Abstract: Recent experiments suggest that Mg condensation at threading dislocations induce current leakage, leading to degradation of GaN-based power devices. To study this issue, we perform first-principles total-energy electronic-structure calculations for various Mg and dislocation complexes. We find that threading screw dislocations (TSDs) indeed attract Mg impurities, and that the electronic levels in the energy gap induced by the dislocations are elevated towards the conduction band as the Mg impurity approaches the dislocation line, indicating that the Mg-TSD complex is a donor. The formation of the Mg-TSD complex is unequivocally evidenced by our atom probe tomography in which Mg condensation and diffusion through [0001] screw dislocations is observed in p-n diodes. These findings provide a novel picture that the Mg being a p-type impurity in GaN diffuses toward the TSD and then locally forms an n-type region. The appearance of this region along the TSD results the reverse leakage current. read less

Abstract: For reproducing the behavior of water molecules adsorbed on gold surfaces in terms of density of both bulk and interfacial water and in terms of structuring of water on top of gold atoms, the implementation of a multibody potential is necessary, thus the Stillinger–Weber potential was tested. The goal is using a single nonbonded potential for coarse-grained models, without the usage of explicit charges. In order to modify the angular part of the Stillinger–Weber potential from a single cosine to a piecewise function accounting for multiple equilibrium angles, employed for Au–Au–Au and Au–Au–water triplets, it is necessary to create a version of the simulation package LAMMPS that supports the assignment of multiple favored angles. This novel approach is able to reproduce the data obtained using quantum mechanical calculations and density profiles of both bulk and adsorbed water molecules obtained using classical polarizable force fields. read less

Abstract: In this article, we study the deposition of AlGaN film on AlN template by molecular dynamics (MD) simulations. The effects of growth temperature and film thickness on the dislocation of deposited AlGaN film are simulated and studied. The atomic structure of deposited AlGaN film is also investigated. We find that the dislocations usually occur at the interface between AlN template and AlGaN film and then extend towards the growth direction. The dislocation density decreases with the increase of AlGaN film thickness, which indicates that increasing the thickness of deposited AlGaN film to a certain extent is beneficial to reducing dislocation. In addition, increasing the growth temperature can also effectively reduce the dislocation in deposited AlGaN film. Furthermore, the crystallinity of deposited AlGaN film could be improved by increasing the growth temperature. This is consistent with the dislocation discussion. The mobility of adatoms increases as the growth temperature increases. So it is easier for adatoms to find their ideal lattice points at higher temperature. Thus the dislocation and other defects can be effectively reduced and the crystal quality of deposited AlGaN film could be improved. GRAPHICAL ABSTRACT read less

Abstract: In order to investigate the tribological property of the gallium nitride (GaN) crystal at the nanoscale, a series of molecular dynamics nanoscratch simulations are carried out on the surfaces of c-GaN, a-GaN, and m-GaN. The key factors of scratch depth and scratch direction that greatly influence the deformation behavior are explored by analyzing the mechanical response, surface wear, and subsurface dislocation nucleation. The friction coefficient, wear rate, and total length of dislocations are all found to increase with the increase of scratch depth. A clear directional dependence could be recognized for c-GaN, where the friction coefficient along the [ 10 1 ¯ 0 ] direction is always lower than that along the [ 1 2 ¯ 10 ] direction, and the wear rate along the [ 10 1 ¯ 0 ] direction is higher than that along the [ 1 2 ¯ 10 ] direction, regardless of the scratch depth. On the contrary, the directional dependence of the wear rate and friction coefficient is unclear for a-GaN and m-GaN. For scratches at a specific depth, dislocations in c-GaN are smallest in length and occupy shallow positions close to the surface, while widely distributed dislocations could be observed in m-GaN.In order to investigate the tribological property of the gallium nitride (GaN) crystal at the nanoscale, a series of molecular dynamics nanoscratch simulations are carried out on the surfaces of c-GaN, a-GaN, and m-GaN. The key factors of scratch depth and scratch direction that greatly influence the deformation behavior are explored by analyzing the mechanical response, surface wear, and subsurface dislocation nucleation. The friction coefficient, wear rate, and total length of dislocations are all found to increase with the increase of scratch depth. A clear directional dependence could be recognized for c-GaN, where the friction coefficient along the [ 10 1 ¯ 0 ] direction is always lower than that along the [ 1 2 ¯ 10 ] direction, and the wear rate along the [ 10 1 ¯ 0 ] direction is higher than that along the [ 1 2 ¯ 10 ] direction, regardless of the scratch depth. On the contrary, the directional dependence of the wear rate and friction coefficient is unclear for a-GaN and m-GaN. For... read less

