Dynamic Effective Charge Research Articles

Temperature and pressure dependences of the dielectric constants of semiconductors

The effects of temperature and hydrostatic pressure on the static dielectric constant ($\ensuremath{\epsilon}$) were investigated for a group of crystalline semiconductors chosen to be representative of III-V compounds (GaAs and GaP), II-VI compounds (ZnS and CdS), and group-IV (Si) materials. When combined with earlier results on the temperature and pressure dependences of the high-frequency optical (i.e., electronic) dielectric constants (${\ensuremath{\epsilon}}_{\ensuremath{\infty}}$), the present results allow, for the compound semiconductors, determination of the lattice contribution to these effects. The results are discussed from both the microscopic and macroscopic points of view. For all the crystals studied, the pressure effects are dominated by the change in polarizability with volume, and the temperature effects by anharmonicities. The pressure dependences of the lattice contributions to the dielectric constants (${\ensuremath{\epsilon}}_{11}$ and ${\ensuremath{\epsilon}}_{33}$) of hexagonal CdS are anomalous in that they increase with pressure. This behavior is most likely due to coupling between the appropriate TO modes and the TA modes which are known to soften on approaching the pressure-induced phase transition in this crystal. The transverse dynamic effective charge was calculated for the compounds, and its pressure dependence was determined for GaAs and GaP. The results and their implications are discussed.

Activités Raman et Infrarouge des Cristaux Piezoélectriques BeSO4, 4H2O et BeSO4, 4D2O. 2—Activité Raman des Modes Polaires

AbstractLes cristaux BeSO4, 4H2O et BeSO4, 4D2O étudiés par diffusion Raman (4000 à 4 cm−1) montrent tous deux des éclatements TO‐LO qui confirment leur structure à caractère piezoélectrique. Des modes obliques distincts montrent un caractére mixte B2 et E. Des charges dynamiques effectives ont été calculées. Un effet électrooptique a été mis en évidence.

Far‐Infrared Reflection Spectra, Optical and Dielectric Constants, Effective Charges, and Lattice Dynamics of the Skutterudites CoP3, CoAs3, and CoSb3

AbstractFrom the far‐infrared reflection spectra of the skutterudite type compounds CoP3, CoAs3, and CoSb3 the TO and LO phonon frequencies at wave vector |q| ≈ 0 are determined by both Kramers‐Kronig analysis and classical oscillator fit method. In the case of CoP3 large free carrier contributions (plasma resonance frequency ω′p ⩽ Ω+ ≈ 800 cm−1) with strong plasmon–phonon interactions are observed. Attempts to calculate the decoupled phonon frequencies of CoP3 using a three and a four parameter model of the dielectric function failed. Lattice dynamical calculations are done by setting up a valence force field consisting of M–X, two X–X and X4–X4, and M–M stretching constants. The obtained force constants, e.g. f(CoSb): 85, f(SbSb): 87 and 59 N m−1, respectively, and also the calculated effective dynamical charges (from TO/LO splittings) show the mainly covalent character of the skutterudites under consideration. The lattice modes of CoSb3 are found to be both mainly internal vibrations of the planary Sb4‐units, v4 and v5, at 174 and 144 cm−1, respectively, and external ones, v1–v3 and v6–v7, at higher and lower wavenumbers than v4 and v5.

LO‐TO Mode Splittings and Dynamic Effective Charges of Oxygen in Reactively Sputtered SiOx Determined by IR Spectroscopy

LO‐TO Mode Splittings and Dynamic Effective Charges of Oxygen in Reactively Sputtered SiO_x Determined by IR Spectroscopy

Direct method of calculation of dynamic effective charges: Application to GaAs

A method is described for the calculation of effective charges and piezoelectric constants in crystals directly from self-consistent electronic calculations. The central equations are based upon moments of the change in electronic charge density $\ensuremath{\delta}n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ caused by the displacement of an atom. The long-range Coulomb interactions are taken into account, and it is shown that the moments are rigorously convergent and define longitudinal effective charges and piezoelectric constants. The method is not limited to small displacements and, in fact, uses exactly the same techniques which have been extensively developed for the calculation of surface and interface dipoles. Results are presented for the effective charge in GaAs using the same ionic pseudopotentials and density functional for the electrons that predict accurately the lattice constant and phonon energies. The predicted charge is ${e}_{L}^{*}=0.16|e|$ (positive on Ga) compared to the experimental value ${e}_{L}^{*}=\frac{{e}_{T}^{*}}{{\ensuremath{\epsilon}}_{0}}=\ifmmode\pm\else\textpm\fi{}0.20|e|$.

