Landau-Khalatnikov Equation Research Articles

Compact modeling of short-channel effects in back-gated 2D negative capacitance (NC) FETs

The negative capacitance field-effect transistor with 2D channel material (2D NC-FET) holds significant promise for low-power applications owing to its remarkable resilience against short-channel effects (SCEs) and favorable noise characteristics. In this study, we establish a compact current–voltage (I–V) model for short-channel back-gated 2D NC-FETs with metal-ferroelectric-metal–insulator–semiconductor structure by self-consistently solving the two-dimensional Poisson, drift–diffusion and Landau–Khalatnikov equations. The proposed model is valid and continuous throughout the entire operating regime, including the fully-depleted region, partly-depleted region, and accumulation region. Furthermore, we derive analytical equations for the threshold voltage ( VTH ) and subthreshold swing ( SS ) of back-gated 2D NC-FETs based on the developed I–V model. Lastly, we elucidate the influence mechanisms of various device parameters and voltage bias on the subthreshold characteristics of short-channel back-gated 2D NC-FETs using the proposed I–V model in conjunction with analytical expressions of VTH and SS . Our findings reveal that back-gated 2D NC-FETs shows unconventional degradation behavior in VTH and SS, resulting from the competition between traditional SCEs and novel negative capacitance effects.

Miller capacitance reduction in negative capacitance TFETs

ABSTRACT A dielectric stacked hetero-gate topology is proposed to reduce the Miller capacitance in a negative capacitance double gate TFET. An analytical charge-based model is introduced for the analysis of the terminal capacitance behaviour of the device. Charge and capacitance models are developed using the surface potential modelling approach by solving the Poisson Equation. The proposed closed-form charge model is SPICE-compatible and can be used for circuit simulations. The model accuracy is validated by combining one-dimensional Landau–Khalatnikov equation with the two-dimensional simulations of the double gate stacked-hetero-gate tunnel field effect transistor. The model shows excellent agreement with device simulations. The proposed topology exhibits Miller capacitance reduction of 30% which results in the gain band width product improvement of 43% more than the stacked homo-gate counterpart.

Computational modelling of cylindrical-ferroelectric-dual metal-nanowire field effect transistor (C-FE-DM-NW FET) using landau equation for gate leakage minimization

In order to address and resolve the significant problem of gate-induced drain leakage (GIDL) current and enhance device reliability, band-to-band tunnelling (BTBT), and OFF-state leakages, a computational model of a cylindrical-ferroelectric-dual-metal-nanowire-field effect transistor (C-FE-DM-NW-FET) has been proposed in this manuscript. The proffered structure is a symmetric gate structure with ferroelectric layer sandwiched between the gate terminal and oxide layer which reduces the BTBT which in term reduces the OFF-state leakage hence making the device definitive for low power applications. In this manuscript, there has been a reduction in the leakage current by a magnitude of 104 times in 50 nm and 107 times in 60 nm channel length which translates to a reduction in gate leakage (IGIDL) of more than 100 % in C-FE-NW-FET over C-NW FET. To analyze the Electric Field, Surface Potential, and IGIDL with the proper boundary conditions, the 2D Poisson's equation is solved analytically with Landau-Khalatnikov (LK) equation. The analytical findings are quite similar to the simulated outcomes.

Understanding magnetoelectric switching in BiFeO3 thin films

In this work we use a phenomenological theory of ferroelectric switching in BiFeO3 thin films to uncover the mechanism of the two-step process that leads to the reversal of the weak magnetization of these materials. First, we introduce a realistic model of a BiFeO3 film, including the Landau energy of isolated domains as well as the constraints that account for the presence of the substrate and the multidomain configuration found experimentally. We use this model to obtain statistical information about the switching behavior—by running dynamical simulations based on the Landau-Khalatnikov time-evolution equation, including thermal fluctuations—and we thus identify the factors that drive the two-step polarization reversal observed in the experiments. Additionally, we apply our model to test potential strategies for optimizing the switching characteristics. Published by the American Physical Society 2024

