Scanning techniques for local characterization of conducting and insulating films are attracting much interest. Many efforts have been made on devel- oping microwave near-field scanning techniques, and various types of near-field microwave micro- scopes have been developed for different pur- poses (Rosner and van der Weide 2002). The near- field microwave microscopes generally fall into the resonant type and the nonresonant type. In a resonant near-field microwave microscope, the probe is a resonator, and it works on the basis of resonant-perturbation theory. While a nonres- onant near-field microwave microscope is usu- ally based on reflection method, and the prop- erties of a sample are obtained from the reflec- tivity due to the presence of the sample. Here we focus on nonresonant near-field microwave microscopes, and the discussions on resonant near- field microwave microscopes can be found in Chapter 6.
In principle, any type of transmission lines can be used to develop near-field microwave micro- scopes. In a near-field microwave microscope developed from rectangular waveguide, the most important part is an aperture in the form of a nar- row rectangular slit. As shown in Figure 3.41, a thin metal diaphragm is mounted across a rect- angular waveguide, and a rectangular slit is cut in the diaphragm parallel to the wide side. For transverse electric (TE) mode propagation, this slit is transparent at a certain wavelength λ,
a a′
b′ b
Figure 3.41 A rectangular slit on a metal diaphragm mounted across a rectangular waveguide
which can be found by solving the following equation (Golosovskyet al. 1996)
a bã
1−
λ 2a
2
= a′ b′ ã
1−
λ 2a′
2
(3.111)
where λis the free-space wavelength,aandbare the wide and narrow sides of the waveguide, and a′ and b′ are the wide and narrow sides of the slit. Equation (3.111) has solution even for arbi- trarily narrow slit. When b′ approaches zero, the solution forλ approaches 2a′. We can also take a rectangular waveguide terminated by a rectangu- lar slit window as a junction of two rectangular waveguides with different dimensions. The reflec- tion from such a junction is determined by the waveguide impedance (Golosovskyet al. 1996)
Z= Z0π b′ 2a′
1−[λ/(2a′)]2 (3.112) where Z0 is the free-space impedance (Z0= 377). By taking the slit as a section of a rectangular waveguide, we can find that for given a′and arbitrarily smallb′, there is always a certain wavelength λ≈2a′ at which Z≈Z0. Therefore, even a very narrow slit may be matched to free space at a narrowband.
When a conducting surface is in the near-field zone of the slit, the microwave is reflected mostly
from the region under the slit. Since reflection from a conducting surface is determined by the resistiv- ity, by measuring the amplitude and phase of the reflected wave while raster scanning the surface, it is possible to map the microwave resistivity of the surface. For conductive layers with thicknesses much larger than the skin depth, we can get sur- face impedance, while for thin layers, we can get sheet resistance. In the determination of microwave resistivity, it is necessary to measure layer thick- ness independently.
In measurement, the sample is placed close to the slit. If the distance between the slit and the sample is smaller than the narrow side of the slit, the spatial resolution in the direction perpendicular to the slit is determined by the narrow side of the slit b′ and maybe as small as λ/100. The spatial resolution in the direction parallel to the slit is determined by the field pattern in the slit and by the wide side of the slit a′, and for a flat slit it is about λ/2.
However, the resolution in this direction may be considerably improved (down toλ/60) if the slit is fabricated in a curved surface. This improvement originates from the strong decay of the field upon increasing distance from the slit, so that the central part of the slit, which is most close to the tested surface, plays a dominant role. Generally speaking, the spatial resolutions in the directions of the wide and narrow sides of the slit are different. However, by doing scans in several directions and using deconvolution techniques and image processing, it is possible to achieve two- dimensional resistivity maps with equal resolution in all directions.
Figure 3.42 shows a dual-frequency electro- magnetic scanning probe for quantitative map- ping of sheet resistance of conducting films (Lann et al. 1998). The high-frequency (82 GHz) mode is used for image acquisition, while the low- frequency (5 MHz) mode is used for distance con- trol. The key component is a thin-slit aperture in a convex end plate of a rectangular waveguide.
This aperture operates as a transmitting/receiving antenna at 82 GHz. A fundamental TE wave is excited in the waveguide and the reflected wave is analyzed. The electric field lines in the TE mode stretch from one side of the slit to the
Metal base Substrate
Conducting film Dielectric spacer
Dielectric screw WR-12 waveguide
mm-wave in/out
5-MHz oscillator
Clamp (optional)
Figure 3.42 A mm-wave near-field probe with a capacitive distance control (Lann et al. 1998). Source:
Lann, A. F. Golosovsky, M. Davidov, D. and Frenkel, A. (1998). “Combined millimeter-wave near-field micro- scope and capacitance distance troll for the quanti- tive mapping of sheet resistance of conducting layers”, Applied Physics Letters,73(19), 2832–2834
Probe Probe
E E
(a) (b)
Figure 3.43 Electric fields near the slit. (a) Electric field of mm-wave operation (inductive mode) and (b) electric field of rf operation (capacitive mode).
