the capacitance is needed. Using the appropriate
calibration procedure C 3is treated as an additional length to the physical length of feed
line. The model 2-2-1 changes to a simpler model shown in figure 2-2-3. In this model
we don’t use lumped components to model A/2 microstrip line for better accuracy.
Copper trace
eflon screw
rass
Figure 2-2-2. Teflon screw is used to mechanically change the coupling capacitance
Zin
z ir
A/2 microstrip
*
Ci
Tip-sample
interaction
Figure 2-2-3. Simplified model of gap capacitor, A/2 microstrip line and load
impedance at the tip because of tip-sample interaction
The input impedance including gap capacitor is
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The Zmcan be calculated from reflection measurement with reference plane just before
the gap capacitor.
=zo
0 1-511
(2-2-5)
The Cj, C2 and j tan fi'l are experimentally determined by the input impedance when the
tip is open (far away from sample) and short (tip is grounded). These conditions are
Z inm o =
z o
1 f l.T
] tan P /
Z;„m
r = Zn
/' tan •B'l
inms
uj
fo r ° P e n
c ir c u it
(2-2-6)
for short circuit
If we evaluate open and short at resonance frequency, we have input impedance
_.
Zino
a + bj
1
h■
j a C ^ a + b* j) + l jcoC2
(2-2-7)
Z2
1
Zinc = ------------+j(oCxZ 0 +a + b* j j(oC2
Where
z -
= z 0
1 n ,; = a +
j tan p i
b *J-
Zino and Zinc can be experimentally measured using reflection coefficients. In all these
input impedance measurements full one port calibration must be done first to correct
directivity, isolation, source match, reflection tracking, load match and transmission
tracking errors. It is important to make sure that the reference plane is carefully calibrated
right before the gap capacitor. C,, C2 and j tan fi'l are solved using numerical iteration
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method by assuming initial j tan fi'l is calculated using physical length of the microstrip
line.
After the parameters of the system are experimentally determined, the (2-2-4) is used to
extract the load impedance at the tip.
*7
ry
i~ o
Z ininmm - Zn
u J/ tan •i31
~ TT 7J7
Z 0
ZrC\ + ;(C, + C2 + ZrC\Cx)
inm
( 2-2 - 8)
(C1+ C2)2 +(CiC2)2Zr2
Zr is input impedance measured at resonant frequency using scalar system. For vector
measurement system,
Z,inm
1
(2-2-9)
These results can be compared with the numerical results. The sensitivity of the
microwave measurement can be determined by this comparison. Measured Cx and C2
are both in the 0.1 pF range in our experiments.
One such extraction process near resonant frequency is shown in figure 2-2-4a (extracted
load impedance at the tip) and figure 2-2-4b (measured input impedance Z in) from 995
MHz to 1000 MHz using vector measurement system. The extracted C, was 2.99e-013 F
and C2 was 3.3979e-013 F at 996 MHz. Frequency depended parameters were used in
the extraction process. The impedance change versus frequency at the tip (figure 2-2-4a)
was very small. The input impedance change (figure 2-2-4b) was very large. The figure
2-2-4b clearly shows a near open condition that is expected! These observations show
that the model described is quite good for load impedance extraction.
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21
J0.5
j0.5
\0.2j
jO 2.
0.2
051
0.51
■j0.2
-J0.2
■j0.5
-j0.5
(a)_
(b)
Figure 2-2-4. Extracted load impedance (a) at the tip from input impedance (a) was
nearly open that is expected.
x 10"
0.3
0.25
0.2
1002.5 MHz
1002.5 MHz
CC 0.1
£r=2.2
0.05
997.5 MHz
997.5 MHz
-0.05
100
300
200
Gap (um)
400
500
100
200
300
Gap (um)
400
500
Figure 2-2-5. Extracted convergent capacitance and resistance change at the tip of a
microstrip resonator versus different gap
The extraction was convergent or self-corrected near resonant frequency. Figure 2-2-5
shows extracted capacitance and resistance change at the tip of a microstrip resonator
with different air gaps. 20 equal-spaced frequencies in 5 MHz bandwidth near resonant
frequency have been used. The convergence of capacitance change was better than the
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22
convergence of resistance change. The nearly same extracted results mean the extraction
is robust and stable to noise and frequency shift. Reliable impedance change can be
obtained by using mean value of multiple frequency measurements. Figure 2-2-6 shows
corresponding magnitude versus gap from I-Q mixer near resonant frequency. The swing
of the magnitude was ultra sensitive to the frequency. Small shift of circuits and
operation frequency chosen affected the output signal drastically.
1002.5 MHz
997.5 MHz
100
200
300
Gap (um)
400
500
600
Figure 2-2-6. Corresponding S lls (Magnitude) near resonant frequency were not
convergent.
2-3. Model of microstrip resonator system using ABCD matrix
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23
The calibration method described above needs accurate model of the feed line, gap
capacitor and resonator system. It is difficult to model this system because it is a
distributed, three dimensional, full-wave and nonlinear system. If we can experimentally
determine the frequency dependent ABCD matrix of the system, the load impedance at
the tip can be extracted by dividing the measured ABCD matrix with the ABCD matrix
of the resonator. The ABCD matrix of microwave resonator is also used to design
resonator using discrete components where the compact system is needed.
The ABCD matrix of the load impedance at the tip is
(2-3-1)
Assume the ABCD matrix of the feed line, gap capacitor and resonator system is
a
b
c
d
(2-3-2)
The voltage and the current at reference plane is
(2-3-3)
In order to calculate reflection coefficient we need
-0
(2-3-4)
From the definition the reflection coefficient is
(2-3-5)
Substitute into equation (2-3-3) and (2-3-4) in to (2-3-5), we have
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24
-[(a + b ) - Z 0(c + d ) ]- b + Z 0d
(2-3-6)
r=
■\la + b)+ Z 0(c + d ) ] - b - Z 0d
, we have
If the reflection coefficient in free space is
h ■Z 0d
(2-3-7)
- b - Z 0d
The reflection coefficient can be written as
r=
Z t ( - b - Z 0d)
[(a + b ) - Z 0(c + d)]+
b+
b - Z 0d
A{ + Z,rm
(2-3-8)
B +Zl
■[(rr + & ) + Z q ( c + ^ ) ] + 1
Z i ( ~ b ~ Z 0d)
where A and B are frequency dependent parameters of the system. For differential
measurement we can write the above equation as
_^= A A .+ z , = a + z^
B +Zl
B +Zt
where A and B are experimentally determined by reflection coefficient on top of copper
ground with different air gap. We have
'- 1
-1
0
0
' A'
0
0
B
0
0
-1
0
r3 - l
Z la
1
0
z^la2
3.
-z la
Z lb
2 - Z lb
1
Z 3 - z lb.
1
J^lb
rx n - 1
0
h
-1
0
0
-1
1
0
0
0
-1
0
1
where q , r2 and r3 are three different position, Z]b,
( 2 - 3 - 10)
and Zfb are corresponding load
impedance using other calibration method.
This method needs calibration using other method first. The parameter vector of one such
experimental system was
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25
“A '
' - 5.4356-23.7854i '
B
-15.7918 + 8.6068i
Z lax = -26.6872 +32.051 li
z2
- 26.8689+ 33.6401i
n .2
N
27.0327 + 34.3880i
1
i
2-4. Discussions of load impedance near the tip
In previous works, the tip is kept soft-contact with samples to maintain constant geometry
of tip-sample[2] or assumed constant air gap without z axis feed back [3]. The
topographic variation may introduce tip distortion and damage the samples because of
contact. The tip distortion will change S l l of the probe. Without feed back control of
contact force, the characterization of material property is not accurate. Non-contact
measurement is therefore preferred especially for some delicate wafers or biological
samples. In non-contact EMP application, stand-off distance, size and electrical property
(permittivity, conductivity) of the substrate determine the output signal. In order to
extract the permittivity and conductivity of the sample, the load impedance should be
calculated, simulated or calibrated using samples with different gap, thickness and
electrical property. These calculations or models of tip-sample interaction will be
compared with the extracted impedance using technique described in this chapter. For
dielectric and semiconductor samples, the ground is put far away from substrate.
In previous works, frequency shift Af , Q factor change [2-3] or magnitude of AM
demodulation signal [4] is used to model capacitance and power loss changes. Af is used
to calibrate permittivity and Q factor is used to calibrate loss tangent or sheet resistance.
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26
In this dissertation we prefer using the impedance near the tip Z( instead of using A f , Q
factor and magnitude of AM demodulation signal in quantitative imaging because of the
following advantages.
1) Z; can be compared with numerical results directly and simulated in commercial
circuit simulation tools as a component to optimize the measurement system.
2) Z, is obtained using fast single frequency measurement. Ultra-stable and low-cost
dielectric oscillator can be used as source. Af and Q factor are property of frequency
spectrum. Complicated phase locking loop circuits may be needed to track Af which limit
the measurement speed and accuracy. Using FM modulation and demodulation to
measure Q factor needs an additional complicated calibration step and may not be
accurate.
3) The experimental determination of Z, is self-corrected. Z, should be almost same
using different carrier frequencies near resonant frequency. In contrast, the input
impedance changes drastically near the resonant frequency.
4) Z; is independent of measurement system and carrier frequency. A f , Q factor and
magnitude of AM demodulation signal depend on measurement system and carrier
frequency.
In order to get Z ,, reflection coefficient measurements with reference plane just before
the gap capacitor are needed.
Referencs
[1] T. C. Edwards, “Foundations of interconnect and microstrip design” Chichester, New
York, John Wiley, (2000)
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27
[2] C. Gao and X.-D. Xiang, ‘Quantitative microwave near-field microscopy of dielectric
properties’, Volume 69, Issue 11, pp. 3846-3851, (1998)
[3] D. E. Steinhauer, C. P. Vlahacos, S. K. Dutta, B. J. Feenstra, F. C. Wellstood, and
Steven M. Anlage, ‘Quantitative imaging of sheet resistance with a scanning near-field
microwave microscope’, Vol 72, Issue 7, pp. 861-863 (1998)
[4] M. Tabib-Azar, D.-P. Su, A. Pohar, S. R. LeClair, and G. Ponchak, ‘0.4 /rm spatial
resolution with 1 GHz (A= 30 cm) evanescent microwave probe’, Rev. Sci. Instrum. Vol
70, 1725 (1999)
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Chapter 3
Model of charge distribution at the tip
3-1. Model of interaction
The axi-symmetric, electrically small structures are important in many applications other
than their applications in EMP. The electrically short monopole antenna [1] for Loran-C
reception is a truncated cone where capacitance and charge density (effective height)
analysis are used to optimize antenna performance. Metallic cylinders and truncated
cones are also widely used in orbital satellites. The conductive atomic force microscope
(c-AFM) [2] or the scanning capacitance microscope (SCM) tips also have conical or
spherical shapes that along with the sample form a capacitor structure with very small but
detectable capacitance. The load impedance depends on the sample’s morphology,
electrical property and tip structure. To increase the lateral spatial resolution of EMP, cAFM and SCM, the tip-sample impedance should be optimized to yield smallest possible
fringing fields and largest response to tip-sample interaction. Thus, the numerical and
experimental determination of load impedance of these structures are very important for
quantitative measurements and optimization of the associated system’s performance. The
imaginary part of this impedance is the gap capacitor between metallic tip and
semiconductor or insulator sample. The sheet resistance of underneath sample determines
the real part of this impedance. In this chapter we develop a fast semi close-form three
dimensional charge density calculation method.
Only tip region of EMP is exposed and the microwave resonator is carefully shielded in
our experiments. Quasi-static analysis is a good approximation because the size of the
probe tip is at least 20 times smaller than wavelength of carrier signal.
28
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The charge distribution and capacitance of axi-symmetric structures are normally
evaluated by the method of moments (MoM) [3] or boundary element method (BEM) [4],
In MoM, the metallic surface is subdivided both in the circumferential direction and axial
direction [3]. Each MoM matrix element is a two-dimensional integral using impulse
response functions as basis and Dirac’s delta functions as test functions. In BEM, twodimensional point matching scheme is used. Fundamental solutions for axi-symmetric
problem are analytically evaluated and used in Galerkin boundary element method [4],
The surface is only subdivided in axial direction. But Galerkin procedure needs to
numerically solve double surface integration of weighted residue. In this technique,
singularity problem also needs to be carefully treated.
In this chapter the metallic or dielectric surface is partitioned into axi-symmetric
subsections. The matrix elements are analytically evaluated without using numerical
integration. The convergence is reliable and fast. The generalized minimal residual
(GMRES) algorithm is used to solve linear equations.