Modeling of negative capacitance underlap graded-channel junction accumulation mode junctionless FET in nano-scale regime

Analytical modeling of negative capacitance (NC) graded-channel (GC) underlap junction accumulation mode (JAM) JL-FET is presented in this literature. Here, the surface potential, threshold voltage, sub-threshold drain current, sub-threshold swing (SS) and DIBL are obtained by solving the 2D Poisson's equation and Landau-Khalatnikov (LK) equation simultaneously. Performances of the proposed NC-GC-JAM-JL-FET is analyzed in detail for the variations in FE-layer thickness, gate-length, underlap length, graded channel ratio and Si-film thickness. The proposed model is calibrated with the experimental data to establish its acceptability. The proposed device is also simulated in the Silvaco ATLAS device simulator, which shows very good agreement with the analytical model. The present paper establishes the remarkable prospect of the proposed architecture to be operated for low-power application in nano-scale regime.

Multiple factors of regulation for transient negative capacitance in PbZr(1−x)Ti(x)O3 ferroelectric thin films

The negative capacitance (NC) of ferroelectric (FE) materials can effectively break the ‘Boltzmann tyranny’ and drive the continuation scaling of Moore’s law. In this work, to find a novel way for amplifying the transient NC, a series network of external resistors and PbZr(1−x)Ti(x)O3 (PZT) FE capacitors was constructed. Uniform modeling and simulation were performed using Kirchhoff’s current law, electrostatics equations, and Landau–Khalatnikov equations. The derived results revealed that the mismatch of switching rate between free charge and polarization during FE domain switching is responsible for the transient NC generation. Some interesting results were obtained for the regulation of the transient NC by various factors such as the strain between the FE film and substrate, the viscosity coefficient, the ratio of Ti components, the external resistance magnitude, and the operating temperature. This work provides considerable insight into the control of FE transient NC, and offers guidance for obtaining larger and longer transient NC in the widely used PZT thin films.

Modeling the Training Effect in Exchange‐Biased Bilayers for Large Numbers of Magnetization Reversal Cycles

The exchange bias (EB) is a unidirectional anisotropy that occurs, e.g., upon field‐cooling ferromagnet/antiferromagnet systems. In many material systems, the EB field is reduced from one hysteresis loop to the next measurement. This so‐called training effect (TE) has been investigated in experiments and by means of theoretical efforts by many research groups. The reduction of the EB field as a result of subsequent magnetization reversal processes is often fitted by a power law, usually with the exception of n = 1, or with an equation based on the discretized Landau–Khalatnikov equation, as first suggested by Binek. Few other models, usually with more fitting parameters, have been proposed yet. Herein, it is shown that for large numbers of subsequent magnetization reversal processes in Co/CoO thin film samples, a modified power law or a logarithmic fit can model the TE in most cases as well as the abovementioned, commonly used models.

Negative Capacitance Dual-Gated ISFETs as Ultra-Sensitive pH Sensors.

Ion-sensitive field-effect transistors (ISFETs) are promising candidates for next-generation pH sensors, enabling highly sensitive and label-free biomolecular and chemical detection. Emerging FETs based on the negative capacitance (NC) effect offer steep-subthreshold switching and higher drive current simply by integrating a ferroelectric (FE) material into the gate stack. Here, we propose a novel NC dual-gated ISFET (NC-DG-ISFET)-based pH sensor, with FE layers integrated into both the top and the bottom gate stacks. The current and voltage sensitivities of the proposed device are extracted from its transfer characteristics, obtained by combining the numerical solutions of the one-dimensional (1D) Landau-Khalatnikov (L-K) equation with three-dimensional (3D) technology computer-aided design (TCAD) simulations. Results show that the NC-DG-ISFET can surpass the sensitivity of some of the state-of-the-art DG-ISFET pH sensors. The inclusion of the FE layers into the gate stacks of a baseline DG-ISFET leads to 51% reduction in subthreshold swing (SS), causing a 5× increase in current sensitivity (SI) in the subthreshold region of operation and a 2× increase in voltage sensitivity (SV). The influence of channel thickness and channel length on the sensor performance is also invesitgated. The findings presented here provide a new pathway to leverage the steep-switching behavior of NCFETs for the next generation of highly sensitive and label-free DG-ISFET pH sensors.

