Variation Of Constants Research Articles

(Invited) Comparison of Empirical Models for Broadband Insertion Losses in TSV-Interconnects

The reliability of through silicon via (TSV)-interconnects depends on various factors including integration schemes, manufacturing process (construction materials, wafer-scale homogeneity, thermal budget) and operating conditions. The magnitude of the frequency-dependent $S_{21}$ microwave scattering parameter quantifies insertion losses in TSV-interconnects. The insertion loss depends on the instantaneous electrical characteristics of the device under test. We attribute insertion loss (which affects device reliability) to reorientation of electrically active defects, cracks, voids, dielectric constant variation, and water molecules affected by heat. We model insertion losses with equivalent circuit models of varying complexity. We compare results determined with global and local models fit to low-frequency and high-frequency subsets of the full spectrum. We estimate model parameters with a stochastic optimization implementation of the Levenberg-Marquadt method. To illustrate the relevance of this methodology, for TSV-interconnects from two different providers, we quantify how estimated model parameters vary with thermal cycles for TSV-interconnects fabricated at particular wafer locations.

A Theoretical Analysis for Arbitrary Residual Stress of Thin Film/Substrate System With Nonnegligible Film Thickness

Abstract Stoney formula is widely used in advanced devices to estimate the residual stress of thin film/substrate system by measuring surface curvature. Many hypotheses including that thin film thickness is ignored are required, thus bringing significant error in characterizing the inhomogeneous residual stress distribution. In this article, arbitrary residual stresses on thin film/substrate structures with nonnegligible film thickness are modeled and characterized. We introduce nonuniform misfit strain and establish the governing equations including mismatched strain, displacements, and interfacial stresses based on the basic elastic theory. The parameterization method and the method of constant variation are used in the process of equation decoupling. The expressions between displacements, surface curvatures, and misfit strain are determined through decoupling calculations. By substituting misfit strain, residual stresses are expressed by parametric equation related to surface curvature. It further indicates that there is a “non-local” part between the film stress and curvature at the same point. Compared to neglecting the film thickness, the proposed method eliminate relative errors up to 58.3%, which is of great significance for stress measurement of thin films and substrates.

Coupling finite and boundary element methods to solve the Poisson-Boltzmann equation for electrostatics in molecular solvation.

The Poisson-Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to the accurate representation of the molecular surface and partial charges, and exact enforcement of the boundary conditions at infinity. However, the boundary element method is limited to linear equations and piecewise constant variations of the material properties. In this work, we present a scheme that couples finite and boundary elements for the linearised Poisson-Boltzmann equation, where the finite element method is applied in a confined solute region and the boundary element method in the external solvent region. As a proof-of-concept exercise, we use the simplest methods available: Johnson-Nédélec coupling with mass matrix and diagonal preconditioning, implemented using the Bempp-cl and FEniCSx libraries via their Python interfaces. We showcase our implementation by computing the polar component of the solvation free energy of a set of molecules using a constant and a Gaussian-varying permittivity. As validation, we compare against well-established finite difference solvers for an extensive binding energy data set, and with the finite difference code APBS (to 0.5%) for Gaussian permittivities. We also show scaling results from protein G B1 (955 atoms) up to immunoglobulin G (20,148 atoms). For small problems, the coupled method was efficient, outperforming a purely boundary integral approach. For Gaussian-varying permittivities, which are beyond the applicability of boundary elements alone, we were able to run medium to large-sized problems on a single workstation. The development of better preconditioning techniques and the use of distributed memory parallelism for larger systems remains an area for future work. We hope this work will serve as inspiration for future developments that consider space-varying field parameters, and mixed linear-nonlinear schemes for molecular electrostatics with implicit solvent models.

