Open-circuit Boundary Conditions Research Articles

Analytical and numerical modelling of the electrostatic behaviour of highly insulating materials in the time domain

The usual response of an insulator subjected to a voltage step involves time power laws. We present here mathematical tools allowing to calculate this time domain response in open circuit after an initial charge deposit, within the framework of linear systems theory, using linear fractional transfer functions. In the time domain, the inverse Laplace transform of the data taken from the frequency domain leads to Mittag-Leffler functions, generalizing the Debye exponential response to an extended fractional α-order response. The open-circuit boundary conditions are different from the closed-circuit ones. We nevertheless demonstrate that using a transfer function deduced from the Cole-Cole response in closed-circuit, a precise analytical formula of the potential decay after an initial charge deposit may be established, and a numerical computation of this decay may be performed using easily available software. Applying the superposition principle, the voltage return following a brief short circuit may also be deduced. Experimental results are presented and the limits of the superposition principle applied to real materials are discussed.

Out-of-plane ferroelectricity and robust magnetoelectricity in quasi-two-dimensional materials.

Thin-film ferroelectrics have been pursued for capacitive and nonvolatile memory devices. They rely on polarizations that are oriented in an out-of-plane direction to facilitate integration and addressability with complementary metal-oxide semiconductor architectures. The internal depolarization field, however, formed by surface charges can suppress the out-of-plane polarization in ultrathin ferroelectric films that could otherwise exhibit lower coercive fields and operate with lower power. Here, we unveil stabilization of a polar longitudinal optical (LO) mode in the n = 2 Ruddlesden-Popper family that produces out-of-plane ferroelectricity, persists under open-circuit boundary conditions, and is distinct from hyperferroelectricity. Our first-principles calculations show the stabilization of the LO mode is ubiquitous in chalcogenides and halides and relies on anharmonic trilinear mode coupling. We further show that the out-of-plane ferroelectricity can be predicted with a crystallographic tolerance factor, and we use these insights to design a room-temperature multiferroic with strong magnetoelectric coupling suitable for magneto-electric spin-orbit transistors.

Giant hyperferroelectricity in LiZnSb and its origin

Hyperferroelectricity (HyFE) is an intriguing phenomenon in which spontaneous polarization persists under an open-circuit boundary condition (OCBC) despite the existence of a depolarization field. However, small polarization and shallow well depth have been found so far in most hyperferroelectric materials, which severely limits their applications. Using first-principles density functional theory, we report the discovery of a giant hyperferroelectricity in LiZbSb. The HyFE spontaneous polarization is shown to be remarkably large with $\mathrm{P}=0.282\phantom{\rule{0.16em}{0ex}}\mathrm{C}/{\mathrm{m}}^{2}$ under OCBC, which is one order of magnitude greater than the HyFE polarization in ${\mathrm{LiNbO}}_{3}$. Furthermore, HyFE in LiZnSb is found to be exceptionally stable with a well depth of electric free energy $\mathrm{\ensuremath{\Delta}}F=\ensuremath{-}332\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$, which makes LiZnSb a possible hyperferroelectric solid at room temperature. The origin of the giant hyperferroelectricity in LiZnSb is identified and is attributed to the large mode effective charge of the soft longitudinal-optic phonon and the large high-frequency dielectric constant.

A refined Bloch mode synthesis framework for fast and accurate analysis of electroelastic metamaterials with piezoelectric resonant shunt damping