Theoretical and numerical study of the Landau-Khalatnikov model describing a formation of 2D domain patterns in ferroelectrics

Among the numerous applications of the Ginzburg-Landau theory to the analysis of significant reaction-diffusion systems, modeling of the behavior of promising polar dielectric materials should be especially highlighted. The paper is devoted to the theoretical and numerical analysis of the Landau-Khalatnikov model describing the dynamics of 2D domain pattern formation in ferroelectrics. The unique solvability of the initial-boundary value problem for the system of 2D cubic-quintic Landau-Khalatnikov equations is proved. The proof is based on the derivation of new a priori estimates for the solution of the system of nonlinear parabolic equations. A series of computational experiments are conducted to examine both spontaneous and polar-induced domain pattern formation in biaxial ferroelectrics. Finite-element simulations allow us to visualize different types of ferroelectric domain structures depending on the varying boundary conditions.

Dynamic antiferroelectric behavior of dielectric susceptibility of a ferroelectric heterostructure

The dynamic antiferroelectric behavior of dielectric susceptibility of a ferroelectric heterostructure (FEH) containing two different ferroelectric (FE) films with an antiferroelectric interfacial coupling between them has been investigated by means of a modified Landau theory appended Landau-Khalatnikov (L-K) equation. Two identical surface transition layers (STLs) within each film and a parameter β described discrepancies of physical properties enter two component films are considered, which is a more realistic model. Due to the competitive action of antiferroelectric coupling, STL, β and frequency of electric field, the dielectric susceptibility of system may present four or two peaks, exhibiting an antiferroelectriclike behavior or a ferroelectric behavior, respectively. We can obtain the characteristics of dielectric susceptibility for our need through appropriate option of these parameters.

Impact of temperature on a ferroelectric interfaced negative capacitance double gate junctionless accumulation mode field effect transistor-compact model

Ferroelectric interfaced negative capacitance field effect transistors are gaining popularity for low power applications; however, as temperature is a constant influencing factor, further study is required to comprehend how these devices are influenced. Through a proposed compact model, this paper analytically investigates the influence of temperature on a ferroelectric interfaced negative capacitance double gate junctionless accumulation mode field effect transistor. This device integrates the benefits of negative capacitance with the junctionless accumulation mode structure. An extensive comparison of the proposed device is made with the existing structure to evaluate the benefits offered by the ferroelectric layer at different temperatures. The Landau–Khalatnikov equation and Pao–Sah integral are employed to obtain the surface potential and drain current model with temperature variation. Various key parameters of the device have been analysed extensively by varying the temperature from 200 to 500 K. It has been found that internal voltage amplification declines as temperature rises, but the sub-threshold swing increases from 46 to 72 mV decade −1 with an increase in temperature. Additionally, with a progressive rise in temperature, the loss of gain and degradation of gate capacitance are observed.

Exploration of temperature stability of linearity and RF performance metrics for PGP negative capacitance FET

The present work focuses on investigating the performance of partial ground plane selective buried oxide negative capacitance (NC) field-effect transistor (NCFET) electrical properties at high temperatures. The performance of the device has been studied between the temperature of 300–400 K using the Landau–Khalatnikov equation with the Poisson’s equation. In NCFET, ferroelectric material in the gate stack generates NC effect that enhances the device performance by the voltage amplification process. Doped is used as the ferroelectric material because of its high dielectric capacitance and reliable polarization rate. This work primarily focuses on examining the effects of temperature change on the device’s dc performance metrics, analog/radio frequency performance parameters, and linearity performance parameters. Compared to kT/q, sub-threshold slope rises more rapidly as temperature rises and diminishing the ferroelectric effect after 350 K. Also reduced intrinsic delay at higher temperatures make the device an great option for ultra-low-power and high switching speed applications. Additionally, the proposed device performs better in terms of linearity at greater temperatures.