Calculating Dielectric Constant at the Interface Between Polyethylene and Copper Using Microscopic Polarization Theory

The relative dielectric constant is the main electric property of polyethylene (PE) as a dielectric material. Based on experimental findings, the dielectric constant of bulk PE has been known to be constant. However, when interfaced with copper –as it is the case in most power applications- the dielectric constant may differ from that value at interface region in atomic scale, which in turn affects the charge injection process. This is further complicated by the inevitable presence of chemical impurities at the interface, where the dielectric constant becomes position-dependent and depends on the type of impurity. In this work, the dielectric constant is calculated for the cases of a pure slab of PE during the interface between PE and copper, and finally with chemical impurities present in the interface region. In those cases, the microscopic polarization theory is used in calculating the position-dependent relative dielectric constant. This theory makes use of the charge density distribution under an applied electric field, which is computed using the density functional theory (DFT). It is found that the calculated dielectric constant varies at the interface region within a range of a few Angstroms, beyond which it becomes constant well within the bulk polyethylene. The dielectric constant variation at the interface region is then used to study the impact on the injection process using the Schottky injection mechanism. The injection current density is computed from Schottky injection law as a function of applied field at different dielectric constant values. It is found that the injection current increased with decreasing the dielectric constant at the interface region. The paper concludes that the relative dielectric constant varies at the interface due to the morphological deformation between the polyethylene chains and the copper atoms. This variation is further enhanced in the presence of chemical impurities. It is further concluded that the injection current density does not only depend on the barrier height, but also on the varying relative dielectric constant.

Impact of temperature on the binding interaction between dsDNA and curcumin: An electrochemical study

In this study, we investigated the binding mode between double-stranded deoxyribonucleic acid (dsDNA) and curcumin (CU) using differential pulse voltammetry (DPV), UV–Vis spectroscopy, and molecular docking. By employing these techniques, we predicted the binding within the minor groove region of dsDNA and CU. Significantly, we employed electrochemistry, specifically cyclic voltammetry (CV), to explore the temperature effect on the dsDNA and CU binding. To the best of our knowledge, this is the first study to utilize electrochemical methods for investigating the temperature-dependent behavior of this binding interaction. Our findings revealed temperature-dependent variations in the binding constants: 2.42 × 103 M−1 at 25 °C, 4.26 × 103 M−1 at 30 °C, 5.44 × 103 M−1 at 35 °C, 6.29 × 103 M−1 at 40 °C, and 7.52 × 103 M−1 at 45 °C. Notably, the binding constant exhibited an increasing trend with elevated temperatures, indicating a temperature-dependent enhancement of the binding interaction.

Constrain the time variation of the gravitational constant via the propagation of gravitational waves

The gravitational constant variation means the breakdown of the strong equivalence principle. As the cornerstone of general relativity, the validity of general relativity can be examined by studying the gravitational constant variation. Such variations have the potential to affect both the generation and propagation of gravitational waves. Here, our focus lies on the effect of gravitational constant variation specifically on the propagation of gravitational waves. In a previous paper (An et al., 2023 [13]) we have studied such effect based on a Maxwell-like equation. That work admits two drawbacks. The assumption that describing gravitational waves with Maxwell-like equation is not solid. And more such treatment can only deal with space dependent gravitational constant. In the current paper we will remedy these two issues. We employ two analytical methods, namely based on the Fierz-Pauli action and the perturbation of Einstein-Hilbert action around Minkowski spacetime, both leading to the same gravitational wave equation. By solving this equation, we find the effects of gravitational constant variation on gravitational wave propagation. The result is consistent with previous investigations based on Maxwell-like equations for gravitational waves for space dependent gravitational constant cases. In addition we can constrain the time variation of the gravitational constant via the propagation of gravitational waves based on GW170817 data. And more, we find that small variations in the gravitational constant result in an amplitude correction at the leading order and a phase correction at the sub-leading order for gravitational waves. These results provide valuable insights for probing gravitational constant variation and can be directly applied to gravitational wave data analysis.

