Showing papers in "Physical Review B in 1980"

Soliton excitations in polyacetylene

Abstract: A theoretical analysis of the excitation spectrum of long-chain polyenes is presented. Because of the twofold degeneracy of the ground state of the dimerized chain, elementary excitations corresponding to topological solitons are obtained. The solitons can have three charge states $Q=0$. $\ifmmode\pm\else\textpm\fi{}e$. The neutral soliton has spin one-half while the charged solitons have spin zero. One electronic state is localized at the gap center for each soliton or antisoliton present. The soliton's energy of formation, length, mass, activation energy for motion, and electronic properties are calculated. These results are compared with experiment.

Critical exponents from field theory

Abstract: We present a detailed study of the methods of summation based on Borel transformation and conformal mapping, which we have used to calculate critical exponents of the $n$-vector model through field theoretical methods. In particular we discuss the sensitivity of the results to various changes in the summation procedure.

Fluctuation-induced tunneling conduction in disordered materials

Abstract: In disordered materials generally characterized by large conducting regions (or long conducting pathways) separated by small insulating barriers, it is shown that the electrical conduction can be ascribed to a novel mechanism, fluctuation-induced tunneling, in which the thermally activated voltage fluctuations across insulating gaps play an important role in determining the temperature and field dependences of the conductivity. By considering the modulating effects induced by voltage fluctuations on either an image-force corrected rectangular potential barrier or a parabolic barrier, a theoretical expression for the tunneling conductivity is derived which displays thermally activated characteristics at high temperatures but becomes identical to the temperature-independent simple elastic tunneling at low temperatures. Between the two limiting behaviors the temperature dependence of the conductivity is controlled by the shape of the tunneling barrier. An expression for the high-field tunneling current is similarly obtained. It is found that, while the tunneling current increases as a nonlinear function of the field, the degree of nonlinearity decreases as the temperature increases, indicating an effective lowering and narrowing of the barrier by voltage fluctuations. The theory is also generalized from the consideration of a single tunnel junction to a random network of tunnel junctions by the application of the effective-medium theory. The theoretical predictions are compared with the experimental results for three disordered systems: (1) carbon-polyvinylchloride composites, (2) heavily doped, closely compensated GaAs, and (3) doped polyacetylene ${(\mathrm{CH})}_{x}$ in the metallic regime. In each case excellent agreement is obtained. It is shown in particular that the nonmetallic temperature dependence of the resistivity in doped metallic ${(\mathrm{CH})}_{x}$ samples can be understood in terms of the present theory.

Renormalization-group approach to the Anderson model of dilute magnetic alloys. I. Static properties for the symmetric case

Abstract: The temperature-dependent impurity susceptibility for the symmetric Anderson model is calculated for all physically relevant values of its parameters $U$ (the Coulomb correlation energy) and $\ensuremath{\Gamma}$ (the impurity-level width). It is shown that, when $Ug\ensuremath{\pi}\ensuremath{\Gamma}$, for temperatures $Tl\frac{U}{(10{k}_{B})}$ the symmetric Anderson model exhibits a local moment and that its susceptibility maps neatly onto that of the spin-\textonehalf{} Kondo model with an effective coupling given by $\ensuremath{\rho}{J}_{\mathrm{eff}}=\ensuremath{-}\frac{8\ensuremath{\Gamma}}{\ensuremath{\pi}U}$. Furthermore, this mapping is shown for remarkably large values of $|\ensuremath{\rho}{J}_{\mathrm{eff}}|$. At very low temperatures (much smaller than the Kondo temperature) the local moment is frozen out, just as for the Kondo model, leading to a strong-coupling regime of constant susceptibility at zero termperature. The results also depict the formation of a local moment from the free orbital as $T$ drops below $U$, a feature not present in the Kondo model. Finally, when $U\ensuremath{\ll}\ensuremath{\pi}\ensuremath{\Gamma}$ there is a direct transition from free-orbital regime for $T\ensuremath{\gg}\ensuremath{\Gamma}$ to the strong-coupling regime for $T\ensuremath{\ll}\ensuremath{\Gamma}$. The calculations were performed using the numerical renormalization group originally developed by Wilson for the Kondo problem. In addition to the actual numerical calculations, analytic results are presented. In particular, the effective Hamiltonians, i.e., fixed-point Hamiltonian plus relevant and marginal operators, are constructed for the free-orbital, local-moment, and strong-coupling regimes. Analytic formulas for the impurity susceptibility and free energy in all three regimes are developed. The impurity specfic heat in the strong-coupling regime is calculated.

