Session X24: Focus Session: Dielectric, Ferroelectric, and Piezoelectric Oxides -- Defects and Relaxors

Evidence for Superhydrogenic Ce Doping of Lu$_{2}$O$_{3}$ Films

In the last decade oxides have exhibited a surprising number of unexpected, novel properties rousing the interest of the research community. One of the unusual property of oxides is their manifesting large dielectric constants as a consequence of which the hydrogenic radii of dopants would be quite large leading to overlap of their orbitals at concentration levels of a few percent. Midgap states formed by such ``superhydrogenic dopants'' may have unusual properties such as antiferromegnetism or ferromagnetism. In this paper we show evidence for the formation of such large Bohr radii dopants by looking at fluorescence quenching in Ce doped Lu$_{2}$O$_{3}$, where by 2{\%} doping all the sharp Lu line features are quenched which can be explained by the formation of large Rydberg radius for the Ce ions in this host. . .   

The electronic structure of O-vacancy at the interface between Si and HfO$_{2}$

We study the electronic properties of oxygen vacancy (V$_{O})$ at the interface structure between Si and HfO$_{2}$ through local density functional calculations. We consider a device model, where HfO$_{2}$ layers are placed on the Si (001) surface. For monoclinic and amorphous HfO$_{2}$, the valence band offsets are estimated to be 2.0--3.0 eV. The defect properties of V$_{O}$ are affected by the local bonding geometry and band offset at the interface. We find that V$_{O}$ defects at the interface, which are surrounded by a mixture of the Hf and Si atoms, have lower formation energies than those in the oxide region. For various interface structures, we find that the defect levels of V$_{O}$ are generally higher in the amorphous phase than in the monoclinic phase due to the smaller valence band offset. Our calculations suggest that the Fermi level pinning in $p$-MOS devices is caused by O-vacancies in the oxide region, more significantly in the amorphous oxide. On the other hand, O-vacancies formed at the interface, which have the unoccupied levels in the Si band gap, are responsible for the Fermi level pinning in $n$-MOS devices.   

Oxygen vacancies in monoclinic hafnia

Hafnia has recently received much attention because of its potential application as high-dielectric material replacing silica in microelectronic devices. Point defects -- in particular oxygen vacancies -- play an important role in this material as electron or hole traps. In this study, we perform electronic structure calculations on oxygen vacancies in hafnia using a combined Density functional Theory (DFT) and GW/BSE formalism. This formalism corrects for the error in calculating formation energy and charge transition levels using standard DFT. While there have been some GW studies on oxygen vacancies in hafnia using small supercells, we perform calculations using large supercells with 96 atoms. Such a large supercell calculation should minimize any spurious defect-defect interactions.   

Point defect chemistry in amorphous HfO$_2$

Neutral and charged native point defects in amorphous HfO$_2$ were studied using first principles computations. Thermodynamically, positively charged O vacancies and negatively charged Hf vacancies are the most probable point defects over a large atomic and electronic chemical potential range. Moreover, of all point defects, the positively charged O vacancy is the one with the lowest migration barrier. Hence, this point defect is identified as the most dangerous one in amorphous HfO$_2$ within the context of high-K gate dielectric applications in microelectronics.   

Point defects and diffusion in Al$_2$ O$_3$

Reconciling experimental measurements of self-diffusion in Al$_2$O$_3$ with theoretical calculations has long been problematic. Measured activation energies and diffusion coefficients are inconsistent with calculations, and the effect of aliovalent impurity doping is much smaller than is usual in such materials. We report \emph{ab initio} calculations using DFT and DFPT of temperature-dependent formation energies and migration barriers of a wide range of native point defects and defect-impurity clusters, parameterized by the constituent species chemical potentials. Using these energies as inputs to a mass-action analysis, we predict how defect concentrations depend on temperature, oxygen partial pressure and impurity doping. Finally, the formation energies are combined with migration barriers to provide diffusion activation energies, and thus an explanation of self-diffusion in alumina. We are able to account in a consistent way for experimental results and resolve the long-standing ``corundum conundrum.'' The importance of determining the Fermi energy self-consistently within a mass-action framework is demonstrated, and the surprising insensitivity of the diffusion coefficients to aliovalent impurity doping is shown to result from a ``buffering'' mechanism relating to clustering of defects and dopants that should also occur in other ionic materials.   