Abstract: ABSTRACT The properties of ohmic contact and thermal boundary conductance between Al and GaN have been studied extensively, but the interface structures and deformation mechanisms in the Al/GaN multilayer can be rarely found in literatures. By molecular dynamics (MD) simulations, we systematically studied the interface structures and structural deformations in the Al/GaN multilayer. Two kinds of interface structures are identified according to the different terminal surfaces of GaN; glide-set terminal interface and shuffle-set terminal interface. Further analysis shows that interface has the maximum stress and misfit lines have the maximum stress values, which serve as the dislocation sources in the Al layer due to the larger stress in the interface. The mechanical responses of the Al/GaN multilayer exhibit a minor stage and some distinctive drops in the stress–strain curve. The first stage is associated with the dislocation nucleation from the interface. Upon further compression, more slip systems appear in the Al layer and dislocation nucleation in GaN could induce drops in curves. Meanwhile, the multiplications of dislocations cause strain hardening behaviours. read less

Abstract: ABSTRACT In this work, we investigated the deposition of AlN film on GaN substrate by using molecular dynamics (MD) simulations. The effects of GaN substrate surface, growth temperature, and injected N: Al flux ratio on the growth of AlN film were simulated and studied. Consequently, the deposited AlN film on the (0001) Ga-terminated GaN surface achieves better surface morphology and crystallinity than that on the (000-1) N-terminated GaN surface due to the different diffusion ability of Al and N adatoms on two GaN surfaces. Furthermore, with the increase of growth temperature, the surface morphology and crystallinity of AlN film were improved owing to the enhanced mobility of adatoms. At the optimised injected N: Al flux ratio of 1, comparatively good surface morphology and crystallinity of deposited AlN films were realised. This method lays a foundation for the follow-up real-time study of defects and stress evolution of AlN on GaN and can be applied to film growth of other materials. GRAPHICAL ABSTRACT read less

Abstract: A relationship between the observation of a density anomaly and the underlying crystalline phase diagram is demonstrated. The crystal phase diagram and temperature of maximum density (TMD) lines are calculated over a range of parameter space using a Stillinger-Weber potential. Relationships between the loci of density maxima in the PT plane for the liquid state and the underlying crystalline phase diagram are investigated. Two key potential parameters are systematically varied in order to control the balance between the model two- and three-body interaction terms, and the relative effects of varying the potential parameters analyzed. The respective TMD lines diverge at extreme values with one set of lines showing a reentrant behavior. For each parameter set the TMD lines are extrapolated to T=0K. The corresponding pressures are related to the crystalline phase diagram and are found to lie on or near specific crystal-crystal coexistence lines for a wide range of potential parameters. The density anomaly is observed to vanish corresponding to regions in the crystal phase diagram which lack crystal-crystal coexistence lines potentially offering a new interpretation for the emergence of anomalous behavior. read less

Abstract: The B3-GaN thin film was investigated by performing large-scale molecular dynamics (MD) simulation of nanoindentation. Its plastic behavior and the corresponding mechanism were studied. Based on the analysis on indentation curve, dislocation density, and orientation dependence, it was found that the indentation depths of inceptive plasticity on (001), (110), and (111) planes were consistent with the Schmid law. The microstructure evolutions during the nanoindentation under different conditions were focused, and two formation mechanisms of prismatic loop were proposed. The “lasso”-like mechanism was similar to that in the previous research, where a shear loop can translate into a prismatic loop by cross-slip; and the extended “lasso”-like mechanism was not found to be reported. Our simulation showed that the two screw components of a shear loop will glide on another loop until they encounter each other and eventually produce a prismatic dislocation loop. read less