In most high-spatial resolution measurement techniques, a sharp tip is used to measure
the local capacitance at the sample’s surface and the parasitic capacitance is usually on
the order of 10"
19
F or larger. The capacitance measurement method in these apparatus
should be able to detect capacitance changes on the order of 10"15F or less. Detecting
small capacitance change (<10‘15 F) with a large background or stray capacitance (>10‘12
F) is very challenging. The capacitance change between AFM tip (20 nm radius) and
90
metal ground can be as small as 10" F. Fortunately, there are synchronization techniques
that can be used to modulate the capacitance while keeping the stray capacitance fixed to
improve the signal. In most cases, the very small capacitance value of the probe tip is
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30
obtained from simulation and the frequency shift of a resonator or other relevant
measured signals.
In this chapter we will compare the numerical capacitance values to their experimental
values. The experimental values were directly extracted from the load impedance
measurements through a suitable resonator structure commonly used in evanescent
microwave imaging systems.
3-2. Charge distribution and capacitance of metal tip over dielectric samples
The axi-symmetric surfaces are the sum of curved surfaces and flat surfaces. These
surfaces are partitioned to axi-symmetric subsections as shown in figure 3-2-1.
't(i)
't(i-l)
Figure 3-2-1. Axi-symmetric surface is the sum of curved surfaces and flat surfaces.
Axi-symmetric subsections are divided.
We assume charge <2, (1 < i < N ) is at the center of the subsection i and the total charge
N
is constant Q (^<2, )• This assumption is as same as Monte Carlo minimization method
i=i
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31
[5]. But we update the Qi using tangent electrical field Et at the interfaces between
subsection i and subsection i+1 instead of stochastically generating numbers. At n+1
iteration
Q r = o : - e o£;{M)Zw
(3-2-la)
Q r = Q ? + e 0E*0lt
(3-2-2b)
where Eq is permittivity , /.is the length of ith interface and eQE"(i)lt is virtual current
because of non-equilibrium charge distribution . The iterations keep Q constant for
isolated conductors. The physical background of this algorithm (dynamics) makes
convergence assured.
The above iteration process converges much faster than stochastic method.
Instead of using this improved iteration method (0(N 2)) we use GMRES (O(N)) to solve
the linear equation.
M
N-l)xN
[l]lxiV
f e
(3-2-2)
I 'x l
The tangent electrical field Et (i, j ) at ith interface because of charge in j th subsection is
Et(i,j) = k(i,j)*Qj = [Ez{i, j)cos(j)-Er(i, j) sin (j>] (3-2-3)
E z (i, j ) and E r (i, j ) are the axial-field component and the radial-field component of ith
section because of jth charge and its image charge respectively:
Ez ( * ’ j) = E z ( r i ’Zj ) - E z ( r i -Zj )
Er (/, j) = E r { r t , Z j ) ~ E r {rt , - z j )
(3-2-4)
where
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32
E. (r:,z ) —
1
E (r z ) -
^_________________ ( z , - Z j ) E ( k )
4 n e 0 27T((>,. - r, ) 2 + ( z , ~ Z j ) 2
+r.)2 +
(z, ~ Z j ) 2)
Qi ( i ^ - r j ) 2 +(zl - z j )2) K ( k ) - ( - r l2 +rf + ( z i - z J)2)E(k) ° ' 2’5)
4n£°
nr,((r, - r,- ) 2 + (z, ~ Zj)2) ^ , + rj)2 + (z, - Zj )2)
where K and E are complete elliptic integral of the first kind and second kind
respectively, k is
k=
2 J^r~
J
-y/((r<+rj f +(z, -
....
(3-2-6)
Zj)2)
Capacitance C can be obtained from charge distribution [<2, ^ i :
C =—
V
(3-2-7)
where,
Af-l
? =1 JL.
(32.8)
j- 147T£0 2Jtrj-Jdri + rs f + (z, - Zj f )
This iteration process is easily expanded to axi-symmetric probe above multiple
stratified dielectric samples [6].
For tip over dielectric sample with thickness h, the charge density p(z) is the
solution to the integral equation
pU )= f ^ L £ ^ )
f
W
J*4ne0 27crl ^ r + r f + ( Z - Zi)
4ne0
dz
)
2nrt ^ ( r + r,)2 + ( z ~ z ;,')
-(3-2-9)
where zu' is given by
zn '= - z ~ 2 h i
11
'
zu ' = - z - 2hl - 2(i - l)hi
(3-2-10)
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33
where hi is z axis of 1th charge on the tip surface when the origin of z axis is at sample
surface.
The ith image charge of 1th charge on the tip surface is p ((zu') = y ,p (z; ).
The scalar factor y . is given by
r
gp
gi
i =
gp T gi
(3-2-11)
g p - g U / 2eo
r, = - ( - — L)
gp + £j
2ei
g0 + £j £0 + £t
where £, is dielectric constant of underneath dielectric sample.
The integration equation again is solved by calculating ‘current’ equation (3-2-2) on the
probe surface using the charge in the tip and image charges in the sample. E z (i, j ) and
E r (/,;') change to:
Ez O',;') = Ez (rt , Z j )
E r (i,; ) =
+
Yi £
^
(y , Zj) + 7 ,■J )
/=i
E z
( ri ’ z u')
(3-2-12)
(r,,
')
If the radius of the probe tip is small compared with sample thickness, computation using
only 1st image charge and charge in the tip is a good approximation. For example, if the
tip radius is 100 |Jm, the dielectric sample has dielectric constant 10 and the thickness of
the sample is 200 pm, the 2nd charge is about 0.27 times 1st image charge and 400 pm
more away from tip surface. The effect of this image charge is smaller than 3 % of the
effect of 1st image charge.
The calculated charge distributions of a 380 pm sphere tip at different gap are shown in
figure 3-2-2. The plot shows more charge is accumulated at the side of the sphere near
ground plane when the gap is smaller. In figure 3-2-2, the total charge in the sphere was
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34
fixed at - 4000 (arbitrary) units. At the sphere-sample stand-off distance (d) of 1 pm, the
sphere had three different charged regions. Near the positively charged metallic sample,
the sphere was strongly negatively charged. Near the sphere’s equator, the charge became
positive and near the top of the sphere the charge was again negative. At d=200 pm, the
whole sphere was effectively negatively charged over the positively charged grounded
metallic sample. In (b) the sphere-sample formed a dipole while in (c) the sphere alone
was polarized and formed two back-to-back dipoles. This situation is also schematically
depicted in the (a) inset. Thus, for the spherical tip, a monopole on top of a metallic plane
is a good approximation when the gap is very small.
From charge distribution, electromagnetic field in the sample and electrostatic forces can
be calculated. Equivalent load impedance then can be determined by post processing the
electromagnetic field.
400
—
200 pm Gap
200
0
-200
0o)>
(0 -400
O
-600
-800
Q
-1000
-1200
1
41
81
121
161
201
241
281
321
361
z (pm)
(a)
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35
Z (m)
-4
-4
r (m)
x 10
-4
r (m)
(c)
x 10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
36
Figure 3-2-2. a) Numerically evaluated charge distribution of the 380 pm diameter
sphere projected along its z axis at two different stand-off distances of d = l pm and
d=200 pm. In (b) the sphere-sample forms a dipole while in (c), the sphere alone is
polarized and forms two back-to-back dipoles. This situation is also schematically
depicted in the (a) inset
6
x 10
-14
Num erical
Equ(3-2-13)
Equ(3-2-14)
5
LL
<D 4
o
c
(0
4-*
<o 3
a
(0
O
2
Expected
capacitance
1
0
0
50
100
150
200
250
300
gap (um)
Figure 3-2-3. Calculated capacitance of 380 pm sphere from formula (3-1-13) and
(3-1-14) are compared with numerical results. Formula (3-1-13) and (3-1-14) used
very poor approxim ation.
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37
The capacitance change of sphere on top of metal ground can be used to determine the
radius of sphere attached to the probe tip or effective radius of probe tip. The capacitance
between sphere and metal ground is approximately [7]
CO
1
C = 4ne0R0 s i n h a T
(3-2-13)
%~2 sinh n a
where R0 is radius of sphere, a = cosh-1 (1 + g / R0), g is gap between sphere and
ground. This approximate formula is first given by E, Durand and quoted by many
authors.
In [8] the capacitance C(z) between ball bearing and base plate is simplified from (3-113) as
C(z) « 27te0R ln(^— ^ )
z
(3-2-14)
Figure 5-2-3 compares computed capacitance from (3-2-13), (3-2-14) and numerical
results for a 380 pm metal sphere. The computed capacitance value from formula (3-213) and (3-2-14) is far away from numerical results when the gap is bigger than 5 pm.
The numerical results have a limit 4ne0R =2.1140xl0'14 F when the gap is large. This
limit capacitance equals the capacitance of isolated copper sphere as expected. The big
difference here is because in the approximation of (3-2-13) and (3-2-14) only one point
charge instead of charge distribution is used to calculate capacitance.
The impedance at the tip was extracted using the technique discussed in chapter 2. The
resonator was tuned to have smallest possible return loss and hence maximum loaded
quality factor in free space near 1 GHz. The input impedance was measured using
experimental TLA system with 20MHz frequency span and frequency resolution of 100
KHz. The insertion loss of the resonator was 40dB at fo and Q factor was around 100 in
free space. The imaginary part (capacitance) of this impedance was used to extract
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
38
capacitance. A copper sphere was attached to the tip during characterization. A sphere
was used because it is geometrically well defined.
5.5
.-14
x 10
Numerical
Experimental
4.5
|
3.5
U
2.5
50
100
150
200
250
300
Gap (pm)
Figure 3-2-4. Capacitance versus gap between a 380 pm diameter sphere and a
metallic base plate.
Figure 3-2-4 shows the capacitance change versus gap between 380 pm ball bearing and
a metallic base plate. For comparison purposes, the measured curve (red) and the
calculated curve (black) from numerical calculations are shifted by +2.1140xl0'14 F to
overlap with the numerical curve (blue). (This constant shift is caused by the assumption
that the load impedance is infinity in free space.) The result agrees with the numerical
capacitance quite well. The experimental stand-off dependence of the capacitance is
remarkably similar to the numerically calculated dependence indicating the validity of the
numerical method.
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39
,-14
2.2
x 10
125 pm
100 pm
50
100
150
200
250
300
Gap (pm)
Figure 3-2-5 Measured and simulated capacitance change of the tungsten tip
For the spherical tip, the load impedance changed from 44.02 +31.44i near surface to
47.89 + 7.78i at 230 pm away. To estimate the sensitivity of the A/2 resonator, we used
an amplitude modulated microwave signal ( I V amplitude) along with a crystal detector
and a lock-in amplifier for coherent signal detection. As before, the measurement
frequency was fixed at the resonant frequency of the probe in free space. As the probesample distance changed from 280 pm to 1 pm. the magnitude of the reflected signal
changed by 0.24V. As noted above, the load capacitance change over 280 stand-off
variation was measure using a network analyzer to be +2.1140xl0'14 F. Thus, the average
sensitivity of this A /2 resonators was 8.47xlO'14F/V. Therefore, for a typical noise level
of 100 )XV / 4Hz, of network analyzer, the capacitance resolution was 8.47x10'
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40
18
F / 4Hz • Lock-in technique along with a synthesized microwave source (resolution
better than 1 KHz at 1GHz and very small phase noise), can be used to further improve
the probe’s sensitivity.
x 10
-14
380 pm dia. spherical tip
Conical Ti tip _________
w
S3
3
ua
aa
U
100
150
200
250
300
Gap (pm)
Figure 3-2-6. Measured capacitances of the spherical and conical (Ti) tips as a
function of tip-sample stand-off distance at 1 GHz.
Scanning tunneling microscope (STM) based measurements use atomically sharp
tungsten tips. Such a tip was next characterized using the above method. Figure 3-2-5
shows the calculated and measured capacitance of an atomically sharp tungsten tip as a
function of the tip-sample stand-off distance at 1 GHz. The tip geometry is depicted in
the inset.
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41
Figure 3-2-6 shows the measured capacitance change of the tungsten tip and that of the
copper sphere for comparison. The spherical tip had 2.8 times larger capacitance than the
conical tungsten tip at small stand-off distances. Although not shown in figure 3-2-6, at
very large stand-off distances the capacitances of the two different tips (conical and
spherical) asymptotically approach each other.
2.5
x 10
-15
Thoery
M easurem ent
LL
o 1.5
0.5
100
40
Gap ( p m )
Figure 3-2-7. Measured capacitances of the spherical and conical (Ti) tips as a
function of tip-sample stand-off distance at 1 GHz
Figure 3-2-7 shows the capacitance change versus gap between 380 pm ball bearing and
0.785 mm thick Duroid substrate (dielectric constant=2.2). Again the result agrees with
the numerical capacitance quite well.
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42
For semiconductor samples, the capacitance at the tip is a series connection of gap
capacitance discussed above and the depletion layer capacitance. The depletion
capacitance at different DC bias can be used to determine the carrier concentration in the
semiconductor. Many efforts have been done to extract dopant profile using inverse
modeling and forward simulation of SCM measurements [9-11].
The researches about tip and semiconductor interactions can be found in numerous
references.
