The percolation exponents for electrical and thermal conductivities and the permittivity and permeability of binary composites
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David S. McLachlan↗
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Results for “Permittivity”
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Correction: Webb et al. In Situ Determination of Dry and Wet Snow Permittivity: Improving Equations for Low Frequency Radar Applications. Remote Sens. 2021, 13, 4617
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Ryan W. Webb↗
Electrical Properties of Lunar Environment Used for Predicting Lunar RF Propagation Characteristics
This contribution treats the lunar propagation environment as a three region medium: lunar exosphere, lunar regolith, and lunar bedrocks. Then it provides models for predicting the electromagnetic characteristics of each region. The electromagnetic characteristics could be electric characteristics represented by the complex relative permittivity, or magnetic characteristics represented by the complex relative permeability or both electric and magnetic characteristics. The lunar exosphere and the lunar bedrocks have only electric characteristics. The lunar regolith has both electric and magnetic characteristics. The complex relative permittivity models for lunar regolith are mapping of the corresponding models for Earth surface components reported in ITU-R P. 527-6. The complex relative permittivity prediction model of lunar exosphere is expressed in terms of a plasma frequency similar to the ordinary wave critical frequency in the corresponding model for the ionosphere. Based on this fascicle the following can be concluded for the frequency bands of 390 MHz and above: • The lunar exosphere can be treated as a free space, • The lunar regolith can be considered as non-magnetic, • The regolith complex relative permittivity has no temperature dependence, • The real part of the regolith complex relative permittivity depends only on regolith bulk density and it has no frequency dependence, and • The variation of regolith complex relative permittivity with regolith depth should be taken into consideration. Moreover, at frequencies of 2400 MHz and above, the lunar regolith can be treated as a uniform medium with complex relative permittivity equal to the corresponding complex relative permittivity at the regolith surface.
Electrical Permittivity↗
Temperature and Frequency Dependent Electrical Properties of AVCOAT and Shuttle Tile Material
This technical memorandum presents the data and results from a series of tests performed on AVCOAT, charred AVCOAT, and different Shuttle Thermal Protection System (TPS) tile coatings to determine their electrical properties as a function of temperature and frequency. Initially, the samples were assumed to be insulators and the complex permittivities were measured from data collected by sandwiching each sample between two conductors to form a sandwich. However, the AVCOAT sample data showed that the material becomes conductive as it begins to char. To get an accurate conductivity reading on these charred samples, a four-point resistance probe was used to collect data. Overall, this testing showed that the virgin AVCOAT starts out as a material that is a good insulator but transitions to one with a conductivity on the order of 1860 S/m as it chars. The deeper layers of AVCOAT (un-charred) all exhibited a temperature and frequency dependence that is possibly indicative of a dielectric relaxation in the material. As the sample temperatures were increased, a knee appears in the real permittivity data sets below 1 kHz. Both the real permittivity and resistivity drop up to several orders of magnitude yet show that the material remains an insulator. The Shuttle High Temperature Reusable Surface Insulation (HRSI) tile coatings studied included Reac- tion Cured Glass (RCG), Aluminum Enhanced Thermal Barrier (AETB), and Toughened Unipiece Fibrous Insulation (TUFI). The purely glass fiber parts of the tile were removed leaving only the outer layers con- taining just the coating. The data collected shows that the RCG, AETB, and outermost layer of the TUFI have similar electrical properties. The real permittivity plots show that there appears to be a relaxation that shows up at frequencies below 1 kHz. The relaxation frequency increases with increasing temperature. Also, the real permittivity increases up to about a factor of four between room temperature and 650K. Likewise, the resistivity (related to the imaginary permittivity) decreases up to five orders of magnitude over the same temperature interval, but still remains an insulator. This data was collected to support a NASA Engineering and Safety Center (NESC) assessment team investigating the source of thermocouple anomalies in both Shuttle TPS material and AVCOAT used for on the Orion spacecraft for Exploration Flight Test 1 (EFT-1). The details of their findings will be documented in a separate report with this document serving as a reference.
