Transient negative differential capacitance (NC), the dynamic reversal of transient capacitance in an electrical circuit is of highly technological and scientific interest since it probes the foundation of ferroelectricity. In this letter, we study a resistor-ferroelectric capacitor (R-FeC) network through a series of coupled equations based on Kirchhoff's law, Electrostatics, and Landau theory. We show that transient NC in a R-FeC circuit originates from the mismatch between rate of free charge change on the metal plate and that of bound charge change in a ferroelectric (FE) capacitor during polarization switching. This transient charge dynamic mismatch is driven by the negative curvature of the FE free energy landscape. It is also analytically shown that a free energy profile with the negative curvature is the only physical system that can describe transient NC during the two-state switching in a FE capacitor. Furthermore, this transient charge dynamic mismatch is justified by the dependence of external resistance and intrinsic FE viscosity coefficient. The depolarization effect on FE capacitors also shows the importance of negative curvature to transient NC. The relation between transient NC and negative curvature provides a direct insight into the free energy landscape during the FE switching.
The capacitance of capacitive energy storage devices can not be directly measured, but can be estimated from the input and output signals expressed in the time or frequency domains. Here the time-domain voltage-charge relationship in non-ideal electrochemical capacitors is treated as an ill-conditioned convolution integral equation where the unknown capacitance kernel function is to be found. This comes from assuming \emph{a priori} that in the frequency domain the charge is equal to the product of capacitance by voltage. The computation of a stable solution to this problem particularly when d…
This paper investigates the thermodynamic driving force of transient negative capacitance (NC) in the series circuit of the resistor and ferroelectric capacitor (R-FEC). We find that the widely used Landau-Khalatnikov (L-K) theory, that is, the minimum of the Gibbs free energy, is inapplicable to explain the transient NC. The thermodynamic driving force of the transient NC phenomenon is the minimum of the difference between the elastic Gibbs free energy and the electric polarization work. The appearance of the transient NC phenomenon is not due to the widely accepted view that the ferroelectri…
The negative capacitance (NC) stabilization of a ferroelectric (FE) material can potentially provide an alternative way to further reduce the power consumption in ultra-scaled devices and thus has been of great interest in technology and science in the past decade. In this article, we present a physical picture for a better understanding of the hysteresis-free charge boost effect observed experimentally in metal-ferroelectric-insulator-metal (MFIM) capacitors. By introducing the dielectric (DE) leakage and interfacial trapped charges, our simulations of the hysteresis loops are in a strong agr…
In this study, we propose a measurement technique for evaluating ferroelectric polarization characteristics in ferroelectric field-effect transistors (FeFETs). Different from standard metal/ferroelectric/metal capacitors, the depletion and inversion phenomena in semiconductor substrates have to be carefully taken into account when evaluating the ferroelectric properties using fast voltage sweep as input. The non-equilibrium deep depletion is found to be the limiting factor for the accurate evaluation of ferroelectric properties in metal/ferroelectric/semiconductor capacitors. By connecting the…
A simulation-based study of variability of remnant polarization $\left (P_r \right)$ in a multi-granular 3-D ultra-thin ferroelectric (FE) capacitor is presented in this paper. The Poisson Voronoi Tessellation Diagram (PVD) is used for the nucleation of grains in the FE region, which corresponds to the physical growth mechanism. The PVD algorithm implemented in MATLAB is coupled with TCAD simulations, to trace the ferroelectric hysteresis loop. It is found that the grains which have linear profile of $P_r$ show larger variability in the FE hysteresis loop, compared to the grains, which follow …
In this letter, the transient behavior of a ferroelectric (FE) metal-oxide-semiconductor (MOS) capacitor is theoretically investigated with a series resistor. It is shown that compared to a conventional high-k dielectric MOS capacitor, a significant inversion charge-boost can be achieved by a FE MOS capacitor due to a steep transient subthreshold swing (SS) driven by the free charge-polarization mismatch. It is also shown that the observation of steep transient SS significantly depends on the viscosity coefficient under Landau's mean field theory, in general representing the average FE time re…
We propose a framework to model ferroelectric negative capacitance: electrostatic Micro Electro Mechanical Systems (MEMS) hybrid actuators and analyze their dynamic (step input) response. Using this framework, we report the first proposal for reduction in the dynamic pull-in and pull-out voltages of the hybrid actuators due to the negative capacitance of the ferroelectric. The proposed model also reveals the effect of ferroelectric thickness on the dynamic pull-in and pull-out voltages and the effect of ferroelectric damping on the energy dissipated during actuation. We infer from our analysis…
In past decades, the application of fractals to electrode design for enhanced signaling and electrochemical performance was a popular subject and enabled the growth of consumer micro-electronics. Supercapacitors, which are energy storage devices with many promising characteristics, have largely grown alongside of such developments in electronics, but little work has been done to use fractal electrodes in supercapacitors. In this work, plane-filling and fractal patterns were used in designing laser scribed graphene supercapacitor electrodes, allowing the scaling laws of capacitance with respect…
We demonstrate that the capacitance of ionic-liquid filled supercapacitors is substantially increased by placing a diode-like structure on the separator membrane. We call the structured separator: gate, and demonstrate that the order of a p-n layout with respect to the auxiliary electrode affects the overall cell's capacitance. The smallest ESR and the largest capacitance values are noted when the p-side is facing the auxiliary electrode.