Sometimes the full-wave solution of tip-sample interaction may be needed. The starting
Maxwell equations are
v
-e = £ e
V x E = - jco p H => V x ( E + jco A) = 0 => E + j(t) A = -V (j)e (3-2-15)
V •J + ~
V x H = J + jco e E <=> V J + jco p = 0
- 0
where
vxa
V
t
(
(
(
t
jj
„ - jk R
V - A = -j(oen<l>e => V 2A + k 2A = - / j J ^ A = - £ - f f |7
dv
4n JJvJ
R
—n
(3-2-16)
J~l
The tip surface has been divided into nn sub-sections and that current density only has z
component has been assumed.
R-Ri
y j ( z - z ’) 2 + (rc o s0 —r ’)2 + (rs in 0 )2
(3-2-17)
I z = 2naK(z)
Electrical field because of Az and virtual current equations are
nn
E? = j(oA[ =
nn
I j )
;= 1
j- 1
nn
j-1
(70 - j c o ^ Qb)K(i, j ) = - « 2£ (Q0 - £ Qb)K(i, j )
=
j =1
b=1
j=l
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6=1
43
nn
£4
y-i
*=i
nn
e“ =-ffl!£<a-2;a mum+£aM(i,y)
/in
y=i
nn
nn
nn
nn-1
nn
OJ22 o oK(i,j)Ci =co2Y ^ Q bK (i,j)C i + 2 Q jm , j ) = (022 Q j J , K ( i , b ) C i + £ e , A 7 ( U )
y=l
> 1 6=1
j= 1
;=1
*=j
;=1
(3-2-18)
The current equation can be solved using GMRES. However this algorithm suffers
convergent problem because J ~ J Zz is a poor assumption for many tips. If this is the
case, 3-D commercial Finite Element Analysis will be a better choice for full wave
analysis.
3-3. Sheet resistance or loss tangent of samples
For thin metallic film and semiconductor sheet resistance is defined by R = — = —
t
to
where o is conductivity and t is thickness of sample. For dielectric samples, the loss
tangent is defined as tan S =
o
. So the ‘sheet resistance’ of dielectric sample is
te
which is used in explaining the measured real part of load impedance.
The model of tip impedance is shown in figure 5-3-1.The capacitance is calculated in
section 5-2. The electromagnetic field in the sample will generate a ‘surface’ impedance
of the sample [8]. The real part of this ‘surface’ impedance is unique compared with
SCM measurement which needs DC bias to determine the carrier concentration in
semiconductor and can not determine loss tangent of dielectric samples.
The real part of ‘surface’ impedance can be obtained by integrating Poynting vector
though the whole surface of probe tip.
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44
References:
[1] John P.Casey, and Ranjeev Bansal, “Analysis and optimization of an electrically
small receiving antenna.” IEEE Trans. Electromag. Compat., vol. 33, pp. 197-204, Aug
(1991).
[2] S.Hudlet, M. Saint Jean, C.Guthmann, and J. Berger, “Evaluation of the capacitive
force between an atomic force microscopy tip and a metallic surface.” The European
Physical Journal B vol. 56 pp. 5-10, Apr (1998).
[3] B.N.Das and S. B.Chakrabaty, “Calculation of electrical capacitance of a truncated
cone.” IEEE Trans. Electromag. Compat., vol. 39. pp. 371-374, Nov (1997).
[4] D. Beatovic, P.L.Levin, S.Sadovic and R.Hutnak, “A Galerkin formulation of a
boundary element method for two dimensional and axi-symmetric Problems in
Electrostatics.” IEEE Trans. Elect. Insulation, vol. 27. pp. 135-142, Feb (1992).
[5] M. Sancho, J. L. Sebastian, S. Munoz, and J. M. Miranda, “Computational method in
electrostatics based on Monte Carlo energy minimisation.” Proc. IEEE Science,
Measurement and Technology, vol. 148. pp.121-124, May (2001).
[6] Yuancheng C. Pan, Weng Cho Chew, “A fast multipole-method-based calculation of
the capacitance matrix for multiple conductors above stratified dielectric media.” IEEE
Trans. Microwave Theory Tech., vol. 49, pp.480-489, Mar. (2001).
[7] C. Gao and X.-D. Xiang, ‘Quantitative microwave near-field microscopy of dielectric
properties’, Volume 69, Issue 11, pp. 3846-3851, (1998).
[8] T. Tran, D. R. Oliver, D. J. Thomson, and G. E. Bridges, ‘"Zeptofarad" (10-21 F)
resolution capacitance sensor for scanning capacitance microscopy’, Rev. Sci. Instrum.
Vol 72 (6), 2618 (2001).
[9] Y. Huang, C. C. Williams, J. Slinkman, ‘Quantitative two-dimensional dopant profile
measurement and inverse modeling by scanning capacitance microscopy’, Vol 66, Issue
3, pp. 344-346 (1995).
[10] J. J. Kopanski, J. F. Marchiando, and J.R. Lowney, J. Vac. Sci. Technol. B12, pp.
242-247(1996).
[11] J.F,Marchiando, J. J. Kopanski, and J. R. L ow ney, J. Vac. Sci. Technol. B 16, pp.
463-470(1998).
[12] D. M. Pozar, Microwave Engineering (Addison-Wesley, New York, 1990).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 4
Designs and Implementations of EMP systems
In this chapter, EMP systems based on modulation, true logarithmic amplifier (TLA) and
self oscillation are discussed. These systems are investigated extensively in our lab and
TLA based EMP system is original idea of this research. Good circuits of EMP systems
should have following characteristics, 1) 60 dB- 80 dB or larger dynamic range is
important for accurate measurement of small signals. Non contact sheet resistance
measurement may require 80 dB dynamic range. 2) Surface mount devices and discrete
solid state devices are good choices for compact system. High quality substrates and
corresponding transmission lines can be used. 3) High stability and low noise devices
should be chosen to suppress the signal shift and increase signal to noise ratio. Dielectric
or phase locked oscillators with low noise figure are used to provide stable source (less
than 60 ppm shifts). The material with small temperature coefficient and low thermal
resistance should be used as substrate. When frequency is lower than 3 GHz, SiGe HBTs
or MOSFETs are preferred than GaAs devices because of lower cost and similar
electrical performance. When operation frequency is larger than 3 GHz GaAs HEMT
devices are preferred because of lowest noise figure. 4) The speed of the EMP system is
determined by the response time of detector and amplification circuit. Fast speed of
circuit enables real time spectrum display and faster imaging process (~100 ns/pixel).
High speed system can eliminate commercial network analyzer during high speed
characterization or imaging. 5) Modulation and demodulation can be used to increase
signal to noise ratio by operating circuits where the 1/f noise is minimum.
45
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46
After the image is obtained, the image can be calibrated using standard samples at fixed
stand-off gap to get quantitative information. In order to compare the measurement
results with numerical results, well defined microspheres with micro or nano-meter scale
are very useful. Commercially available .015" to .062" diameter copper or silver spheres
have 5% or smaller tolerance. The sphere is attached using conductive epoxy or
fabricated to the thin probe tip used in our experiments.
4-1. AM modulation, FM modulation and microwave diode detector
The noise spectrum of measurement system shows noise can be less than 200 n V / -JHz
with 100 ms time constant if phase locking amplifier is used and RF signal is modulated
to minimize low frequency flicker (1/f) noise and thermo-noise in electronic systems.
Phase lock-in amplifier also has dynamic range more than 110 dB with 50 ppm stability.
The speed of phase lock in amplifier is limited by its time constant. The accepted signal
to noise ratio of EMP system requires at least 10 ms time constant. The phase information
of tip-sample interaction can not kept using modulation and demodulation techniques.
Vector measurements can only be done at resonant frequency where z position feedback
is needed to track the resonant frequency. However the modulation and demodulation
method is straightforward and simple. AM modulation based EMP system is used
extensively in our lab to explore the capability of EMP before [1-5]. FM modulation and
demodulation of carrier signal has been used to get approximate Q factor for sheet
resistance map and used in the phase locked loop as feed back signal. The modulation by
exciting samples’ mechanical vibration is also a valuable method explored.
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47
Sample
HP8341B
/
XK
Circulator
Synthesizec L
Sweeper
x, y, z control
PC
Pre-Amplifier “ Vo
Lock in
Amplifie
Detector
Modulation Signal
Figure 3-1-1. EMP system using AM or FM modulation. In these systems phase
lock-in amplifier (PLA) is the key instrument.
The typical measurement system is shown in figure 4-1-1. The x, y and z axis DC servo
motors are controlled using a PCI 64 bit MIPS based controller in the computer. These
16-bit DC motors have reliable 1 |Jm spatial resolution, 3.3 KHz servo filters and larger
than 5 inches X 5 inches scan range. The integration constant of the PID loop normally
set to 1000 for smallest error using smallest time. The speed of these motors can go up to
106 step (0.017 pm /step in our system) per second. The probe is going up and down to
track the resonant frequency during imaging process using feed back schemes with
operation frequency fixed. The magnitude of demodulated AM signal is smallest and the
phase change of demodulated FM signal is digitized 180 degrees change at resonant
frequency. These two signals can be used as the feed back signals. The time of feed back
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48
is determined by the time constant of phase lock in amplifier, the average steps that the
feed back takes, the communication delay between computer and phase lock-in amplifier
and the computation time of the software. 10 ms/ pixel has been achieved for this setup.
The Narrow band (<20%) ferrite circulator used in this system may have 60dB directivity
for reflection measurement. This excellent directivity assures best accuracy. Wide band
(100%) directional coupler with 30dB directivity can be surface mounted to get compact
systems. AC coupled Preamplifier with band pass filter may be needed just before the
phase lock-in amplifier.
For AM modulation Vr is
Vr = aAmARF cos((omt)cos(a)RFt)
(4-1-1)
The output of the phase lock-in amplifier is
Vo = aAmARF
(4-1-2)
where a is determined by the sensitivity of crystal detector and the AM modulation
index. At resonant frequency of microwave resonator, the phase of SI 1 is zero. For AM
modulation system with fixed AM modulation amplitude and AM modulation index, the
reflection coefficient measured at resonant frequency is
^_
(AI Amplification o f test)
(Aq / Amplification o f calibration)
(4 13 )
FM modulation is obtained by using sinusoidal signal as control signal of VCO or GUNN
oscillator. For FM modulation the FM source signal Yin from VCO is as follows.
Vin = V sin( 2n f0 +
J 2tzKvVfm
co s
(
2n f FMt)dt = V sin( 2jrf0 + /3 sin( 2n f FMt)) (4-1-4)
Where modulation index (3 = K vVFM/ f FM, K v is FM sensitivity of the VCO which 10
MHz/V or 1 MHz/V is used in our system. The modulation signal is a sinusoidal signal
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49
with amplitude V fm and carrier frequency fpM- Vin can be expanded using Besssel
function.
Vin/ V = J 0(l3)cos(27tf0t) + J 1(p){cos[2n(f0 - f FM) t ] - cos [ 2n( f 0 + f FM)t)]}
^
+ J 2(£){cos[2n ( f 0 - 2 f FM)t] + cos[2n ( f Q+ 2 f FM» ] } + ...
If we use phase lock in amplifier at fFM., the useful detected output RF signal at fo +fpM
and fo +fFM is V o u t.
v 0ut IV = V ( f 0 - f FM) / 1(JS)cos[2^(/0 - f FM) t ] - V ( f 0 + f FM)71(i8)cos[2n ( f 0 + f FM)t]
= / 1(J8 ) ( - 2 /m ) y '( / 0)co s(2 ^ FMO cos(2^00 + y i(jS)2F(/0)sin(27?fm O sin(2^00
(4-1-6)
The envelope of Vout is the output signal Ven after demodulation using crystal diode.
Ven = 7 j( ^ ) ( - 2 /fm )V' ( f 0)cos(27tfFMt) + J x(P)2V ( f 0)sin(2rtfFMt)
(4-1-7)
If f FMis much smaller than the bandwidth of resonant spectrum, we have
V ( f 0 - f FM) ~ V ( f 0 + f FM)
(4-1-8)
In the case of RF resonator operating near the dip of the spectrum, we have
k , ( /3 ) ( - 2 /„ )V'(/„ ) |» |y, (P)2 V(/„ )|
and Ven =
)V \f„ )c o s(2 ltf„ t)
(4-1-9)
The phase and magnitude of the output envelope signal are corresponding to the phase
change and the first derivative of high frequency S21 respectively if the frequency
deviation is much less than the bandwidth of resonant spectrum. The FM modulation
signal is chosen to make the frequency deviation as small as 100 KHz. This is reasonable
compared with the typical bandwidth (>10 MHz) of the microstrip resonators. The
optimum modulation frequency should be chosen to make Ven biggest. This can be done
by generating a plot of J^/3) versus f as shown in figure 4-1-2. Stable demodulation
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50
signal can be obtained when the magnitude of FM modulation signal is as small as 10
mV. This is a good characteristic for the low power and wireless electronic application.
x 10"
5
S3
4
-4a-i
t/3
S3
O
<J
dJ
-O
3
B
2
0A
CO
2
1
'2
0
1
0
10
20
30
40
50
60
70
80
90
100
(khz)
f FM
Figure 4-1-2. Optimum FM modulation frequncy must be chosen to make
magnitude constant as large as possible. 90 KHz is chosen
High sensitivity and accurate sensing can be obtained using FM modulation because the
effective Q factor (frequency band of 180 phase change/center frequency) is 10 times
larger than Q factor of AM modulation. This is shown in figure 3-1-3 for a typical over
coupled 30dB microstrip resonator where near digital phase change in frequency domain
has been observed. The effective Q for this resonator was 3400 compared with Q= 100 of
S l l . T h i s F M d e t e c t i o n m e t h o d c a n g o u p t o 2 0 G H z e a s i l y b e c a u s e t h e p h a s e d e t e c t i o n is
done using low frequency modulation signal and the output envelope signal. The whole
system based on this is very compact and cheap in terms of cost. It needs to be pointed
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51
out the phase detected here is different from real microwave phase. Meaningful data
should be carefully calibrated.