Mark A Nurge↗
(abstract) A Polarimetric Model for Effects of Brine Infiltrated Snow Cover and Frost Flowers on Sea Ice Backscatter
A polarimetric scattering model is developed to study effects of snow cover and frost flowers with brine infiltration on thin sea ice. Leads containing thin sea ice in the Artic icepack are important to heat exchange with the atmosphere and salt flux into the upper ocean. Surface characteristics of thin sea ice in leads are dominated by the formation of frost flowers with high salinity. In many cases, the thin sea ice layer is covered by snow, which wicks up brine from sea ice due to capillary force. Snow and frost flowers have a significant impact on polarimetric signatures of thin ice, which needs to be studied for accessing the retrieval of geophysical parameters such as ice thickness. Frost flowers or snow layer is modeled with a heterogeneous mixture consisting of randomly oriented ellipsoids and brine infiltration in an air background. Ice crystals are characterized with three different axial lengths to depict the nonspherical shape. Under the covering multispecies medium, the columinar sea-ice layer is an inhomogeneous anisotropic medium composed of ellipsoidal brine inclusions preferentially oriented in the vertical direction in an ice background. The underlying medium is homogeneous sea water. This configuration is described with layered inhomogeneous media containing multiple species of scatterers. The species are allowed to have different size, shape, and permittivity. The strong permittivity fluctuation theory is extended to account for the multispecies in the derivation of effective permittivities with distributions of scatterer orientations characterized by Eulerian rotation angles. Polarimetric backscattering coefficients are obtained consistently with the same physical description used in the effective permittivity calculation. The mulitspecies model allows the inclusion of high-permittivity species to study effects of brine infiltrated snow cover and frost flowers on thin ice. The results suggest that the frost cover with a rough interface significantly increases the backscatter from thin saline ice and the polarimetric signature becomes closer to the isotropic characteristics. The snow cover also modifies polarimetric signatures of thin sea ice depending on the snow mixture and the interface condition.
thin sea ice radar backscatter frost flowers snow ↗
Patterned Ferroelectric Films for Tunable Microwave Devices
Tunable microwave devices based on metal terminals connected by thin ferroelectric films can be made to perform better by patterning the films to include suitably dimensioned, positioned, and oriented constrictions. The patterns can be formed during fabrication by means of selective etching processes. If the width of the ferroelectric film in such a device is reduced at one or more locations, then both the microwave field and any applied DC bias (tuning) electric field become concentrated at those locations. The magnitudes of both the permittivity and the dielectric loss of a ferroelectric material are reduced by application of a DC field. Because the concentration of the DC field in the constriction(s) magnifies the permittivity- and loss-reducing effects of the applied DC voltage, the permittivity and dielectric loss in the constriction(s) are smaller in the constriction(s) than they are in the wider parts of the ferroelectric film. Furthermore, inasmuch as displacement current must flow through either the constriction(s) or the low-loss dielectric substrate, the net effect of the constriction(s) is equivalent to that of incorporating one or more low-loss, low-permittivity region(s) in series with the high-loss, high-permittivity regions. In a series circuit, the properties of the low-capacitance series element (in this case, the constriction) dominate the overall performance. Concomitantly, the capacitance between the metal terminals is reduced. By making the capacitance between the metal terminals small but tunable, a constriction increases the upper limit of the frequency range amenable to ferroelectric tuning. The present patterning concept is expected to be most advantageous for devices and circuits that must operate at frequencies from about 4 to about 60 GHz. A constriction can be designed such that the magnitude of the microwave electric field and the effective width of the region occupied by the microwave electric field become functions of the applied DC electric field, so that tunability is enhanced. It should even be possible to design the constriction to obtain a specific tuning-versus-voltage profile.
