A Scanned Perturbation Technique For Imaging Electromagnetic Standing Wave Patterns of Microwave Cavities

We have developed a method to measure the electric field standing wave distributions in a microwave resonator using a scanned perturbation technique. Fast and reliable solutions to the Helmholtz equation (and to the Schrodinger equation for two dimensional systems) with arbitrarily-shaped boundaries are obtained. We use a pin perturbation to image primarily the microwave electric field amplitude, and we demonstrate the ability to image broken time-reversal symmetry standing wave patterns produced with a magnetized ferrite in the cavity. The whole cavity, including areas very close to the walls, can be imaged using this technique with high spatial resolution over a broad range of frequencies.Comment: To be published in Review of Scientific Instruments,September, 199

Microwave shielding of transparent and conducting single-walled carbon nanotube films

The authors measured the transport properties of single-walled carbon nanotube (SWCNT) films in the microwave frequency range from 10 MHz to 30 GHz by using the Corbino reflection technique from temperatures of 20-400 K. Based on the real and imaginary parts of the microwave conductivity, they calculated the shielding effectiveness for various film thicknesses. Shielding effectiveness of 43 dB at 10 MHz and 28 dB at 10 GHz are found for films with 90% optical transmittance, which suggests that SWCNT films are promising as a type of transparent microwave shielding material. By combining their data with those from the literature, the conductivity of SWCNT films was established in a broad frequency range from dc to visible.Comment: 4 pages, 4 figure

Noncontact electrical metrology of Cu/low-k interconnect for semiconductor production wafers

We have demonstrated a technique capable of in-line measurement of dielectric constant of low-k interconnect films on patterned wafers utilizing a test key of ~50x50 \mu m in size. The test key consists of a low-k film backed by a Cu grid with >50% metal pattern density and <250 nm pitch, which is fully compatible with the existing dual-damascene interconnect manufacturing processes. The technique is based on a near-field scanned microwave probe and is noncontact, noninvasive, and requires no electrical contact to or grounding of the wafer under test. It yields <0.3% precision and 2% accuracy for the film dielectric constant

A near-field scanned microwave probe for spatially localized electrical metrology

We have developed a near-field scanned microwave probe with a sampling volume of approximately 10 micron in diameter, which is the smallest one achieved in near-field microwave microscopy. This volume is defined to confine close to 100 percent of the probe net sampling reactive energy, thus making the response virtually independent on the sample properties outside of this region. The probe is formed by a 4 GHz balanced stripline resonator with a few-micron tip size. It provides non-contact, non-invasive measurement and is uniquely suited for spatially localized electrical metrology applications, e.g. on semiconductor production wafers.Comment: 6 pages, 3 figures, submitted to Appl. Phys. Let

Superconducting RF Metamaterials Made with Magnetically Active Planar Spirals

Superconducting metamaterials combine the advantages of low-loss, large inductance (with the addition of kinetic inductance), and extreme tunability compared to their normal metal counterparts. Therefore, they allow realization of compact designs operating at low frequencies. We have recently developed radio frequency (RF) metamaterials with a high loaded quality factor and an electrical size as small as $\sim$$\lambda$658, ($\lambda$ is the free space wavelength) by using Nb thin films. The RF metamaterial is composed of truly planar spirals patterned with lithographic techniques. Linear transmission characteristics of these metamaterials show robust Lorentzian resonant peaks in the sub- 100 MHz frequency range below the $T_c$ of Nb. Though Nb is a non-magnetic material, the circulating currents in the spirals generated by RF signals produce a strong magnetic response, which can be tuned sensitively either by temperature or magnetic field thanks to the superconducting nature of the design. We have also observed strong nonlinearity and meta-stable jumps in the transmission data with increasing RF input power until the Nb is driven into the normal state. We discuss the factors modifying the induced magnetic response from single and 1-D arrays of spirals in the light of numerical simulations.Comment: 4 pages, 7 figure

Frequency- and electric-field-dependent conductivity of single-walled carbon nanotube networks of varying density

We present measurements of the frequency and electric field dependent conductivity of single walled carbon nanotube(SWCNT) networks of various densities. The ac conductivity as a function of frequency is consistent with the extended pair approximation model and increases with frequency above an onset frequency $\omega_0$ which varies over seven decades with a range of film thickness from sub-monolayer to 200 nm. The nonlinear electric field-dependent DC conductivity shows strong dependence on film thickness as well. Measurement of the electric field dependence of the resistance R(E) allows for the determination of a length scale $L_{E}$ possibly characterizing the distance between tube contacts, which is found to systematically decrease with increasing film thickness. The onset frequency $\omega_0$ of ac conductivity and the length scale $L_{E}$ of SWCNT networks are found to be correlated, and a physically reasonable empirical formula relating them has been proposed. Such studies will help the understanding of transport properties and benefit the applications of this material system.Comment: 7 pages and 6 figure