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The electrical conductivity of a CdS thin film, controlled by grain structures is essential to enhance its photoconductivity to be able to be fit as a window material in CdS/CdTe heterojunction solar cell. In order to characterize a thin film, electromagnetically, we employed an open cavity resonator with a sub-millimeter VNA (Vector Network Analyzer). Our technique is capable of measuring complex dielectric permittivity, $\tilde{\epsilon}$, of a photovoltaic film as thin as 0.1 $\mu$m. We measured the real part of the complex dielectric permittivity, $\epsilon_{re}$, and electrical conductivity, $\sigma_{re}$ (derived from the imaginary part, $\epsilon_{im}$), of unannealed and annealed CdS films with thicknesses $\sim$ 0.15 $\mu$m on $\sim$ 3 mm thick-borosillicate glass substrates, at room temperature. We obtain the (thermally activated) electrical conductivity between 100 and 312 GHz, which is less in annealed samples than in unannealed one by $\sim$ 2 orders of magnitude. Contrary to our expectations, the carrier concentrations extracted from these data by fitting a Drude model, are $\sim$ 10$^{16}$ cm$^{-3}$ (unannealed) and $\sim$ 10$^{14}$ cm$^{-3}$ (annealed). We investigate the connection between grain size and carrier concentration., Comment: (In press), (2016) Applied Physics Letters

Complex dielectric variations can address neatly the maturity of organic-rich mudrocks. We, therefore, apply an open hemispherical cavity resonator to measure complex dielectric permitivitties of five thin sections of oil (bakken) shales (with different maturity) of $\sim$ 30 $\mu$m thickness on glass-substrates around 2.15 mm thick in 100 - 165 GHz. The real part of complex dielectric permittivity ($\epsilon_{re}$) are constant but show significant differences in magnitude based on maturity: (1) lowest, $\sim$ 1.9, for immature or early maturation stage, (2) higher than the immature one, $\sim$ 3.0 (also bundled up together), for three oil-matured stages, and (3) highest, $\sim$ 4.9, for late or overmatured stage. The conductivity ($\sigma_{re}$) from imaginary part of the complex dielectric constant ($\epsilon_{im}$) emphasizes two important features of conductivity of oil shales: (1) frequency dispersion, and (2) maturity-dependence. We obtain increases of $\sigma_{re}$ with maturity and frequency.

We implement a technique to characterize electromagnetic properties at frequencies 100 to 165 GHz (3 cm$^{-1}$ to 4.95 cm$^{-1}$) of oriented montmorillionite samples using an open cavity resonator connected to a sub-millimeter wave VNA (Vector Network Analyzer). We measured dielectric constants perpendicular to the bedding plane on oriented Na$^{+}$ and Ca$^{++}$-ion stabilized montmorillionite samples deposited on a glass slide at ambient laboratory conditions (room temperature and room light). The clay layer is much thinner ($\sim$ 30 $\mu$m) than the glass substrate ($\sim$ 2.18 mm). The real part of dielectric constant,$\epsilon_{re}$, is essentially constant over this frequency range but is larger in Na$^{+}$- than in Ca$^{++}$-ioned clay. The total electrical conductivity (associated with the imaginary part of dielectric constant, $\epsilon_{im}$) of both samples increases monotonically at lower frequencies ($<$ 110 GHz), but shows rapid increase for Na$^{+}$ ions in the regime $>$ 110 GHz. The dispersion of the samples display a dependence on the ionic strength in the clay interlayers, i.e., $\zeta$-potential in the Stern layers.

A basic issue in optimization, inverse theory,neural networks, computational chemistry and many other problems is the geometrical characterization of high dimensional functions. In inverse calculations one aims to characterize the set of models that fit the data (among other constraints). If the data misfit function is unimodal then one can find its peak by local optimization methods and characterize its width (related to the range of data-fitting models) by estimating derivatives at this peak. On the other hand, if there are local extrema, then a number of interesting and difficult problems arise. Are the local extrema important compared to the global or can they be eliminated (e.g., by smoothing) without significant loss of information? Is there a sufficiently small number of local extrema that they can be enumerated via local optimization? What are the basins of attraction of these local extrema? Can two extrema be joined by a path that never goes uphill? Can the whole problem be reduced to one of enumerating the local extrema and their basins of attraction? For locally ill-conditioned functions, premature convergence of local optimization can be confused with the presence of local extrema. Addressing any of these issues requires topographic information about the functions under study. But in many applications these functions may have hundreds or thousands of variables and can only be evaluated pointwise (by some numerical method for instance). In this paper we describe systematic (but generic) methods of analysing the topography of high dimensional functions using local optimization methods applied to randomly chosen starting models. We provide a number of quantitative measures of function topography that have proven to be useful in practical problems along with error estimates., Comment: 14 figures and an appendix containing proof of main result

In analogy with optical near-field scanning methods, we use tapered dielectric waveguides as probes for a millimeter wave vector network analyzer. By scanning thin samples between two such probes we are able to map the spatially varying dielectric properties of materials with sub-wavelength resolution; using a 150 GHz probe in transmision mode we see spatial resolution of around 500 microns. We have applied this method to a variety of highly heterogeneous materials. Here we show dielectric maps of granite and oil shale.

We exploit millimeter wave technology to measure the reflection and transmission response of random dielectric media. Our samples are easily constructed from random stacks of identical, sub-wavelength quartz and Teflon wafers. The measurement allows us to observe the characteristic transmission resonances associated with localization. We show that these resonances give rise to enhanced attenuation even though the attenuation of homogeneous quartz and Teflon is quite low. We provide experimental evidence of disorder-induced slow light and superluminal group velocities, which, in contrast to photonic crystals, are not associated with any periodicity in the system. Furthermore, we observe localization even though the sample is only about four times the localization length, interpreting our data in terms of an effective cavity model. An algorithm for the retrieval of the internal parameters of random samples (localization length and average absorption rate) from the external measurements of the reflection and transmission coefficients is presented and applied to a particular random sample. The retrieved value of the absorption is in agreement with the directly measured value within the accuracy of the experiment., Comment: revised and expanded

Natural sedimentation processes give rise to fine layers in shales. If these layers alternate between organic-rich and organic-poor sediments, then the contrast in dielectric properties gives rise to an effective birefringence as the presence of hydrocarbons suppresses the dielectric constant of the host rock. We have measured these effects with a quasioptical millimeter wave setup that is rapid and noncontacting. We find that the strength of this birefringence and the overall dielectric permittivity provide two useful diagnostic of the organic content of oil shales., Comment: to appear in Applied Physics Letters

One region of the electromagnetic spectrum that is relatively unexploited for materials characterization is the millimeter wave band (frequencies roughly between 40 and 300 GHz). Millimeter wave techniques involve free-space (non-contacting) measurements which have a length scale that makes them ideal for characterizing bulk properties of multicomponent composites where the scale of homogeneity is on the order of millimeters. Such composites include granular materials such as rocks, fluid mixtures, suspensions and emulsions. Here we show measurements on partially saturated rocks and an oil/water mixture, demonstrating that millimeter wave spectroscopy is sensitive yet rapid measure of changing composition.