Macroscopic Dielectric Constant Research Articles

A review of first-principles calculation methods for defects in semiconductors

Doping and defect control in semiconductors are essential prerequisites for their practical applications. First-principles calculations of defects based on density functional theory offer crucial guidance for doping and defect control. In this paper, the developments in the theoretical methods of first-principles semiconductor defect calculations are introduced. Firstly, we introduce the method of calculating the defect formation energy and finite-size errors to the formation energy caused by the supercell method. Then, we present corresponding image charge correction schemes, which include the widely used post-hoc corrections (such as Makov-Payne, Lany-Zunger, Freysoldt-Neugebauer-van de Walle schemes), the recently developed self-consistent potential correction which performs the image charge correction in the self-consistent loop for solving Kohn-Sham equations, and the self-consistent charge correction scheme which does not require an input of macroscopic dielectric constants. Further, we extend our discussion to charged defect calculations in low-dimensional semiconductors, elucidate the issue of charged defect formation energy divergence with the increase of vacuum thickness within the jellium model and introduce our theoretical model which solves this energy divergence issue by placing the ionized electrons or holes in the realistic host band-edge states instead of the virtual jellium state. Furthermore, we provide a brief overview of defect calculation correction methods due to the DFT band gap error, including the scissors operator, LDA+<i>U</i> and hybrid functionals. Finally, in order to describe the calculation of defect formation energy under illumination, we present our self-consistent two-Fermi-reservoir model, which can well predict the defect concentration and carrier concentration in the Mg doped GaN system under illumination. This work summarizes the recent developments regarding first-principles calculations of defects in semiconducting materials and low-dimensional semiconductors, under whether equilibrium conditions or non-equilibrium conditions, thus promoting further developments of doping and defect control within semiconductors.

Reaction Entropies in Solution from Analytical Three-Dimensional Reference Interaction Site Model Derivatives with Application to Redox and Spin-Crossover Processes.

An analytical approach to compute the excess entropy of solvation at constant pressure in three-dimensional reference interaction site model (3D-RISM) calculations is presented. It includes the changes in the macroscopic dielectric constant of the solvent upon variation of temperature and density. The approach is exact within the framework of force-field descriptions of the solute and gives reasonable results for self-consistently determined electrostatics as used in the 3D-RISM-self-consistent field approach, particularly for entropy differences. The new method is applied to simple examples of reaction entropies of iron complexes in aqueous solution, for which simple gas-phase calculations and many other approaches give unreliable estimates. For both redox half-reactions and spin-crossover processes, (semi)quantitative agreement with experimental reaction entropies can be achieved out of the box.

Accuracy trade-off between one-electron and excitonic spectra of cuprous halides in first-principles calculations.

Because of the sophisticated error cancellation in the density functional theory (DFT)-based calculations, a theoretically more accurate input would not guarantee a better output. In this work, our first-principles GW plus Bethe-Salpeter equation calculations using pseudopotentials show that cuprous halides (CuCl and CuBr) are such extreme cases for which a better one-electron band is not accompanied with a better exciton binding energy. Moreover, we find that the exchange interaction of Cu core electrons plays a crucial role in their ground-state electronic properties, especially in the energy gap and macroscopic dielectric constant. Our work provides new insights into the understanding of the electronic structure of cuprous halides from the DFT perspective.

Избирательная сольватация красителя 4-DASPI в бинарном растворителе вода-этиленгликоль

Solvatochromic shifts of the absorption spectra maxima of the dye 4-DASPI (4- [4- (dimethylamino) styryl] -1-methylpyridinium iodide) in a binary solvent water-ethyleneglycol in the concentration range 0-100% were experimentally investigated. The dependence of the solvatochromic shift on the macroscopic dielectric constant of the solution and the concentration of ethyleneglycol was determined. The Onsager-Liptay model was used for the theoretical interpretation of the experimental data. It made it possible to estimate the effective dielectric constant in the microscopic area that contacts with dye chromophore taking into account the measured solvatochromic shifts. It was found that the value of the dielectric constant in the solvation shell of this dye differs significantly from the macroscopic value. The solvation shell is significantly enriched by ethyleneglycol (preferential solvation) over the components’ concentration range. The enrichment reaches its maximum approximately in the middle of this range. The composition of the dye solvation shell at different concentration is discussed.