Bloch mode synthesis (BMS) is a model order reduction method that was originally formulated to accelerate band-structure calculations of periodic elastic materials. In this paper, the BMS framework is expanded to offer a platform suitable for analysis of electroelastic metamaterials with piezoelectric resonant shunt damping. First, a transformation of coordinates formed by a set of dominant fixed-interface modes and a set of static-constraint modes is used in combination with Bloch periodicity boundary conditions to derive the classical BMS method in the context of electroelastic metamaterials. Then, a set of residual modes that is simply truncated in the classical BMS, is augmented into the reduction process, leading to an enhanced BMS method, denoted RMH-BMS.Currently available model order reduction techniques for electroelastic metamaterials adopt a reduction basis obtained from one of the limiting eigenvalue problems associated with short-circuit (SC) and open-circuit (OC) boundary conditions. In either case, the electrical circuit parameters are ignored during modal reduction. In this paper, it is shown that such approximation leads to inaccurate band-structure predictions for electroelastic metamaterials equipped with periodic array of resonant shunt circuits. To this end, two versions of the proposed BMS methods are evaluated and compared. In the first version, the reduced order model is constructed following the widely used OC basis approach. The second version, on the other hand, exploits a coupled basis approach, which requires knowledge of the electrical circuit parameters prior to the interior modal reduction step. A comprehensive error analysis is conducted to assess the computational performances of the BMS methods, and the results revealed that whether the classical BMS or the RMH-BMS is employed to construct the reduced order model, the coupled basis approach produces significantly more accurate results compared to the OC basis approach. The results presented in this work expose the limitations of implementing the OC basis approach in wave propagation analysis of electroelastic metamaterials with piezoelectric resonant shunt damping and shed light on the associated consequences in predicting the bandgap properties of such metamaterials.

Possible existence of tristable polarization states in LiNbO3 under an open-circuit boundary condition

Hyperferroelectricity is an intriguing phenomenon in that electric polarization persists under the open-circuit boundary condition (OCBC). Using first-principles density functional calculations, we investigate the hyperferroelectric properties of ${\mathrm{LiNbO}}_{3}$, a technologically important ferroelectric solid. We find that (i) the longitudinal-optic ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}_{1})$ phonon is soft with imaginary frequency $96i\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ when centrosymmetric ${\mathrm{LiNbO}}_{3}$ is under OCBC, and this soft LO phonon is shown to differ drastically from the corresponding transverse-optic ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{TO}}_{1})$ phonon. (ii) The ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}_{1})$ phonon is able to yield, under OCBC, a free-energy minimum with well depth of $\ensuremath{-}9$ meV at a nonzero polarization of 0.023 C/${\mathrm{m}}^{2}$, thereby capable of producing hyperferroelectricity. (iii) The origin that ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}_{1})$ is capable of inducing HyFE is determined, and it stems from the extraordinarily small mode effective charge of this soft LO phonon. This finding also provides a key guiding principle for searching and designing new hyperferroelectrics. (iv) Despite that ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}_{1})$ is able to induce HyFE, we find that the ground state of ${\mathrm{LiNbO}}_{3}$ under OCBC is nevertheless not polar, revealing that the existence of a soft LO phonon does not guarantee HyFE. (v) Interestingly, we further show that ${\mathrm{LiNbO}}_{3}$ under OCBC may exhibit unusual tristable polarization states, with two potential wells of depth $\ensuremath{-}23$ meV and $\ensuremath{-}1.9$ meV, respectively. Besides providing insightful knowledge for understanding HyFE in general, these results reveal that there is rich and interesting hyperferroelectric physics in ${\mathrm{LiNbO}}_{3}$ under OCBC, in particular.

Ferroelectricity and multiferroicity in anti–Ruddlesden–Popper structures

Combining ferroelectricity with other properties such as visible light absorption or long-range magnetic order requires the discovery of new families of ferroelectric materials. Here, through the analysis of a high-throughput database of phonon band structures, we identify a structural family of anti-Ruddlesden-Popper phases [Formula: see text]O (A=Ca, Sr, Ba, Eu, X=Sb, P, As, Bi) showing ferroelectric and antiferroelectric behaviors. The discovered ferroelectrics belong to the new class of hyperferroelectrics that polarize even under open-circuit boundary conditions. The polar distortion involves the movement of O anions against apical A cations and is driven by geometric effects resulting from internal chemical strains. Within this structural family, we show that [Formula: see text]O combines coupled ferromagnetic and ferroelectric order at the same atomic site, a very rare occurrence in materials physics.