Source: Lann, A. F. Golosovsky, M. Davidov, D. and Frenkel, A. (1998). “Combined millimeter-wave near- field microscope and capacitance distance troll for the quantitive mapping of sheet resistance of conducting layers”,Applied Physics Letters,73(19), 2832–2834
other, as shown in Figure 3.43(a), and they are mostly tangential to the sample surface and induce currents in the sample. The magnitude of the induced currents is determined by the sample resistivity and thickness. In this high-frequency operation mode, the probe behaves inductively and provides information on the resistance of the sample.
In order to enable a simultaneous low-frequency operation mode, a short waveguide section containing the probe is electrically isolated from the rest of the mm-wave circuitry by a thin mylar sheet, as shown in Figure 3.42. A 5-MHz oscil- lator is connected to the waveguide section with the probe, while the ground of the oscillator is connected to the rest of the mm-wave circuitry and to the conducting sample. As the slit size for the rf-operation mode is much smaller than the rf wavelength, the surface of the probe is equipotential. So, as shown in Figure 3.43(b), the electric field lines stretch from the probe to the sample surface, and they are almost normal to the sample and induce charges rather than cur- rents. Thus the probe behaves capacitively, and is almost insensitive to the sample resistance.
The resonant frequency of the oscillator strongly depends upon the probe-sample capacitance that is determined by the probe-sample distance. There- fore by measuring the resonant frequency of the oscillator, the probe-sample distance can be pre- cisely controlled.
REFERENCES
Anderson, L. S. Gajda, G. B. and Stuchly, S. S. (1986).
“Analysis of an open-ended coaxial line sensor in layered dielectrics”,IEEE Transactions on Instrumen- tation and Measurement,35(1), 13–18.
Anderson, L. S. Gajda, G. B. and Stuchly, S. S. (1994).
“Dielectric measurements using a rational functional model”,IEEE Transactions on Microwave Theory and Technique,42, 199–204.
Athey, T. W. Stuchly, M. A. and Stuchly S. S. (1982).
“Measurement of radio-frequency permittivity of biological tissues with an open-ended coaxial line- Part I”,IEEE Transactions on Microwave Theory and Techniques,30(1), 82–86.
Baker-Jarvis, J. (1990). Transmission/reflection and short-circuit line permittivity measurements, NIST Technical Note 1341, National Institute of Standards and Technology, U.S. Department of Commerce.
Baker-Jarvis, J. Janezic, M. D. Grosvenor, J. H. Jr. and Geyer, R. G.
(1993). Transmission/Reflection and Short-Circuit Line Methods for Measuring Permittivity and Perme- ability, NIST Technical Note 1355 (revised), National Institute of Standards and Technology, U.S. Depart- ment of Commerce.
Baker-Jarvis, J. Domich, M. D. and Geyer, R. G. (1994).
“Analysis of an open-ended coaxial probe with lift- off for nondestructive testing”,IEEE Transactions on Instrumentation and Measurement,43(5), 711–718.
Bakhtiari, S. Ganchev, S. I. and Zoughi, R. (1994).
“Analysis of radiation from an open-ended coax- ial line into stratified dielectrics”, IEEE Transac- tions on Microwave Theory and Techniques, 42(7), 1261–1267.
Berube, D. Ghannouchi, F. M. and Savard, P. (1996).
“A comparative study of four open-ended coaxial probe models for permittivity measurements of lossy dielectric biological materials at microwave frequen- cies”, IEEE Transactions on Microwave Theory and Techniques,44(10), 1928–1934.
Booth, J. C. Wu, D. H. and Anlage, S. M. (1994). “A broadband method for the measurement of the sur- face impedance of thin films at microwave fre- quencies”, Review of Scientific Instruments, 65 (6), 2082–2090.
Brady, M. M. Symons, S. A. and Stuchly, S. S. (1981).
“Dielectric behavior of selected animal tissues in vitro at frequencies from 2 to 4 GHz”,IEEE Transactions on Biomedical Engineering,28(3), 305–307.
Brekhovskikh, L. M. (1980). Waves in Layered Media, 2ndedition, Academic Press, New York.