Image charge interaction correction in charged-defect calculations

Charged-defect calculation using a periodic supercell is a significant class of problems in solid state physics. However, the finite supercell size induces an undesirable long-range image charge Coulomb interaction. Although a variety of methods have been proposed to eliminate such image Coulomb interaction, most of the previous schemes are based on a rough approximation of the defect charge screening. In this work, we present a rigorous derivation of the image charge interaction with a new defect screening model where the use of bulk macroscopic dielectric constant can be avoided. We have verified this approach in comparison with a widely used approach for 12 different defects. Our correction scheme offers a much faster convergence concerning the supercell size for cases with considerable image charge interactions. In those cases, we also found that the nonlinear dielectric screening might play an important role. The proposed new defect screening model will also shed new light on understanding the defect screening properties and can be applied to other defect systems.

Macroscopic Dielectric Constant Model for Layered Media With Rough Surfaces

A macroscopic dielectric constant (MDC) model is proposed to describe the impact of a dielectric layered medium with two-layer rough surfaces (TLRSs) on 2-D electromagnetic scattering. The MDC model is based on the Kirchhoff approximation (KA) method to find an equivalence between the total fields on a TLRS and on a single-layer rough surface (SLRS). With this model, evaluating the scattering over a TLRS can be reduced to a simple SLRS scattering problem. The KA method is used in conjunction with the MDC model to calculate the bistatic scattering coefficients at different surface roughness conditions. The results are in good consistency with the values obtained using the method of moments. Extensive numerical results confirm that the MDC varies along the profile of the top surface as the surface roughness increases, and the variations in the surface roughness and medium depth can significantly affect the fluctuation and mean value of MDC.

Vacuum metrology based on refractive index of gas

With the development of vacuum technology, subject to the influence of directional flow and uneven temperature, the thermodynamic equilibrium state is destroyed. In this case, the pressure reference is not suitable for characterizing the vacuum state. To ensure the long-term stability and reproducibility of the measurement system, vacuum metrology will be characterized by gas density. The precisive measurement of gas refractive index based on a Fabry-Perot cavity can be used to derive the gas density. This kind of an optical measurement of vacuum links macroscopic dielectric constants of gases with microscopic polarization parameters of atoms and molecules. It replaces the physical standard based on the mercury pressure gauge with the quantum standard. In this paper, we discuss the reverse process from refractive index to gas pressure, and use the laser-locked Fabry-Perot cavity method to measure the refractive index of argon gas. The contribution of related parameters to the uncertainty of determined gas pressure is analyzed. The influences of material parameters and experimental parameters such as gas molar susceptibility, molar susceptibility, dielectric second Virial coefficient and temperature on gas pressure accuracy are analyzed. The result shows that the uncertainty in our measurement of argon within 1 atm is <inline-formula><tex-math id="M2">\begin{document}$u = \sqrt {{{(6\;{\rm{mPa}})}^2} + {{(73 \times {{10}^{ - 6}}p)}^2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20200706_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20200706_M2.png"/></alternatives></inline-formula>. Currently, the uncertainty mainly comes from the measurement deviation of gas temperature inside the cavity. After repeating the measurement a few times, the results show that the statistical uncertainty of refractive index is within 100 ppm, which is limited by the accuracy of the pressure gauge used here. In addition, we compare the dipole calculated by the <i>ab initio</i> method with that by the DOSD method. The results show that the dynamic polarizability obtained by the <i>ab initio</i> method is consistent with our experimental results. In conclusion, these experimental results show that the measurement of gas pressure based on the gas refractive index has high repeatability and accuracy. If the temperature control and corresponding measurement accuracy of the gas are further improved, this method can also be used to obtain high-precision microscopic parameters such as the polarizabilities of atoms and molecules. In the future work, we will focus on improving the temperature control and the design of the cavity to reduce cavity leakage and deflation. It is possible that the measurement accuracy of the gas pressure will be increased to 10 ppm level, which is the same level as the current standard pressure gauge and will become a new standard for pressure measurement in the future.

