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Principles of Near-Field Microwave Microscopy

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1 Introduction1.1 What is the “Near-Field”? 2 General Principles of Microwave Microscope Design2.4.2 Atomic Force based distance control2.4.3 Scanning Tunneling based distance control3 Detailed description of one microscope4 Theory of Near-Field Microwave Microscopy4.1 Lumped Element Model for Sample-to-Tip Interaction4.5 Full Wave Analysis4.6 Cavity Perturbation ApproachPrinciples of Near-Field Microwave Microscopy Steven M. Anlage, Vladimir V. Talanov, and Andrew R. Schwartz Published as: Steven M. Anlage, Vladimir V. Talanov, Andrew R. Schwartz, "Principles of Near-Field Microwave Microscopy," in Scanning Probe Microscopy: Electrical and Electromechanical Phenomena at the Nanoscale, Volume 1, edited by S. V. Kalinin and A. Gruverman (Springer-Verlag, New York, 2007, ISBN: 978-0-387-28667-9), pages 215-253. Near-field microwave microscopy is concerned with quantitative measurement of the microwave electrodynamic response of materials on length scales far shorter than the free-space wavelength of the radiation. Here we review the basic concepts of near-field interactions between a source and sample, present an historical introduction to work in the field, and discuss a novel quantitative modeling approach to interpreting near-field microwave images. We discuss the spatial resolution and a number of concrete applications of near-field microwave microscopy to materials property measurements, as well as future prospects for new types of microscopy. 1 Introduction Much of our understanding of materials comes from studying the interaction of electromagnetic fields with matter. The optical properties of metals, semiconductors and dielectrics have revealed many aspects of charge and lattice dynamics in condensed matter and the study of materials at lower frequencies has also been a fruitful area of investigation [1]. For example, early evidence for a gap in the spectroscopic properties of superconductors came from microwave transmission experiments. Evidence for case-II coherence effects was also seen in measurements of the complex conductivity of superconductors [2]. The study of magnetization dynamics in ferromagnets came through measurements of ferromagnetic resonance and anti-resonance at microwave frequencies [3-5]. One thing that all of these techniques have in common is that they are carried out with measurement systems that are on the scale of the free-space wavelength of the radiation employed. For example, transmission experiments are done in the far-field of a source, and typically require a sample on the scale of the wavelength in size. Many other experiments are carried out in resonant cavities, which are on the order of the wavelength in at least one dimension. One result is that the electrodynamic properties of the sample are averaged overS. M. Anlage, V. V. Talanov, A. R. Schwartz 2 macroscopic length scales. The properties of the material may in fact be varying on much shorter length scales, even into the nanometer range. Hence to measure the intrinsic response, such traditional measurements require remarkably large, pure and homogeneous samples to study. Most materials of interest today are complex multi-component compounds or nano-scale composites and can rarely be made homogeneous on the mm- or cm-length scales required for traditional electrodynamics measurements. In addition, the typical dimensions of devices into which some of these functional materials are integrated are orders of magnitude smaller than the wavelength at the frequency of operation of the device. Additional constraints of traditional measurements are imposed by the sample geometry. Ideally, one would like to measure the properties of ellipsoidally-shaped samples to eliminate de-magnetization and de-polarization effects, but such samples are rarely available, particularly for novel and interesting materials. Thin film samples often have such large de-magnetization factors that results of measurements in perpendicular fields are extremely challenging to interpret, particularly on anisotropic materials. A related issue concerns the edges and corners of superconductors in the Meissner state, at which screening currents are known to become singular [6]. These extraordinarily large current densities result in an extreme type of weighted average of the sample properties. The properties of edges and corners, which may not be representative of the bulk, will dominate such measurements. This is an issue for single crystal, ceramic and thin film samples. A new paradigm of electrodynamics measurements in condensed matter physics has emerged in recent years. This is associated with the concept of so-called near-field interactions between a source and a sample in which near-zone fields and/or evanescent waves with high spatial frequency are created and interact with the sample. The recovery of these signals gives insight into the localized electrodynamic properties of the sample. The art of near-field microwave microscopy of materials is one aspect of this new paradigm. We are motivated in part by the deficiencies of traditional far-field measurements, as outlined above. We are also motivated by the desire to examine new physics on nanometer-length scales present in highly-correlated electron systems and biological systems, as well as technologically motivated investigations of semiconductor and other functional materials on the nm-scale. In this review we arbitrarily confine ourselves to situations where the following four conditions are simultaneously met: (1) measurements are performed at frequencies between 100 MHz and 100 GHz (this ranges from the bottom of A-band to the top of M-band in the EU/NATO spectrum or I-band to W-band in the IEEE US electronic warfare spectrum); (2) measurements of material properties are performed; (3) there is scanning of the probe relative to the sample; and (4) the spatial resolution of the measurement is substantially (≤ 10-1) less than the free-space wavelength. Even with such stringent constraints, there is a great deal of interesting work to discuss. Although we have attempted to be comprehensive in our coverage of this field, it is inevitable that important work has been accidentally overlooked. WePrinciples of Near-Field Microwave Microscopy 3 apologize to the reader in advance for these oversights. Some other review articles on microwave near-field imaging that are of possible interest to the reader include references [7], [8] and [9]. We do not


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