Nanoscale molecular junctions are celebrated nanoelectronic devices for mimicking several electronic functions including rectifiers, sensors, wires, switches, transistors, and memory but capacitive behavior is nearly unexplored. Capacitors are crucial energy storage devices that store energy in the form of electrical charges. A capacitor utilizes two electrical conductors separated by a dielectric material. However, many oxides-based dielectrics are well-studied for integrating capacitors, however, capacitors comprised of thin-film molecular layers are not well-studied. The present work descri…
We present an integrated circuit capable of scavenging energy from repetitive changes in finger touch capacitance. A finger tapping on this ASIC generates a capacitive change of approximately 770pF. These changes feed into a charge-pump circuit which stores 320pJ of energy on a 1nF storage capacitor. We present measurement results and simulations that demonstrate operation. As a proof-of-concept, we also demonstrate that the harvested energy can power a ring oscillator which outputs a series of chirps with frequencies ranging from 80Hz to 30kHz as the storage capacitor voltage charges and disc…
Most capacitors do not satisfy the conventional assumption of a constant capacitance. They exhibit memory which is often described by a time-varying capacitance. It is shown that the classical relation, $Q\left(t\right)=CV\left(t\right)$, that relates the charge, $Q$, with the capacitance, $C$, and the voltage, $V$, is not applicable for capacitors with a time-varying capacitance. The expression for the current, $dQ/dt$, that is subsequently obtained following the substitution of $C$ by $C\left(t\right)$ in the classical relation corresponds to an inconsistent circuit. In order to address the …
Half of the energy is always lost when charging a capacitor. Even in the limit of vanishing resistance, half of the charging energy is still lost--to radiation instead of heat. While this fraction can technically be reduced by charging adiabatically, it otherwise places a fundamental limit on the charging efficiency of a capacitor. Here we show that this 1/2 limit can be broken by coupling a ferroelectric to the capacitor dielectric. Maxwell's equations are solved for the coupled system to analyze energy flow from the perspective of Poynting's theorem and show that (1) total energy dissipation…
This study simulated negative-capacitance double gate FinFETs with channel lengths ranging from 25nm to 100nm using TCAD. The results show that negative capacitance significantly reduces subthreshold swing as well as drain induced barrier lowering effects. The improvement is found to be significantly more prominent for short channel devices than long ones, which demonstrates the tremendous advantage of negative capacitance gate stack for scaled MOSFETs. A compact analytical formulation is developed to quantify sub-threshold swing improvement for short channel devices.
Epitaxial ferroelectric Hf0.5Zr0.5O2 films have been successfully integrated in a capacitor heterostructure on Si(001). The orthorhombic Hf0.5Zr0.5O2 phase, [111] out-of-plane oriented, is stabilized in the films. The films present high remnant polarization Pr close to 20 μC/cm2, rivaling with equivalent epitaxial films on single crystalline oxide substrates. Retention time is longer than 10 years for writing field of around 5 MV/cm, and the capacitors show endurance up to 1E9 cycles for writing voltage of around 4 MV/cm. It is found that the formation of the orthorhombic ferroelectric phase d…
In this paper, we present the dynamics and modeling of multi-domains in the ferroelectric FET (FeFET). Due to the periodic texture of domains, the electrostatics of the FeFET exhibit an oscillatory conduction band profile. To capture such oscillations, we solve coupled 2-D Poisson's equation with the net ferroelectric energy density (gradient energy + free energy + depolarization energy) equation. Multi-domain dynamics are captured by minimizing the net ferroelectric energy leading to a thermodynamically stable state. Furthermore, we show that the motion of domain walls originates local bound …
Analytical modeling and dynamics of multidomain in metal-ferroelectric-insulator-semiconductor (MFIS)-FETs are presented in this paper. The formation of multi-domain (MD) leads to oscillations in the conduction band in the channel and periodicity in the local electric field in the ferroelectric region. The impact of 2-D local electric field on the MD switching is captured in the model using the domain wall velocity concept. The optimum values of oxide thickness, ferroelectric thickness and channel length are calculated which corresponds to mono-domain device operation. Deviation from the optim…
In graphene based materials, the energy storage capacity is usually improved by rich porous structures with extremely high surface area. By utilizing surface corrugations, this work shows an alternative strategy to activate graphene materials for large capacitance. We demonstrate how to simply fabricate such activated graphene and how these surface structures helped to realize considerable specific capacitance (e.g., electrode capacitance of ~340 F g-1 at 5 mV s-1 and device capacitance of ~ 343 F g-1 at 1.7 A g-1) and power performance (e.g., power density of 50 and 2500 W kg-1 at the energy …