200
Q f =3400
150 -
ft -50
1.825
1.849
1.873
1.897
1.921
Fr equency (GHz)
(a)
-10
- -
-20
--
-50
-
1.850
1,875
1.92
f (G H z )
(b)
Figure 4-1-3. (a)Effective Q factor was 3400 which was 34 times larger than Q factor
of S ll. (b) S l l of the resonator
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Both AM demodulation and FM demodulation needs high quality wide band diodes.
The wide band microwave detectors in EMP imaging should have the following
advantages. 1) low noise index. 2) high speed operation which is very useful for real time
measurement. 3) low threshold voltage. Point contact diode and Schottky barrier diode
are good choices for such purpose. When the RF power is small linear response is good
approximation for these diodes as shown in figure 4-1-4 for an example. The typical
sensitivity of biased schottky diode used is about 2000mV/mW. The schottky diode can
also be fabricated at the tip of the probe.
600
500
5 - 400
£ 300
>
200
100
0
■2
0
2
4
6
8
10
Power (dBm)
Figure 4-1-4. The output of schottky diode versus RF power. The magnitude of
modulation signal was fixed at 0.4 V.
The point-contact diode was developed in WWII. Figure 4-1-5 shows a typical pointcontact diode. The cathode of the diode consists of a small rectangular crystal of n-type
silicon or GaAs. A thin metal (berylium-copper, bronze-phosphor, or tungsten for silicon
and platinum, titanium, gold for GaAs) wire called the catwhisker presses against the
crystal and forms the anode of the diode. It needs to point out that a metal AFM tip over
semiconductor sample has similar setup. A small region of p-type material around the
crystal in the vicinity of the point contact is formed by passing though a relatively large
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53
current from the catwhisker to the semiconductor substrate during manufacturing. Thus, a
P/N junction is formed which behaves in the same way as a normal P/N junction.
Oxide
Catwhisker
wire
Metal
Ptype
Sem iconductor^^
N type material
Figure 4-1-5. Biased schottky diode and Point-contact diode
The pointed thin wire or probe is used to produce a high-intensity electric field at the
point contact without using a large external source voltage. It may damage the
semiconductor because of the excessive heating if large voltages across the average
semiconductor are applied.
The capacitance (~1 pF) between the catwhisker and the crystal is less than the
capacitance between the two terminals of the junction diode (~ 20 pF).
Schottky barrier diode has a large contact between the sputtered metal (anode) and the
semiconductor (normally n type). It is can be integrated with other integrated circuits
easily. Lower forward resistance and lower noise index are the most important
advantages of the Schottky barrier diode. The forward bias voltage is less than 0.6 V
normally.
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54
The I_V curves of Schottky barrier diode used in our system have shown the forward bias
voltage is less than 0.2 V.
The Schottky barrier diode is a majority carrier device without minority carrier. The
conduction of the Schottky barrier diode is controlled by thermionic emission of majority
carrier because of work function difference. Low cost Schottky barrier diodes up to 300
GHz are commercially available.
The junction capacitance changes with bias voltage
(4-1-10)
where C]a is the junction capacitance at zero bias voltage (V=0) and (j)m is barrier height
(difference of Fermi level and peak of conduction band). The current of the Schottky
barrier diode is
I(V) = I 0[e{qVlnkT)- l \ = A T 2We{-q^ lkT)[e(qVlnkT) - l j
(4-1-11)
where A is the modified Richardson constant, W is width of junction area, T is absolute
temperature, k (1.37e-23 J/K) is Boltzman constant, q is the charge of single electron and
n is slope parameter or ideality factor usually between 1.05 to 1.25 . The modified
Richardson constant is approximately 96 Am'4 K'2 for silicon and 4.4 Am'4 K'2 for GaAs.
The Schottky diode effects of EMP metal probe have been used to image the carrier
concentration in semiconductor samples. Planar GaAs Schottky barrier diodes are
commercially available up to 300 GHz.
DC bias voltage is applied through a RF blocked coil inductor at k/4 away from the open
end of X/2 resonator.
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55
4-2. High-speed EMP system based on true logarithmic amplifier (TLA)
In EMP application the reflected signal of microwave resonator may have 20dB-50dB
(contact) and 80dB (non-contact) dynamic range normally. The true logarithmic amplifier
(TLA) can be utilized to maintain the phase information and compress the reflected
signal. The TLA is composed of multi dual gain stages. Each stage has an input bufferdivider, a unit gain amplifier, a low power level limiting amplifier and an adder. Every
single stage has moderate gain (typically lOdB) at low power level and gain approaching
unity at higher power levels. Barber and Brown have shown that the best fit straight line
response of this cascaded stages is Vout={N+l/A+log(A+i)[AVin/V L]}VL where V l is
output limiting voltage, A is the voltage gain of each stage, and N is the number of
stages. [6-7] The phase information is kept in the output digitized limiting signal. The dc
output of true logarithmic amplifier is proportional to the logarithm or phase of the
reflected signal. The number of dual gain stages determines the deviation from best-fit
strait line. Maximum 0.8dB deviation can be achieved using lOdB gain stages. The
response time of the TLA is typically less than 100ns witch is significantly smaller than
lms(smallest time constant for most commercial phase lock-in amplifiers). Monolithic
GaAs MESFET technology or SiGe technology can be used to fabricate the TLA and
integrated EMP system. Low cost TLA with 100 dB dynamic range is commercially
available.
Both directional couplers and ferrite circulators can be used in reflection coefficient
measurement systems.3-port directional coupler is connected so that its coupled port
samples the reflected signal from the microwave resonator. Higher coupling value is
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preferred for lower main line insertion loss. 30dB coupling value can achieve main line
insertion loss less than O.OldB. Coupling value in this system is determined by matching
the center of dynamic range of the TLA inputs. Higher directivity is desirable for smaller
reflection measurement error. Mathematical analysis shows that the error is less than ldB
when the directivity is 20dB greater than the resonator’s return loss. Bulky and narrow
band ferrite circulators have better directivity. But directional couplers can be surface
mounted and low cost devices under 5 GHz. The wide band directional couplers with 30
dB coupling value and 40dB directivity are easily obtained up to 110 GHz. The
rectangular waveguide directional couplers are full band compared with only 10% band
of circulators.
In our prototype system design we choose AD8302 [8] chip from Analog Device Inc. The
AD8302 is a fully integrated RF IC for measuring amplitude and the phase between two
independent input signals using BiCMOS process. The device can be used from low
frequencies up to 2.7 GHz. The AD8302 integrates two closely matched wideband
logarithmic amplifiers, a wideband linear multiplier / phase detector, precision 1.8 V
reference, and analog output scaling circuits. The applied input signal can range from -60
dBm to OdBm (ref 50ohm), which corresponds to a 60 dB dynamic range. The AD8302
output provides an accurate amplitude measurement over +/-30dB range scaled to 30
mV/dB and the phase measurement over a 0 to 180 degree range scaled to 10 mV/degree.
The response time of any 15° change (10%-90%) is less than 5 0ns. The rise time and
fall time of any 20 dB change (10%-90%) is less than 60 ns. The settling time of full
scale 60 dB change is 300ns. This means the sweeping frequency can be 3 MHz.
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57
Resonator/probe
LOGA
Mag
Phase
VCO
LOGB
ATTE
Figure 4-2-1. High-speed EMP system based on TLA
The AD8302 chip has magnitude and phase outputs [8]
V „ , = R r i Su. log(V„
/v„)+ v„
whereRFI SLP =3 0 mV / d B , RFI 0 - l O m V / degree and Vcp = 900mF when the output
pins are connected directly to the feedback set-point input pins. This device actually
measures channel A dividing channel B.
The schematic of experimental system is shown in figure 4-2-1. One two way 0 degree
power splitter is used to split the incoming signal to two identical signals for two arms.
Attenuator may be used to balance the center of dynamic range of two arms.
The phase error of measurement can be calibrated assuming the error is introduced by
frequency depended electrical length of lossless transmission line. This phase error can
be recorded in processing unit or calibrated using voltage controlled varactor electrically.
The calibrated phase is
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where 0O is because of electrical length difference between channel A and channel B. At
resonant frequency in free space phase 6 should be zero.
a -af
y 0 — Vina
(4-2-3)
-Qf
V inb
If the operation frequency / ' is far away from resonant frequency, ideal reflection
coefficient should be 1. The magnitude calibration factor is
h | = V,„/V„#
(4-2-4)
The magnitude of calibrated reflection coefficient is
(4-2-5)
In figure 3-2-1, we compute magnitude using the measured magnitude at / ' a s reference
and compute phase using measured phase at resonant frequency as reference
V /nagf ~ V m a g f ' =
V phsf
V phsr
SLP
^F^
\ m
’in a f^ \n b f' ^ i n b f ' ^ i n a f ' )
naf ) - W
(4-2-6)
n bf ) | - \ W n a r ) “ W
r f , ) |)
From the calibration process, the equations change to
^ magf ~ ^ m a g f l ~ ^ F ^ S L P
(\
inaf ^ i n b f ' )
\\
- V , ^ ^~ -~ R^ FPII<!>^^( V inaf) - m n bf)\)
( 4 - 2 -7 )
! phs f ~ V p h s r
The technique described above guarantee we have correct reference plane right before the
gap capacitor. One calibration curve from 500 MHz -1000 MHz is shown in figure 4-32. The plot shows the offset magnitude and phase voltage when channel A was 50 Q
terminated.
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59
2000
2000
£ 1000
a
600
700
800
f r e q u e n c y (G H z)
900
Figure 4-2-2. The offset phase and magnitude of experimental system from 0.5 GHz1 GHz were measured for calibration.
For some measurements full differential measurement schemes (figure 4-2-3) are used to
achieve best dynamic range improvement. The dynamic range of measurement can be
expanded further by using a reference arm with similar response spectrum. The devices
and connections between devices of each arm are identical. These two resonators are
calibrated on top of standard samples to get identical frequency spectrum before imaging.
One resonator (probe A) has a longer tip which is scanning over sample surface. The tip
of another probe (probe C) is much shorter to keep the tip/sample interaction of reference
arm negligible. The common mode of both linear and nonlinear response is canceled out
for these balanced two arms. If the probe C on top of standard sample with constant
response is used as channel B, one more calibration factor is needed to extract the input
impedance. Use 50 Q arm as channel A and probe C as channel B. We denote and record
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60
the magnitude and phase of this measurement as r' and 6". The calibration is
corresponding to the transformation of measurement results using probe C as channel B.
6 ina ~ 6 i n b
0 ina ~ ®inb + 0 "
r'Vina IV.,
mb
v ma IV.mbh
(4-2-8)
1 RF in
Power splitter
50 Q
CHA
CHB
Figure 4-2-3. The full Differential measurements use two identical probes at two
arms. The third arm is reserved for calibration.
After transformation is performed, the reflection coefficient can be obtained using same
procedure when 50 Q arm is used as channel B. We can also calculate the impedance
using probe B as reference and plot it in Smith chart o f course. The effective impedance
calculated using this method has different meaning from the impedance with standard
reference arm. It is more sensitive to the impedance change at the tip.
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61
If ferrite circulators with large directivity are used instead of directional couplers, open
circuit at port 2 is better choice as reference arm instead of 50 Q terminal. We have
ro “ 1
and r'~ 1 when the operation frequency is far away from resonant frequency
T LA
NA
-10
-3 -15
-25
-30
-35
70
975
980
985
990
995
1000
Frequency (GHz)
Figure 4-2-4. The measured magnitude of S l l using experimental system fits quite
well with the measured magnitude of S l l using HP8720C network analyzer.