Dynamic polarization-regulated metasurface with variable focal length

Polarization and focal length are both critical optical parameters with many applications in many fields, such as optical communications and imaging. The development of metasurfaces provides a new realization of optical systems. In this paper, based on metasurfaces’ powerful electromagnetic modulation capability, we integrate polarization conversion with continuous zoom function and propose a dynamic polarization-regulated metasurface with variable focal length. It realizes the reversible conversion of polarization state, which can convert linearly polarized light into elliptically polarized light and circularly polarized light and convert circularly polarized light to linearly polarized light. At the same time, it achieves a 4.4× zoom range, with a constant focal length variation from 70 µm to 309 µm. The metasurface has the advantages of small size, easy integration, and reconfigurability, providing a new design idea for complex functional optical systems.

DFT calculations for electronic and magnetic properties of full Heusler Fe2MnAs alloy in perfect and defect structures

First-principles calculations within the framework of the density functional theory were conducted using the FP-LAPW method to investigate the electronic and magnetic properties of the Full-Heusler Fe2MnAs alloy. The study encompassed the examination of its perfect structure as well as the variation of lattice constants around the ground state. The negative value of the calculated formation energy suggests that the alloy may form spontaneously. From a magnetic perspective, Fe2MnAs exhibit a ferromagnetic order. The alloy also shows a high spin-polarization that may be increased, transforming the alloy into a half-metal, with the contraction of the lattice constant. Furthermore, the investigation delved into the effect of point defect formation. The calculated formation energies for vacancies, antisite, and exchange defects suggest the likely occurrence of some of these defects within the Fe2MnAs compound. Significantly, certain defects contribute to the spin-polarization of the alloy, effectively rendering it a fully half-metallic material.

Kirigami-inspired deployable mechanisms with a type-preserving feature and controllable Poisson’s ratio

A spatial deployable mechanism is capable of adapting to different operating requirements by adjusting its shape and size. However, most current deployable mechanisms fail to maintain the type of their reflective surface during the folding process, which limits their ability to adjust the optimal operating frequency. To address this issue, this paper presents a novel design of a deployable mechanism with a type-preserving feature inspired by kirigami techniques. By preserving the type of its reflective surface, this mechanism allows for the adjustment of the optimum operating frequency according to specific requirements. This makes it well-suited for deployment on commercial satellites that undergo constant mission variations. The mechanism is constructed using porous kirigami cells, ensuring that the type of the working surface is maintained throughout the deployment process. The construction of deployable units and networks based on porous cells is also discussed. Additionally, deployable mechanisms with controllable Poisson’s ratios are developed. The kinematics of the mechanism are analyzed to verify the type-preserving characteristics. Finally, four case studies are conducted to illustrate and validate the proposed design and analysis.

First-principles investigation on structural, electronic, magnetic, mechanical and thermodynamic properties of half-metallic Zn-based all-d-metal equiatomic quaternary Heusler alloys

This study employs first-principles calculations based on density functional theory (DFT) to investigate the structural, electronic, magnetic, mechanical, and thermodynamic properties of Zn-based all-d-metal equiatomic quaternary Heusler alloys (EQHAs) XX'YZn (X = Fe, Ni, Co; X' = V, Cr; Y = Nb, Ti, Zr, Hf). The investigation encompasses three distinct structural types of all-d EQHAs, with the energy calculations revealing the Type-I configuration as the most stable. The electronic structure of the all-d EQHAs demonstrate 100% spin polarization. Specifically, NiVTiZn and NiVZrZn exhibit characteristics of half-metallic ferromagnets, while FeVNbZn, CoCrTiZn, CoCrZrZn, and CoCrHfZn manifest traits of half-metallic ferrimagnets. Notably, we have conducted computations concerning the magnetic properties of these six alloys, revealing that their principal magnetic moments stem from V and Cr atoms. This study analyzes the influence of lattice constant variations on the magnetic properties of the alloys and the width of the spin down energy gap. Results demonstrate that within the ranges of lattice constants from 5.6 Å to 6.4 Å for FeVNbZn, 5.5–6.6 Å for NiVTiZn, 5.8–6.8 Å for NiVZrZn, 5.8–6.7 Å for CoCrTiZn, 5.9–6.8 Å for CoCrZrZn and 6.0–6.9 Å for CoCrHfZn, these alloys maintain their stable half-metallic attributes. Furthermore, the investigated alloys demonstrate mechanical stability, exhibiting ductility and anisotropic characteristics. These investigations underscore the potential application prospects of half-metallic all-d EQHAs in spintronic devices.