We analyze the distributions of electric potential and field, polarization and charge, and the differential capacitance of a silicon metal-oxide-ferroelectric field effect transistor (MOSFET), in which a gate insulator consists of thin layers of dielectric SiO2 and weak ferroelectric HfO2. It appeared possible to achieve a quasi-steady-state negative capacitance of the HfO2 layer, C_(HfO_2 )<0, if the layer thickness is close to the critical thickness of the size-induced ferroelectric-paraelectric phase transition. The quasi-steady-state negative capacitance, being a very slow-varying transien…
In this work, we analyze the ferroelectric (FE) domain-wall (DW) induced negative capacitance (NC) effect in Metal-FE-Insulator-Metal (MFIM) and Metal-FE-Insulator-Semiconductor (MFIS) stacks. Our analysis is based on 2D phase field simulations. Considering HZO as the FE material, we study 180 FE domain formation in MFIM and MFIS stacks and their voltage-dependent DW motion. Our analysis signifies that, when FE is in multi-domain (MD) state with soft-DW, the stored energy in the DW leads to non-hysteretic NC effect in FE, which provides an enhanced charge response in the MFIM stack, compared t…
We exploit the premises of exceptional points of degeneracy (EPDs) induced in linear time-periodic (LTP) systems to achieve extremely sensitive biosensors. The EPD is formed in a single LC resonator where the total capacitance is comprised of a time-varying capacitor in parallel to a biosensing capacitor. We use the time-periodic variation of a system parameter (e.g., capacitance) to achieve a second order EPD aiming at improving the sensitivity of liquid based radio frequency biosensors, leading to an intrinsic ultra sensitivity. We show the emergence of EPDs in such a system and the ultra se…
Since many years, sub-60mV/decade switching has been reported in ferroelectric FETs. However, thus far these reports have lacked full physical explanation since they typically use a negative capacitance in the ferroelectric layer to be able to explain the experimental observations. Because negative capacitance as such is not a physical concept, we propose an alternative model that relies on the non-linear and non-equilibrium behavior of the ferroelectric layer. It is shown that a steep subthreshold slope can be obtained by a 2-step switching process, referred to as nucleation and propagation. …
Physical phenomena underlying operation of ferroelectric field-effect transistors (FeFETs) is treated within a unified simulation framework. The framework incorporates the Landau mean-field treatment of free energy of a ferroelectric and the polarization dynamics according to Landau-Khalatnikov (LK) equation. These equations are self-consistently solved with the one-dimensional metal-oxide-semiconductor (MOS) structure electrostatics and the drift-diffusion solution for the current in the semiconductor channel. Numerical simulations demonstrate, depending on the ferroelectric (FE) thickness, b…
Designing high endurance Hf0.5Zr0.5O2 capacitors through engineered recovery from fatigue for non-volatile ferroelectric memory and neuromorphic hardware
Ion-Sensitive Field-Effect Transistors (ISFETs) form a wide-spread technology for sensing, thanks to their label-free detection and intrinsic CMOS compatibility. Their current sensitivity, ΔID/ID, for a given ΔpH, however, is limited by the thermionic limit for the Subthreshold Slope (SS) of Metal-Oxide-Semiconductor Field-Effect Transistors(MOSFET) and by the Nernst limit. Obtaining ISFETs with a steep slope transfer characteristics is extremely challenging. In this paper we combine the merits of traditional ISFETs with the performance boosts offered by the insertion of a Negative Capacitor i…
Domain Morphology, Electrocaloric Response, and Negative Capacitance States of Ferroelectric Nanowires Array
Institute of Physics, National Academy of Sciences of Ukraine（乌克兰国家科学院物理研究所）；Taras Shevchenko National University of Kyiv（基辅塔拉斯舍甫琴科国立大学）；V. Lashkariov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine（乌克兰国家科学院V.拉什卡廖夫半导体物理研究所）；Slovenia Jožef Stefan Institute（斯洛文尼亚约瑟夫斯蒂芬研究所）；Frantsevich Institute for Problems in Materials Science, National Academy of Sciences of Ukraine（乌克兰国家科学院弗兰采维奇材料科学问题研究所）；Zone 5 Technologies（Zone 5科技有限公司）
Tunable Defect Engineering of Mo/TiON Electrode in Angstrom-Laminated HfO$_2$/ZrO$_2$ Ferroelectric Capacitors towards Long Endurance and High Temperature Retention
The ferroelectric polarization switching in ferroelectric hafnium zirconium oxide (Hf0.5Zr0.5O2, HZO) in the HZO/Al2O3 ferroelectric/dielectric stack is investigated systematically by capacitance-voltage and polarization-voltage measurements. The thickness of dielectric layer is found to have a determinant impact on the ferroelectric polarization switching of ferroelectric HZO. A suppression of ferroelectricity is observed with thick dielectric layer. In the gate stacks with thin dielectric layers, a full polarization switching of the ferroelectric layer is found possible by the proposed leaka…