Dynamically Tunable Subthermionic Subthreshold Swing and Hysteresis in a Hf0.5Zr0.5O2-Based Ferroelectric Device Unit

In this article, we propose a universal way to tune subthermionic subthreshold swing (SS) and hysteresis dynamically in an amphibious basic functional unit, which can operate in memory- or steep-slope logic mode. The observed largest hysteresis is 4.59 V with gate-voltage tunability down to approximately 0 V. A sub-60 mV/decade SS can also be dynamically achieved and the smallest value is as low as 19.9 mV/decade. Theoretical simulations based on the multidomain temporal Landau–Khalatnikov equation clearly show that this dynamic tunability is endowed by the external bias-dependent competition between the ferroelectric polarization of Hf0.5Zr0.5O2 (HZO) and the charge screening effect of the control transistor. This work proposes the way to dynamically modulate SS to sub-60 mV/decade independent of the gate-stack, which breaks the limitations of conventional static optimization and shows potential in promoting the development of HZO-based steep-slope and multifunctional devices.

Distribution of Order Parameter in Solids under High Pressure Torsion.

Severe plastic deformation (SPD) can lead to various phase transformations. High-pressure torsion (HPT) is one of the most important variants of SPD. In principle, HPT can continue almost indefinitely long, as long as the plungers are not destroyed. However, the number of defects in a material during HPT deformation cannot increase indefinitely. When the rate of defects production becomes equal to the rate of their annihilation, a steady state or dynamic equilibrium is reached. Unexplored is the issue of establishing equilibrium at the initial stage of plunger torsion, when there is an angular acceleration. The parameters of the steady state are described here using the idea of an order parameter in solids in the framework of Landau phenomenological theory and the Landau–Khalatnikov equation.

Low-power double-gate MoS2 negative capacitance transistors with near-zero DIBL

Negative capacitance (NC) devices hold great promise for improving subthreshold slope (SS). However, the theoretical exploration of the short-channel effect in NC and two-dimensional (2D) materials remains an ongoing challenge in device scaling. The present work demonstrates a double-gate MoS2 negative capacitance field-effect transistor (MoS2 DG-NCFET) with low power and near-zero drain-induced barrier lowering (DIBL) by exploring its design space considering the impact of various MoS2 layers, with the aid of the developed 2D short-channel model containing the NC effect and numerical simulation. The proposed monolayer MoS2 DG-NCFET model is solved by unifying the long and short channel models coupled with the one-dimensional Landau-Khalatnikov equation. The study indicates that a lower SS, considerable voltage saving (), and even the ability to achieve zero DIBL are seen in monolayer MoS2 devices when compared with those of non-2D MoS2, due to the combination of the atomic-scale thickness of channels and the double-gate structure. This study provides an insight for further reducing the feature size of ultralow power transistors.

Leveraging negative capacitance ferroelectric materials for performance boosting of sub-10 nm graphene nanoribbon field-effect transistors: a quantum simulation study

In this paper, an ultrascaled ballistic graphene nanoribbon field-effect transistor (GNRFET) endowed with a compound double-gate based on metal-ferroelectric-metal (MFM) structure is proposed to overcome the limitations encountered with its conventional counterpart. The ballistic transistor is computationally investigated by solving self-consistently the non-equilibrium Green’s function formalism and the Poisson solver in conjunction with the Landau–Khalatnikov equation. The numerical investigation has included the ferroelectric-induced amplified internal metal voltage, the role of the ferroelectric thickness in boosting the device performance, the assessment of the switching and subthreshold performance, and the analysis of the FE-GNRFET scaling capability. The simulations revealed that the MFM-based gate can significantly boost the performance of GNRFETs, including the switching behavior, the on-current, the off-current, the current ratio, the swing factor, the intrinsic delay, and the scaling capability. More importantly, the proposed MFM GNRFET was found able to provide sub-thermionic subthreshold swing even with sub-10 nm gate lengths, which is very promising for low-power applications. The obtained results indicate that the MFM-based gating approach can give new impulses to the GNRFET technology.