Bucci, O. M. and Franceschetti, G. (1974). “Input admit- tance and transient response of spheroidal antennas in dispersive media”,IEEE Transactions Antennas and Propagation,22(4), 526–536.
Burdette, E. C. Clain, F. L. and Seals, J. (1980). “In vivo probe measurement technique for determining dielectric properties at VHF through microwave frequencies”, IEEE Transactions on Microwave Theory and Techniques,28, 414–427.
Courtney, C. C. (1998). “Time-domain measurement of the electromagnetic properties of materials”, IEEE Transactions on Microwave Theory and Techniques, 46(5), 517–522.
Courtney, C. C. and Motil, W. (1999). “One-port time- domain measurement of the approximate permittivity and permeability of materials”, IEEE Transactions on Microwave Theory and Techniques, 47(5), 551–
555.
Deschamps, A. (1972). “Impedance of an antenna in a conducting medium”,IEEE Transactions on Antennas and Propagation,10, 648–650.
Fan, S. Staebell, K. F. and Misra, D. (1990). “Static analysis of an open-ended coaxial line sensor in lay- ered dielectrics”,IEEE Transactions on Instrumenta- tion and Measurement,39, 435–437.
Gajda, G. and Stuchly, S. S. (1983). “An equivalent cir- cuit of an open-ended coaxial line”, IEEE Transac- tions on Instrumentation and Measurement, 32 (4), 506–508.
Ganchev, S. I. Qaddoumi, N. Bakhtiari, S. and Zoughi, R. (1995). “Calibration and measurement of dielec- tric properties of finite thickness composite sheets
with open-ended coaxial sensors”, IEEE Transac- tions on Instrumentation and Measurement, 44 (6), 1023–1029.
Ghannouchi, F. M. and Bosisio, R. G. (1989). “Mea- surement of microwave permittivity using six-port reflector with an open-ended coaxial line”, IEEE Transactions on Instrumentation and Measurement, 38(2), 505–508.
Golosovsky, M. Galkin, A. and Davidov, D. (1996).
“High-spatial resolution resistivity mapping of large- area YBCO films by a near-field millimeter-wave microscope”, IEEE Transactions on Microwave The- ory and Techniques,44(7), 1390–1392.
Huang, Y. (2001). “Design, calibration and data inter- pretation for a one-port large coaxial dielectric mea- surement cell”,Measurement Science and Technology, 12(1), 111–115.
Kalachev, A. A. Kukolev, I. V. Matytsin, S. M. Novo- grudsiy, L. N. Rozanov, K. N. and Sarychev, A. K.
(1991). “The methods of investigation of complex dielectric permittivity of layer polymers contain- ing conductive inclusions”, in Optical and Electri- cal Properties of Polymers, Materials Research Soci- ety Symposia Proceedings, Vol. 214, J. A. Emerson and J. M. Torkelson, Ed., Materials Research Society, Pittsburgh, pp. 119–124.
Keam, R. B. and Holdem, J. R. (1997). “Permittivity measurements using a coaxial-line conical-tip probe”, Electronics Letters,33(5), 353–355.
Langhe, P. D. Martens, L. and Zutter, D. D. (1994).
“Design rules for an experimental setup using an open-ended coaxial probe based on theoretical modeling”, IEEE Transactions on Instrumentation and Measurement,43(6), 810–817.
Lann, A. F. Golosovsky, M. Davidov, D. and Fren- kel, A. (1998). “Combined millimeter-wave near-field microscope and capacitance distance troll for the quantitive mapping of sheet resistance of conducting layers”, Applied Physics Letters, 73 (19), 2832–
2834.
Levine, H. and Papas, C. H. (1951). “Theory of the circular diffraction antenna”, Journal of Applied Physics,22, 29–43.
Marcuvitz, N. (1965). Waveguide Handbook, Dover Publications, New York.
Otto, G. P. and Chew, W. C. (1991). “Improved cali- bration of a large open-ended coaxial probe for dielec- tric measurement”,IEEE Transactions on Instrumen- tation and Measurement,40(4), 742–746.
Panariello, G. Verolino, L. and Vitolo, G. (2001). “Effi- cient and accurate full-wave analysis of the open- ended coaxial cable”, IEEE Transactions on Micro- wave Theory and Techniques, 49 (7), 1304–
1309.
Pournaropoulos, C. L. and Misra, D. K. (1994). “A study on the coaxial aperture electromagnetic sensor and its application in material characterization”,IEEE
Transactions on Instrumentation and Measurement, 43(2), 111–115.