Abstract: A series of molecular dynamics simulations are carried out to investigate the plastic deformation in wurtzite GaN. Besides the formation of an amorphous zone under the contact region, plastic slips nucleated on the m plane (10-10), c plane (0001), r plane (10-12), and s plane (10-11) are observed in the indentation. Combined with a close analysis of critical stress that induces a specific slip on different crystalline planes, the defect evolution is discussed in detail. Slip systems of [10-1-1](10-12) and 1/3[2-1-1-3](10-11) on the pyramidal planes are not supposed to nucleate easily since higher stress is required to activate them. However, a significant decrease in the shear stress that induces a pyramidal slip could be expected if the slip evolves gradually following a two-step procedure. The gradual slips on both the r plane (10-12) and s plane (10-11) are observed in our indentation simulation; the mechanism is studied by the calculation of generalized stacking fault energy.A series of molecular dynamics simulations are carried out to investigate the plastic deformation in wurtzite GaN. Besides the formation of an amorphous zone under the contact region, plastic slips nucleated on the m plane (10-10), c plane (0001), r plane (10-12), and s plane (10-11) are observed in the indentation. Combined with a close analysis of critical stress that induces a specific slip on different crystalline planes, the defect evolution is discussed in detail. Slip systems of [10-1-1](10-12) and 1/3[2-1-1-3](10-11) on the pyramidal planes are not supposed to nucleate easily since higher stress is required to activate them. However, a significant decrease in the shear stress that induces a pyramidal slip could be expected if the slip evolves gradually following a two-step procedure. The gradual slips on both the r plane (10-12) and s plane (10-11) are observed in our indentation simulation; the mechanism is studied by the calculation of generalized stacking fault energy. read less

Abstract: The growth of AlGaN has been extensively studied, but corresponding research related to the effect of AlN substrate surface has rarely been reported in literature. In this article, the effects of AlN substrate surface on deposition of AlGaN films were investigated by molecular dynamics (MD) simulations. (0001) Al-terminated and (0001¯) N-terminated AlN were considered as substrates. The quality of surface morphology and atomic scale structure of deposited AlGaN film are discussed in detail. The results show that the surface morphology and crystal quality of AlGaN film grown on (0001) Al-terminated AlN surface are better than for that grown on (0001¯) N-terminated AlN surface under various growing temperatures and Al/Ga injection ratios between Al and Ga. This can be attributed to the higher mobility of Al and Ga adatoms on the (0001) Al-terminated AlN surface. These findings can provide guidance for the preparation of high-quality AlGaN thin films on AlN substrate. read less

Abstract: In this theoretical investigation of the miscibility in quaternary alloys, we stay in the regular solution model and determine the interaction parameters from the enthalpy of mixing calculated using a modified Stillinger–Weber (SW) potential for III‐nitride ternary alloys. From our calculation, the values of the interaction parameters are 6.605, 10.523, and 0.677 kcal mol−1, respectively, for InGaN, InAlN, and AlGaN at x = 0.5 (where x is the In and Al fraction in InGaN, InAlN, and AlGaN, respectively). These values are in good agreement with those predicted by the improved delta lattice parameter (DLP) model for nitride ternary alloys. To determine the unstable regions characterized by the spinodal decomposition of the quaternary alloy InxAlyGa1−x−yN, we consider the composition ranges of 0.06 ≤ x ≤ 1 and 0 ≤ y ≤ 0.94. Our calculations show that the phase separation temperature increases with the increase of indium concentration. For In concentration lower than 9.4%, the quaternary alloy is miscible independent of the Al and Ga compositions in the usual growth temperature range for metalorganic vapor phase epitaxy. read less

Abstract: We report our findings on the optical properties of grain boundaries in GaN films grown on graphene layers and discuss their atomistic origin. We combine electron backscatter diffraction with cathodoluminescence to directly correlate the structural defects with their optical properties, enabling the high-precision local luminescence measurement of the grain boundaries in GaN films. To further understand the atomistic origin of the luminescence properties, we carefully probed atomic core structures of the grain boundaries by exploiting aberration-corrected scanning transmission electron microscopy. The atomic core structures of grain boundaries show different ordering behaviors compared with those observed previously in threading dislocations. Energetics of the grain boundary core structures and their correlation with electronic structures were studied by first principles calculation. read less