Lattice dynamics of BaFBr

A normal coordinate and force constant calculation for BaFBr was carried out on the basis of the rigid ion model. There is a strong anisotropy of the effective dynamical charges of the barium, fluoride, and bromide ions, which are 1.57e, −0.78e, and −0.79e for the degenerate vibrations and 1.04e, −0.71e, and −0.33e for the vibrations in the z-direction. In accordance with the ionic nature of BaFBr the short range force constants have only small values.

Ionicity scale and piezoelectricity of crystals with zincblende- and wurtzite-type structure

We have tried to determine the ionicity of crystals with a dynamical effective ionic charge defined by the observed TO- LO splitting. We find excellent agreement between our results and the ionicity scale derived by Phillips from band gap theory. We confirm that the observed piezoelectric constants can be well accounted for on the basis of the Born lattice-dynamical treatment by adding the concept of charge transfer, and we have made an estimate of the latter.

Activité Raman du m‐Chloronitrobenzène, Cristal Piézo‐électrique

AbstractThe piezo‐electric crystal m‐C6H4ClNO2 was studied by Raman scattering. TO–LO splitting of 1–7 cm−1 was observed for some internal modes and correlated to the infrared intensities. The observed Raman lines corresponding to the vsNO2 mode are interpreted through an analysis using G0(k,–k) subgroups of the factor group G0(0). The effective dynamical charges were calculated. The polaritons corresponding to the vs(NO2)A1 mode and skeletal mode at 1123 cm−1 were observed.

Vibrational excitations and structure of CO chemisorbed on Cu(100)

The local adsorption site for CO chemisorbed on Cu(100) at 80 K has been investigated by vibrational spectroscopy at different structural situations as defined by low-energy electron diffraction. The high-resolution electron energy loss spectrum for the c(2 × 2) CO structure (coverage 0.5) is compatible with a terminal CuCO bond. The spectrum shows two vibrational loss lines at 43 and 260 meV due to excitations of the CuC and CO stretcning vibrations respectively. The CO stretchning vibration is excited via dipole interaction for primary electron energies 1–4 eV. An effective dynamic charge of 0.64 e is deduced in good agreement with infrared reflection-absorption data. The preceeding CO lattice gas is also characterized by the terminal bond configuration. The spectrum for the CO compression structure at coverage 0.57 is tentatively interpreted in terms of an alternative site (terminal and bridge) absorption model proposed by Pritchard. A brief comparision with the Ni(100)-CO system is made.

Dynamic effective charge and surface reconstruction on Si(111)

The previously developed soft-mode theory of surface reconstruction is applied to the (111) surface of silicon. It is shown that the mutual interaction of surface dynamic effective charges can cause the ideal equilibrium configuration of the surface atoms to be unstable, thus leading to reconstruction. This instability is studied in detail using lattice-dynamical methods and it is found that dynamic effective charges on the order of $0.5e$ can lead to the 2 \ifmmode\times\else\texttimes\fi{} 1 reconstruction observed experimentally. The directions in which the atoms displace due to the instability are shown and a new atomic configuration for the reconstructed surface is thereby predicted. The results are found to be nearly independent of the details of surface relaxation, of the distribution of the dynamic effective charges, and of the supposed weakening of the short-range forces in the surface region.

Dynamical effective charges in semiconductors: A pseudopotential approach

A method for an ab-initio calculation of transverse dynamical effective charges Z* in partially covalent semiconductors within the framework of pseudopotential theory is presented. It is based on previously established expressions for Z* in terms of the inverse microscopic dielectric function of the crystal but circumvents the direct inversion of the latter. In contrast to earlier calculations the results are definitely boundary insensitive. Moreover, the acoustic sum rule expressing charge neutrality is inherently guaranteed. Within the local empirical pseudopotential method a simple analytical model calculation, which is compared with the bond orbital model, as well as a full numerical computation is performed. For III-V compounds the resulting Z* underestimate the experimental effective charges by approximately 30% while good agreement for II-VI materials is obtained. Reasons for these findings are discussed and the effects of several refinements are estimated.

Interaction of low-energy electrons with surface lattice vibrations

In the present article, we examine the interaction of low-energy electrons near the crystal surface with lattice vibrations of the surface region. Our primary attention is devoted to the use of the inelastic scattering of low-energy electrons to elucidate the nature of this interaction, and to obtain information about the nature of atomic vibrations in and near the surface. We review both the theoretical and the experimental literature in this area, within the framework of a discussion of the concepts which are required to interpret the data. We also present a discussion of a number of closely related topics, such as the origin of the image potential in ionic crystals, the properties of the surface polaron, the surface dynamic effective charge and its possible relation to the phenomenon of surface reconstruction, and the scattering by electronic excitations of low-energy electrons incident on the surface.