Structural and electronic properties of bulk and ultrathin layers of V2O5 and MoO3

The structural and electronic properties of bulk and ultrathin films of V2O5 and MoO3 layered oxides have been studied with first-principles density functional theory calculations including Van der Waals dispersion corrections. The U parameter in the DFT + U approach has been determined in order to properly reproduce geometry, band-gap, macroscopic dielectric constant, and formation enthalpies of the two materials. The mono-, and multi-layers are cleaved along the 〈0 0 1〉 and 〈0 1 0〉 stable crystallographic orientations for V2O5 and MoO3, respectively. Three layers are needed in order to recover bulk-like properties of V2O5 and MoO3. Spin-orbit effects have been incorporated in our simulations, and they result in marginal effects (∼20–30 meV) on the electronic band-gap of V2O5 and a more pronounced (∼200 meV) effect on the band gap of bulk MoO3. We also discuss the importance of including local field effects for the reproduction of the anisotropy of the dielectric constant, which reflects the crystal structure of these materials.

The behavior of ions in water is controlled by their water affinity.

The strong, long-range electrostatic forces described by Coulomb's law disappear for ions in water, and the behavior of these ions is instead controlled by their water affinity - a weak, short-range force which arises from their charge density. This was established experimentally in the mid-1980s by size-exclusion chromatography on carefully calibrated Sephadex® G-10 (which measures the effective volume and thus the water affinity of an ion) and by neutron diffraction with isotopic substitution (which measures the density and orientation of water molecules near the diffracting ion and thus its water affinity). These conclusions have been confirmed more recently by molecular dynamics simulations, which explicitly model each individual water molecule. This surprising change in force regime occurs because the oppositely charged ions in aqueous salt solutions exist functionally as ion pairs (separated by 0, 1 or 2 water molecules) as has now been shown by dielectric relaxation spectroscopy; this cancels out the strong long-range electrostatic forces and allows the weak, short-range water affinity effects to come to the fore. This microscopic structure of aqueous salt solutions is not captured by models utilizing a macroscopic dielectric constant. Additionally, the Law of Matching Water Affinity, first described in 1997 and 2004, establishes that contact ion pair formation is controlled by water affinity and is a major determinant of the solubility of charged species since only a net neutral species can change phases.

Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators

We present a general scheme of range-separated hybrid functionals in which the mixing parameters of Fock exchange are fully nonempirical and determined solely from the dielectric function. We show that the full dielectric dependence leads to an unscreened Fock exchange in the short range, while in the long range the Fock exchange is correctly screened by the macroscopic dielectric constant. The range separation is obtained by fitting to the calculated static dielectric function in the long-wavelength limit. The resulting hybrid functional accurately accounts for electronic and structural properties of various semiconductors and insulators spanning a wide range of band gaps.

Insights into the Impact of Native Defects on the Conductivity of CuVO3 Material for Photovoltaic Application: A First-Principles Computational Study.

We report a theoretical study on the impact of native defects present in CuVO3 material on its conductivity using first-principles calculations based on density functional theory. We find a low and direct band gap of 1.4 eV for the pristine cell together with relatively high solar absorption efficiency, high macroscopic dielectric constant, and delocalized orbital characters of photogenerated charge carriers. This result highlights CuVO3 as a good candidate for photovoltaic application. Among the various explored native defects (including vacancies, interstitials, and antisites), we demonstrate that only those associated with O vacancies are shallow donors and with Cu vacancies are shallow acceptors, leading respectively to n-type and p-type conductivities under O-poor and O-rich growing conditions.

Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices

Efficient analytical image charge models are derived for the full spatial variation of the electrostatic self-energy of electrons in semiconductor nanostructures that arises from dielectric mismatch using semi-classical analysis. The methodology provides a fast, compact and physically transparent computation for advanced device modeling. The underlying semi-classical model for the self-energy has been established and validated during recent years and depends on a slight modification of the macroscopic static dielectric constants for individual homogeneous dielectric regions. The model has been validated for point charges as close as one interatomic spacing to a sharp interface. A brief introduction to image charge methodology is followed by a discussion and demonstration of the traditional failure of the methodology to derive the electrostatic potential at arbitrary distances from a source charge. However, the self-energy involves the local limit of the difference between the electrostatic Green functions for the full dielectric heterostructure and the homogeneous equivalent. It is shown that high convergence may be achieved for the image charge method for this local limit. A simple re-normalisation technique is introduced to reduce the number of image terms to a minimum. A number of progressively complex 3D models are evaluated analytically and compared with high precision numerical computations. Accuracies of 1% are demonstrated. Introducing a simple technique for modeling the transition of the self-energy between disparate dielectric structures we generate an analytical model that describes the self-energy as a function of position within the source, drain and gated channel of a silicon wrap round gate field effect transistor on a scale of a few nanometers cross-section. At such scales the self-energies become large (typically up to ~100 meV) close to the interfaces as well as along the channel. The screening of a gated structure is shown to reduce the self-energy relative to un-gated nanowires.

A comprehensive study on carrier mobility and artificial photosynthetic properties in group VI B transition metal dichalcogenide monolayers

Artificial photosynthesis in group VI B transition metal dichalcogenide monolayers.

Empirical Multiphase Dielectric Mixing Model for Cement-Based Materials Containing Alkali-Silica Reaction Gel

Alkali-silica reaction (ASR) is a common cause of concrete deterioration. Water (either in free or bound form), in the presence of reactive aggregates, plays a major role in the reaction itself and in the formation and expansion of the deleterious gel produced. Since microwave signals are sensitive to the presence of water in dielectric materials, microwave materials characterization techniques have the potential to detect and monitor ASR gel in concrete structures. Dielectric mixing models are physics-based models that relate the macroscopic (i.e., effective) dielectric constant of a material to the dielectric constant of its constituents and their respective volumetric contents. In this investigation, an empirical multiphase dielectric mixing model is developed in conjunction with measured dielectric constants of two sets of mortar samples with ASR-reactive and nonreactive aggregates at R-band (1.7–2.6 GHz). The proposed model is capable of closely predicting the effective (temporal) dielectric constant of the samples. The modeling results are validated by a comparison with the measured temporal dielectric constant of the samples, showing good agreement. Through this investigation, quantitative information on the influence of constituents of ASR-reactive mortar samples (including ASR gel) are obtained, and the pertinent results indicate significant potential for microwave materials characterization techniques for ASR detection and evaluation.

Fully converged plane-wave-based self-consistentGWcalculations of periodic solids

The $GW$ approximation is a well-known method to obtain the quasiparticle and spectral properties of systems ranging from molecules to solids. In practice, $GW$ calculations are often employed with many different approximations and truncations. In this work, we describe the implementation of a fully self-consistent $GW$ approach based on the solution of the Dyson equation using a plane wave basis set. Algorithmic, numerical, and technical details of the self-consistent $GW$ approach are presented. The fully self-consistent $GW$ calculations are performed for GaAs, ZnO, and CdS including semicores in the pseudopotentials. No further approximations and truncations apart from the truncation on the plane wave basis set are made in our implementation of the $GW$ calculation. After adopting a special potential technique, a $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{Ry}$ energy cutoff can be used without the loss of accuracy. We found that the self-consistent $GW$ (sc-$GW)$ significantly overestimates the bulk band gaps, and this overestimation is likely due to the underestimation of the macroscopic dielectric constants. On the other hand, the sc-$GW$ accurately predicts the $d$-state positions, most likely because the $d$-state screening does not sensitively depend on the macroscopic dielectric constant. Our work indicates the need to include the high-order vertex term in order for the many-body perturbation theory to accurately predict the semiconductor band gaps. It also sheds some light on why, in some cases, the ${G}_{0}{W}_{0}$ bulk calculation is more accurate than the fully self-consistent $GW$ calculation, because the initial density-functional theory has a better dielectric constant compared to experiments.