Polarization switching in nanoscale ferroelectric composites containing PVDF polymer film and graphene layers

Modeling and computer study of a composite nanostructure containing a ferroelectric PVDF polymer and graphene layers were carried out in this work by molecular dynamic simulation and semiempirical quantum PM3 RHF method using the HyperChem software. It is shown here that the inclusion of graphene layers into the PVDF ferroelectric polymer increases the coercive field and decreases the polarization switching time of this composite structure. It is possible due to decrease in the damping coefficient of the Landau-Khalatnikov kinetic equation of the Landau-Ginzburg-Devonshire theory for two-dimensional ferroelectrics. Heterostructures with adjustable polarization switching times can be constructed based on such approach.

Physics-Based Models for Magneto-Electric Spin-Orbit Logic Circuits

Spintronic devices are a promising beyond-CMOS device option thanks to their energy efficiency and compatibility with CMOS. To accurately capture their multi-physics dynamics, a rigorous treatment of both spin and charge and their inter-conversion is required. Here we present physics-based device models based on 4x4 matrices for the spin-orbit coupling part of the magneto-electric spin-orbit (MESO) device. Also, a more rigorous physics model of ferroelectric and magnetoelectric switching of ferromagnets, based on Landau-Lifshitz-Gilbert (LLG) and Landau-Khalatnikov (LK) equations, is presented. With the combined model implemented in a SPICE circuit simulator environment, simulation results were obtained which show feasibility of MESO implementation and functional operation of buffers, oscillators, and majority gates.

Nonlinear terahertz pulse induced polarization dynamics in ferroelectric Ba0.8Sr0.2TiO3 thin film

The ultrafast ferroelectric polarization dynamics excited by intense THz pulses (with an electric field up to 23 MV/cm) in a multidomain Ba0.8Sr0.2TiO3 thin film has been experimentally demonstrated using optical second harmonic generation (SHG) probe. The obtained nonlinear dependence of the SHG intensity on the electric field of the THz pulse can be explained in terms of Landau-Khalatnikov equation by a transient ferroelectric polarization reversal. The best agreement between the experimental and simulated data was obtained when taking into account the multidomain structure of the film and carrying out convolution of the simulated polarization dynamics and the optical probe pulse.

Device and Circuit Level Assessment of Negative Capacitance TFETs for Low-Power High-Performance Digital Circuits

In this paper, we propose and analyse the performance of negative capacitance tunnel field-effect-transistors (NC-TFETs) at device and circuit level. We design and simulate four NC-TFETs, two are Silicon based “Si NC N-TFET,” “Si NC P-TFET” and two are Heterojunction Silicon-Germanium source based “SiGe NC N-TFET,” “SiGe NC P-TFET.” The effect of NC is incorporated with 5 nm thick layer of ferroelectric Hafnium Zirconium Oxide HfZrO2 (FE-HZO) in gate stack of TFETs by using of Landau-Khalatnikov (L-K) equations in MATLAB. The results show that at reduced NC gate voltage, the ON current (ION), On to OFF current (ION/IOFF) in NC devices is enhanced by while reduction in the threshold voltage (VTH) and Average subthreshold slope (SSAV) is observed. The SiGe NC-TFETs showed the best response with maximum ION range, ION/IOFF ratio of lowest SS as compare to Si NC-TFETs. The circuit transient analysis is done using the Verilog-A model based on look-up table (LUT) approach. The propagation delay of NC NAND circuits is reduced 90%, the SiGe NC-TFETs based circuits showing the smallest propagation delay and fast transient characteristics. This paper also demonstrates that the impact of FE-HZO thickness (TFE) on the device-circuit characteristics.