Point Defects in Al$_2$O$_3$ and their impact on novel CMOS performance

The desire for III-V CMOS devices has stimulated interest in novel dielectrics, which form high-quality interfaces III-V semiconductors. Recent significant progress has been reported using Al$_2$O$_3$. However, there is concern about defects that could degrade device quality. Therefore, we have performed a first-principles study of point defects in Al$_2$O$_3$. We analyze native point defects such as vacancies, self-interstitials, antisites, and dangling bonds, as well as hydrogen-related defects. Our first-principles calculations utilize state-of-the-art hybrid-functional methods within the HSE formalism. We also use calculated band offsets to make predictions about the location of defect levels with respect to the band edges of relevant III-V semiconductors. We find that the oxygen vacancy defect introduces defect levels near the conduction-band edge of relevant channel materials. Also, we find that vacancies can be responsible for accumulation of fixed charge in the crystal. Finally, hydrogen is considered as a passivation agent for defect states and fixed charge introduced by vacancy-related defects. Work supported by the Semiconductor Research Corporation and by NSF.   

Effects of adding HfO$_{2}$ on the microstructure and dielectric properties of giant dielectric constant ceramic CaCu$_{3}$Ti$_{4}$O$_{12}$

CaCu$_{3}$Ti$_{4}$O$_{12}$ (CCTO), an unusual perovskite-like ceramic, is known for its extraordinarily high ($\sim $10$^{4})$ and relatively frequency independent dielectric constant. It has drawn a lot of attention recently because of its potential applications in microelectronics and microwave devices. In this investigation, HfO$_{2}$ powder was added to a pre-reacted CCTO powder, which was synthesized by a conventional solid-state reaction, at different concentrations from 1 to 70 wt{\%} and the mixture was sintered into disc-shaped ceramic samples. The effects of adding HfO$_{2 }$on the microstructure and dielectric properties of CCTO ceramics were investigated. In general, we found that the dielectric constant tends to increase with HfO$_{2}$ addition up to 8 wt{\%} and then decrease with further addition. Moreover, the dielectric loss was also influenced by the addition of HfO$_{2}$, and a low loss tangent of $\sim $0.035 was obtained. The ac conductivity, impedance, complex dielectric permittivity and electric modulus graphs were used to analyze the data. These observations were explained on the basis of the internal-barrier-layer capacitor model with Maxwell-Wagner relaxations.   

Comparison of Structural Properties of a Pb-free relaxor to PMN

The Pb-free perovskite, BaZn$_{0.317}$Nb$_{0.633}$Ti$_{0.05}$O$_3$, has been reported to be a ferroelectric relaxor with a permittivity that has a stronger frequency shift than Pb-based relaxors [1]. We report neutron powder diffraction measurements which were performed over a 450 K temperature range on this compound. The results are compared to PMN, and it is shown that the atomic displacements and the thermal expansion of these two compounds are very dissimilar. [1] L. Khemakhem et al., J. Alloys Compd. 452, 451 (2008).   

Ultrasonic Wave Propagation Study of Phase Transitions in PZN-PT and PMN-PT Relaxor Single Crystals

Ultrasonic wave propagation provides an invaluable tool for the investigation of elastic properties of materials. The compressional and shear acoustic waves serve as an unique and sensitive noninvasive probe to investigate very subtle changes in the material (phase transition, onset of mechanical failure, etc), due to both the microstructure and also due to external mechanical parameters such as strain, applied field or temperature. The technique developed in this work is based on measuring attenuation variation and relative velocity change of ultrasonic pulse in the MHz frequency range while superimposing a harmonic or quasi-static bias load or during the temperature scan. Ultrasonic wave interaction with solids under stress at various temperatures in oriented, poled (1--$x)$Pb(Zn$_{1/3}$Nb$_{2/3})$O$_{3}-x$PbTiO$_{3}$ with $x$ = 0.045, 0.06 and 0.08 (PZN-PT) single crystal is studied. A strong temperature and stress hysteresis of ultrasonic and in ferroelectric rhombohedral (R)-tetragonal (T) transition occurred under uniaxial compressive stress with magnitude similar to those used in sound projectors. Dramatic changes in the velocity and the attenuation of the acoustic wave in the sample was an indication of the stress induced rhombohedral-orthorombic phase transition. The effect of composition, stress, and temperature have been investigated and experimental results will be presented   