Magnetoresistance and Hall effect in a disordered two-dimensional electron gas

Abstract: Two models of disorder in two dimensions are discussed. The first is a localization theory that treats noninteracting particles by perturbation theory in the weak scattering limit. A weak magnetic field is found to have strong effects on the previously predicted logarithmic rise in resistivity at low temperatures. No logarithmic divergence is found for the Hall constant. A second model treats the disorder scattering by conventional diagramatic technique but includes the effects of interactions. In a short communication it has previously been reported that the resistivity and Hall constant both show a logarithmic increase at low temperatures. The details of the calculation are reported here, together with an extension to thin wires which shows a ${T}^{\ensuremath{-}\frac{1}{2}}$ divergence in the resistivity.

New method for a scaling theory of localization

Abstract: We base a scaling theory of localization on an expression for conductivity of a system of random elastic scatterers in terms of its scattering properties at a fixed energy. This expression, proposed by Landauer, is first derived and generalized to a system of indefinite size and number of scattering channels (a "wire"), and then an exact scaling theory for the one-dimensional chain is given. It is shown that the appropriate scaling variable is $f(\ensuremath{\rho})=\mathrm{ln}(1+\ensuremath{\rho})$ where $\ensuremath{\rho}$ is the dimensionless resistance, which has the property of "additive mean," and that scaling leads to a well-behaved probability distribution of this variable and to a very simple scaling law not previously given in the literature.

Continuum model for solitons in polyacetylene

Abstract: Solitons in a one-dimensional charge-density-wave system with half-filled electron bands are studied theoretically with a continuum model. This model is a continuum version of the one of polyacetylene recently considered by Su, Schrieffer, and Heeger (SSH). We have analyzed a variational solution with the displacement order parameter $\ensuremath{\Delta}(x)={\ensuremath{\Delta}}_{0}tanh(\frac{x}{\ensuremath{\xi}})$ with $\ensuremath{\xi}$ as a variational parameter. It is shown within the weak-coupling limit that the soliton (creation) energy takes the minimum value $(\frac{2}{\ensuremath{\pi}}){\ensuremath{\Delta}}_{0}$ with $\ensuremath{\xi}=\frac{\ensuremath{\hbar}{v}_{F}}{{\ensuremath{\Delta}}_{0}}$, where $2{\ensuremath{\Delta}}_{0}$ and ${v}_{F}$ are the dimerization energy gap and the Fermi velocity, respectively. These results agree quite well with numerical results by SSH for the discrete system. Furthermore, we show that the above $\ensuremath{\Delta}(x)$ is an exact solution of the self-consistent Bogoliubov-de Gennes equation.