Abstract: Aberration-corrected scanning transmission electron microscopy was used to investigate the core structures of threading dislocations in plan-view geometry of GaN films with a range of Si-doping levels and dislocation densities ranging between (5 ± 1) × 108 and (10 ± 1) × 109 cm−2. All a-type (edge) dislocation core structures in all samples formed 5/7-atom ring core structures, whereas all (a + c)-type (mixed) dislocations formed either double 5/6-atom, dissociated 7/4/8/4/9-atom, or dissociated 7/4/8/4/8/4/9-atom core structures. This shows that Si-doping does not affect threading dislocation core structures in GaN. However, electron beam damage at 300 keV produces 4-atom ring structures for (a + c)-type cores in Si-doped GaN. read less

Abstract: GaN nanowires are being pursued for optoelectronic and high-power applications. In either use, increases in operating temperature reduce both performance and reliability making it imperative to minimize thermal resistances. Since interfaces significantly influence the thermal response of nanosystems, the thermal boundary resistance between GaN nanowires and metal contacts has major significance. In response, we have performed systematic molecular dynamics simulations to study the thermal boundary conductance between GaN nanowires and Al films as a function of nanowire dimensions, packing density, and the depth the nanowire is embedded into the metal contact. At low packing densities, the apparent Kapitza conductance between GaN nanowires and an aluminum film is shown to be larger than when contact is made between films of these same materials. This enhancement decreases toward the film-film limit, however, as the packing density increases. For densely packed nanowires, maximizing the Kapitza conductance can be achieved by embedding the nanowires into the films, as the conductance is found to be proportional to the total contact area. read less

Abstract: Fracture and buckling are major failure modes of thin and long nanowires (NWs), which could be affected significantly by an electric field when piezoelectricity is involved in the NWs. This paper aims to examine the issue based on the molecular dynamics simulations, where the gallium nitride (GaN) NWs are taken as an example. The results show that the influence of the electric field is strong for the fracture and the critical buckling strains, detectable for the fracture strength but almost negligible for the critical buckling stress. In addition, the reversed effects are achieved for the fracture and the critical buckling strains. Subsequently, the Timoshenko beam model is utilized to account for the effect of the electric field on the axial buckling of the GaN NWs, where nonlocal effect is observed and characterized by the nonlocal coefficient e0a=1.1 nm. The results show that the fracture and buckling of piezoelectric NWs can be controlled by applying an electric field. read less

Abstract: Gallium Nitride (GaN) possesses superior electronic properties for RF power electronics that play critical roles in various wireless communication technologies and military applications [1]. Heat generated as a byproduct of operation in these devices, increases their operating temperature and degrades their performance and lifetime. While bulk GaN has a high thermal conductivity (k) approaching 250 W/m-K, [2, 3] GaN thin films and devices experience a much lower k due to the presence of additional phonon scattering mechanisms and departures from Fourier transport [4, 5]. We will review thermal transport in GaN based devices, broadly addressing the impact of heat source dimensions, film thicknesses, interfaces, and defects. read less

Abstract: Thermal boundary resistance (inverse of conductance) between different material layers can dominate the overall thermal resistance in nanostructures and therefore impact the performance of the thermal property limiting nano devices. Because relationships between material properties and thermal boundary conductance have not been fully understood, optimum devices cannot be developed through a rational selection of materials. Here we develop generic interatomic potentials to enable material properties to be continuously varied in extremely large molecular dynamics simulations to explore the dependence of thermal boundary conductance on the characteristic properties of materials such as atomic mass, stiffness, and interfacial crystallography. To ensure that our study is not biased to a particular model, we employ different types of interatomic potentials. In particular, both a Stillinger-Weber potential and a hybrid embedded-atom-method + Stillinger-Weber potential are used to study metal-on-semiconductor compound interfaces, and the results are analyzed considering previous work based upon a Lennard-Jones (LJ) potential. These studies, therefore, reliably provide new understanding of interfacial transport phenomena particularly in terms of effects of material properties on thermal boundary conductance. Our most important finding is that thermal boundary conductance increases with the overlap of the vibrational spectra between metal modes and the acoustic modes of the semiconductor compound, and increasing the metal stiffness causes a continuous shift of the metal modes. As a result, the maximum thermal boundary conductance occurs at an intermediate metal stiffness (best matched to the semiconductor stiffness) that maximizes the overlap of the vibrational modes. read less