Structural and electronic properties of monodomain ultrathin PbTiO3/SrTiO3/PbTiO3/SrRuO3 heterostructures: A first-principles approach

First-principles calculations within the local density approximation were carried out to explain the ground state and electronic properties of a vacuum/PbTiO3/SrTiO3/PbTiO3/SrRuO3 multilayer in a monodomain phase. Open-circuit boundary conditions were assumed, considering the electric displacement field, D, as the fundamental electrical variable. The direction and the magnitude of D can be monitored by proper treatment of the PbO surface layer, introducing external fractional charges Q in the surface atomic layers by means of virtual crystal approximation. Different excess or deficit surface charges (from Q=±0.05 to Q=±0.15) were considered, corresponding to small values of the polarization (up to ±0.16C/m2) in both directions. The layer-by-layer electric polarization, tetragonality, and the profile of the electrostatic potential were computed, as well as the projected density of states, as a function of electric displacement field. The magnitude of D is preserved across the dielectric layers, which translates into a polarization of the SrTiO3 spacer layer. The tetragonality of the two PbTiO3 layers is different, in good agreement with experimental x-ray diffraction techniques, with the layer closer to the free surface exhibiting a smaller value. This is attributed to the interplay with surface effects that tend to contract the material in order to make the remaining bonds stronger. Our calculations show how the final structure in this complex oxide heterostructure comes from a delicate balance between electrical, mechanical, and chemical boundary conditions.

Vibration attenuation and dynamic control of piezolaminated plates with coupled electromechanical actuation

Vibration attenuation and dynamic control of the piezolaminated plate actuated with coupled electromechanical loading are aimed and achieved in the present work. Efficient finite element methodology with higher-order shear deformation theory is assisted to blend the effects of shear strains in the computational model. An isoperimetric eight-noded rectangular element is implemented through linear electric potential distribution along the thickness to set up the relations. Coupled electromechanical loading is considered in the formulation to consider the piezoelectric sensing and actuation mechanism. Piezolaminated plates with both cross-ply and angle-ply orientation of bonded substrate lamina are considered in the analysis. Vibration responses of multilayered composite plates with surface-mounted piezolaminates are evaluated for open-circuit and closed-circuit boundary conditions of the electric field. Results obtained from the analysis are well revealed for frequencies of various modes of simply supported piezolaminated plates. Dynamic vibrational response and effect of the control gain (Gv) in terms of velocity feedback on the dynamic characteristics of a piezoelectric laminated plate are examined. Another aim of proposing this FE model is to demonstrate the effect of placement of fibers in a different orientation for the PVDF layer to achieve active damping, and attenuation of vibrations of the laminated composite plate is also achieved and demonstrated.

Electrical Response of a Multiferroic Composite Semiconductor Fiber Under a Local Magnetic Field

We study the electrical response of a multiferroic composite semiconductor fiber consisting of a piezoelectric semiconductor layer and two piezomagnetic layers under a transverse magnetic field applied locally to a finite part of the fiber. The phenomenological theory of piezomagnetic-piezoelectric semiconductors is employed. A one-dimensional model is derived for magnetically induced extension of the fiber. For open-circuit boundary conditions at the two ends of the fiber, an analytical solution is obtained from the model linearized for small carrier perturbations. The solution shows a local electric polarization and a pair of local electric potential barrier-well. When the two ends of the fiber are under a voltage, a nonlinear numerical solution shows that the potential barrier and well forbid the passage of currents when the voltage is low. The results have potential applications in piezotronic devices when magnetic fields are involved for manipulating the devices or sensing and transduction.