Core-level binding-energy shifts for the metallic elements

Abstract: A general treatment of core-level binding-energy shifts in metals relative to the free atom is introduced and applied to all elemental metals in the Periodic Table. The crucial ingredients of the theoretical description are (a) the assumption of a fully screened final state in the metallic case and (b) the ($Z+1$) approximation for the screening valence charge distribution around the core-ionized site. This core-ionized site is, furthermore, treated as an impurity in an otherwise perfect metal. The combination of the complete screening picture and the ($Z+1$) approximation makes it possible to introduce a Born-Haber cycle which connects the initial state with the final state of the core-ionization process. From this cycle it becomes evident that the main contributions to the core-level shift are the cohesive energy difference between the ($Z+1$) and $Z$ metal and an appropriate ionization energy of the ($Z+1$) atom (usually the first ionization potential). The appearance of the ionization potential in the shift originates from the assumption of a charge-neutral final state, while the contribution from the cohesive energies essentially describes the change of bonding properties between the initial and final state of the site. The calculated shifts show very good agreement with available experimental values (at present, for 19 elements). For the other elements we have made an effort to combine experimental ionization potentials with theoretical calculations in order to obtain accurate estimates of some of the atomic-core-level binding energies. Such energies together with measured metallic binding energies give "pseudoexperimental" shifts for many elements. Our calculated core-level shifts agree exceedingly well also with these data. For some of the transition elements the core-level shift shows a deviating behavior in comparison with that of neighboring elements. This is shown to be due to a difference in the atomic ground-state configuration, such as, for example, ${d}^{5}s$ in chromium relative to the ${d}^{n}{s}^{2}$ configuration in vanadium and manganese. When the core-level shift is referred to, the ${d}^{n}{s}^{2}$ (or ${d}^{n+1}s$) atomic configuration for all the elements in a transition series, a quite regular behavior of the shift is found. However, some structure can still be observed originating from a change of screening within the $d$ band from a bonding to an antibonding type as one proceeds through the series. For elements beyond the coin metals the screening of a core hole is performed by $p$ electrons, which provide a less effective screening mechanism than the $d$ electrons for the transition metals. The coin metals are intermediate cases, partly due to a dominating $s$-electron screening and partly due to $d$-electron bonding in the initial state. The effect of the electron-density redistribution between the free atom and the solid on the core-level shift is particularly striking in the case of the rare-earth elements Pr-Sm and Tb-Tm. Here the remarkable situation is that a deep core electron is less bound in the atom than in the solid. Also for the actinides the electronic redistribution upon condensation gives rise to pronounced effects on the core-level shifts. Further, it is shown that the measured $6{p}_{\frac{3}{2}}$ binding energy in metallic uranium provides a clear demonstration of the occupation of the $5f$ level in this metal. The present treatment of the core-level shift for bulk metallic atoms can easily be generalized to surface atoms. From an empirical relation for the surface energy a simple expression for the shift of the surface core-level relative to the bulk can be derived. For the earlier transition metals, it is found that the core electrons are more bound at the surface than in the bulk, while for the heavier ones the opposite situation exists. This change of sign of the surface shift depends on the bonding-antibonding division of the $d$ band. To illustrate how the present approach can be applied to alloy systems, a treatment of core-level shifts for rare-gas atoms implanted in noble metals is undertaken.

Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works

Abstract: A complete wave-vector analysis has been made of the gradient coefficient for the exchange-correlation energy of a nonuniform electronic system. It is shown that the majority of the contribution comes from a very small but universal region of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space near the origin. From this it can be concluded that random-phase-approximation-like calculations, like the present one or that of Rasolt and Geldart, which treat this region correctly, are likely to provide accurate results for the gradient coefficient and hence for the energy and structure of a system whose density is truly slowly varying. However, it also shows that the criterion for the validity of the gradient approximation itself is much more severe than previously supposed, so that the usual type of application, to say a surface or bulk material, is incorrect. For the surface case this is verified in unequivocal detail. On the other hand, a generalization of the gradient scheme based on an average slope instead of a local slope is proposed. This gives good agreement with limiting cases where they exist, and rough agreement with the interpolation scheme proposed previously by the authors.

Ising model with solitons, phasons, and "the devil's staircase"

Abstract: We have analyzed the modulated phase of an Ising model with competing interactions in an effort to increase the understanding of the spatially modulated phases found in many physical systems. The analysis has three stages. First, the mean-field phase diagram is calculated numerically. A large, possibly infinite, number of phases where the periodicity of the ordered structure is commensurate with the lattice is found. The resulting periodicity-versus-temperature curve thus probably has an infinity of steps; i.e., it exhibits "the devil's staircase" behavior. Then the mean-field theory is analyzed analytically, and it is shown that the stability of the commensurate phases can be understood within a domain-wall or "soliton" theory. The solitons from a regular lattice near the transitions to the commensurate phases. The elementary excitations in the solition lattice are the phasons. Third, the effects of temperature-induced fluctuations, ignored in the mean-field theory, are estimated by calculating the entropy contribution to the free energy from the phasons. It is found that the stability ranges of the commensurate phases are reduced, but the staircase survives at finite temperatures. On the basis of our calculations a phase diagram is constructed.