Electronegativity, Ionicity, and Effective Atomic Charges

This paper reviews the concepts of electronegativity and ionicity, together with the concept of effective static atomic charge which is associated with them. It is briefly recalled that the ionicity of a chemical bond has two components: a chemical component linked to the valency of the atoms and to their short distance spatial arrangement, and an electrostatic component linked to their effective charge. In solids, however, the appearance of group vibrations of the atoms also introduces the concept of effective dynamic charge, taking account of dielectric phenomena. Emission, absorption, and diffraction of x‐rays are related to these two kinds of effective atomic charges and may be used for evaluating them. The substitution, in the second component of ionicity, of the dynamic charge for the static charge probably defines something different from what is usually called ionicity.

Bond charge model for the transverse dynamic effective charge and the piezoelectric constant of zincblende‐type crystals

AbstractA bond charge model for the transverse dynamic effective charge and the piezoelectric constant of the zincblende structure is presented. It works with analytical pseudopotentials and leads to simple analytical results, which yield numerical agreement with experimental data. The transverse dynamic effective charge is obtained from ionic and electronic polarizations arising in an optic‐mode sublattice displacement. The piezoelectric constant is calculated regarding additionally the effects of a macroscopic strain in a deformable‐ion model. It consists of an internal‐displacement term and a charge redistribution term, the latter comes from the bond charge. Both are of the same order of magnitude but of opposite sign and confirm quantitatively Lawaetz' qualitative local‐field analysis of Martin's theory of the piezoelectric effect.

Comment on calculations of electric polarization in crystals

A calculation of lattice dynamical effective charges by Bennett and Maradudin is shown to be based upon an incorrect expression for the electric polarization produced by displacement of the atoms. The basic point is that the polarization of a crystal cannot be derived solely in terms of the charge density in a unit cell in an infinite periodic crystal. The correct polarization is most readily evaluated from well-known finite-wave-vector expressions.

The dielectric and lattice vibrational spectrum of cuprous oxide

The i.r. reflection and Raman spectra of single crystal specimens of cuprous oxide have been studied between 20 and 900 cm−1 over a wide temperature range. The optical and dielectric parameters have been derived by Kramers-Krönig analysis and the effective dynamic charge calculated. The Raman spectrum is far more complex than a group theoretical analysis suggests and this is interpreted in terms of a selection rule breakdown in the crystal due to nonstoichiometry. Variable temperature and polarisation measurements have been made in order to characterise some of the structure in the spectrum. The implications of the results for the lattice dynamical calculations is discussed.

Soft Surface Phonons and Surface Reconstruction

We propose a new mechanism which can lead to reconstruction in the surface region of a large class of materials. The mechanism is based on the fact that the dynamic effective charges present on the atoms near the surface can be different from those on the atoms in the bulk. The long-range interaction of these charges can cause the surface phonon to be lowered in frequency. We present numerical calculations of the normal-mode frequencies of a simple-cubic monatomic slab [(001) faces] of 15 layers when surface-induced dynamic effective charges are present near one of the surfaces. For reasonable values of the short-range atomic force constants, and for values of the dynamic effective charge on the surface layer of the order of 0.5e, the surface is unstable and recontruction occurs. Various patterns of reconstruction can be obtained depending upon the values of the short-range force constants.

Piezoelectricity in Zincblende‐ and Wurtzite‐Type Crystals

AbstractA phenomenological model for the piezoelectric effect in zincblende‐ and wurtzite‐type crystals is proposed on the basis of optic and dielectric lattice properties. By introduction of a deformation charge it is shown that the sign of the longitudinal piezoelectric constant is determined by the ionicity of the chemical bond. The piezoelectric constant is calculated with correct sign and found to be in good numerical agreement with experimental data. For a number of I–VII, II–VI, and III–V compounds piezoelectric constants are predicted. With the piezoelectric effect the sign of the dynamic effective charges is determined.

Soft-Mode Theory of Surface Reconstruction

We present a mechanism capable of explaining surface reconstruction which is based on the fact that the presence of the surface can change the value of the dynamic effective charge on the atoms near the surface. We perform a lattice dynamical calculation and find that the long-range interaction between these induced charges can lower the frequency of the surface phonon to the point where the surface region becomes unstable and reconstruction must occur.

Dynamic Effective Charge of a Finite Linear Chain

A formalism for calculating the dynamic effective charge induced on the atoms of a homopolar crystal by the presence of a surface is presented in the framework of the tight-binding approximation. The method is applied to a one-dimensional chain of two-electron atoms for the purposes of illustration and identification of the critical model parameters. The wave function of the chain is constructed from a linear combination of $s$-like and $p$-like atomic orbitals. In the infinite chain, symmetry requires the dynamic effective charge of each atom to vanish. The presence of the free ends in the finite chain, however, induces dynamic effective charges on the atoms which decay in magnitude with increasing distance from the ends. It is found that the important model parameters are the energy band gap and the hopping integral between $s$ and $p$ states centered on adjacent sites. The dependence of the dynamic effective charge on these two parameters is presented.