Solvent effect on protonation of tpps in water-DMF mixtures

The protonation of 5,10,15,20-tetrakis(4-sulfonatophenyl)porphyrin was investigated in aqueous solutions of N,N-dimethyformamide at 25 °C and 0.1 mol.dm-3 sodium perchlorate. The solvent effect on value of protonation constant was examined by using the linear solvation energy relationship concept. The value of logK1,logK2 and logKt was correlated with the macroscopic (dielectric constant) and microscopic Kamlet-Taft parameters (a, b and p*) of binary mixtures. The solvent effects were analyzed in the terms of Kamlet, Abboud and Taft model (KAT). Multiple linear regression were used to find the contribution of the microscopic parameters containing a (hydrogen-bond acidity), p* (dipolarity/polarizability) and b (hydrogen-bond basicity). It was found that a and b were the most predominant descriptors. Also, relationship with reciprocal of dielectric constant was obtained based on Born’s model, showing the significance of specific solute-solvent interactions. Therefore the hydrogen bonding interactions between solute and solvent components are mainly responsible for the change in protonation constants of 5,10,15,20-tetrakis(4-sulfonatophenyl)porphyrin in water- N,N-dimethyformamid binary mixtures. KEY WORDS: Protonation, TPPS, Solvent effects, Aqueous mixture, DMF Bull. Chem. Soc. Ethiop. 2016, 30(3), 457-464DOI: http://dx.doi.org/10.4314/bcse.v30i3.14

Computing the Kirkwood g-Factor by Combining Constant Maxwell Electric Field and Electric Displacement Simulations: Application to the Dielectric Constant of Liquid Water.

In his classic 1939 paper, Kirkwood linked the macroscopic dielectric constant of polar liquids to the local orientational order as measured by the g-factor (later named after him) and suggested that the corresponding dielectric constant at short-range is effectively equal to the macroscopic value just after "a distance of molecular magnitude" [ Kirkwood, J. Chem. Phys., 1939, 7, 911 ]. Here, we show a simple approach to extract the short-ranged Kirkwood g-factor from molecular dynamics (MD) simulation by superposing the outcomes of constant electric field E and constant electric displacement D simulations [ Zhang and Sprik, Phys. Rev. B: Condens. Matter Mater. Phys., 2016, 93, 144201 ]. Rather than from the notoriously slow fluctuations of the dipole moment of the full MD cell, the dielectric constant can now be estimated from dipole fluctuations at short-range, accelerating the convergence. Exploiting this feature, we computed the bulk dielectric constant of liquid water modeled in the generalized gradient approximation (PBE) to density functional theory and found it to be at least 40% larger than the experimental value.

Atomistic electrodynamics simulations of bare and ligand-coated nanoparticles in the quantum size regime.

The optical properties of metallic nanoparticles with nanometre dimensions exhibit features that cannot be described by classical electrodynamics. In this quantum size regime, the near-field properties are significantly modified and depend strongly on the geometric arrangements. However, simulating realistically sized systems while retaining the atomistic description remains computationally intractable for fully quantum mechanical approaches. Here we introduce an atomistic electrodynamics model where the traditional description of nanoparticles in terms of a macroscopic homogenous dielectric constant is replaced by an atomic representation with dielectric properties that depend on the local chemical environment. This model provides a unified description of bare and ligand-coated nanoparticles, as well as strongly interacting nanoparticle dimer systems. The non-local screening owing to an inhomogeneous ligand layer is shown to drastically modify the near-field properties. This will be important to consider in optimization of plasmonic nanostructures for near-field spectroscopy and sensing applications.