Mott's formula for the thermopower and the Wiedemann-Franz law

Abstract: The Mott formula for the thermopower, $S=\frac{(\frac{{\ensuremath{\pi}}^{2}}{3})(\frac{{k}_{B}^{2}T}{e}){\ensuremath{\sigma}}^{\ensuremath{'}}}{\ensuremath{\sigma}}$, and the Wiedemann-Franz law, $\frac{K}{\ensuremath{\sigma}T}={(\frac{{k}_{B}}{e})}^{2}(\frac{{\ensuremath{\pi}}^{2}}{3})$, are shown to be exact for independent electrons interacting with static impurities and phonons treated in the adiabatic approximation. This is true irrespective of the interaction strength. These results are derived using a Green's-function technique that emphasizes the importance of corrections to the free-electron heat current operator. These corrections have frequently been neglected in the past. The Green's-function technique is well suited for going beyond the adiabatic phonon approximation, and the implications of doing so are briefly discussed.

Calculating properties with the coherent-potential approximation

Abstract: It is demonstrated that the expression that has hitherto been used for calculating the Bloch spectral-density function ${A}^{B}(E,\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ in the Korringa-Kohn-Rostoker coherent-potential-approximation theory of alloys leads to manifestly unphysical results. No manipulation of the expression can eliminate this behavior. We develop an averaged Green's-function formulation and from it derive a new expression for ${A}^{B}(E,\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ which does not contain unphysical features. The earlier expression for ${A}^{B}(E,\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ was suggested as plausible on the basis that it is a spectral decomposition of the Lloyd formula. Expressions for many other properties of alloys have been obtained by manipulations of the Lloyd formula, and it is now clear that all such expressions must be considered suspect. It is shown by numerical and algebraic comparisons that some of the expressions obtained in this way are equivalent to the ones obtained from a Green's function, while others are not. In addition to studying these questions, the averaged Green's-function formulation developed in this paper is shown to furnish an interesting new way to approach many problems in alloy theory. The method is described in such a way that the aspects of the formulation that arise from the single-site approximation can be distinguished from those that depend on a specific choice for the effective scatterer.

Low-temperature properties of the random Heisenberg antiferromagnetic chain

Abstract: The one-dimensional quantum spin-\textonehalf{} Heisenberg antiferromagnetic model with randomly distributed interaction strengths is solved approximately for several different distributions. Ground-state energy and low-temperature properties are evaluated. Universal qualitative features are found in the specific heat and the magnetic susceptibility, which display a power-law dependence on temperature. Such features hold for nonsingular distributions as well as for distributions with power-law divergence at the origin. The approximate method of solution is based on successive eliminations of spins coupled by the maximum coupling constant.

Dynamics of superfluid films

Abstract: A theory of the dynamical properties of a helium film near its superfluid transition is presented. Details are given of previously published results on the linear response of the film to a substrate oscillation. A key role is played by the diffusive motion of quantized vortices, which become free above the thermodynamic Kosterlitz-Thouless temperature ${T}_{c}$ but which only exist as bound pairs below ${T}_{c}$. An analogy with a two-dimensional plasma is presented and used. Contact is made with experiments involving oscillating substrates. The nucleation of single vortices from pairs is calculated, and this process is balanced against pair recombination to calculate the rate of decay of superflow below ${T}_{c}$. Formulas are worked out for the propagation and damping of third sound, and a discussion is given of hydrodynamic modes. An analogy between the dynamical equations for the film and Maxwell's equations is exploited.

