David Vanderbilt

Spontaneous polarization and piezoelectric constants of III-V nitrides

The spontaneous polarization, dynamical Born charges, and piezoelectric constants of the III-V nitrides AlN, GaN, and InN are studied ab initio using the Berry-phase approach to polarization in solids. The piezoelectric constants are found to be up to ten times larger than in conventional III-V and II-VI semiconductor compounds, and comparable to those of ZnO. Further properties at variance with those of conventional III-V compounds are the sign of the piezoelectric constants ~positive as in II-VI compounds! and the very large spontaneous polarization. @S0163-1829~97!51740-1# In this paper we report an ab initio study of the spontaneous polarization, piezoelectric constants, and dynamical charges of the III-V nitride semiconductors AlN, GaN, and InN. 1 This class of polarization-related properties is of obvious importance for the study of nitride-based piezodevices 2 and multilayer structures. In particular, knowledge of these properties allows an insightful treatment of the polarization ~and ensuing electric fields! in strained and polarized nitride junctions and superlattices under any strain condition, as discussed elsewhere. 3 From the present study, one of the first applications of the modern theory of polarization in solids 4,5 to real and ‘‘difficult’’ materials of technological interest, the nitrides emerge as highly unusual III-V materials, resembling II-VI oxides and in some respects ferroelectric perovskites. The results we report here are of special interest in view of the scarcity of the data ~both experimental and theoretical! available at present for the nitrides. In the absence of external fields, the total macroscopic polarization P of a solid is the sum of the spontaneous polarization P eq in the equilibrium structure, and of the straininduced or piezoelectric polarization dP. In the linear regime, the piezoelectric polarization is related to the strain e by

First-principles study of structural, vibrational, and lattice dielectric properties of hafnium oxide

Crystalline structures, zone-center phonon modes, and the related dielectric response of the three low- pressure phases of HfO2 have been investigated in density-functional theory using ultrasoft pseudopotentials and a plane-wave basis. The structures of low-pressure HfO2 polymorphs are carefully studied with both the local-density approximation ~LDA! and the generalized gradient approximation. The fully relaxed structures obtained with either exchange-correlation scheme agree reasonably well with experiment, although LDA yields better overall agreement. After calculating the Born effective charge tensors and the force-constant matrices by finite-difference methods, the lattice dielectric susceptibility tensors for the three HfO2 phases are computed by decomposing the tensors into the contributions from individual infrared-active phonon modes. have, in a previous paper, 4 investigated the bulk structures and lattice dielectric response of ZrO 2 polymorphs. We found that the dielectric responses vary dramatically with the crystal phase. Specifically, we found that the monoclinic phase has a strongly anisotropic lattice dielectric tensor and a rather small orientationally averaged dielectric constant ow- ing to the fact that the mode effective charges associated with the softest modes are relatively weak. This Brief Report presents the corresponding work on HfO2, providing the first thorough theoretical study of the structural, vibrational, and lattice dielectric properties of the HfO2 phases. Such properties are naturally expected to be similar to those of ZrO2 in view of the chemical similarities mentioned above. We find that this is generally true, although we also find some significant quantitative differences in some of the calculated properties. The calculation of the lattice contributions to the static dielectric tensor e 0 entails the computations of the Born ef- fective charge tensors Z* and the force-constant matrices F. The Z* tensors, defined via DP5(e/V)( iZ iiDui , are ob- tained by finite differences of polarizations ~P! as various sublattice displacements ( u i ) are imposed, with the elec- tronic part of the polarizations computed using the Berry- phase approach. 5,6 Here V is the volume of the unit cell, e is the electron charge, and i labels the atom in the unit cell. We then calculate the force-constant matrix, F ij 52)F i /)u j .2DF i /Du j b by calculating all the Hellmann-Feynman forces Fi caused by making displacements u j of each atom in each Cartesian direction in turn ~Greek indices label the Cartesian coordinates!. The resulting F matrix is symme- trized to clean up numerical errors, the dynamical matrix D ij 5( MiM j) 21/2 F ij is constructed, and the latter is then diagonalized to obtain the eigenvalues v l and eigenvectors j i,lb .