Miranda, Felix A.↗
Subcritical-Water Extraction of Organics from Solid Matrices
An apparatus for extracting organic compounds from soils, sands, and other solid matrix materials utilizes water at subcritical temperature and pressure as a solvent. The apparatus, called subcritical water extractor (SCWE), is a prototype of subsystems of future instrumentation systems to be used in searching for organic compounds as signs of past or present life on Mars. An aqueous solution generated by an apparatus like this one can be analyzed by any of a variety of established chromatographic or spectroscopic means to detect the dissolved organic compound( s). The apparatus can be used on Earth: indeed, in proof-of-concept experiments, SCWE was used to extract amino acids from soils of the Atacama Desert (Chile), which was chosen because the dryness and other relevant soil conditions there approximate those on Mars. The design of the apparatus is based partly on the fact that the relative permittivity (also known as the dielectric constant) of liquid water varies with temperature and pressure. At a temperature of 30 C and a pressure of 0.1 MPa, the relative permittivity of water is 79.6, due to the strong dipole-dipole electrostatic interactions between individual molecular dipoles. As the temperature increases, increasing thermal energy causes increasing disorientation of molecular dipoles, with a consequent decrease in relative permittivity. For example, water at a temperature of 325 C and pressure of 20 MPa has a relative permittivity of 17.5, which is similar to the relative permittivities of such nonpolar organic solvents as 1-butanol (17.8). In the operation of this apparatus, the temperature and pressure of water are adjusted so that the water can be used in place of commonly used organic solvents to extract compounds that have dissimilar physical and chemical properties.
Amashukeli, Xenia↗
Variance of phase fluctuations of waves propagating through a random medium
As an electromagnetic wave propagates through a random scattering medium, such as a forest, its energy is attenuated and random phase fluctuations are induced. The magnitude of the random phase fluctuations induced is important in estimating how well a Synthetic Aperture Radar (SAR) can image objects within the scattering medium. The two-layer random medium model, consisting of a scattering layer between free space and ground, is used to calculate the variance of the phase fluctuations induced between a transmitter located above the random medium and a receiver located below the random medium. The scattering properties of the random medium are characterized by a correlation function of the random permittivity fluctuations. The effective permittivity of the random medium is first calculated using the strong fluctuation theory, which accounts for large permittivity fluctuations of the scatterers. The distorted Born approximation is used to calculate the first-order scattered field. A perturbation series for the phase of the received field in the Rytov approximation is then introduced and the variance of the phase fluctuations is also calculated assuming that the transmitter and receiver are in the paraxial limit of the random medium, which allows an analytic solution to be obtained. Results are compared using the paraxial approximation, scalar Green's function formulation, and dyadic Green's function formulation. The effects studied are the dependence of the variance of the phase fluctuations on receiver location in lossy and lossless regions, medium thickness, correlation length and fractional volume of scatterers, depolarization of the incident wave, ground layer permittivity, angle of incidence, and polarization.
Chu, Nelson C.↗
Method and Apparatus for Measuring Fluid Flow
The invention is a method and apparatus for monitoring the presence, concentration, and the movement of fluids. It is based on utilizing electromagnetic measurements of the complex permittivity of the fluids for detecting and monitoring the fluid. More particularly the apparatus uses one or more microwave probes which are placed at the locations where the measurements are to be made. A radio frequency signal is transmitted to the probe and the reflected signal is phase and amplitude detected at a rapid rate for the purpose of identifying the fluids, based on their dielectric constant at the probe. The apparatus can be used for multiple purposes including measures of flow rates, turbulence, dispersion, fluid identification, and changes in flow conditions of multiple fluids or multiple states of a single fluid in a flowline or a holding container. The apparatus includes a probe consisting of two electrical conductors separated by an insulator. A radio frequency signal is communicated to the probe and is reflected back from the portion of the probe exposed to the fluid. The radio frequency signal also provides a reference signal. An oscillator generates a second signal which combined with each of the reference signal and the reflected signal to produce signals of lower frequencies to facilitate filtering and amplifying those signals. The two signals are then mixed in a detector to produce an output signal that is representative of the phase and amplitude change caused by the reflection of the signal at the probe exposed to the fluid. The detector may be a dual phase detector that provides two such output signals that are in phase quadrature. A phase shifter may be provided for selectively changing the phase of the reference signal to improve the sensitivity of at least one of the output signals for more accurate readings and/or for calibration purposes. The two outputs that are in quadrature with respect to each other may be simultaneously monitored to account for drift errors. The output signals are digitized and provided to a computer at a sample rate which may be very high. The computer is operable to identify the fluid based on its complex permittivity as may be useful for identifying the flow rates, determining the fluid mixture ratio, detecting impurities in the fluid, and so forth. Novelty is believed to reside in the use of the real part of complex permittivity to measure small difference in permittivity of the fluid.