Pournaropoulos, C. L. and Misra, D. K. (1997). “The co-axial aperture electromagnetic sensor and its appli- cation in material characterization”,Measurement Sci- ence and Technology,8(11), 1191–1202.
Razaz, M. and Davies, J. B. (1979). “Capacitance of the abrupt transition from coaxial-to-circular waveguide”, IEEE Transaction on Microwave Theory and Tech- niques,27(6), 564–569.
Rosner, B. T. and van der Weide, D. W. (2002). “High- frequency near field microscopy”,Review of Scientific Instruments,73(7), 2505–2525.
Rzepecka, M. A. and Stuchly, S. S. (1975). “A lumped capacitance method for the measurement of the per- mittivity in the frequency and time domain – a further analysis”,IEEE Transactions on Instrumentation and Measurement,24(1), 27–32.
Saed, M. A. Riad, S. M. and Elshabini-Riad, A. (1989).
“Wide-band measurement of the complex permittiv- ity of dielectric materials using a wide-band cavity”, IEEE Transactions on Instrumentation and Measure- ment,38(2), 488–495.
Saed, M. A. Riad, S. M. and Davis, W. A. (1990).
“Wide-band characterization using a dielectric filled cavity adapted to the end of a transmission line”, IEEE Transactions on Instrumentation and Measure- ment,39(3), 485–489.
Smith, G. S. and Nordgard, J. D. (1985). “Measurement of the electrical constitutive parameters of materials using antennas”, IEEE Transactions Antennas and Propagation,33(7), 783–792.
Staebell, K. F. and Misra, D. (1990). “An experimen- tal technique for in vivo permittivity measurement of materials at microwave frequencies”, IEEE Transac- tions on Microwave Theory and Techniques, 38 (3), 337–339.
Stuchly, M. A. Athey, T. W. Samaras, C. M. and Tay- lor, G. E. (1982). “Measurement of radio frequency permittivity of biological tissues with an open-ended coaxial line: Part II-experimental results”, IEEE Transactions on Microwave Theory and Techniques, 30(1), 87–91.
Stuchly, S. S. Sibbald, C. L. and Anderson, J. M.
(1994). “A new admittance model for open-ended waveguides”,IEEE Transactions on Microwave The- ory and Techniques,42(2), 192–198.
Stuchly, M. A. and Stuchly, S. S. (1980). “Coaxial line reflection methods for measuring dielectric properties of biological substances at radio and microwave frequencies – a review”, IEEE Transac- tions on Instrumentation and Measurement, 29 (3), 176–183.
Umari, M. H. Ghodgaonkar, D. K. Varadan, V. V. and Varadan, V. K. (1991). “A free-space bistatic cali- bration technique for the measurement of parallel and perpendicular reflection coefficients of planar
samples”,IEEE Transactions on Instrumentation and Measurement,40(1), 19–24.
Von Hippel, A. R. Ed. (1995).Dielectric Materials and Applications, Artech House, Boston.
Wang, Y. and Fan, D. (1994). “Accurate global solu- tions of EM boundary-value problems for coaxial radiators”, IEEE Transactions Antennas and Propa- gation,42(5), 767–770.
Wang, S. J. Niu, M. D. and Xu, D. M. (1998). “A frequency-varying method for simultaneous mea- surement of complex permittivity and permeability with an open-ended coaxial probe”, IEEE Transac-
tions on Microwave Theory and Techniques, 46(12), 2145–2147.
Xu, Y. S. Ghannouchi, F. M. and Bosisio, R. G. (1992).
“Theoretical and experimental study of measure- ment of microwave permittivity using open-ended elliptical coaxial probes”, IEEE Transactions on Microwave Theory and Techniques, 40 (1), 143–
150.
Zheng, H. M. and Smith, C. E. (1991). “Permittivity measurements using a short open-ended coaxial line probe”,IEEE Microwave and Guided Wave Letters,1 (11), 337–339.
Transmission/Reflection Methods
In a transmission/reflection method, the sample under test is inserted into a segment of trans- mission line, and the permittivity and permeabil- ity of the sample are derived from the reflec- tion and transmission of the sample-loaded unit.
After analyzing the working principle and calcu- lation algorithms, we discuss four types of trans- mission/reflection methods, including coaxial air- line method, hollow metallic waveguide method, surface-wave method and free-space method. We then make a brief review of the modifications of the conventional transmission/reflection methods.
At the end of this chapter, we discuss the measure- ment of complex conductivity of superconductors using transmission/reflection methods.