A detailed analysis of stochastic models applied to temporal gravity field recovery with GRACE observations

Summary In this study, we analyzed the impacts of errors in background force models and observed non-gravitational forces on the pseudo-observations (pre-fits) during gravity field recovery based on the GRACE satellite gravity mission. To reduce these effects, we introduced the stochastic parameters into the functional model of the variational equation integration approach to absorb this type of noise contribution. Simultaneously, the prior variances of observed orbits and K-Band range rates used in traditional method are re-estimated with least-square variance component estimation (LS-VCE) after considering these stochastic parameters. To improve the computing efficiency, a modified method of the calculation of sensitivity matrices related to the introduced stochastic parameters is proposed. Compared to the method of variation of constants widely used in the precise orbit determination and gravity field recovery, the modified method decreases the computational time of these matrices by about four times. Furthermore, an efficient LS-VCE algorithm is derived in a more generalized case. The efficient algorithm only costs 1% of the time of the unoptimized method. With the GRACE data, we analyzed the benefits of these refinements in gravity field recovery, and the results show that these improvements can mitigate the impacts of errors in background force models and accelerometer data on recovered gravity field models, especially in the high degree signals. Furthermore, the quality of results has less dependence on parameterization.

AN ELECTROMETRIC METHOD FOR THE DETERMINATION OF IMPACT OF DMSO-WATER MIXTURES ON pKa VALUES OF SALICYLIC ACID DERIVATIVES

Objective: The main objective of this present study is to conduct an experiment to analyze the variation of protonation-deprotonation equilibria with regards to the dielectric constants of an organic medium, influence of errors on protonation constants and effect of pH on the percentage of species. Methods: The present investigation was carried out by using pH meter at a temperature of 303 K and ionic strength of 0.16 mol dm-3 in Dimethyl sulfoxide (DMSO)-water mixtures. The processing of data was done by using Gran plot titration. The advanced principles of mathematics and fuzzy logic have been employed to correlate chemical problems, known as chemometrics. To obtain best-fit chemical models, a modelling strategy such as SCPHD is used and a computer program MINIQUAD 75 is also employed for the refinement of results. Results: In the present study, we found the influence of dielectric constants of a medium Dimethyl sulfoxide (DMSO)-water on protonation constants of 5-Sulfosalicylic acid and 5-Hydroxysalicylic acid has been studied. The species distribution diagrams were presented and understood the effect of pH on the percentage of species. The obtained skewness values are ranging from 0.11-0.36 and–0.56-0.38, for 5-Sulfosalicylic acid (5-SSA) and 5-Hydroxysalicylic acid (5-HSA), respectively, which describes the distribution curves are right skewed and left skewed. The kurtosis values are ranging from 2.12-3.56, which indicates the peak of the distribution curve exhibits both platykurtic and leptokurtic pattern. The changes in the concentrations of some influential parameters such as log F, acid, alkali, volume of titrands, ligand causes variation of stability constants and the order of the effect of influential parameters on stability constants are as alkali>acid>ligand>volume of titrand>log F. Conclusion: It is observed that the significant influence of co-solvent Dimethyl sulfoxide (DMSO)-Water mixtures on the protonation constants of ligands also studied how some factors such as changes in concentrations of ligand, acid, base log F and volume of the solution have influence on the protonation constants.