Arndt, G. Dickey↗
SYNTHESIS OF NOVEL ALL-DIELECTRIC GRATING FILTERS USING GENETIC ALGORITHMS
We are concerned with the design of inhomogeneous, all dielectric (lossless) periodic structures which act as filters. Dielectric filters made as stacks of inhomogeneous gratings and layers of materials are being used in optical technology, but are not common at microwave frequencies. The problem is then finding the periodic cell's geometric configuration and permittivity values which correspond to a specified reflectivity/transmittivity response as a function of frequency/illumination angle. This type of design can be thought of as an inverse-source problem, since it entails finding a distribution of sources which produce fields (or quantities derived from them) of given characteristics. Electromagnetic sources (electric and magnetic current densities) in a volume are related to the outside fields by a well known linear integral equation. Additionally, the sources are related to the fields inside the volume by a constitutive equation, involving the material properties. Then, the relationship linking the fields outside the source region to those inside is non-linear, in terms of material properties such as permittivity, permeability and conductivity. The solution of the non-linear inverse problem is cast here as a combination of two linear steps, by explicitly introducing the electromagnetic sources in the computational volume as a set of unknowns in addition to the material unknowns. This allows to solve for material parameters and related electric fields in the source volume which are consistent with Maxwell's equations. Solutions are obtained iteratively by decoupling the two steps. First, we invert for the permittivity only in the minimization of a cost function and second, given the materials, we find the corresponding electric fields through direct solution of the integral equation in the source volume. The sources thus computed are used to generate the far fields and the synthesized triter response. The cost function is obtained by calculating the deviation between the synthesized value of reflectivity/transmittivity and the desired one. Solution geometries for the periodic cell are sought as gratings (ensembles of columns of different heights and widths), or combinations of homogeneous layers of different dielectric materials and gratings. Hence the explicit unknowns of the inversion step are the material permittivities and the relative boundaries separating homogeneous parcels of the periodic cell.
Zuffada, Cinzia↗
Application of strong fluctuation random medium theory to scattering of electromagnetic waves from a half-space of dielectric mixture
The strong fluctuation random medium theory is applied to calculate scattering from a half-space of dielectric mixture. The first and second moments of the fields are calculated, respectively, by using the bilocal and the distorted Born approximations, and the low frequency limit is taken. The singularity of the dyadic Green's function is taken into account. Expressions for the effective permittivity for the full space case are derived. It is shown that the derived result of the effect permittivity is identical to that of the Polder and van Santern mixing formula. The correlation function of the random medium is obtained by using simple physical arguments and is expressed in terms of the fractional volumes and particle sizes of the constituents of the mixture. Backscattering coefficients of a half-space dielectric mixture are also calculated. Numerical results of the effective permittivity and backscattering coefficients are illustrated using typical parameters encountered in microwave remote sensing of dry and wet snow. It is also shown that experimental data can be matched with the theory by using physical parameters of the medium as obtained from ground truth measurements.
Tsang, L.↗
Relating ground truth collection to model sensitivity
The importance of collecting high quality ground truth before a SAR mission over a forested area is two fold. First, the ground truth is used in the analysis and interpretation of the measured backscattering properties; second, it helps to justify the use of a scattering model to fit the measurements. Unfortunately, ground truth is often collected based on visual assessment of what is perceived to be important without regard to the mission itself. Sites are selected based on brief surveys of large areas, and the ground truth is collected by a process of selecting and grouping different scatterers. After the fact, it may turn out that some of the relevant parameters are missing. A three-layer canopy model based on the radiative transfer equations is used to determine, before hand, the relevant parameters to be collected. Detailed analysis of the contribution to scattering and attenuation of various forest components is carried out. The goal is to identify the forest parameters which most influence the backscattering as a function of frequency (P-, L-, and C-bands) and incident angle. The influence on backscattering and attenuation of branch diameters, lengths, angular distribution, and permittivity; trunk diameters, lengths, and permittivity; and needle sizes, their angular distribution, and permittivity are studied in order to maximize the efficiency of the ground truth collection efforts. Preliminary results indicate that while a scatterer may not contribute to the total backscattering, its contribution to attenuation may be significant depending on the frequency.
