This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

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Phonons and related crystal properties from density-functional perturbation theory

First-principles calculations have evolved from mere aids in explaining and supporting experiments to powerful tools for predicting new materials and their properties. In the first part of this review we describe the state-of-the-art computational methodology for calculating the structure and energetics of point defects and impurities in semiconductors. We will pay particular attention to computational aspects which are unique to defects or impurities, such as how to deal with charge states and how to describe and interpret transition levels. In the second part of the review we will illustrate these capabilities with examples for defects and impurities in nitride semiconductors. Point defects have traditionally been considered to play a major role in wide-band-gap semiconductors, and first-principles calculations have been particularly helpful in elucidating the issues. Specifically, calculations have shown that the unintentional n-type conductivity that has often been observed in as-grown GaN cannot be a...

First-principles calculations for defects and impurities: Applications to III-nitrides

This review covers important advances in recent years in the physics of thin-film ferroelectric oxides, the strongest emphasis being on those aspects particular to ferroelectrics in thin-film form. The authors introduce the current state of development in the application of ferroelectric thin films for electronic devices and discuss the physics relevant for the performance and failure of these devices. Following this the review covers the enormous progress that has been made in the first-principles computational approach to understanding ferroelectrics. The authors then discuss in detail the important role that strain plays in determining the properties of epitaxial thin ferroelectric films. Finally, this review ends with a look at the emerging possibilities for nanoscale ferroelectrics, with particular emphasis on ferroelectrics in nonconventional nanoscale geometries.

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Physics of thin-film ferroelectric oxides

A grid-based real-space implementation of the projector augmented wave (PAW) method of Bl\"ochl [Phys. Rev. B 50, 17953 (1994)] for density functional theory (DFT) calculations is presented. The use of uniform three-dimensional (3D) real-space grids for representing wave functions, densities, and potentials allows for flexible boundary conditions, efficient multigrid algorithms for solving Poisson and Kohn-Sham equations, and efficient parallelization using simple real-space domain-decomposition. We use the PAW method to perform all-electron calculations in the frozen core approximation, with smooth valence wave functions that can be represented on relatively coarse grids. We demonstrate the accuracy of the method by calculating the atomization energies of 20 small molecules, and the bulk modulus and lattice constants of bulk aluminum. We show that the approach in terms of computational efficiency is comparable to standard plane-wave methods, but the memory requirements are higher.

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Real-space grid implementation of the projector augmented wave method

An overview of the state of art in ferroelectric thin films is presented. First, we review applications: microsystems' applications, applications in high frequency electronics, and memories based on ferroelectric materials. The second section deals with materials, structure (domains, in particular), and size effects. Properties of thin films that are important for applications are then addressed: polarization reversal and properties related to the reliability of ferroelectric memories, piezoelectric nonlinearity of ferroelectric films which is relevant to microsystems' applications, and permittivity and loss in ferroelectric films-important in all applications and essential in high frequency devices. In the context of properties we also discuss nanoscale probing of ferroelectrics. Finally, we comment on two important emerging topics: multiferroic materials and ferroelectric one-dimensional nanostructures. (c) 2006 American Institute of Physics.

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Ferroelectric thin films: Review of materials, properties, and applications

Phonon excitations play an important role in electronic transport, nonradiative electron-relaxation processes, and other properties of interest for materials characterization, device engineering, and design. We have calculated the phonon dispersions and density of states for wurtzite AlN, GaN, and InN using state-of-the-art density-functional perturbation theory. The calculations are in good agreement with the existing experimental data for zone-center modes and predict the full phonon dispersions throughout the Brillouin zone. In particular, it is found that the three-phonon decay of the LO phonon in two acoustic phonons is not allowed in GaN and InN, since the LO frequency is much larger than the acoustic frequencies over the entire spectrum. The substantial potential of the group-III nitrides and their alloys for applications in optoelectronic and high speed devices has attracted a great deal of interest. AlN, GaN, and InN have direct energy gaps which span a substantial range, from the visible to the ultraviolet region of the spectrum. Consequently, their alloys have direct gaps that can be tuned to any value within this range simply by varying the alloy composition. This tunability offers many possibilities for device engineering. In particular, InGaN alloys were used in the realization of light emitting diodes and laser diodes operating in the blue and UV spectral region. Under ambient conditions, the III nitrides crystallize in a hexagonal, wurtzite ~2H! structure, although thin films having a cubic, zincblende ~3C! structure have also been grown. 1 Properties of interest for device engineering and design, such as electronic transport, nonradiative electron relaxation processes, lattice specific heat, etc., are strongly influenced by phonon excitations. Furthermore, a number of nondestructive experimental techniques of sample characterization, for instance, Raman spectroscopy or IR reflectivity, involve phonon measurements. A characterization of the phonon dispersions and densities of states for the group-III nitrides is therefore desirable. However, since it is very challenging to grow single crystals of suitable size for neutron-scattering experiments, there are no experimental data for the phonon dispersions of these compounds. Only very recently have the phonon density of states for AlN and GaN been obtained from time-of-flight neutron spectroscopy using bulk powders. 2,3 In addition, numerous studies of the zone-center phonons in GaN and AlN films have been conducted using Raman and IR spectroscopy. Due to the lack of latticematched substrates, these samples are affected by the high density of defects and strain present in the films and it is therefore unclear how well these data represent the true bulk values. The least studied of the three nitrides is InN for which there are only few Raman studies. 4,5