Simple resonant magnitude spectrums of a microstrip resonator near 984 MHz measured
using experimental system (TLA) and HP8720C network analyzer (NA) are compared in
figure 4-2-4. The experimental TLA system used 1 GHz ferrite circulator with open at
terminal 2. Measurements at two hundred frequency points have been used to generate
the TLA spectrum. The effects of frequency shift (about 1.1 MHz in this experiment)
between signal generator and network analyzer because of not perfect frequency
calibration have been got rid of in this comparison. The power of the RF generator was
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62
fixed at -10 dBm compared with the source voltage of the network analyzer was fixed at
1 V. The attenuator was not used in this experiment.
After reflection coefficients are obtained, the load impedance can be calculated and
plotted in Smith chart. One example is shown in figure 4-2-5. In figure 4-2-5 the input
impedance of a microstrip resonator with 380 |Jm sphere tip on top of copper ground with
1 pm, 125 pm and 250 pm gap are shown. The resonant frequency of the experiment
resonator was 996.3 MHz in free space. The start frequency was 995 MHz. The
frequency span was 5 MHz. Un-calibrated transmission line will introduce frequency
depended electrical delay or equivalent linear phase shift and rotate the impedance curve
in Smith chart. It can be seen that the two channels of the measurement system were well
balanced with Q circle center on the real axis. In figure 4-2-5, we also observe
1 pm gap
25 pm gap
250 pm gap
-ii
Figure 4-2-5. The input impedance of a microstrip resonator with 380 pm sphere
tip over copper ground with 1 pm gap, 125 pm gap and 250 pm gap.
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63
1) The impedance is more capacitive when the frequency is smaller than resonant
frequency. At resonant frequency the inductive component cancels out capacitive
component.
2) The gap between metal and probe tip is smaller, the resonant frequency is smaller.
3) We also have Z ( f + A/, g ) « Z ( f , g - Ag) which means resonant frequency shift is a
good measure of the gap between the tip and metallic surface. The spectrums follow
same path in Smith chart at different gap.
4-3. Coupling of microstrip resonator
Resonant
Insertion
frequency
loss (dB)
Over
980.8
couple
MHz
Critical
983.6
Couple
MHz
Less
986.9
Couple
MHz
-17.5
Z at fr
64.86
C l (pF)
C2 (pF)
0.4
0.37
-41
51
0.36
0.33
-14.5
38.6
0.51
0.47
Table 3-3-1. Some important parameters of a microstrip resonator with resonant
frequency near 1 GHz operating at three different coupling conditions
The coupling or matching of microstrip resonator is very important and valuable in
verification and sensitivity improvement of EMP system design.
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64
The microstrip resonator can be over coupled, critical coupled and less coupled. The real
part of the input impedance is closest to 50 Q at resonant frequency for critical coupled
resonator. This also means the resonator has largest insertion loss when the resonator is
critical coupled. Different coupling leads to different sensitivity and stability. Table 4-1-1
shows some important parameters of a microstrip resonator with resonant frequency near
1 GHz operating at three different coupling conditions. The tuning at the tip region is also
valuable. The appropriate matching circuits may increase the sensitivity of resonators.
j0.5
J0.2,
ritical
03
cTa
less
-j0.2
-j0.5
ovei
Figure 4-3-1. The Smith chart of less, near critical and over coupled resonator using
the system described in section 4-2.
Bigger coupling is obtained by moving Teflon screw at the feed line/resonator gap closer
to the microstrip line. Figure 4-3-1 shows the Smith chart of these three conditions from
976 MHz to 996 MHz. All these measurements were done using the experimental system
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65
described in section 3-2 with 200 frequency points. Figure 4-3-1 shows larger coupling
means the radius of impedance circle in Smith chart is larger and the impedance circle of
critical coupling corresponds to 50 Q circle. This figure also clear shows the resonant
frequency becomes lower when coupling is larger. Many researchers have tried to
understand and fitted these impedance circles to get Q factor and other important
parameters [9-10].
200
150 ■
100 ■
50 ■
a
o.<
J3
On -50 -100
0.980
98
0.988
0.992
0.996
Frequency (GHz)
■
-150 -200
Figure 4-3-2. The phase of less, critical and over coupled resonator with open at the
end of probe.
It is interesting to note the phase change near resonant frequency is exactly 180° and the
phase change is larger/smaller than 180° if the coupling is larger/smaller than critical
coupling as shown in figure 4-3-2. The measurement system has been calibrated to get rid
of the feed line section in figure 4-3-2. The phase becomes positive when frequency is
larger than resonant frequency for open-ended electrical probes. This information is very
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66
useful to calibrate and verify vector microwave measurement system. When the resonator
is over-coupled, the special care is given to the phase signal to ensure the corrected phase
pattern in our experimental TLA system. The rotation of the impedance circle in Smth
chart can be used to calibrate capacitive (clockwise) or inductive (anti-clockwise) change
near the tip. The radius of the impedance circle can be used to calibrate the sheet
resistance or loss tangent if coupling of the resonator is fixed.
4-4. Self resonant EMP probe [11]
The EMP systems described in section 4-1 to section 4-2 are open loop systems where
microwave resonator for imaging is not in the loop of the microwave oscillator.
EMP forms part of an oscillator circuit that when coupled to a sample, oscillates at a
different frequency determined by the combined EMP-sample system. This simple
arrangement enables frequency tracking as well as quality factor mapping with a very
small circuitry suitable fo r direct integration with the EMP on silicon. The selfoscillating probe always operates at its resonant frequency and it is very compact.
Moreover, it is well known that in second-order circuits at resonance, the capacitive
effects cancel out inductive effects significantly simplifying the analysis.
Another important aspect of these self-oscillating probes is that they can be integrated
on silicon with all the necessary electronics. The development of high frequency
resonators on silicon substrates has been limited by the performance degradation
associated with silicon at high frequencies. Since the resistivity of common grade silicon
wafers is in the range of 1-20 £2.cm, circuit elements and transmission lines fabricated on
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67
silicon have high loss resulting in low quality factors. Alternative techniques have been
developed to solve this problem. For example, one can use commercially available high
resistivity silicon wafers (p~2500 Q.cm). All of the circuit elements in this case may be
implemented in the same way as they are implemented on GaAs, ceramic, or duroid
substrates. We have shown that resonators fabricated on high-p silicon can be tuned to
achieve external quality factor two orders of magnitude higher than the un-tuned
resonators. In the present work, we only discuss self-oscillating resonators on duroid and
we will report characteristics of fully integrated resonators on silicon substrate with
electronics in the near future.
The self-oscillating evanescent microwave probe is composed of three essential parts.
The microstripline resonator, which is also the heart of the probe, constitutes the first part
of the probe and it is depicted in figure 4-4-1. The second part of the probe is a
microwave amplifier that compensates for dissipation of energy in the resonator. The
third part of the probe is its tip region that interacts with the sample. All these different
regions are schematically shown in figure 4-4-1.
Schottky Diode
Detector ^
Mixei
Amp
Figure 4-4-1. Schematic of the self-oscillating evanescent microwave probe (SO
EMP) with an integrated RF amplifier.
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68
The full-wave finite element simulation of microstripline resonator structure was carried
out to optimize resonator’s behavior. The presence of a sample near the tip modifies the
density of these charges enabling the microwave sensor to characterize the microwave
properties of the sample. Thus, it is essential that at the operation frequency of the
oscillator, the tip should be located in the high charge density part of the resonator and
not on a node. The resonator consisted of a 1-mm thick duroid substrate, with 3.5 mm
wide 14 cm long copper strip (Zo~50 £2). 125 /xm diameter tip used in the experiment.
-10
100
CM
-20
-100
-25
1.8
2.0
2.2
2.4
2.6
2.8
F requency (GHz)
Figure 4-4-2. The experimental S21 (both phase and amplitude) spectrum of the SO'
EMP resonator with the amplifier turned off.
The S21 parameter of the over-coupled resonator is shown in figure 4-4-2. In the
present work we used a commercially available 20dB rf amplifier (VNA-25) with its
measured 5-parameters shown in figure 4-4-3. The oscillation criteria (gain>l or 0 dB
and phase=0, 2n, ..) was met at fo~2.2 GHz. At 2.2-2.3 GHz, the amplifier produced a
linear phase shift that along with the more than 180 degree phase shift introduced by the
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resonator. At the same frequency near the magnitude peak, the phase requirement is
satisfied. Moreover, the amplifier gain of 16-17 dB was also sufficient to compensate for
the radiative losses (-10 dB) occurred in the resonator (figure 4-4-2) around 2.2 GHz. The
S21 of the SO-EMP with the amplifier in place is shown with the measured 3.4 dB gain
at 2.227 GHz. It should be noted that the resonant frequency of the resonator is different
when measured using the S-parameter technique (fcr^2.315 GHz) compared to the self­
oscillation frequency ifd^2.223 GHz). We also noted that the presence of the amplifier
(turned off) affected the/o in the S?t measurement as well (fd^-2.21 GHz). These small
differences in the measure fo s are the result of differences in the loading and parasitic
capacitance effects associated with different modes of measurements.
150
100
SP
so i
0
-50
£
<8
I
-100
0.5
1.0
1.5
2.0
Frequency (GHz)
2.5
3.0
A
Figure 4-4-3. The experimental S21 spectrum of the RF amplifier (VNA-25) used in
the SO-EMP.
Figure 4-4-4 shows two oscillation spectra of the SO-EMP that were obtained with the
probe in air and with a metallic sample in front of the probe. These spectra were obtained
using a spectrum analyzer rather than a network analyzer that was used in S-parameter
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70
measurements discussed before. The change in /0 was around 3 MHz for a metallic
sample.
M e ta l
A ir
60
5PL
2.21
2.215
2.225
2.22
2.23
2.235
2.24
Frequency (GHz)
Figure 4-4-4. The oscillation spectra obtained using a spectrum analyzer of the SOEMP with and without a metallic sample.
The SO-EMP was scanned over different samples using a x-y-z stage controlled by a
computer as schematically shown in figure 4-1-1. The change in the oscillation spectrum
of the SO-EMP was detected using a phase detection circuit that produced a dc output
that was monitored by the computer to produce line-scans and x-y maps. Figure 4-4-5
shows two SO-EMP line scans over a 12.5 pm square wire (figure 4-4-5a) and 4 pm
carbon fibers (figure 4-4-5b). The corresponding EMP scans indicate much lower spatial
resolution. The stand-off distance in the scans shown in figure 4-4-5 was around 5 pm
and the wire as well as the carbon fibers were grounded and were attached to an
insulating glass substrate. Based on figure 4-4-5b, the spatial resoltion of the SO-EMP
can be determined to be around 4 pm for high contrast objects.
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1.4
1.2
12.5 |jm
1
>
w 0.8
cl
x
w 0.6
o
w 0.4
0.2
0
0
100
200
D istance (urn)
300
(a)
xlO"3
8
ft.
^W
I
O
6*
t/5
4
182
184
186
188
Distance (Mm)
190
192
(b)
Figure 4-4-5. The SO-EMP linescans over a 12.5 |im square wire (a) and three 4-(jm
diameter carbon fibers (b).
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72
300
100
0
100
150
Distance (|im)
50
200
250
(a )
0.45
0.4
0.35
0.3
>
w
a 0.25
z
^ 0.2
o
on
0.15
0.05
0
100
200
300
400
500
600
Distance (pm)
(b )
Figure 3-4-6. The SO-EMP output (a) and the EMP output (b) versus distance (in
the z-direction) using a metallic (copper) sample. The SO-EMP decay length is
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73
around 70 fim while that of the EMP decay length is in excess of 400 jim. Both
probes had similar tapering and tip sections.
Figure 4-4-6a shows the SO-EMP output as a function of the stand-off distance. The
decay length is around 70 pm. We also used the SO-EMP’s resonator section as an EMP
and measured its output as a function of stand-off distance as well. As shown in figure 44-6b, the decay length of fields near the EMP probe was around 400 pm. The 4-fold
decrease in the SO-EMP’s decay characteristics can be attributed to the more confined
nature of the fields near the probe tip operated in self-ocsillating mode. It is as though
the field patterns attain a lower energy configuration in self-oscillation mode compared to
field patterns resulting from an external signal source. This also reflects itself in the
measured quality factor of these two different modes, the Q factor is higher almost by a
factor of 10 indicating less radiative losses. Radiative losses are usually the result of
larger spatial changes in the field pattern. Thus, in the self-oscillating mode, the field
patterns are less dispersed resulting in sharper field decays near the probe tip.
References
[1] M. Tabib-Azar and Y. Wang, "Design and Microfabriation of Atomic Force
Microscope Compatible Scanning Near-Field Electromagnetic Probes." To be Presented
in 2002 ASME Conference, 17-22 New Orleans, Louisiana.
[2] M. Tabib-Azar and D. Akinwande, ‘Real-time imaging of semiconductor spacecharge regions using high-spatial resolution evanescent microwave microscope’, Rev.
Sci. Instrum., Vol 71(3), pp. 1460-1465(2000).