Monoclinic and triclinic phases in higher-order Devonshire theory

Devonshire theory provides a successful phenomenological description of many cubic perovskite ferroelectrics such as BaTiO3 via a sixth-order expansion of the free energy in the polar order parameter. However, the recent discovery of a novel monoclinic ferroelectric phase in the PZT system by Noheda et al. (Appl. Phys. Lett. 74, 2059 (1999)) poses a challenge to this theory. Here, we confirm that the sixth-order Devonshire theory cannot support a monoclinic phase, and consider extensions of the theory to higher orders. We show that an eighth-order theory allows for three kinds of equilibrium phases in which the polarization is confined not to a symmetry axis but to a symmetry plane. One of these phases provides a natural description of the newly observed monoclinic phase. Moreover, the theory makes testable predictions about the nature of the phase boundaries between monoclinic, tetragonal, and rhombohedral phases. A ferroelectric phase of the lowest (triclinic) symmetry type, in which the polarization is not constrained by symmetry, does not emerge until the Devonshire theory is carried to twelfth order. A topological analysis of the critical points of the free-energy surface facilitates the discussion of the phase transition sequences.

A Monte Carlo simulated annealing approach to optimization over continuous variables

Abstract Numerical optimization methods based on thermodynamic concepts are extended to the case of continuous multidimensional parameter spaces. Techniques which allow this strategy to be implemented efficiently and reliably, including a self-regulatory mechanism for choosing the random step distribution, are described. The method is applied to a set of standard global minimization problems, and to a typical non-linear least-squares functional fitting problem.

Maximally localized Wannier functions for entangled energy bands

We present a method for obtaining well-localized Wannier-like functions (WFs) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual maximally localized WFs method [N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12 847 (1997)] that the bands of interest should form an isolated group, separated by gaps from higher and lower bands everywhere in the Brillouin zone. An energy window encompassing N bands of interest is specified by the user, and the algorithm then proceeds to disentangle these from the remaining bands inside the window by filtering out an optimally connected N-dimensional subspace. This is achieved by minimizing a functional that measures the subspace dispersion across the Brillouin zone. The maximally localized WFs for the optimal subspace are then obtained via the algorithm of Marzari and Vanderbilt. The method, which functions as a postprocessing step using the output of conventional electronic-structure codes, is applied to the s and d bands of copper, and to the valence and low-lying conduction bands of silicon. For the low-lying nearly-free-electron bands of copper we find WFs which are centered at the tetrahedral-interstitial sites, suggesting an alternative tight-binding parametrization.

Thermal contraction and disordering of the Al(110) surface

Al(110) has been studied for temperatures up to 900 K via ensemble density-functional molecular dynamics. The strong anharmonicity displayed by this surface results in a negative coefficient of thermal expansion, where the first interlayer distance decreases with increasing temperature. Very shallow channels of oscillation for the second-layer atoms in the direction perpendicular to the surface support this anomalous contraction, and provide a novel mechanism for the formation of adatom-vacancy pairs, preliminary to the disordering and premelting transition. Such characteristic behaviour originates in the free-electron-gas bonding at a loosely packed surface. [S0031-9007(99)08925-5].

Phonons and lattice dielectric properties of zirconia

We have performed a first-principles study of the structural and vibrational properties of the three low-pressure (cubic, tetragonal, and especially monoclinic) phases of

First-principles theory of ferroelectric phase transitions for perovskites: The case of BaTiO3.

{\mathrm{ZrO}}_{2},

Ab initio study of ferroelectric domain walls in PbTiO 3

with special attention to the computation of the zone-center phonon modes and related dielectric properties. The calculations have been carried out within the local-density approximation using ultrasoft pseudopotentials and a plane-wave basis. The fully relaxed structural parameters are found to be in excellent agreement with experimental data and with previous theoretical work. The total-energy calculations correctly reproduce the energetics of the

Pseudopotentials for high-throughput DFT calculations

{\mathrm{ZrO}}_{2}