Large-cell Monte Carlo renormalization group for percolation

Abstract: We obtain the critical parameters for the site-percolation problem on the square lattice to a high degree of accuracy (comparable to that of series expansions) by using a Monte Carlo position-space renormalization-group procedure directly on the site-occupation probability. Our method involves calculating recursion relations using progressively larger lattice rescalings, $b$. We find smooth sequences for the value of the critical percolation concentration ${p}_{c}(b)$ and for the scaling powers ${y}_{p}(b)$ and ${y}_{h}(b)$. Extrapolating these sequences to the limit $b\ensuremath{\rightarrow}\ensuremath{\infty}$ leads to quite accurate numerical predictions. Further, by considering other weight functions or "rules" which also embody the essential connectivity feature of percolation, we find that the numerical results in the infinite-cell limit are in fact "rule independent." However, the actual fashion in which this limit is approached does depend upon the rule chosen. A connection between extrapolation of our renormalization-group results and finite-size scaling is made. Furthermore, the usual finite-size scaling arguments lead to independent estimates of ${p}_{c}$ and ${y}_{p}$. Combining both the large-cell approach and the finite-size scaling results, we obtain ${y}_{p}=0.7385\ifmmode\pm\else\textpm\fi{}0.0080$ and ${y}_{h}=1.898\ifmmode\pm\else\textpm\fi{}0.003$. Thus we find ${\ensuremath{\alpha}}_{p}=\ensuremath{-}0.708\ifmmode\pm\else\textpm\fi{}0.030$, ${\ensuremath{\beta}}_{p}=0.138(+0.006,\ensuremath{-}0.005)$, ${\ensuremath{\gamma}}_{p}=2.432\ifmmode\pm\else\textpm\fi{}0.035$, ${\ensuremath{\delta}}_{p}=18.6\ifmmode\pm\else\textpm\fi{}0.6$, ${\ensuremath{ u}}_{p}=1.354\ifmmode\pm\else\textpm\fi{}0.015$, and $2\ensuremath{-}{\ensuremath{\eta}}_{p}=1.796\ifmmode\pm\else\textpm\fi{}0.006$. The site-percolation threshold is found for the square lattice at ${p}_{c}=0.5931\ifmmode\pm\else\textpm\fi{}0.0006$. We note that our calculated value of ${\ensuremath{ u}}_{p}$ is in considerably better agreement with the proposal of Klein et al. that ${\ensuremath{ u}}_{p}=\frac{\mathrm{ln}\sqrt{3}}{\mathrm{ln}(\frac{3}{2})}\ensuremath{\cong}1.3548$, than with den Nijs' recent conjecture, which predicts ${\ensuremath{ u}}_{p}=\frac{4}{3}$. However, our results cannot entirely rule out the latter possibility.

Quasiatoms: An approach to atoms in nonuniform electronic systems

Abstract: A method of estimating the energy of an impurity in a host electronic system using density-functional theory is presented. The impurity ion plus its electronic screening cloud is treated as a unit and is used to define a quasiatom. The energy of the quasiatom is a functional of the host electron density in which it is immersed. In the simplest approximation it is given by the energy of the impurity in a uniform electron gas having a density equal to that of the host at the position of the impurity nucleus. This uniform-density approximation (UDA) is tested for light atoms in a variety of model and realistic situations and is found to be successful in reproducing qualitative trends. By developing a perturbation expansion for a weakly inhomogeneous host the UDA is shown to be the leading term in a rigorous expansion of the quasiatom energy in gradients of the host electron density, and corrections to second order in gradients are determined. As an example, these corrections are used in the calculation of the binding energy of a helium atom to a vacancy and excellent agreement with exact results is achieved. The perturbation expansion also suggests an ansatz for the quasiatom energy in which the host electron density is sampled by the quasiatom electrostatic potential. Tests of this ansatz are equally successful.

Phase diagrams and critical behavior in Ising square lattices with nearest- and next-nearest-neighbor interactions