[3] M. Tabib-Azar, D.-P. Su, A. Pohar, S. R. LeClair, and G. Ponchak, ‘0.4 pm spatial
resolution with 1 GHz (A= 30 cm) evanescent microwave probe’, Rev. Sci. Instrum. Vol
70, 1725 (1999).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
[4] M. Tabib-Azar, J.L.Katz , and S.R.Leclair,” Evanescent microwaves: A novel super­
resolution noncontactive imaging technique for biological applications”, IEEE Trans.
Instrum. And Meas., Vol. 48 pp. 1111-1116 (1999).
[5] Tao Zhang and M.Tabib Azar, ‘Phase Detection in Evanescent Microwave
Microscopy’, ASNT 11th Annual Research Symposium, Portland, Oregon, March 18-22,
( 2002).
[6] Barber, W.L.; Brown, E.R., ‘A true logarithmic amplifier for radar IF applications’,
Solid-State Circuits, IEEE Journal o f , Vol 15 (3) pp. 291-295 (1980).
[7] Smith, M.A., ‘A 0.5 to 4 GHz true logarithmic amplifier utilizing monolithic GaAs
MESFET technology’, Microwave Theory and Techniques, IEEE Transactions on , Vol
36 (12), pp. 1986-1990(1988).
[8] Analog Device ‘AD8320 Datasheet’.
[9] Kajfez, D., ‘Linear fractional curve fitting for measurement of high Q factors’,
Microwave Theory and Techniques, IEEE Transactions on , Vol 42 (7), Jul 1994.
[10] Vanzura, E.J.; Rogers, J.E., ‘Resonant circuit model evaluation using reflected Sparameter data’, Instrumentation and Measurement Technology Conference, IMTC-91.
Conference Record., 8th IEEE , pp.150 -155,14-16 May (1991).
[11] Tabib-Azar, M.; Tao Zhang; LeClair, S.R., ‘Self-oscillating evanescent microwave
probes for nondestructive evaluations of materials’, Instrumentation and Measurement,
IEEE Transactions on , Vol 51 (5), pp. 1126 -1132 (2002).
[12] M.Tabib-Azar, A.Garcia.Vanlenzuela and G.ponchak, ‘Evanescent microwave
microscopy for high resolution characterization of material’, Nowell, MA, Kluwer,
( 2002 ).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 5
Microwave AFM System
Conventional EMP systems use PE) controlled DC servo motors to get point-to-point
positioning. The servo motor normally has spatial resolution larger than 1 pm because of
hysteresis of spring. It is useful to integrate established nano-meter positioning and image
processing techniques of AFM system with EMP probes when spatial resolution of EMP
is smaller than 100 nm.
AFM system uses PID controlled stiff piezoelectric ceramics to get accurate and smooth
nano-meter movement where the response is very fast. The noise displacement is 0.4
pm 14Hz, if the rms drive amplifier noise is 3 flV / -J~Hz [1]. Both contact and noncontact operation of SPM microscope AFM can give 300 X 300 topographic maps of
sample surface from 1 pm XI pm to 100 pm X 100 pm. Laser is used to detect the
deflection or vibration of beam of AFM tip. The soft-contact is quantitatively
characterized by feed back controlled set-point which is important for accurate
microwave measurement. The data processing system of AFM normally provides several
inputs during imaging process. The outputs of internal sensor of AFM can be monitored
simultaneously with forward and backward outputs of EMP. Point positioning function of
AFM system which can move the tip to specified positions and keep the tip at the
positions shown in topography plot is also very valuable for microwave characterization
and measurement. The crosstalk between interface circuits of external inputs and internal
circuits should be paid attention.
Microwave AFM system (pAFM ) uses delicate motion control system of AFM and one
or two inputs of AFM. The challenge here is the limited space for microwave probe and
75
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76
very tiny impedance change of tip-sample interaction. The small space and wire
connection introduce large parasitic impedance at high frequency and affect the electrical
behavior of probe drastically. In this thesis the AFM tip is DC and microwave
characterized, three setups of microwave AFM system are proposed and used to get
images of metal, semiconductor and dielectric samples.
5-1. Characterization of AFM tip
S ill* *
s"
5 .0
kV
*
x 5 0 . 0 k ' '6 0 0n m
Figure 5-1-1. Fabricated coaxial shielded AFM compatible tip by Yaqiang wang in
our group.
DC I-V and S parameters characterization are standard procedures for characterization
and modeling of high frequency devices.
Coaxial shielded AFM compatible tips (figure 5-1-1) fabricated on low loss SOI wafers
in our group were used [2-3] in the calibration. These sharp tips are carefully shielded
near the tip region using sputtered metallic (Al) ground to get localized field distribution
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77
0.04
0.03
0. 02
S3
<
u
t*
u
3
U
0.01
-
0.02
-0.04
0.10-0.08-0.06-0.040.020.000.02 8.04 0.048.08 0.10
Voltage (V)
(a)
/
l.E-05
l.E-05
Bn
8.E-06
^ > 0
'
2
+4
fl
<a>
u
mm
3
u
6.E-06
A
c
’---------- *
4.E-06
2.E-06
0.E+00
-2.E-06
-1.0
-0.7
-0.4
-0.1
0.2
0.5
0.8
Voltage (V)
(b)
Figure 5-1-2. The I-V characteristic of coaxial AFM compatible tips
near the tip. The high quality beams o f these AFM compatible tips are 50 pm X 2-5 pm X
500-1000 pm with mechanical resonant frequency from 10 KHz to 100 KHz and high
mechanical Q factor. The mechanical response of these beams is excellent. The tip radius
of these tips is around 20 nm. The DC I-V characterization is to make sure good electrical
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78
isolation between tip and coaxial shield and low tip-copper ground contact resistance as
assumed. The measured I-V results using HP 4155 B semiconductor parameter analyzer
are shown at figure 5-l-2a (contact resistance) and figure 5-l-2b (leakage). The leakage
was only 2 pA at 0.5 V. The contact resistance was around 2.8 Q. The I-V characteristic
of this tip was better than commercial AFM tips which normally have contact resistance
about 20 Q.
The load impedance of the AFM tip from 0.05 GHz to 20 GHz was one-port
characterized using HP8720C as shown in figure 5-1-3. Single cable was used to connect
To HP 8720C
Z ir,
t
Test cable
<hn
v
"AI M tip
Figure 5-1-3. Load impedance characterization using a single cable and HP8720C
network analyzer
the AFM tip to the network analyzer. First the network analyzer was very carefully full
one port calibrated to remove frequency response, directivity and source match errors in
reflection measurement without cable connected. The near open condition should be
observed in Smith chart after calibration. The AFM tip was fixed on top of a grounded A1
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79
sample holder with its shield ground connected to A1 plate. The test probe can move up
and down for best control of probe-AFM tip contact. A single cable with high microwave
quality was used to connect the HP 8732C and the AFM tip. When the tip is far away
from the AFM tip (open), the input impedance is
Z° —— ^ —
m ju m p I
where p =
2n
(5-1-1)
j a is determined by wavelength A in the test cable and attenuation
constant a , I is the sum of physical length and effective length of the test cable, Z0 is
characterize impedance (50 Q in our measurement). From (5-1-1) the j tan p i of the
cable is experimentally determined.
When the test probe was contacting with the signal line of the AFM tip, the input
impedance was changed by the load impedance Z t at the tip
Z .+ jZ .ta n /H
Z0 + jZ t tan p i
After Zz is determined, the parallel resistance and capacitance were experimentally
determined. The test results of three coaxial AFM tips are shown in Figure 5-1-4. From
figure 5-1-4, we can see these tips normally have capacitance in the order of 0.1 pF that
includes the capacitance of the coaxial transmission line on SOI substrate. The isolation
was good till 5 GHz (~KQ) for these tips. Tip 3 is a ‘bad’ tip. It has been verified that this
method can detect capacitance change as small as IfF using a single transmission line.
We used a grounded flat copper foil perpendicularly approaching one AFM tip at 10
GHz. The parallel resistance and capacitance change are shown in figure 5-1-5.
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80
i-12
3 .5
x 10'
2 .5
0 .5
- 0 .5
-1 - 5 .
0 .5
f (Hz)
x 10
f (Hz)
x 10
10
x 10'
0.8
0.6
Tip2
/T ip i
0 .4
0.2
E
JZ
-
0.2
-0.4
-
0.6
-
0.8
Tip3
0.5
10
Figure 5-1-4. Extracted resistance and capacitance of three AFM tips
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81
PC
AFM tip
Single RF
cable
Sample
holder
HP8720C
Xyz stage
n
Figure 5-1-5. Setup used to characterize the coaxial AFM compatible tip
2 .0 6
>-13
x 10
Grounded copper foil
2 .0 5
2 .0 4
AFM tip
2.02
2.01
100
200
300
400
500
600
z (um)
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82
125
120
105
100
100
200
300
Z (um)
400
500
600
Figure 5-1-6. Extracted resistance and capacitance of one AFM tip using grounded
copper foil to perpendicularly approaching the AFM tip at 10 GHz. Z was smaller,
gap was smaller. Z=0 corresponding to about 0.5mm gap between ground and AFM
tip.
Figure 5-1-7. AFM compatible co-coaxial tip was mounted on the metal half washer.
The half washer was mounted on the AFM head and connected to EMP system.
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83
#
-5
-10
-15
«
-20
S
-25
3
-30
-35
-40
0.60
0.60
0.7*
#.87
0.96
1.05
0.96
1.05
1.14
0
S I 1 ^ ------►
-10
-20
pa
l-H
rH
tz5
-30
-40
-SO
— 60 n
-60
1 ------
0.6
L-
0.69
1
1
0.78
1
1
0.87
i
■
.
1. 14
Frequency (GHz)
(b)
Figure 5-1-8. AFM compatible co-coaxial tip was in the air or touch ground. The
S l l of AFM tip was sensitive to set-point of AFM system.
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0.7 mm well calibrated coaxial cable and conductive epoxy were used to connect the
AFM tip on half-washer as shown in 5-1-7. The half-washer was then mounted on the
magnetized AFM head (ground) as shown. After the tip was mounted and DC connection
was verified, the tip was characterized using SI 1 from HP 8720C network analyzer.
Figure 5-1-8a shows the SI 1 of an AFM in the air before approaching and after
approaching copper ground and feed back established. Different set point of AFM tip
means different contact force between AFM tip and ground witch will change S 11 of the
AFM tip shown in figure 5-l-8b. In figure 5-l-8b the set-point value was larger, contact
force was smaller. The largest insertion loss was obtained when the set-point was 20 nA.
This means the S 11 can be used as feed back signal in AFM system instead of signal
from photo detector because S ll was a sensitive function of contact force.
At very high frequency large S l l changes because of metallic or dielectric sample have
been observed.
5-2. Microwave AFM system
The characterization of AFM tip showed very sensitive S ll response to tip-sample
interaction. In order to get images, three microwave AFM setups have been proposed and
built.
(a) The first kind of microwave AFM system is based on conventional AM modulation,
FM modulation or TLA vector measurement. It is reflection measurement based and well
established as discussed in chapter 4. The most difficult part of this setup is constructing
high Q resonance near the tip region.
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85
(b) AFM tip as receiving antenna
The electrically short antennas have a lot of applications. The second method is shown in
figure 4-2-1. The AM or FM modulation is not a must and is used to suppress the low
frequency noise. It is observed that DC output has good enough S/N for this setup. This
method has a lot of advantages. (1) This setup can be easily expanded to higher
frequency. Low cost Gunn oscillator, Schottky diode and horn antenna up to 110 GHz is
commercially available. The rectangular waveguide to coaxial cable transition is well
established up to 110 GHz. (2) No power splitting and directional coupling are needed. It
uses transmission mode. (3) Wireless application maybe valuable for some special
applications. The transmission resonance is much more controllable than fixed
transmission line in commercial AFM system. The position of the horn antenna in this
setup is determined by optimizing the transmission parameter from hom to conductive
AFM tip. For most hom antennas, maximum radiation is directed along z-axis of
antennas in free apace.
The Thevenin equivalent circuit of the AFM tip as receiving antenna is capacitor C in
series with surface impedance which can be modeled as a resister R and an inductor L in
parallel. The capacitance C is determined by the gap between tip and sample, the
dimensions of the tip and the electrical property (permittivity and conductivity) of the
sample. Because the AFM tip size is much smaller than microwave wavelength, quasi­
static theory is a good assumption. The capacitance because of these factors is in the
18
order of 10' F for AFM tip with 20 nm diameter. If the sample is semiconductor sample,
applying DC bias will add another series junction capacitance to the capacitance C. The
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86
resistance R includes radiation loss and ohmic loss in the sample. The L is related to
inductive component in high conductive sample.
The AFM conductive tip is used as an electrically short monopole antenna in this method.
Because of a uniform incident electric field Ein directed parallel to the AFM tip the open
circuit voltage is [3]
(5-2-1)
o
where effective height heff of the tip is determined by the current l{s) distribution along
the generating curve of the axis-symmetric probe. 7(0) is the current at the antenna
terminal. v(.v) is the angle between the tangent to the generating curve and the tip axis.