Abstract: A clear visualization of the origin and characteristics of threading dislocations (TDs) of GaN-based light emitting diode epitaxial layers on (0001) sapphire substrates have been carried out. Special experimental set up and chemical etchant along with field emission scanning electron microscopy are employed to study the dynamics of GaN TDs at different growth stages. Cross-sectional transmission electron microscopy analysis visualized the formation of edge TDs is arising from extension of coalescences at boundaries of different tilting-twining nucleation grains “mosaic growth.” Etch pits as representatives of edge TDs are in agreement with previous theoretical models and analyses of TDs core position and characteristics. read less

Abstract: We present a rigorous Green-Kubo methodology for calculating transport coefficients based on on-the-fly estimates of: (a) statistical stationarity of the relevant process, and (b) error in the resulting coefficient. The methodology uses time samples efficiently across an ensemble of parallel replicas to yield accurate estimates, which is particularly useful for estimating the thermal conductivity of semi-conductors near their Debye temperatures where the characteristic decay times of the heat flux correlation functions are large. Employing and extending the error analysis of Zwanzig and Ailawadi [Phys. Rev. 182, 280 (1969)] and Frenkel [in Proceedings of the International School of Physics "Enrico Fermi", Course LXXV (North-Holland Publishing Company, Amsterdam, 1980)] to the integral of correlation, we are able to provide tight theoretical bounds for the error in the estimate of the transport coefficient. To demonstrate the performance of the method, four test cases of increasing computational cost and complexity are presented: the viscosity of Ar and water, and the thermal conductivity of Si and GaN. In addition to producing accurate estimates of the transport coefficients for these materials, this work demonstrates precise agreement of the computed variances in the estimates of the correlation and the transport coefficient with the extended theory based on the assumption that fluctuations follow a Gaussian process. The proposed algorithm in conjunction with the extended theory enables the calculation of transport coefficients with the Green-Kubo method accurately and efficiently. read less

Abstract: The promise of the broad range of direct band gaps of the {Al, Ga, In}N system is limited by the crystal quality of current material. As grown defect densities of InN, when compared with the more mature GaN, are extremely high and InN is strongly influenced by these defects. This is particularly important due to the unusual position of the charge neutrality level of InN, leading to both the well‐known surface charge accumulation and difficulties in p‐type doping. While impurities and native defects clearly impact on the bulk carrier density in InN, the effects of threading dislocations on the electrical properties are still in dispute. Issues such as whether the dislocation line is charged or contains dangling bonds remain open. We present the results of a global search for possible dislocation core reconstructions for a range of screw dislocations in wurtzite III‐N material, utilizing empirical Stillinger–Weber inter‐atomic potentials. In addition, we investigate a wide range of non‐stoichiometric core structures. read less

Abstract: Past molecular dynamics studies of thermal transport have predominantly used Stillinger–Weber potentials. As materials continuously shrink, their properties increasingly depend on defect and surface effects. Unfortunately, Stillinger–Weber potentials are best used for diamond-cubic-like bulk crystals. They cannot represent the energies of many metastable phases, nor can they accurately predict the energetics of defective and surface regions. To study nanostructured materials, where these regions can dominate thermal transport, the accuracy of Tersoff potentials in representing these structures is more desirable. Based upon an analysis of thermal transport in a GaN system, we demonstrate that the cutoff function of the existing Tersoff potentials may lead to problems in determining the thermal conductivity. To remedy this issue, improved cutoff schemes are proposed and evaluated. read less

Abstract: Many methodologies have been proposed to build reliable and computationally fast coarse-grained potentials. Typically, these force fields rely on the assumption that the relevant properties of the system under examination can be reproduced using a pairwise decomposition of the effective coarse-grained forces. In this work it is shown that an extension of the multiscale coarse-graining technique can be employed to parameterize a certain class of two-body and three-body force fields from atomistic configurations. The use of explicit three-body potentials greatly improves the results over the more commonly used two-body approximation. The method proposed here is applied to develop accurate one-site coarse-grained water models. read less