Active vibration control of thin constrained composite damping plates with double piezoelectric layers

Vibrations and the damping behaviour of thin constrained composite plates with double piezoelectric layers are analytically explored by using Fourier transformation and classical laminated plate theory. Electric potential equations in the double piezoelectric layers are solved with respect to closed and open circuit boundary conditions, an exterior dielectric slab and active control. The natural frequencies and loss factors of the constrained smart composite plates with passive control methods are not notably changed in comparison with those of the constrained composite plates without piezoelectric effects since vibrational energy does not efficiently convert to electrical energy. The loss factors of the composite plates with active constrained damping increase and the natural frequencies have significant variations as the proportional derivative gains increase. Transverse displacement power spectra of the piezoelectric composite plates with active control are compared with those of the piezoelectric composite plates with passive control showing that active control has the best suppression performance of vibrations for the constrained laminated plates with double piezoelectric layers. Radial power spectral density, phase angles and cylindrical-wave power spectral density are calculated. Interesting patterns of wave propagation are explained when plane wave expansion is used to obtain Bessel cylindrical waves.

Hyperferroelectricity in ZnO: Evidence from analytic formulation and numerical calculations

Hyperferroelectricity is an interesting phenomenon. The hexagonal ABC-type semiconductor LiZnAs was discovered to be hyperferroelectric (HFE) [Garrity et al., Phys. Rev. Lett. 112, 127601 (2014)]. ZnO is a technologically important semiconductor and possesses a wurtzite crystal structure similar to LiZnAs. It raises an intriguing question of whether ZnO is HFE. Here we use various approaches to address this important question by determining the electric equation of state, the free energy of ZnO under an open-circuit boundary condition (OCBC), and the vibration properties of a LO phonon. We find the following: (i) The $D\ensuremath{\sim}\ensuremath{\lambda}$ curve of ZnO, where $D$ is electric displacement and $\ensuremath{\lambda}=P/0.844$ is a parameter directly proportional to polarization $P$, exhibits one and only one root at $\ensuremath{\lambda}=0$. (ii) Under OCBC, the free energy of ZnO does not produce a minimum at the structural phase of nonzero polarization. (iii) The LO phonon with computed frequency ${\ensuremath{\omega}}_{\mathrm{LO}}=255\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ in centrosymmetric ZnO is not soft and does not have an imaginary frequency. These results corroborate the others and consistently lead to the conclusion that, although ZnO is interestingly on the edge of becoming a HFE, it is not yet a HFE. We further provide a physical origin explaining why ZnO is not HFE and reveal a possibility that may turn ZnO into a HFE.

Exact Solution for Driven Oscillations in Plasmonic Field-Effect Transistors

High-mobility field effect transistors can serve as resonant detectors of terahertz radiation due to excitation of plasmons in the channel. The modeling of these devices previously relied either on approximate techniques, or complex full-wave simulations. In this paper, we obtain an exact solution for driven electrical oscillations in plasmonic field-effect transistor with realistic contact geometry. The obtained solution highlights the importance of evanescent plasma waves excited near the contacts, which qualitatively modify the detector responsivity spectra. We derive the boundary condition on the ac floating electrodes of plasmonic FET which interpolates between open-circuit (Dyakonov-Shur) and short-circuit (clamped voltage) boundary conditions. In both limits, the FET photovoltage possesses resonant fringes, however, the absolute value of voltage is greater in the open-circuit regime.

Active vibration control of piezoelectric smart beams with radial basis function generated finite difference collocation method

A local collocation method based on finite difference generated radial basis functions considering supplementary polynomials is used to solve the governing equations of cantilever piezoelectric smart beams. The natural modes of vibration of a bimorph and a three-layered smart beam with an interior aluminium core are analysed for both open-circuit and closed-circuit electrical boundary conditions. Very accurate results are obtained at a low computational cost. Subsequently, a constant gain velocity feedback active vibration control system is implemented, and the time and frequency response functions of both beams subjected to initial impulse and displacement conditions are investigated. Different values of the applied gain and varying thickness of the piezoelectric layers are analysed. The governing equations are established using equivalent-single-layer first-order-shear-deformation theory with through-the-thickness quadratic layerwise electric potential for improved accuracy.