Heterogeneous electron transfer of ferrocene in acetonitrile-LiTFSI highly concentrated electrolyte

Highly concentrated electrolytes (HCE) are mixtures of equivalent or near-equivalent amounts of salt and solvent displaying a liquid phase at room temperature. HCE have intensively studied for application in energy storage devices with a particular focus on batteries since the demonstration of the lack of reactivity of lithium metal in an acetonitrile HCE. The lack of "free" solvent molecules in HCE is responsible for their stability. This feature also suggests that heterogeneous electron transfer (ET) in HCE could be different from conventional electrolytes because of the importance of solvent reorganization during ET. Thus, we investigated the heterogeneous electron transfer of the ferrocenium/ferrocene (Fc+/Fc) redox couple as a function of concentration of the salt Li bis(trifluoromethanesulfonyl)imide in acetonitrile, a model system for HCE. We show that while the diffusivity of Fc (Shoup-Szabo) follows the trend with viscosity (η) expected from the Stokes-Einstein relation over the entire concentration range, the ET rate constant (k0) variation with η on the other hand diverges from ideality. Using Raman spectroscopy in the solution and on the surface (EC-SERS), we show that the most likely cause for the difference in ET rate constant between dilute and highly concentrated electrolytes involves a strong coordination of the ferrocenium with the complexes found in HCE. This new knowledge highlights the importance of increasing fundamental research on the topic of electrochemistry in HCE.

Cosmologically varying kinetic mixing

The portal connecting the invisible and visible sectors is one of the most natural explanations of the dark world. However, the early-time dark matter production via the portal faces extremely stringent late-time constraints. To solve such tension, we construct the scalar-controlled kinetic mixing varying with the ultralight CP-even scalar’s cosmological evolution. To realize this and eliminate the constant mixing, we couple the ultralight scalar within 10−33eV ≲ m0 ≪ eV with the heavy doubly charged messengers and impose the ℤ2 symmetry under the dark charge conjugation. Via the varying mixing, the keV – MeV dark photon dark matter is produced through the early-time freeze-in when the scalar is misaligned from the origin and free from the late-time exclusions when the scalar does the damped oscillation and dynamically sets the kinetic mixing. We also find that the scalar-photon coupling emerges from the underlying physics, which changes the cosmological history and provides the experimental targets based on the fine-structure constant variation and the equivalence principle violation. To ensure the scalar naturalness, we discretely re-establish the broken shift symmetry by embedding the minimal model into the ℤN-protected model. When N ~ 10, the scalar’s mass quantum correction can be suppressed much below 10−33eV.

Searching for a secular variation of the gravitational constant using strong gravitational fields

Searching for a secular variation of the gravitational constant using strong gravitational fields

Impact of pH levels on the morphological, dielectric and impedance spectral behaviour of cobalt oxide nanomaterials

Pure Co3O4 nanomaterials were synthesized by using Sol-Gel technique at various pH levels (7, 8 and 9). Morphological and structural analysis was done by X-ray diffraction method (XRD), scanning electron microscope (SEM) and energy-dispersive spectroscopy EDX. The X-ray diffraction patterns revealed that the prepared samples crystallized in a cubic structure without any impurities. SEM micrographs validated the influence of pH in altering the morphology of the synthesized compound. The elemental spectrum analysis EDX confirms the presence of cobalt and oxygen without any impurities. Variation of dielectric constant, dielectric loss and impedance were analyzed for various temperatures and different pH values. Dielectric loss value increases at high temperature due to the thermal disturbance of the atoms. Cole-Cole impedance plot gives the information about grain and grain boundaries. DC electrical conductivity values of Co3O4 nanomaterials in the temperature range 40ºC to 250ºC increases with increase in pH level from 7 to 9. Arrhenius plot of Co3O4 nanoparticles confirmed that the activation energy at various temperature increases with increase in pH levels upto 8, then decreases for pH level 9.