The effective height can be calculated after the charge density on the tip surface is
determined. The effective height of AFM tip and load impedance near AFM tip are two
most important design parameters to boost the S/N if AFM tip is treated as a monopole
antenna in transmission mode. Einis corresponding to Ee (0=7t/2) in E plane of hom
antenna. Since the current density is largest at the tip of the probe, Voc is localized with
spatial resolution in the same order of tip radius. Parasitic capacitance is smaller when
tip height is larger and width of cantilever beam is smaller. This is why extensive
fabrication efforts have been done to make sharper and higher tips.
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87
In the experiment the home made coax-rectangular wave guide transition is though a
probe at a small opening in the center of the wider side wall of waveguide about 1 cm
following hom antenna.
Schottky
Diode
AFM tip
sample
Horn antennaA k
RF
source *
r
i
j Modulatioij
i source
i
i
i
i
i
Figure 5-2-1. AFM compatible tips used as monopole antenna
(c) AFM tip as transmitting antenna
This method uses the conductive AFM tip as transmitting antenna instead of receiving
antenna. Stable synthesized microwave sweeper can be used as source. The detecting
principle is similar to setup (b).
5-3. Experimental results of microwave AFM system
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88
In the experiments we used 100 pm tripode scanner from ThermoMicroscopes. Several
special microwave probes had been developed. However in this experiment we only used
commercial conductive AFM tip to verify the proposed system prototypes. The radius of
these full metallic contact conductive tips was about 20 nm with a height about 10 pm.
The nominal cantilever width was 60 pm. The tip was intentionally tilted to get smaller
parasitic capacitance change in the measurement. The outputs of the pAFM were fed into
the analog inputs of ECU (Electronic Control Unit). Same image processing software was
used for pAFM and AFM images. The resolution of the images in experiments was
300x300 pixels. The contact force between AFM tip and sample was set to smaller than 10 nN. The forward and backward internal images and the forward and backward pAFM
images were monitored at same time.
In method 1 using commercially available components, systems based on TLA were
readily constructed up to 20 GHz. In this system the electrical length and loss from VCO
outputs to logarithmic amplifiers were made to be equal for channel A and channel B.
Input voltage of VCO was swept at 1 MHz and used as x axis of x-y mode of
oscilloscope. The spectrum (magnitude and phase) was monitored real time to choose the
most sensitive operation frequency when the AFM tip was scanning over the surface of
sample. The scanning speed of AFM tip was set to largest scanning speed (100 pm /s)
which AFM system can provide. This system was used to image a fresh cell sample. The
small contact force between tip and cell sample guaranteed no damage to the cell sample.
The pAFM image of cells was compared with AFM image as shown in figure 5-3-1. In
microwave image, the nuclei of the cell are visible which cannot be seen in standard
AFM images [4].
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iu u pim
50 p.m
0 (im
0.00 nm
1.50 um
(a)
Cell
100p.m
100nm
Cell
50 p.m
50 (nm
- J
0tJ.m
100pim
50 um
■10.000V
-3.389V
(b)
0 |im
100nm
50 nm
■10.000 V
-9.851V
(C)
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90
Figure 5-3-1. (a) cell AFM image; (b) Cell jtAFM (magnitude) image using method 1
at 1GHz; (c) Cell pAFM (phase) image using method 1 at 1GHz.
In method 2 we used X-band (8.2-12.4 GHz) pyramidal hom antenna. The horn produced
17dB forward gain. The AFM tip was carefully placed along the axis of the hom in E
Plane.
S v . ..
0 pim
50 pm
100 pm
Figure 5-3-2. pAFM image of semiconductor sample using method 2 at 10.5 GHz.
The bright line was SisN,*.
The S21 from the coax-hom transition to AFM tip showed the peaks of the spectmm can
be -lOdB when hom was about 10cm away from the tip. In order to increase the signal to
noise ratio, whole pAFM system was enclosed in a metal box to shield external radiation
source. The operation frequency was chosen near the peaks of S21. This was good for
feed-back or self oscillation based measurement. A Si3N 4line on Si substrate was
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91
scanned. Figure 5-3-2 shows pAFM image. pAFM image was clear and had many visible
details of the sample even when the mechanical quality of the tip was bad after a long
time (1 week) intensive usage.
Oum
(a)
10.17 tim
20.33 nm
(b)
0 nm
948.89 nm
1897.78 nm
(C)
Figure 5-3-3. (a) pAFM of sputtered 2000A Au on glass substrate using method 3 at
18GHz. (a) AFM of sputtered 2000A Au on glass substrate using method 3 at
18GHz. (c) The spatial resolution was smaller than 20 nm at the edge of the Au
layer.
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92
In method 3 we used same antenna as in method 2. The AFM image in figure 5-3-4a was
not clear because the Au layer was very thin and the feature size was very small.
However similar features between AFM images and p.AFM images can be identified.
Figure 5-3-3c is zoomed in image from 5-3-3b. The details of Au edge had spatial
resolution about 20nm in pAFM image.
References:
[1] Thomas. R.Hicks, Paul. D. Atherton, ‘The Nanopositioning Book’, ISBN
0953065804, UK, (1997).
[1] M. Tabib-Azar and Y. Wang, ‘Design and Microfabriation of Atomic Force
Microscope Compatible Scanning Near-Field Electromagnetic Probes.’ To be Presented
in 2002 ASME Conference, 17-22 New Orleans, Louisiana.
[2] Yaqiang Wang; Tabib-Azar, M., ‘Microfabricated near-field scanning microwave
probes’, Electron Devices Meeting, 2002. IEDM '02. Digest. International, pp. 905 -907
(2002).
[3] John P.Casey and Rajeev Bansal “Analysis and Optimization of an Electrically Small
Receiving Antenna” IEEE Trans. Electromag. Comp. Vol. 33(3), pp 197-204.(1991).
[4] Scott, Adina, Tao Zhang, Y, Wang and M.Tabib Azar, “Microwave Atomic Force
Microscopy”, ASNT 11th Annual Research Symposium, Portland, Oregon, March 18-22,
(2002 ).
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Chapter 6
Quantitative characterization of materials using EMP
Nano-metrology tools for conductivity, permittivity and material uniformity imaging are
of great importance in microfabrication and other high-tech industries. For example, high
spatial resolution sheet resistance characterization of semiconductors is important for
improving the yield of microfabrication techniques and performance of high frequency
integrated circuits. Moreover, in sub-micron complementary metal-oxide-semiconductor
(CMOS) devices, better current drivability is achieved by decreasing the contact
resistance between metal and source/drain. Annealing at higher temperature, ion
implantation of SiGe layer [1] and plasma doping [2] of shallow junctions are used for
this purpose. Real time monitoring the sheet resistance of wafers can be used to optimize
the above steps. The permittivity of substrate material will determine characteristic
impedance of transmission line and the Q factor of passive devices.
The tip can be soft-contact with samples to get rid of the effects of stand-off distance.
However the figure 4-2-1 has shown that different contact force which needs PID feed
back control itself can affect S ll drastically. Constant stand-off distance without z axis
feedback control is also used to map sheet resistance. These measurements will be
affected by the topography and alignment of samples in a ‘large’ area. The assumption of
constant stand-off distance without z axis feedback control during imaging is not
accurate. Figure 6-0-1 shows the gap between tip and ‘flat’ wafer surface that was
obtained by feed back control. The variation of the gap was about 70 (am in 15 mm circle
area that was not negligible. Non-contact EMP with z feed back or correction is proposed
93
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94
in this chapter. These non-contact EMPs are clean and have no damage to the underneath
samples.
Figure 6-0-1. Gap between probe tip and ‘flat’ GaAs wafer. The step size was 0.017
pm.
6-1. z decay of EMP probe in Smith chart
The input impedance spectrum of microwave resonator at different gap is valuable
information to determine spatial resolution, sensitivity of the probe and detection
schemes. Smith chart is two dimensional tool to show the impedance trend of tip-sample
interaction compared to z-decay curve of only magnitude or phase. The difference of
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input impedance in Smith chart is bigger. The signal is easier to detect. Figure 6-1-1
shows input impedance spectrum at different gaps for metal (red), 5880 Duroid substrate
(black) and GaAs wafer (green). The reference plane of the input impedance was just
before the gap capacitor. 60 equally spaced gaps were used and the largest gap was 510
pm in this plot. The frequency range was 970 MHz-990 MHz with 20 frequency points.
The resonator had -30 dB return loss at its resonant frequency. The experimental TLA
measurement system with 60dB dynamic range described in section 4-2 has been used in
the experiment.
j0.5
jo .z
0.2
0.5
-jO-2
Metal
-j0.5
Duroid
GaAs
Figure 6-1-1. z decay of metal (red), GaAs (green) and Duroid substrate (black).
In figure 6-1-1, we observe
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96
1) Near resonant frequency the input impedance becomes more inductive when the
frequency is larger than resonant frequency. The gap is smaller. The resonant
frequency is smaller. The tip-sample interaction is like a small additional wire
attached to the open end of the tip that is capacitive.
2) The impedance change because of gap almost follows same path in Smith chart. The
resonant frequency shift is very good measure of gap for metallic, dielectric sample
with constant permittivity and semiconductor sample without DC bias applied.
3) The input impedance paths for metal, GaAs (80 Q/square) and 0.785 mm 5880
Duroid sample (loss tangent=0.0009) are fairly close which means the capacitance
component of tip-sample interaction is dominant for this tip. Large dynamic range of
measurement system is important to characterize sheet resistance that determines the
real part of load impedance at the tip.
6-2. Permittivity characterization
The permittivity of substrate is a very important parameter to determine characteristic
impedance of transmission line and performance of fabricated devices. Non-uniformity
in dielectric material is utilized to get image of cells, detect corrosion and characterize
other interesting properties in materials. Non-contact EMP is preferred in these
applications.
In this thesis two methods are used to characterize permittivity. Stand-off distance is
estimated using matrix interpolation using two measured capacitance changes in the first
method. In the second method stand-off distance is made to be equal experimentally.
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97
The capacitance change matrix (CGP) which uses gap and permittivity as indexes for
specific tip is numerically estimated using algorithm discussed in chapter 5. From CGP
permittivity matrix (PCC) and topography matrix (TCC) which use capacitance at gap gl
and gap g2 (g2=gl-d, d is constant) can be estimated from CGP. Because the indexes Cgl
and C 2 are both monotonic versus gap, two-dimensional data interpolation algorithm
can be used to determine the permittivity and gap. Accurate determination of probe size
or a z-decay measurement above metallic ground is the only calibration step using this
method.
10
c 9
Dielectric constant
Figure 6-2-1. Measured permittivity versus the value using IPC-TM-550
The capacitance changes at gap gl and gap g2 were experimentally extracted and used as
indexes of PCC and TCC. The step of the gap used to generate the matrixes was 8.5 pm,
d was 17 pm and the dielectric constant step was 0.2 from 2-12 in our experiment. The
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98
measured permittivity versus the value from the manufactures was plotted in figure 6-2-1.
Manufactures used low spatial resolution IPC-TM-550 to measure these permittivity
values. Less than 7% difference between measured p permittivity and value provided by
manufactures has been achieved.
301
201
151
101
51
50
4,00
5.00
dielectric co n sta n t
Figure 6-2-2.Calibration curve of permittivity with air gap about 50 pm using true
log amplifier (TLA) based EMP.
Sometimes more straightforward calibration methods are needed instead of numerical
calculations and matrix interpolations. The calibration curve can be generated by
measuring magnitude or phase change using same stand-off distance for different
samples. Very good alignment and ‘flat’ surface are required in this method. Figure 6-2-2
shows a calibration curve at 50 pm stand-off. The insertion loss of resonator was about
30 dB and resonant frequency was 923 MHz in the air. A 200 pm diameter tungsten tip
was used in these experiments. The error was less than 0.5 mV in figure 6-2-2. The
voltage output of phase change was about 43 mV (~1.5dB in our system) when
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99
permittivity changes from 3 to 4.5. For typical TLA system (BiCMOS) the signal
stability is about 0.05 mV/ °C. So for this specific tip and TLA system the permittivity
sensitivity of the probe
(A s/ e )
was estimated to be 3.87xl0'4 at 50 pm stand-off. The
Figure 6-2-3 shows calibration curve of permittivity with same air gap using phase lockin amplifier based EMP (PLA). For this specific tip and PLA system the permittivity
sensitivity of the probe was estimated to be 8.07xl0'4 at 50 pm stand-off. 100 ms time
constant and noise level 250 nV / 4H z were used in the estimation. The power level of
the RF source was -10 dBm in the experiments.
3.2
2.8
£
.§2 6
> c
«OS
S
2.4
3.00
4.00
5.00
9.00
dielectric constant
Figure 6-2-3.Calibration curve of permittivity with air gap about 50 pm using phase
lock-in amplifier (PLA) based EMP.