Optic modes in PbMg$_{1/3}$Nb$_{2/3}$O$_{3}$ relaxor by hyper-Raman scattering

Hyper-Raman scattering (HRS) experiment is performed in three different single crystals of PbMg$_{1/3}$Nb$_{2/3}$O$_{3}$ (PMN) relaxor [1]. The relative intensities of the band near 250 cm$^{-1}$ in various polarization geometries are fully compatible with the HRS tensor of the $F_{2u} `$silent' mode of the parent $O_{h}$ cubic structure. The temperature dependence of the three $F_{1u }$polar modes was investigated between 20 K and 800 K. High-resolution data reveal that the lowest $F_{1u}$ mode is splitted up to the highest investigated temperatures. On cooling, the low frequency component strongly decreases in frequency and exhibits clear soft mode behaviour with a crossover from a vibrational to a relaxational behaviour around $T_{d} \quad \approx $ 620 K [2]. This observation gives a new insight into the low-frequency dynamics of PMN-type relaxor systems. \\[4pt] [1] A. Al-Zein \textit{et al.}, PRB \textbf{78}, 134113 (2008)~; B. Hehlen \textit{et al.}, PRB \textbf{75}, 052104 (2007). \\[0pt] [2] A. Al-Zein \textit{et al.}, submitted to PRL.   

A Molecular Dynamics Study of Dielectric Response in a Relaxor Ferroelectric

We use atomistic molecular dynamics simulations to study relaxor behavior in the 0.75Pb(Mg,Nb)O$_3$-0.25PbTiO$_3$ material. Even for a fairly small simulation size of 1000 atoms, the system exhibits frequency dispersion and deviation from the Curie-Weiss law typical of relaxor materials. Analysis of the time autocorrelation functions for individual atoms allows us to identify the Nb atoms with a high concentration of neighboring Ti atoms as the nucleation sites for the relaxor behavior. This is due to the higher coupling between the cation displacements induced by the presence of overbonded oxygen atoms located between Nb and Ti atoms.   

First principles study of the structure and properties of lead indium niobate and its effect on relaxor based materials

Recent advanced in the growth of single crystals of relaxor based materials have shown that when Pb(In$_{1/2}$Nb$_{1/2}$)O$_3$ (PIN) is alloyed into Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$-PbTiO$_3$ (PMN-PT) it significantly improves both the depoling temperature and coercive field,\footnote{G. Hu \textit{et al}, Appl. Phys. Lett. \textbf{90}, 032901, (2007)} overcoming the major drawbacks of these types of systems when compared to PZT. For example, PIN-PMN-PT at a composition of 24/44/32 was shown to have a coercive field more than double that of PMN-PT.\footnote{J. Tian \textit{et al}, Appl. Phys. Lett. \textbf{91}, 222903 (2007)} Using first-principles methods, we investigate and compare properties of highly ordered PIN systems to allow us to gain some insight into the role of PIN in changing the properties of relaxor-system crystals. This includes an analysis of the most energetically favorable structure and ordering based on the most ordered PIN structures and their possible distortions. Our calculations show that the most stable ordering involves a rocksalt arrangement of the B-site cations. We have also calculated the polarizations, Born effective charges and piezoelectric constants of these structures. The work represents a step towards a more complete understanding of these relaxor-based systems.   

Neutron Scattering Study of the Relaxor Ferroelectric PZN -4.5{\%}PT under an [001]-Oriented Electric Field

Polar nano-regions (PNR) are believed to play important roles in determining many special properties of relaxor ferroelectric materials. We have performed a series of neutron diffuse scattering and neutron spin echo measurements on single crystals of Pb[(Zn$_{1/3}$Nb$_{2/3})_{0.955}$Ti$_{0.045}$]O$_{3 }$(PZN-4.5{\%}PT) to study the PNR under the influence of an [001] oriented electric field. Our results suggest that the short-range polar structure in this compound is complicated. In addition to the previously known PNR having $<$110$>$-oriented polarizations, we found PNR with $<$100$>$-oriented polarizations. The diffuse scattering intensity from $<$100$>$-oriented PNR can be partially suppressed by an external electric field applied along [001], while that from the $<$110$>$-oriented PNR exhibits little to no change. Our neutron spin echo measurements further show that the diffuse scattering intensity from the $<$100$>$-oriented PNR contains both static and dynamic components. On cooling, the static to dynamic ratio increases, suggesting that the short-range polar order freezes gradually.   

Electric Field and Polarization Distributions in Relaxor Ferroelectrics

Relaxor ferroelectric crystals (or simply relaxors) show high dielectric constants and low dielectric losses over a broad range of temperatures. There is consensus that the dielectric properties of the relaxors are due to the formation of polar nanoregions (PNR) below the Burns temperature. Each PNR possesses a net polarization that has many equivalent orientations. The gradient in the polarization leads to charge accumulation on the PNR surfaces. Such charge accumulation produces electric fields, which in turn affect the direction of the polarizations themselves. Knowledge of the electric field and of the polarization distributions is critical to understand the dielectric properties of these systems. Here, we present results on the calculated probability distribution of the electric fields and of the polarizations in the relaxors. Comparison to results obtained from neutron scattering experiments is provided.