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Ab initio phonon dispersions of wurtzite AlN, GaN, and InN

Using a combination of first-principles and effective-Hamiltonian approaches, we map out the structure of ${\text{BaTiO}}_{3}$ under epitaxial constraints applicable to growth on perovskite substrates. We obtain a phase diagram in temperature and misfit strain that is qualitatively different from that reported by Pertsev, Zembilgotov, and Tagantsev [Phys. Rev. Lett. 80, 1988 (1998)], who based their results on an empirical thermodynamic potential with parameters fitted at temperatures in the vicinity of the bulk phase transitions. In particular, we find a region of ``$r$ phase'' at low temperature where Pertsev et al. have reported an ``$ac$ phase.'' We expect our results to be relevant to thin epitaxial films of ${\text{BaTiO}}_{3}$ at low temperatures and experimentally achievable strains.

Ab initio study of the phase diagram of epitaxial BaTiO 3

The phonon-dispersion relations and elastic constants for ferromagnetic ${\mathrm{Ni}}_{2}\mathrm{MnGa}$ in the cubic and tetragonally distorted Heusler structures are computed using density-functional and density-functional-perturbation theory within the spin-polarized generalized-gradient approximation. For $0.9lc/al1.06,$ the ${\mathrm{TA}}_{2}$ transverse- acoustic branch along $[110]$ and the symmetry-related directions exhibit a dynamical instability at a wave vector that depends on $c/a.$ Through examination of the Fermi-surface nesting and electron-phonon coupling, this is identified as a Kohn anomaly. In the parent cubic phase the computed tetragonal shear elastic constant, ${C}^{\ensuremath{'}}{=(C}_{11}\ensuremath{-}{C}_{12})/2,$ is close to zero, indicating a marginal elastic instability towards a uniform tetragonal distortion. We conclude that the cubic Heusler structure is unstable against a family of energy-lowering distortions produced by the coupling between a uniform tetragonal distortion and the corresponding $[110]$ modulation. The computed relation between the $c/a$ ratio and the modulation wave vector is in excellent agreement with structural data on the premartensitic $(c/a=1)$ and martensitic $(c/a=0.94)$ phases of ${\mathrm{Ni}}_{2}\mathrm{MnGa}.$

First-principles study of lattice instabilities in ferromagnetic Ni 2 MnGa

The effect of layer-by-layer heterostructuring and epitaxial strain on lattice instabilities and related ferroelectric properties is investigated from first principles for the [001]-(PbTiO$_3$)$_1$(PbZrO$_3$)$_1$ superlattice and pure PbTiO$_3$ on a cubic substrate. The results for the superlattice show an enhancement of the stability of the monoclinic r-phase with respect to pure PbTiO$_3$. Analysis of the lattice instabilities of the relaxed centrosymmetric reference structure computed within density functional perturbation theory suggests that this results from the presence of two unstable zone-center modes, one confined in the PbTiO$_3$ layer and one in the PbZrO$_3$ layer, which produce in-plane and normal components of the polarization, respectively. The zero-temperature dielectric response is computed and shown to be enhanced not only near the phase boundaries, but throughout the r-phase. Analysis of the analogous calculation for pure PbTiO$_3$ is consistent with this interpretation, and suggests useful approaches to engineering the dielectric properties of artificially structured perovskite oxides.

Epitaxially strained [001]-(PbTiO 3 ) 1 (PbZrO 3 ) 1 superlattice and PbTiO 3 from first principles

The phonon dispersion relation of NiTi in the simple cubic $B2$ structure is computed using first-principles density-functional perturbation theory with pseudopotentials and a plane-wave basis set. The structure is shown not to be a local energy minimum, so that its observation at high temperatures must be due to entropic stabilization by large fluctuations around the average atomic positions. Lattice instabilities are observed to occur across nearly the entire Brillouin zone, excluding three interpenetrating tubes of stability along the (001) directions and small spheres of stability centered at R. The strongest instability is that of the doubly degenerate ${M}_{{5}^{\ensuremath{'}}}$ mode. The distorted structure produced by freezing a particular choice of unstable ${M}_{{5}^{\ensuremath{'}}}$ eigenvector into the reference cubic structure yields, with an appropriate choice of overall amplitude, an excellent approximation to the observed ground-state ${B19}^{\ensuremath{'}}$ structure.

Claudia Bungaro

Papers

Ab initio phonon dispersions of wurtzite AlN, GaN, and InN

Ab initio study of the phase diagram of epitaxial BaTiO 3

First-principles study of lattice instabilities in ferromagnetic Ni 2 MnGa

Epitaxially strained [001]-(PbTiO 3 ) 1 (PbZrO 3 ) 1 superlattice and PbTiO 3 from first principles

Lattice instabilities of cubic NiTi from first principles