6-3. Sheet resistance characterization
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Non-contact sheet resistance measurement using microwave and infrared light resulting
from ohmic heating has been developed [3] for semiconductors. These techniques and
other far-field techniques have spatial resolutions in the millimeter range. Quantitative
measurement of sheet resistance using evanescent microwave microscopy was
investigated by using contact measurement [4] or by monitoring frequency shift and
quality factor (Q) of an open-ended coaxial probe resonator [5]. Our group used fixed
frequency EMP to detect and image depletion regions in solar cell p-n junctions at f x or
near / 0 [6]. In that work, stand-off distance was not fixed and phase information was
omitted.
Furthermore, we note that the sheet resistance extracted from frequency shift and Q may
not be accurate. This is because it is not easy to differentiate between the load impedance
change at the tip and the impedance change of the resonator itself (coupling
capacitance/transformer between the feed-line and the resonator section) [7] when the
change due to the sheet resistance is very small. Experiments have shown impedance
change at the tip is comparable or even smaller than the impedance change of the
resonator itself at 1 GHz. Because of these considerations, it is desirable to use fixed
frequency evanescent microwave microscopy to make the sheet resistance extraction
more accurate. We demonstrate a fixed frequency quantitative evanescent microwave
microscopy of semiconductor samples with constant permittivity using a A/2 microstrip
resonator with resonant frequency of 1 GHz in this section.
The measurement apparatus is schematically shown in figure 3-1-1. The HP8731B
sweep synthesizer produces an amplitude modulated RF signal, with 10 KHz resolution,
that is applied to the high directivity circulator witch is capacitively coupled to the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
microstrip resonator through gap capacitor. The modulation frequency was 40 KHz in our
experiments. The insertion loss of the SI 1 at fo was largest when the tip was very close to
the underneath sample. In scanning experiments, the output of the circulator was detected
using a crystal detector, pre-amplified and amplified using a lock in amplifier
synchronized with the AM signal. This signal is shown as Vo was monitored instead of
return loss £0which is its complement. The x-y-z stage was controlled using the
computer that also controlled the experiment and collected the data. The step size of the
x-y-z motors was as small as 0.017 pm.
In our measurements the operation frequency of the probe was chosen to co-inside with
the resonant frequency of the probe at some reference point over the sample. Keeping the
operation frequency constant at that frequency, the probe’s z-coordinate was then
changed to minimize the probe output at any other point on the sample. Thus, probe’s zcoordinate was changed to keep the stand-off distance constant between the probe tip and
the sample. This procedure assumes that the probe’s resonant frequency is predominantly
determined by the stand-off distance and dielectric constant of underneath sample which
is verified in section 6-1.
The probe’s spatial resolution is directly determined by its tip curvature, sharp tips were
preferred for high spatial resolution imaging. In our current measurements, we used 150
pm diameter tip with flat apex rather than the atomically sharp tips that were used in the
past. The 2-mm long tip was attached to the microstripline resonator. The imaginary part
of load impedance (i.e., the capacitance) at the tip was evaluated using a network
analyzer shown in figure 6-3-1. The horizontal axis in this figure shows the tip-sample
stand-off distance with negative stand-off referring to the fact that the tip touches the
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102
sample and bends due to the applied force that applies a contact force and pushes the tip
against the sample’s surface.
0.45
209 ohm/sq
80ohm/sq
0.15
-51 -41 -31 -20 -10 0
10 20 31 41 51
Gap (um)
Figure 6-3-1. Capacitive part of the load impedance at the tip as a function of
stand-off distance obtained using a network analyzer. Negative stand-off distance
refers to tip-sample contact that also results in tip bending and application of
contact force.
According to figure 6-3-1, there is an abrupt change in the value of the tip-sample
capacitance when the tip stops touching the sample. Two semiconducting samples were
used in these experiments with resistivities of 209 and 80 Q/square. Impedance
difference between 80 Q/square sample and 209 ^square sample as detected by the
resonant probe was only significant after the tip contacted the sample. This so-called
“soft touch” mode operation is used by other researchers in the past and it is undesirable
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103
in ultra-clean semiconductor industries and difficult to get constant contact force during
imaging process.
The loss measurement monitors the magnitude of the voltage output Vo of lock-in
amplifier. If the amplitude of input RF signal of feed-line is Vin, we can get
z,„ Z0
vin- v 0
(3)
Vin + V0
Both real and imaginary parts of Z l can shift f 0 and change Q factor. If the permittivity
of the samples is fixed,
Vo
at the fixed operation frequency (that co-insides with
fo)
is
directly affected by the sheet resistance. Clearly, to properly calibrate this probe, the
stand-off distance should be taken into account.
We used silicon (esj =11.9) samples with different sheet resistance that were
independently measured using the four-point probe technique. The samples had a wide
range of four-point probe sheet resistance from 1 62/square to 25062/square.
1058
1057.5
„
rsl
1057
209 ohm /sq
80 ohm /sq
4.6 ohm /sq
1056.5
1056
1055.5
50
10 0
z (um )
150
200
Figure 6-3-2. Resonant frequency (fo) as a function of the stand-off distance is three
different samples.
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104
Figure 6-3-2 shows resonant frequency as a function of stand-off for three different
silicon wafers ranging in sheet resistance from 4.6 £2/square to 209 Q/square. Although
there is a small dependence on the sheet resistance, the fo seems to be dominantly
determined by the stand-off distance rather than the samples’ sheet resistance as
expected. In contrast, Vo as a function of stand-off distance, as shown in figure 6-3-3,
exhibited a very strong sample dependence.
70
60
50
>
E,
>
209 o h m /s q
80 o h m /s q
4.6 o h m /s q
40
*»
30
20
10
50
150
200
Figure 6-3-3. Probe’s output voltage at the resonant frequency (V0) as a function of
stand-off distance for different samples. The sheet resistance of sample is shown in
inset.
The measured Vo as a function of sheet resistance at three different stand-off distances of
20, 50 and 100 pm are shown in figure 6-3-4 with better than 1% reproducibility and
excellent signal stability and the error bar was less than 1%. In these measurements the
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105
input power of the RF signal was fixed at 0 dBm. The amplitude of the modulation signal
was 0.5V. The maximum output of the microwave detector was 13.9 mV. The output
signal of the detector at resonant frequency was on the order of microvolt (pV). The
dynamic range of this measurement apparatus was more than 80 dB (in contrast, the
experimental TLA system has 60 dB dynamic range) which expected in observation 3 in
section 6-1.
so
75
70
65
60
>
E
X
5
55
50
20 pm
50 pm
100 pm
45
40
35
30
20
40
60
80
100
120
140
160
180
200
R (o h m /sq )
Figure 6-3-4. V0 as a function of sheet resistance at three different stand-off
distances.
The effect of the stand-off distance was to reduce the change in the microwave sensor
output as a function of sample’s sheet resistance. The sheet resistance calibration should
take into account the stand-off distance as well as the operation frequency to account for
microwave impedance of the sample. The effect of stand-off on the calibration curve is
shown in figure 6-3-5.
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106
Best noise level of our sensor was about 100 nV / 4~Hz using 100 ms time constant at the
output stage of the lock-in amplifier. Thus, we estimate the sheet resistance sensitivity of
9
9
the probe (Apa/pCT) to be 3x10' at 210 pm stand-off, 1.5x10' at 50 pm stand-off and
5x10' at 5 pm stand-off for the 80fysquare sheet resistance at 1 GHz. Better sensitivity
is expected by adding a custom matching network near tip region.
£40
300
200
200
100
100
R (ohm/Sq)
Figure 6-3-5. V 0 as a function o f sheet resistance and stand-off distance.
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107
Log-Scale
p
X1
15
10
5
0
-5
-10
-15
2.17E6
1.59E6
-20
Figure 6-3-6. Sheet resistance map using non-contact EMP and contact CoReMa
technique.
9
3500
12000
Figure 6-3-7. Sheet resistance map of conductive SiC
This technique was used to quantitatively map the sheet resistance of 6H SiC wafer.
Figure 6-3-6 shows side-by-side two sheet resistance maps taken from two sister-wafers
cut from the same SiC boule # A5-197. In the left picture is the map of wafer A5-197-14
produced by technique discussed in this section; on the right is the map produced by a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
capacitance technique (CoReMa) which is a contact technique and large DC voltage
(>100 V) is applied to a MOS structure. The resemblance is striking. The EMP technique
has better spatial resolution and larger dynamic range.
Figure 6-3-7 shows a resistivity map of a conductive SiC wafer # 434-2. A higher sheet
resistance core visible in the center is quite characteristic for these N-doped crystals
because of their manufacturing process.
The TLA based EMP system also can be used to characterize the sheet resistance. The
phase signal is used as the set-point in a PID loop in this case.
1
0.5
0
>
tjO.5
o
>
-1
-1.5
"20
50
100
150
200
R (o h m .cm )
Figure 6-3-8. Sheet resistance calibration curve of TLA based EMP system. 200 mV
DC bias and 100 times amplification have been used.
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109
0.64
0.62
0.6
>
0.58
O
>
0.56
0.54
0.52
0
50
100
R (o h m .c m )
150
200
Figure 6-3-9. Sheet resistance calibration curve of PLA based EMP system. RF
power was -10 dBm. 5000 times amplification has been used.
Figure 6-3-8 shows the calibration curve of sheet resistance using experimental TLA
system and figure 6-3-9 shows the calibration curve of PLA based EMP system at 50 pm
stand-off. A 200 pm diameter tungsten tip was used in these experiments. In the
measurement frequency was fixed at 922.6 MHz. The error of TLA measurements was
about 25 mV. For CMOS devices the error can be decrease to less than 5 mV by carefully
controlling the environmental temperature. The average slope of this calibration curve
was about 14 mV/Q*cm. Without changing the parameters of microstrip resonators,
phase lock-in amplifier based EMP system (figure 3-1-1) was used to calibrate same
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110
samples. The measured error of PLA measurements was about 2.5 mV. The average
slope of this calibration curve was about 0.6 mV/Q*cm. The sheet resistance sensitivity
of TLA system was at least 2.3 times better than the sensitivity of PLA based system in
this experiment.
Sheet resistance of sputtered Au layers on glass have been calibrated and summarized in
figure 6-3-10 (TLA) and 6-3-11 (PLA). 0.2 Q«cm has been detected using TLA based
EMP system with 200 pm diameter tungsten tip. For phase lock-in based EMP system
this error is relatively larger as shown in 6-3-11.
1.6
1.55
1.5
01.35
1.3
1.25
1.2
1.15
0.5
1.5
R (o h m .c m )
Figure 6-3-10.Sheet resistance calibration curve of TLA based EMP system. 100 mV
DC bias and 100 times amplification have been used. The samples were sputtered
gold layers.
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111
610
605
>
£
600
595
590
585
0.5
1.5
R (o h m .c m )
Figure 6-3-1 l.Sheet resistance calibration curve of TLA based EMP system. RF
power was -10 dBm. AM modulation index was 5 %. 10000 times amplification was
used.
6-4. Proposed future work
1) Only one probe should be used or one probe is much longer than reference probe.
Alignment may be difficult if two probes with nearly same length are used. The good
reference probe will create best DC bias of the outputs and keep sensitive response to the
load impedance change at the tip.
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112
2) The matching circuit near the tip region is very important and should be carefully
designed and implemented. The probe that is sensitive to permittivity may not be
sensitive to conductivity too. Specialized probes enable more accurate and sensitive
measurement.
3) The response of the sensor should be monotonic versus gap between tip and sample for
accurate data interpolation in calibration procedure.
4) The signal response should be easy for feed back control of z axis. It is better to
calibrate the stand-off distance using phase signal.
References:
[1] H. Kurata, K. Suzuki, T. Futatsugi, and N. Yokoyama, ‘Shallow p-type SiGeC layers
synthesized by ion implantation of Ge, C, and B in Si’, Appl. Phys. Lett. Vol 75, 1568
(1999).
[2] S.B. Felch, Z. Fang, B. W. Koo, R. B. Liebert, S. R. Walther, and D. Hacker,
Surface and Coatings Technology, Vol. 156, pp229-236 (2002).
[3] Krzysztof Kempa, J. Martin Rommel, Roman Litovsky, Peter Becla, Bohumil Lojek,
Frank Bryson, and Julian Blake, ‘Noncontact sheet resistance measurement technique for
wafer inspection’, Rev. Sci. Instrum. Vol. 66, 5577 (1995).
[4] M. Golosovsky, A. Galkin, and D. Davidov, IEEE trans. Microwave Theory Tech.
Vol. 44, 1390 (1996).
[5] D. E. Stemhaucer, C. P. Vlahacos, S. K. Dutta, B. J. Feenstra, F. C. Wellstood, and
Steven M. Anlage, ‘Appl. Phys. Lett. Vol. 72, 861 (1998).
[6] M. Tabib-Azar and D. Akinwande, Rev. Sci. Instrum. V ol 71, 1460 (2000).
[7] T. C. Edwards, “Foundations of interconnect and microstrip design” Chichester, New
York, John Wiley, (2000).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.