Abstract: The phase diagrams of Ising antiferromagnets in a magnetic field $H$ are investigated for various values of the ratio $R$ between nearest- and next-nearest-neighbor interaction. While meanfield approximations and the existing real-space renormalization-group treatments yield phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from Monte Carlo calculations. For $Rl0$ only an antiferromagnetically ordered phase exists. Its transition to the disordered phase is first order for temperatures below the tricritical point (${T}_{t}$,${H}_{t}$). For $R\ensuremath{\rightarrow}0$ also ${T}_{t}\ensuremath{\rightarrow}0$. For $R=0$ we find very good agreement with the results of M\"uller-Hartmann and Zittartz. For $Rg0$ and ${H}_{1}lHl{H}_{2}$ a new phase with anomalous high ground-state degeneracy is found (two sublattices have only one-dimensional order). These sublattices undergo order-disorder transitions at $T=0$, such that for $Tg0$ one is left with a "superantiferromagnetic" phase. At low temperatures in this phase a pronounced tendency is observed to form a simpler (2 \ifmmode\times\else\texttimes\fi{} 2) superstructure but with many antiphase domain boundaries. For $R\ensuremath{\rightarrow}\frac{1}{2}$ and $Hl{H}_{1}$ the regime of the antiferromagnetic phases goes to zero temperature, while for $Rg\frac{1}{2}$ the superantiferromagnetic phase exists also for $Hl{H}_{1}$. The order-disorder transition associated with this phase seems to have non-Ising critical exponents which vary as a function of $R$ and $H$. Estimates for the exponents lead us to suggest that Suzuki's "weak universality" is valid. The behavior of the model at $T=0$ is related to known results on hard-core lattice gases. It is shown that it is useful to interpret the transitions at $T=0$ as generalized percolation transitions. Since the model may have applications to adsorbate phases in registered structures at (100) surfaces of cubic crystals, the transcription of our results to temperature-coverage phase diagrams and adsorption isotherms is discussed in detail, and possible experimental applications are mentioned.

Effective-medium theory of chemical binding: Application to chemisorption

Abstract: An approximate theory of the total energy change connected with the embedding of an atom in an inhomogeneous host is developed. The primary effect of the inhomogeneous environment is included by replacing it with a homogeneous electron gas of a density equal to that of the host at the atom site. The lowest-order corrections to this simple picture are derived. The scheme, which is computationally very simple, is tested against first-principles calculations for several chemisorption systems. It is found that including a simple first-order correction gives excellent agreement for H and O adsorbates. For less electronegative atoms like Si and Li, it seems that a second-order term involving the polarizability of the atom in a homogeneous electron gas must be included.

Self-consistency and sum-rule tests in the Kramers-Kronig analysis of optical data: Applications to aluminum

Abstract: An iterative, self-consistent procedure for the Kramers-Kronig analysis of data from reflectance, ellipsometric, transmission, and electron-energy-loss measurements is presented. This procedure has been developed for practical dispersion analysis since experimentally no single optical function can be readily measured over the entire range of frequencies as required by the Kramers-Kronig relations. The present technique is applied to metallic aluminum as an example. The results are then examined for internal consistency and for systematic errors by various optical sum rules. The present procedure affords a systematic means of preparing a self-consistent set of optical functions provided some optical or energy-loss data are available in all important spectral regions. The analysis of aluminum discloses that currently available data exhibit an excess oscillator strength, apparently in the vicinity of the L edge. A possible explanation is a systematic experimental error in the absorption-coefficient measurements resulting from surface layers: possibly oxides: present in thin-film transmission samples. A revised set of optical functions has been prepared by an ad hoc reduction of the reported absorption coefficient above the L edge by 14%. These revised data lead to a total oscillator strength consistent with the known electron density and are in agreement with dc-conductivity and stopping-power measurementsmore » as well as with absorption coefficients inferred from the cross sections of neighboring elements in the periodic table. The optical functions resulting from this study show evidence for both the redistribution of oscillator strength between energy levels and the effects on real transitions of the shielding of conduction electrons by virtual processes in the core states.« less

Interactions and the Anderson transition

Abstract: We examine the effects of the electron-electron interaction on the Anderson transition. It is shown that the dimensionality of the system and the range of the interaction are crucial in determining the decay properties of a single-particle citation. For a long-range interaction we find that the appropriate one-electron excitations, when localized, decay via a ${(\ensuremath{\epsilon}\ensuremath{-}\ensuremath{\mu})}^{\frac{1}{d}}$ law where ($\ensuremath{\epsilon}\ensuremath{-}\ensuremath{\mu}$) is the energy above the Fermi energy and $d$ is the dimensionality. At finite temperatures this becomes a ${T}^{\frac{1}{d}+1}$ law. The single-particle excitations are bound for short-range forces. The conditions for the persistence of the Anderson transition are presented in terms of the nature of the "$m$-basis" (that in which the Green's function is diagonal) and the convergence of a series for the renormalized self-energy.