Structural phase transition, electronic structures and optical properties of ZnTe

The equations of state and phase transition of ZnTe in zinc blende (ZB) and cinnabar (CB) structures under high pressure are investigated by the projected augmented wave method in the scheme of density functional theory. The primitive cell volumes, electronic structures and optical properties are also predicted before and after phase transition. The variations of the calculated total energy with volume, for the structures of ZB and CB, yield the information about the static equation of state and phase stability. The results show that the ZB phase of ZnTe has lower energy, and is more stable than its CB phase. The pressure-induced transition occurs along the common tangent line connecting the tangential points on the two enthalpy-volume curves. The calculations show that the phase transition pressure is 8.6 GPa from the ZB structure to the CB structure. The value is also compatible with those of other available theoretical and experimental results. Just before the ZB phase is transferred to the CB phase at about 8.6 GPa, the volume is reduced by 13.0% relative to the former volume at the ambient pressure condition. The calculated critical volumes and volume compressibilities by using two methods agree well with other results in the literature. The lattice parameters and equations of state of the two structures are also obtained. Metallization case of other similar materials such as ZnS caused by high pressure does not occur here. The CB phase has the behavior of indirect band gap with 0.98 eV along the symmetry of GK. After phase transition, the distributions of density of states of Zn and Te atoms of the CB structure shift towards lower energy, especially in the conduction band bottom, and the band gap decreases. Energy level overlapping is more obvious in the CB structure, and orbital hybridizations still exist, that is the reason why it is the stable phase under high pressure condition. Stronger orbital hybridization helps the transitions between Te 5p and Zn 3d electrons. The main peak of imaginary part of dielectric constant is enhanced apparently with abnormal red shift, while other two peaks disappear at the same time. Macroscopic dielectric constant of ZB structure decreases as pressure increases. For CB structure, the macroscopic dielectric constant with 13.60 eV is not affected by pressure. The results provide a theoretical basis for the polarization research of ZnTe material in static electric field under high pressure.

Electrostatics-based finite-size corrections for first-principles point defect calculations

Finite-size corrections for charged defect supercell calculations typically consist of image-charge and potential alignment corrections. A wide variety of schemes for both corrections have been proposed for decades. Regarding the image-charge correction, Freysoldt, Neugebauer, and Van de Walle (FNV) recently proposed a novel method that enables us to accurately estimate the correction energy a posteriori through alignment of the defect-induced potential to the model charge potential [Freysoldt et al., Phys. Rev. Lett. 102, 016402 (2009)]. This method, however, still has two issues in practice. Firstly, it uses planar-averaged potential for determining the potential offset, which cannot be readily applied to relaxed system. Secondly, the long-range Coulomb interaction is assumed to be screened by a macroscopic dielectric constant. This is valid only for cubic systems and can bring forth huge errors for defects in anisotropic materials. In this study, we use the atomic site electrostatic potential as a potential marker instead of the planar-averaged potential, and extend the FNV scheme by adopting the point charge model in an anisotropic medium for estimating long-range interactions. We also revisit the conventional potential alignment correction and show that it is fully included in the image-charge correction and therefore unnecessary. In addition, we show that the potential alignment corresponds to a part of first-order and full of third-order image-charge correction; thus the third-order image-charge contribution is absent after the potential alignment. Finally, a systematic assessment of the accuracy of the extended FNV correction scheme is performed for a wide range of material classes. The defect formation energies calculated using around 100-atom supercells are successfully corrected even after atomic relaxation within a few tenths of eV compared to those in the dilute limit.