Amar, Faouzi↗
Electromechanical Materials for Cryogenic Use
Electromechanical materials can be used in smart sensor and actuator devices. Yet none performing at low temperatures are available. To meet this need, Pb((MgNi)(1/3)Ta(2/3))03 was synthesized as an electrostrictive ceramic for applications in cryogenic environments. Employing the columbite precursor route, samples with 0% to 100% Ni substitution for Mg were prepared, but only samples with Ni-substitutions less than or equal to 20% yielded primarily the desired perovskite phase. For these compositions the temperature of highest permittivity decreased linearly with increasing Ni content to yield a minimum value of -124 C for 20% Ni-substitution. This composition showed good relaxor dielectric behavior with a maximum relative permittivity of 5890 at 1 kHz. Additionally, in samples with excess MgO, the magnitude of permittivity doubled. In this effort, Pb((MgNi)(1/3)Ta(2/3))03 (PMNiTa) was fabricated to lower its transition temperature by substituting Ni for Mg successively.
Leidinger, Peter↗
Polarimetric scattering from layered media with multiple species of scatterers
Geophysical media are usually heterogeneous and contain multiple species of scatterers. In this paper a model is presented to calculate effective permittivities and polarimetric backscattering coefficients of multispecies-layered media. The same physical description is consistently used in the derivation of both permittivities and scattering coefficients. The strong permittivity fluctuation theory is extended to account for the multiple species of scatterers with a general ellipsoidal shape whose orientations are randomly distributed. Under the distorted Born approximation, polarimetric scattering coefficients are obtained. These calculations are applicable to the special cases of spheroidal and spherical scatterers. The model is used to study effects of scatterer shapes and multispecies mixtures on polarimetric signatures of heterogeneous media. The multispecies model accounts for moisture content in scattering media such as snowpack in an ice sheet. The results indicate a high sensitivity of backscatter to moisture with a stronger dependence for drier snow and ice grain size is important to the backscatter. For frost-covered saline ice, model results for bare ice are compared with measured data at C band and then the frost flower formation is simulated with a layer of fanlike ice crystals including brine infiltration over a rough interface. The results with the frost cover suggest a significant increase in scattering coefficients and a polarimetric signature closer to isotropic characteristics compared to the thin saline ice case.
Nghiem, S. V.↗
Validation of an Accurate Three-Dimensional Helical Slow-Wave Circuit Model
The helical slow-wave circuit embodies a helical coil of rectangular tape supported in a metal barrel by dielectric support rods. Although the helix slow-wave circuit remains the mainstay of the traveling-wave tube (TWT) industry because of its exceptionally wide bandwidth, a full helical circuit, without significant dimensional approximations, has not been successfully modeled until now. Numerous attempts have been made to analyze the helical slow-wave circuit so that the performance could be accurately predicted without actually building it, but because of its complex geometry, many geometrical approximations became necessary rendering the previous models inaccurate. In the course of this research it has been demonstrated that using the simulation code, MAFIA, the helical structure can be modeled with actual tape width and thickness, dielectric support rod geometry and materials. To demonstrate the accuracy of the MAFIA model, the cold-test parameters including dispersion, on-axis interaction impedance and attenuation have been calculated for several helical TWT slow-wave circuits with a variety of support rod geometries including rectangular and T-shaped rods, as well as various support rod materials including isotropic, anisotropic and partially metal coated dielectrics. Compared with experimentally measured results, the agreement is excellent. With the accuracy of the MAFIA helical model validated, the code was used to investigate several conventional geometric approximations in an attempt to obtain the most computationally efficient model. Several simplifications were made to a standard model including replacing the helical tape with filaments, and replacing rectangular support rods with shapes conforming to the cylindrical coordinate system with effective permittivity. The approximate models are compared with the standard model in terms of cold-test characteristics and computational time. The model was also used to determine the sensitivity of various circuit parameters including typical manufacturing dimensional tolerances and support rod permittivity. By varying the circuit parameters of an accurate model using MAFIA, these sensitivities can be computed for manufacturing concerns, and design optimization previous to fabrication, thus eliminating the need for costly experimental iterations. Several variations were made to a standard helical circuit using MAFIA to investigate the effect that variations on helical tape and support rod width, metallized loading height and support rod permittivity, have on TWT cold-test characteristics.