Analysis of second-harmonic generation at metal surfaces

Abstract: We discuss the second-harmonic generation of light at metal surfaces within the hydrodynamic theory of the electron gas; expressions for the phenomenological parameters $a$ and $b$ of Rudnick and Stern are presented, and the possibility of a resonance in $a$ at optical or near-uv frequencies is discussed. A recent plasmon-enhanced experiment of Simon et al. is analyzed, and the use of such experiments to determine $a$ and $b$ is considered; new experiments are proposed to aid in such a determination.

Many-particle effects in the optical spectrum of a semiconductor

Abstract: A local-orbital treatment of the two-particle Green's function for the electron-hole interaction is presented which takes into account both screened electron-hole attraction and its exchange counterpart. They give rise to the excitonic effects including Frenkel and intermediate coupling regimes and to the random-phase approximation local-field effects, respectively. An alternative formulation based on the Kohn-Sham density-functional scheme is also given and numerically tested. Quantitative calculations of the absorption and modulation spectra in Si show that electron-hole interaction effects significantly modify the absorption line shape and give rise to shifts of critical-point structure up to 0.2 eV. A model analysis indicates that deviations of the one-particle spectra of column IV, III-V, and II-VI semiconductors from experiment should similarly be accounted for.

Site effect on the impurity levels in 4 H , 6 H , and 1 5 R SiC

Abstract: The existence of site-dependent impurity levels caused by inequivalent sites in $4H$, $6H$, and $15R$ SiC has been verified from a study of configuration coordinate phonons. From analyses of donor-acceptor pair and free-to-acceptor luminescence, two kinds of impurity levels of A1, Ga, and B acceptors and N donors substituted cubic-like and hexagonal-like sites are determined. All the impurities in cubic-like sites take deeper levels than those in hexagonal-like sites. Ratios of the ionization energies are approximately constant independent of polytypes and the kind of impurities, 1.0-1.08 for acceptors and 1.55-1.88 for donors, in spite of a wide range of the ionization energies. The origin of the site effect on the impurity level is explained by assuming the existence of a local dielectric constant and a local effective mass. Haynes' rule is found to apply relatively well to N donors in different sites in various polytypes SiC.

Extended x-ray absorption fine structure analysis of interatomic distances, coordination numbers, and mean relative displacements in disordered alloys

Abstract: A procedure is described for determining interatomic distances $r$, coordination numbers $N$, and mean relative displacements $\ensuremath{\sigma}$ from extended x-ray absorption fine structure (EXAFS) data on disordered metallic systems. This procedure includes the case when the spectrometer has finite energy resolution. It is shown how the absolute value of the EXAFS can be determined. A way has been developed to determine the inelastic loss factors of the photoelectrons from model compounds of known structure. The procedure has been checked on four metallic systems (Cu, $\ensuremath{\alpha}\ensuremath{-}\mathrm{Al}\mathrm{Cu}$-AlCu, ${\ensuremath{\theta}}^{\ensuremath{'}}$ and $\ensuremath{\theta}$ AlCu). The accuracy of the analysis is 1% for the interatomic distances, 15% for the coordination numbers, and 20% for $\ensuremath{\sigma}$. The reliability of the data analysis, which depends strongly on the number of different atoms in a shell, on the magnitude of their mean relative displacement and on the difference in their backscattering power will be discussed at length.