Effect of Cr cations addition on the structural, morphological, optical, and photocatalytic properties of Er-doped ZnO structures

In this work, we have investigated the effect of Cr3+ cations addition on the structural, morphological, optical, and photocatalytic properties of Er-doped ZnO structures. The Zn(1-(x-y))ErxCryO compound, where [(x; y) = (0.00; 0.00), (0.02; 0.01), (0.02; 0.02) and (0.02; 0.03)] was synthesized by the co-precipitation method and thermally treated at 100 °C for 6 h. The structural study showed that the dopant cations concentrations, cause variations in lattice constants, and increase the crystallite size and the strain in the ZnO crystal lattice. The structural atomic disorder was confirmed by Raman and photoluminescence spectroscopies, with VO, VO+, and VO++ type oxygen vacancy defects dominating. The samples exhibited different morphologies depending on the dopant concentration (plates-like, irregular hemispherical particles, and octahedrons-like structures). In the photocatalytic test, the methylene blue (MB) dye degradation under UV irradiation increased as a function of Cr3+ cations concentration, achieving a degradation rate of 37.4 ± 1.9% for the sample containing 2% of Er3+ cations and 3% of Cr3+ cations. In addition, the MB dye removal capacity by the Zn(1-(x-y))ErxCryO compound was incremented to above 85% using an optimized H2O2 concentration. Finally, the irradiated solution did not show toxicity against Artemia salina, indicating that the intermediate photoproducts formed are not toxic.

Analysis of Stress Concentration in Functionally Graded Plates with Linearly Increasing Young’s Modulus

In this article, the strain and stress analyses of functionally graded plates with circular holes that are subject to a uniaxial far-field traction load are analytically considered. The Young’s modulus is assumed to vary linearly along the radial direction around the hole. The adoption of such a type of inhomogeneity variation can be justified as follows. Firstly, and among all the possible variations of stiffness, the linear one is indeed the simplest inhomogeneity distribution. Surprisingly however, according to our knowledge extent, the associated elastic fields were not yet addressed in the literature. Secondly, a linearly varying stiffness could reasonably imply a remarkable advantage from a technological point of view. In fact, unlike nonlinearly varying stiffness plates, manufacturing routes are only required to handle constant variations throughout the radial domain. After recalling the basic equations for plane stress elasticity, the displacement, strain, and stress fields around the hole were numerically tackled and discussed for different stiffness ratios. A comparison was also carried out with other Young’s modulus distributions that have been commonly employed in the literature.

All-coupling solution for the continuous polaron problem in the Schrödinger representation

The solution for the large-radius Fröhlich polaron in the Schrödinger representation of the quantum theory is constructed in the entire range of variation of the coupling constant. The energy and the effective mass of the polaron are calculated by simple algebraic transformations and are analogous to the results found by Feynman on the basis of the variational principle for the path-integrals of this system. It allows us to solve the long-lived problem of the inequalities of the functional and operator approaches for the polaron problem.The developed method is important for other models of particle-field interaction including those ones for which the standard perturbation theory is divergent.

Studies on temperature-dependent bandgap and gap-to-midgap ratio in diamond lattice photonic crystal with biosensing applications

The present study examines the temperature dependence of the photonic bandgap, the corresponding wavelength and the gap-to-midgap ratio in a three-dimensional diamond lattice photonic crystal. The bandgap calculations establish that the structure shows a complete photonic bandgap centered around 1550 nm at 300 K. The thermo-optic effect, observed in silicon, is employed to compute the photonic bandgap, band-edge wavelengths and mid-bandgap wavelength at various temperatures in the range of 300 K–400 K. The gap-to-midgap ratio, for the proposed structure, is also evaluated at different temperatures. It is seen that the upper and lower band-edge wavelengths and the mid-bandgap wavelength show a linear temperature dependence. The sensitivity of the structure is observed to be 0.0518 nm/K, thus supporting temperature sensing applications. It is found that the gap-to-midgap ratio, for the proposed diamond lattice structure, shows linear variation with temperature. The effect of variation of the dielectric constant and the fill factor on the gap-to-midgap ratio for the diamond structure has also been analyzed. The proposed design has also been analyzed as a refractive index sensor with a sensitivity of 254.9 nm/RIU for sensing the different components of blood.