Kory, Carol L.↗
Measurement of the Dielectric Constant of Seawater at L-Band: Techniques and Measurements
Satellite instruments, that will monitor salinity from space in the near future, require an accurate relationship between salinity/temperature and seawater dielectric constant. This paper will review measurements that were made of the dielectric constant of seawater during the past several years. The objective of the measurements is to determine the dependence of the dielectric constant of seawater on salinity and on temperature, more accurately than in the past. by taking advantage of modem instrumentation. The measurements of seawater permittivity have been performed as a function of salinity and temperature using a transmission resonant cavity technique. The measurements have been made in the salinity range of 10 to 38 psu and in the temperature range of IOU C to 35 C. These results will be useful in algorithm development for sensor systems such as SMOS and Aquarius. The measurement system consists of a brass microwave cavity that is resonant at 1.413 GHz. The seawater is introduced into the cavity through a capillary glass tube having an inner diameter of 0.1 mm. The diameter of the tube has been made very small so that the amount of seawater introduced in the cavity is small - thus maintaining the sensitivity of the measurements and allowing the use of perturbation theory predicting the seawater permittivity. The change in resonant frequency and the change in cavity Q can be used to determine the real and imaginary pare of the dielectric constant of seawater introduced into the slender tube. The microwave measurements are made by an HPS722D network analyzer. The cavity has been immersed in a u~ateriethylene-glycol bath which is connected to a Lauda circulator. The circulator keeps the brass cavity at a temperature constant to within 0.01 degrees. The system is automated using a Visual Basic program to control the analyzer and to collect the data. The results of the dielectric constant measurements of seawater will be presented. The measurement results will be compared with permittivity values generated from the Kline and Swift relationship. Two methods of calibration will be discussed, The errors that each technique introduces into the measurement resulls will be reviewed. Temperature stability, frequency drift and the effect of increasing cavity transmission loss on the unloaded cavity Q will also be discussed.
Lang, R.↗
Metal Standards for Waveguide Characterization of Materials
Rectangular-waveguide inserts that are made of non-ferromagnetic metals and are sized and shaped to function as notch filters have been conceived as reference standards for use in the rectangular- waveguide method of characterizing materials with respect to such constitutive electromagnetic properties as permittivity and permeability. Such standards are needed for determining the accuracy of measurements used in the method, as described below. In this method, a specimen of a material to be characterized is cut to a prescribed size and shape and inserted in a rectangular- waveguide test fixture, wherein the specimen is irradiated with a known source signal and detectors are used to measure the signals reflected by, and transmitted through, the specimen. Scattering parameters [also known as "S" parameters (S11, S12, S21, and S22)] are computed from ratios between the transmitted and reflected signals and the source signal. Then the permeability and permittivity of the specimen material are derived from the scattering parameters. Theoretically, the technique for calculating the permeability and permittivity from the scattering parameters is exact, but the accuracy of the results depends on the accuracy of the measurements from which the scattering parameters are obtained. To determine whether the measurements are accurate, it is necessary to perform comparable measurements on reference standards, which are essentially specimens that have known scattering parameters. To be most useful, reference standards should provide the full range of scattering-parameter values that can be obtained from material specimens. Specifically, measurements of the backscattering parameter (S11) from no reflection to total reflection and of the forward-transmission parameter (S21) from no transmission to total transmission are needed. A reference standard that functions as a notch (band-stop) filter can satisfy this need because as the signal frequency is varied across the frequency range for which the filter is designed, the scattering parameters vary over the ranges of values between the extremes of total reflection and total transmission. A notch-filter reference standard in the form of a rectangular-waveguide insert that has a size and shape similar to that of a material specimen is advantageous because the measurement configuration used for the reference standard can be the same as that for a material specimen. Typically a specimen is a block of material that fills a waveguide cross-section but occupies only a small fraction of the length of the waveguide. A reference standard of the present type (see figure) is a metal block that fills part of a waveguide cross section and contains a slot, the long dimension of which can be chosen to tailor the notch frequency to a desired value. The scattering parameters and notch frequency can be estimated with high accuracy by use of commercially available electromagnetic-field-simulating software. The block can be fabricated to the requisite precision by wire electrical-discharge machining. In use, the accuracy of measurements is determined by comparison of (1) the scattering parameters calculated from the measurements with (2) the scattering parameters calculated by the aforementioned software.
