Piezoelectric materials, which convert mechanical to electrical energy (and vice versa), are crucial in medical imaging, telecommunication and ultrasonic devices. A new generation of single-crystal materials, such as Pb(Zn1/3Nb2/3)O3-PbTiO3 (PZN-PT) and Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), exhibit a piezoelectric effect that is ten times larger than conventional ceramics, and may revolutionize these applications. However, the mechanism underlying the ultrahigh performance of these new materials-and consequently the possibilities for further improvements-are not at present clear. Here we report a first-principles study of the ferroelectric perovskite, BaTiO3, which is similar to single-crystal PZN-PT but is a simpler system to analyse. We show that a large piezoelectric response can be driven by polarization rotation induced by an external electric field. Our computations suggest how to design materials with better performance, and may stimulate further interest in the fundamental theory of dielectric systems in finite electric fields.

Bulk ferroelectrics undergo structural phase transformations at low temperatures, giving multi-stable (that is, multiple-minimum) degenerate states with spontaneous polarization. Accessing these states by applying, and varying the direction of, an external electric field is a key principle for the operation of devices such as non-volatile ferroelectric random access memories (NFERAMs). Compared with bulk ferroelectrics, low-dimensional finite ferroelectric structures promise to increase the storage density of NFERAMs 10,000-fold. But this anticipated benefit hinges on whether phase transitions and multi-stable states still exist in low-dimensional structures. Previous studies have suggested that phase transitions are impossible in one-dimensional systems, and become increasingly less likely as dimensionality further decreases. Here we perform ab initio studies of ferroelectric nanoscale disks and rods of technologically important Pb(Zr,Ti)O3 solid solutions, and demonstrate the existence of previously unknown phase transitions in zero-dimensional ferroelectric nanoparticles. The minimum diameter of the disks that display low-temperature structural bistability is determined to be 3.2 nm, enabling an ultimate NFERAM density of 60 x 10(12) bits per square inch-that is, five orders of magnitude larger than those currently available. Our results suggest an innovative use of ferroelectric nanostructures for data storage, and are of fundamental value for the theory of phase transition in systems of low dimensionality.

We present a pseudopotential approach to the calculation of the excitonic spectrum of semiconductor quantum dots. Starting from a many-body expansion of the exciton wave functions in terms of singlesubstitution Slater determinants constructed from pseudopotential single-particle wave functions, our method permits an accurate and detailed treatment of the intraconfiguration electron-hole Coulomb and exchange interactions, while correlation effects can be included in a controlled fashion by allowing interconfiguration coupling. We calculate the exciton fine structure of InP and CdSe nanocrystals in the strong-confinement regime. We find a different size dependence for the electron-hole exchange interaction than previously assumed ͑i.e., R Ϫ2 instead of R Ϫ3). Our calculated exciton fine structure is compared with recent experimental results obtained by size-selective optical spectroscopies. ͓S0163-1829͑99͒00227-1͔

A first-principles-derived approach is developed to study the effects of uncompensated depolarizing electric fields on the properties of Pb(Zr,Ti)O 3 ultrathin films for different mechanical boundary conditions. A rich variety of ferroelectric phases and polarization patterns is found, depending on the interplay between strain and amount of screening of surface charges. Examples include triclinic phases, monoclinic states with in-plane and/or out-of-plane components of the polarization, homogeneous and inhomogeneous tetragonal states, as well as, peculiar laminar nanodomains.Typeset using REVT E X 1

We present pseudopotential plane-wave electronic-structure calculations on InP quantum dots in an effort to understand quantum confinement and surface effects and to identify the origin of the long-lived and redshifted luminescence. We find that ͑i͒ unlike the case in small GaAs dots, the lowest unoccupied state of InP dots is the ⌫ 1c-derived direct state rather than the X 1c-derived indirect state and ͑ii͒ unlike the prediction of k•p models, the highest occupied state in InP dots has a 1sd-type envelope function rather than a ͑dipole-forbidden͒ 1p f envelope function. Thus explanations ͑i͒ and ͑ii͒ to the long-lived redshifted emission in terms of an orbitally forbidden character can be excluded. Furthermore, ͑iii͒ fully passivated InP dots have no surface states in the gap. However, ͑iv͒ removal of the anion-site passivation leads to a P dangling bond ͑DB͒ state just above the valence band, which will act as a trap for photogenerated holes. Similarly, ͑v͒ removal of the cation-site passivation leads to an In dangling-bond state below the conduction band. While the energy of the In DB state depends only weakly on quantum size, its radiative lifetime increases with quantum size. The calculated ϳ300-meV redshift and the ϳ18 times longer radiative lifetime relative to the dot-interior transition for the 26-Å dot with an In DB are in good agreement with the observations of full-luminescence experiments for unetched InP dots. Yet, ͑vi͒ this type of redshift due to surface defect is inconsistent with that measured in selective excitation for HF-etched InP dots. ͑vii͒ The latter type of ͑''resonant''͒ redshift is compatible with the calculated screened singlet-triplet splitting in InP dots, suggesting that the slow emitting state seen in selective excitation could be a triplet state. ͓S0163-1829͑97͒04428-7͔

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Properties of BaTiO3 colloidal quantum dots and wires are simulated using a first-principles-based approach. Large atomic off-center displacements (that are robust against capping matrix materials) are found to exist in very small (<5 nm) dots. We further determine the size dependences of electrical and electromechanical responses in the studied nanostructures, as well as provide microscopic understanding of these responses.

An atomistic approach allowing an accurate and efficient treatment of depolarizing energy and field in any low-dimensional ferroelectric structure is developed. Application of this approach demonstrates the limits of the widely used continuum model (even) for simple test cases. Moreover, implementation of this approach within a first-principles-based model reveals an unusual phase transition -from a state exhibiting a spontaneous polarization to a phase associated with a toroid moment of polarization -in a ferroelectric nanodot for a critical value of the depolarizing field.