Paramagnetic-spin-glass-antiferromagnetic phase transitions in Cd 1-x Mn x Te from specific heat and magnetic susceptibility measurements

Abstract: Low-temperature specific heat and low-field magnetic susceptibility were measured in ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$ mixed crystals for $0.002l~xl~0.70$. Three regions of composition can be distinguished in both experiments. For $xl0.17$ the crystal is paramagnetic at all temperatures. For $0.17lxl0.7$, a spin-glass phase is observed, as evidenced by the characteristic cusp in the susceptibility and a linear temperature dependence of the specific heat in the low-temperature regions. Because the material is an insulator at low temperatures, and the Mn interactions are only antiferromagnetic, we believe that the observed spin-glass phase is produced by the frustration of the lattice. For $x=0.7$ an antiferromagnetic phase is observed. To understand the experimental behavior of the specific heat and susceptibility as a function of temperature and magnetic field for $0.002lxl0.17$, we must assume that the distribution of Mn ions deviates strongly from a random distribution. The number of pairs is more than doubled for $x=0.05$, and 30% higher for $x=0.1$, than statistically predicted. The number of larger clusters, like triplets, is also significantly higher. Analysis of the data yielded the value of the exchange integral for the nearest-neighbor interaction to be $\frac{{J}_{\mathrm{NN}}}{k}=\ensuremath{-}0.55\ifmmode\pm\else\textpm\fi{}0.05$ K. The interaction is stronger within the larger clusters, and is described by a different exchange constant $\frac{{J}_{\mathrm{NN}}^{\ensuremath{'}}}{k}=\ensuremath{-}4.3$ K.

Scattering by ionization and phonon emission in semiconductors

Abstract: Calculations of the pair-creation energy $\ensuremath{\epsilon}$, the Fano factor $F$, and the quantum yield for semiconductors are done for the assumptions that in each scattering event all possible sets of product particles are equally probable, that the energy bands are those of free particles separated by a band gap ${E}_{g}$, and that there is a single phonon energy $\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$. A new method of calculating these quantities is advanced. In it a pair-number probability distribution ${p}_{n}(E)$, the probability that a particle with energy $E$ ultimately creates $n$ pairs, is calculated recursively with increasing $E$. The first and second moments of the ${p}_{n}(E)$ distribution yield $\ensuremath{\epsilon}$, $F$, and the quantum yield as functions of $\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$, ${E}_{g}$, and a parameter $A$, proportional to the ratio of the matrix elements for electron scattering by phonon emission and by ionization. We find that a single value of $A$, which fits the $\ensuremath{\epsilon}$ observed for Si, gives values for these quantities in good accord with experiments for many semiconductors. The calculated $\ensuremath{\epsilon}$ is found insensitive in many semiconductors to electron-energy loss to plasmons and to differences in the threshold energy for ionization representing real band-structure features. The assumption that all possible sets of product particles are equally probable in each scattering event leads to ultimate nonuniform population of the states with energies below the threshold for ionization, in contrast to the uniform population assumed in some earlier approaches. Results of other existing approaches in which the final-state distribution is calculated, an alternate method, were duplicated using this new method. A simple paradigm is used to illustrate these methods and assumptions.

Optical properties of Au: Sample effects

Abstract: Reported optical data for Au are investigated to determine the origin of their differences. A single-parameter model representing voids in an otherwise homogeneous medium is shown to account for the major discrepancies in the above-band-gap ($Eg2.5$ eV) ${\ensuremath{\epsilon}}_{2}$ spectra for Au samples prepared in different ways. Ellipsometric measurements on transmission-electron-microscopy (TEM) characterized thin-film samples on an energy range of 1.5-5.8 eV support the void model but show the importance of measuring both ${\ensuremath{\epsilon}}_{1}$ and ${\ensuremath{\epsilon}}_{2}$ to separate volume from surface film effects. Differences in below-band-gap data arise from at least two mechanisms: grain-size effects in samples with a large volume fraction of imperfections, and increased surface scattering, probably from thermal grooving, in annealed samples. Two mechanisms are required because the lowest values of ${\ensuremath{\epsilon}}_{2}$ in the Drude region are shown to occur for unannealed but smooth, moderately thick film samples evaporated on room-temperature substrates. Our best below-band-gap data, taken on electron-beam evaporated samples, show directly the linearly increasing $d$-band to Fermi-level transition threshold near $X$ at 1.8 eV unobstructed by the Drude tail. These data have an ${\ensuremath{\epsilon}}_{2}$ value at 1.5 eV equal to within experimental error to that calculated from the scattering lifetime derived from the known resistivity of the bulk metal, indicating a grain size and quality better than anything previously used for optical measurements in Drude region.