Fracture analysis of flexoelectric double cantilever beams based on the strain gradient theory

In this article, the fracture behavior of a flexoelectric double cantilever beam (DCB) under large deformation is investigated using strain gradient theory. Incorporation of electric field-strain gradient coupling, known as flexoelectricity, in the constitutive equations of a 1D cantilever beam is studied. Moreover, due to the enormous surface area to volume ratio at micro/nanoscale, surface effects are also included in the theoretical formulations. The solutions of the cantilever beam deflections and strain energy release rates of the DCB with different configurations are numerically evaluated and compared. Numerical results anticipate significant size effect (higher structural stiffness) as the values of the material length scale parameter (l) and the material flexoelectric coefficient (f31) are increased. DCB with the open circuit boundary condition demonstrates higher stiffness than the short circuit boundary condition. At micro/nanoscale, the effect of uncracked part of the DCB is found to be substantial in determining the strain energy release rate and it must not be ignored even for the slender beams.

Buckling analysis of orthotropic smart laminated nanoplates based on the nonlocal continuum mechanics using third-order shear and normal deformation theory

In this article, the nonlocal buckling behavior of biaxially loaded graphene sheet with piezoelectric layers based on an orthotropic intelligent laminated nanoplate model is studied. The nonlocal elasticity theory is used in the buckling analysis to show the size scale effects on the critical buckling loads. The electric potential in piezoelectric layers satisfies Maxwell’s equation for either open- or closed-circuit boundary conditions. Based on the third-order shear and normal deformation theory, the nonlinear equilibrium equations are obtained. In order to obtain the linear nonlocal stability equations, the adjacent equilibrium criterion is used. The linear nonlocal governing stability equations are solved analytically, assuming simply supported boundary condition along all edges. To validate the results, the critical buckling loads are compared with those of molecular dynamics simulations. Finally, the effects of different parameters on the critical buckling loads are studied in detail. The results show that by increasing the nonlocal parameter, the critical buckling load decreases. The piezoelectric effect increases the critical buckling load for both open- and closed-circuit boundary conditions. For open-circuit boundary condition, the variation in the critical buckling load is due to the stiffness and piezoelectric effects, but for closed circuit, it is due to the stiffness effect only. Also, the critical buckling load for open circuit is bigger than that of closed one.

Off-plane polarization ordering in metal chalcogen diphosphates from bulk to monolayer

Vertically (off-plane) ferroelectric ordering in ultrathin films has been pursued for decades. We predict the existence of intrinsic vertical polarization orderings in ultrathin metal chalcogen-diphosphates (MCDs). Taking ${\mathrm{CuInP}}_{2}{\mathrm{Se}}_{6}$ as an example, the first-principles calculation and electrostatic-energy model show that, under the open-circuit boundary condition, the ground state of bulk ${\mathrm{CuInP}}_{2}{\mathrm{Se}}_{6}$ is ferroelectric (FE) while that of monolayer is antiferroelectric (AFE), and the critical thickness for this FE/AFE transition is around six layers. Interestingly, under the closed-circuit boundary condition, the FE state can hold even for monolayer. Particularly, because of the small energy difference but the large barrier between FE and AFE orderings, the FE state can be stabilized in a free-standing monolayer, giving rise to intrinsic, off-plane two-dimensional ferroelectrics. Applying Monte Carlo simulations, we further calculate the ferroelectric Curie temperature (${T}_{c}$) and electric hysteresis.