Abstract: Recent molecular dynamics simulation methods have enabled thermal conductivity of bulk materials to be estimated. In these simulations, periodic boundary conditions are used to extend the system dimensions to the thermodynamic limit. Such a strategy cannot be used for nanostructures with finite dimensions which are typically much larger than it is possible to simulate directly. To bridge the length scales between the simulated and the actual nanostructures, we perform large-scale molecular dynamics calculations of thermal conductivities at different system dimensions to examine a recently developed conductivity vs dimension scaling theory for both film and wire configurations. We demonstrate that by an appropriate application of the scaling law, reliable interpolations can be used to accurately predict thermal conductivity of films and wires as a function of film thickness or wire radius at realistic length scales from molecular dynamics simulations. We apply this method to predict thermal conductivities for GaN wurtzite nanostructures. read less

Abstract: Significant differences exist among literature for thermal conductivity of various systems computed using molecular dynamics simulation. In some cases, unphysical results, for example, negative thermal conductivity, have been found. Using GaN as an example case and the direct nonequilibrium method, extensive molecular dynamics simulations and Monte Carlo analysis of the results have been carried out to quantify the uncertainty level of the molecular dynamics methods and to identify the conditions that can yield sufficiently accurate calculations of thermal conductivity. We found that the errors of the calculations are mainly due to the statistical thermal fluctuations. Extrapolating results to the limit of an infinite-size system tend to magnify the errors and occasionally lead to unphysical results. The error in bulk estimates can be reduced by performing longer time averages using properly selected systems over a range of sample lengths. If the errors in the conductivity estimates associated with each of the sample lengths are kept below a certain threshold, the likelihood of obtaining unphysical bulk values becomes insignificant. Using a Monte Carlo approach developed here, we have determined the probability distributions for the bulk thermal conductivities obtained using the direct method. We also have observed a nonlinear effect that can become a source of significant errors. For the extremely accurate results presented here, we predict a [0001] GaN thermal conductivity of $185\text{ }\text{W}/\text{K}\text{ }\text{m}$ at 300 K, $102\text{ }\text{W}/\text{K}\text{ }\text{m}$ at 500 K, and $74\text{ }\text{W}/\text{K}\text{ }\text{m}$ at 800 K. Using the insights obtained in the work, we have achieved a corresponding error level (standard deviation) for the bulk (infinite sample length) GaN thermal conductivity of less than $10\text{ }\text{W}/\text{K}\text{ }\text{m}$, $5\text{ }\text{W}/\text{K}\text{ }\text{m}$, and $15\text{ }\text{W}/\text{K}\text{ }\text{m}$ at 300 K, 500 K, and 800 K, respectively. read less

Abstract: III–N compound semiconductors are nowadays widely used in electronic device technology. Due to the complexity of their structures planar and linear defects may have various atomic configurations. Since in the wurtzite structure of AlN and InN the second‐neighbor distance is very close to the stable “metallic” Al–Al and In–In distances respectively, a III‐species environment approach based on a Tersoff empirical bond order interatomic potential is developed in which the cut‐off distance for Al–Al and In–In interactions is tuned. In particular, the work is focused on two issues: the development of an approach for the calculation of defected structures in III‐nitrides and the application of this method on a series of planar defects in wurtzite structure. Various structural and energy‐related conclusions are drawn that are attributed to the complexity of the III–III metal type and N–N interactions in connection with the difference of the lattice parameters and the elastic constants. Molecular dynamic simulations are led to the conclusion that structural transformations may also occur. The Austerman–Gehman and Holt models for the inversion domain boundary (IDB) on the (10$ \bar 1 $0) plane are higher in energy than the IDB* model of Northrup, Neugebauer, and Romano. The model of Blank et al. for the translation domain boundary (TDB) on the {1$ \bar 2 $10} plane is unstable with respect to Drum's model. The Austerman model for the IDB on the {1$ \bar 2 $10} plane is unstable with respect to the IDB* model appropriate for this plane. The Austerman {10$ \bar 1 $0} IDB model is recognized as a strong candidate, among the IDB atomic configurations. Moreover, models for IDBs on {10$ \bar 1 $0} planes in which the boundary plane intersects two bonds (type‐2 models) are less stable than models in which the boundary plane intersects one bond (type‐1 models), in all cases considered. It is confirmed that the III‐species environment approach describes the “wrong”‐bonded defect local configuration structures more realistically with respect to the standard approach. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) read less