Lambert, Kevin M.↗
Carbon Nanofiber-Based, High-Frequency, High-Q, Miniaturized Mechanical Resonators
High Q resonators are a critical component of stable, low-noise communication systems, radar, and precise timing applications such as atomic clocks. In electronic resonators based on Si integrated circuits, resistive losses increase as a result of the continued reduction in device dimensions, which decreases their Q values. On the other hand, due to the mechanical construct of bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators, such loss mechanisms are absent, enabling higher Q-values for both BAW and SAW resonators compared to their electronic counterparts. The other advantages of mechanical resonators are their inherently higher radiation tolerance, a factor that makes them attractive for NASA s extreme environment planetary missions, for example to the Jovian environments where the radiation doses are at hostile levels. Despite these advantages, both BAW and SAW resonators suffer from low resonant frequencies and they are also physically large, which precludes their integration into miniaturized electronic systems. Because there is a need to move the resonant frequency of oscillators to the order of gigahertz, new technologies and materials are being investigated that will make performance at those frequencies attainable. By moving to nanoscale structures, in this case vertically oriented, cantilevered carbon nanotubes (CNTs), that have larger aspect ratios (length/thickness) and extremely high elastic moduli, it is possible to overcome the two disadvantages of both bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators. Nano-electro-mechanical systems (NEMS) that utilize high aspect ratio nanomaterials exhibiting high elastic moduli (e.g., carbon-based nanomaterials) benefit from high Qs, operate at high frequency, and have small force constants that translate to high responsivity that results in improved sensitivity, lower power consumption, and im - proved tunablity. NEMS resonators have recently been demonstrated using topdown, lithographically fabricated ap - proaches to form cantilever or bridgetype structures. Top-down approaches, however, rely on complicated and expensive e-beam lithography, and often require a release mechanism. Reso - nance effects in structures synthesized using bottom-up approaches have also recently been reported based on carbon nanotubes, but such approaches have relied on a planar two-dimensional (2D) geometry. In this innovation, vertically aligned tubes synthesized using a bottom- up approach have been considered, where the vertical orientation of the tubes has the potential to increase integration density even further. The simulation of a vertically oriented, cantilevered carbon nanotube was performed using COMSOL Multi - physics, a finite element simulation package. All simulations were performed in a 2D geometry that provided consistent results and minimized computational complexity. The simulations assumed a vertically oriented, cantilevered nanotube of uniform density (1.5 g/cu cm). An elastic modulus was assumed to be 600 GPa, relative permittivity of the nanotube was assumed to be 5.0, and Poisson s ratio was assumed to be 0.2. It should be noted that the relative permittivity and Poisson s ratio for the nanotubes of interest are not known accurately. However, as in previous simulations, the relative permittivity and Poisson s ratios were treated as weak variables in the simulation, and no significant changes were recognized when these variables were varied.
Kaul, Anupama B.↗