Advanced methodology for measuring the extensive elastic compliance and mechanical loss directly in k31 mode piezoelectric ceramic plates

Dielectric, elastic, and piezoelectric constants, and their corresponding losses are defined under constant conditions of two categories; namely, intensive (i.e., E, electric field or T, stress), and extensive (i.e., D, dielectric displacement or x, strain) ones. So far, only the intensive parameters and losses could be measured directly in a k31 mode sample. Their corresponding extensive parameters could be calculated indirectly using the coupling factor and “K” matrix. However, the extensive loss parameters, calculated through this indirect method, could have large uncertainty, due to the error propagation in calculation. In order to overcome this issue, extensive losses should be measured separately from the measurable intensive ones in lead-zirconate-titanate (PZT) k31 mode rectangular plate ceramics. We propose a new mechanical-excitation methodology, using a non-destructive testing approach by means of a partial electrode configuration, instead of the conventional full electrode configuration. For this purpose, a non-electrode sample was prepared, where the electrode covered only 10% of the top and bottom surfaces at the center to actuate the whole sample, and also monitor the responding vibration. The admittance spectrum of this sample, corresponds to PZT properties under dielectric displacement D constant condition. Furthermore, ceramics with partial-electrodes were also prepared to create short and open circuit boundary conditions, attributing to resonance and anti-resonance modes. In the proposed way, we were able to measure both intensive and extensive elastic compliances and mechanical losses directly for the first time. The accuracy of this new method is compared with the conventional measurements by use of indirect calculations. The preliminary results (by neglecting the 10% actuator part difference at this point) were obtained, which were in good agreements (less than 3% difference) with the previous indirect method.

Free vibration of functionally graded carbon nanotube reinforced composite plates integrated with piezoelectric layers

In the present research, free vibration behavior of carbon nanotube reinforced composite (CNTRC) plates integrated with piezoelectric layers at the bottom and top surfaces is analyzed. Plate is modeled according to the first order shear deformation plate theory. Distribution of CNTs across the plate thickness may be functionally graded (FG) or uniformly distributed (UD). Properties of the composite media are obtained according to a modified rule of mixtures approach which contains efficiency parameters. Distribution of electric potential across the piezoelectric thickness is assumed to be linear. The complete set of motion and Maxwell equations of the system are obtained according to the Ritz formulation suitable for arbitrary in-plane and out-of-plane boundary conditions. Besides, two types of electrical boundary conditions, namely, closed circuit and open circuit are considered for the free surfaces of the piezoelectric layers. Chebyshev polynomials are used as the basis functions in Ritz approximation. The resultant eigenvalue system is solved to obtain the frequencies of the system as well as the mode shapes. It is shown that, fundamental frequency of a closed circuit plate is always higher than a plate with open circuit boundary conditions.

Topology optimization of piezoelectric nanostructures

We present an extended finite element formulation for piezoelectric nanobeams and nanoplates that is coupled with topology optimization to study the energy harvesting potential of piezoelectric nanostructures. The finite element model for the nanoplates is based on the Kirchoff plate model, with a linear through the thickness distribution of electric potential. Based on the topology optimization, the largest enhancements in energy harvesting are found for closed circuit boundary conditions, though significant gains are also found for open circuit boundary conditions. Most interestingly, our results demonstrate the competition between surface elasticity, which reduces the energy conversion efficiency, and surface piezoelectricity, which enhances the energy conversion efficiency, in governing the energy harvesting potential of piezoelectric nanostructures.

Phase-transition character in (Ba0.50,Sr0.50)TiO3 nanodots from first principles

A first-principles-derived scheme combined with an efficient Monte Carlo technique is performed to investigate the character of phase transitions in (Ba0.50,Sr0.50)TiO3 (BST50) nanodots under ideal short-circuit (SC) and open-circuit (OC) electrical boundary conditions, and the corresponding properties are subsequently compared to the properties of bulk BST50. Our calculations indicate that the ferroelectric properties change dramatically when transitioning from 3D (bulk) to 0D (nanodot) systems under short-circuit conditions. While BST bulk exhibits three first-order ferroelectric phase transitions, BST dot shows a single second-order ferroelectric phase transition. On the other hand, new insight into the character and signature of the phase transition associated with a toroid moment of polarization, which occurs in nanodots under open-circuit conditions, is provided.