Abstract: An atomistic simulation of the threading $(\mathbf{a}+\mathbf{c})$-mixed dislocation core in wurtzite GaN has been carried out. Starting from models generated in the framework of continuum elasticity theory, two core configurations are obtained independently by using an empirical potential and a tight-binding based ab initio method. The most energetically favorable core with a $5∕7$-atoms ring structure is fully coordinated without wrong bonds, whereas the other with a complex double $5∕6$-atoms ring structure contains two rows of dangling bonds. Both core configurations introduce empty states spread over the upper half of the band gap. read less

Abstract: Various properties of ceramics can be significantly influenced by the presence of grain boundaries. The influence on the properties is closely related to the grain-boundary atomic structures. As different grain boundaries have different atomic structure, different grain boundaries have different influence on the properties. It is difficult to examine the atomic structure and properties of individual grain boundaries in ceramics. In order to understand the atomic–structure–property relationships, well-defined single grain boundaries should be characterized. In the present paper, we review our recent results on the investigations of atomic structures and electrical properties of ZnO single grain boundaries. The relationships between the atomic structures and the electrical properties were investigated using ZnO bicrystals, whose grain-boundary orientation relationship and grain-boundary planes can be arbitrarily controlled. The discussion focuses on the microscopic origin of nonlinear current–voltage (I–V) characteristics across ZnO grain boundaries. High-resolution transmission electron microscopy (HRTEM) observations and lattice-statics calculations revealed the atomic structures of the undoped ZnO [0001] Σ7 and Σ49 grain boundaries, enabling a comparison between coincidence site lattice (CSL) boundaries with small and large periodicity. These grain boundaries contained the common structural units (SUs) featuring atoms with coordination numbers that are unusual in ZnO. The Σ49 boundary was found to have characteristic arrangement of the SUs, where two kinds of the SUs are alternatively formed. It is considered that the characteristic arrangement was formed to effectively relax the local strain in the vicinity of the boundary. Such a relaxation of local strain is considered to be one of dominant factors to determine the SU arrangements along grain boundaries. I–V measurements of the undoped ZnO bicrystals showed linear I–V characteristics. Although the coordination and bond lengths of atoms in the grain boundaries differ from those in the bulk crystal, this does apparently not generate deep unoccupied states in the band gap. This indicates that atomic structures of undoped ZnO grain boundaries are not responsible for the nonlinear I–V characteristics of ZnO ceramics. On the other hand, the nonlinear I–V characteristic appeared when doping the boundaries with Pr. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of Pr-doped boundaries revealed that Pr segregates to specific atomic columns, substituting Zn at the boundary. However, the Pr itself was not the direct origin of the nonlinear I–V characteristics, as the Pr existed in the three-plus state and would not produce acceptor states in the boundary. First-principles calculations revealed that Pr doping instead promotes the formations of acceptor-like native defects, such as Zn vacancies. We believe that such acceptor-like native defects are microscopic origin of the nonlinear I–V characteristics. Investigations of various types of grain boundaries in the Pr and Co-codoped ZnO bicrystals indicated that the amounts of Pr segregation and the nonlinear I–V characteristics significantly depend on the grain-boundary orientation relationship. Larger amount of Pr segregation and, as a result, higher nonlinearity in I–V characteristics was obtained for incoherent boundaries. This indicates that Pr doping to incoherent boundaries is one of the guidelines to design the single grain boundaries with highly nonlinear I–V characteristics. Finally, a Pr and Co-codoped bicrystal with an incoherent boundary was fabricated to demonstrate a highly nonlinear I–V characteristic. This result indicates that ZnO single-grain-boundary varistors can be designed by controlling grain-boundary atomic structures and fabrication processes. Summarizing, our work firstly enabled us to gain a deeper understanding for the atomic structure of ZnO grain boundaries. Secondly, we obtained important insight into the origin of nonlinear I–V characteristics across the ZnO grain boundaries. And, finally, based on these results, we demonstrated the potential of this knowledge for designing and fabricating ZnO single-grain-boundary varistors. read less