Drift-diffusion Formalism Research Articles

Finite Element Approach for the Simulation of Modern MRAM Devices.

Because of their nonvolatile nature and simple structure, the interest in MRAM devices has been steadily growing in recent years. Reliable simulation tools, capable of handling complex geometries composed of multiple materials, provide valuable help in improving the design of MRAM cells. In this work, we describe a solver based on the finite element implementation of the Landau-Lifshitz-Gilbert equation coupled to the spin and charge drift-diffusion formalism. The torque acting in all layers from different contributions is computed from a unified expression. In consequence of the versatility of the finite element implementation, the solver is applied to switching simulations of recently proposed structures based on spin-transfer torque, with a double reference layer or an elongated and composite free layer, and of a structure combining spin-transfer and spin-orbit torques.

Finite Element Method for MRAM Switching Simulations

The development of reliable simulation tools provides a valuable help in the design of modern MRAMdevices. Thanks to its versatility in the choice of meshes and discretization, the finite element method is a useful framework for the numerical solution of the magnetization dynamics. We review a finite element implementation of both the Landau-Lifshitz-Gilbert equation and the spin and charge drift-diffusion formalism in a solver employing open source software. The presented approach is successfully applied to emerging multilayered MRAM cells.

Comprehensive evaluation of torques in ultra-scaled MRAM devices

We present a generalization of the coupled spin-charge drift-diffusion formalism capable of accurately describing the spin and charge transport properties through magnetic tunnel junctions. Correction terms enable reproducing oscillations of the spin current in ferromagnets typical for quasi-ballistic transport. Our approach proves necessary to accurately capture an interplay between the interfacial Slonczewski and bulk-like Zhang-Li contributions to the torque in ultra-scaled MRAM devices.

Response competition between neurons and antineurons in the mushroom body

SummaryThe mushroom bodies of Drosophila contain circuitry compatible with race models of perceptual choice. When flies discriminate odor intensity differences, opponent pools of αβ core Kenyon cells (on and off αβc KCs) accumulate evidence for increases or decreases in odor concentration. These sensory neurons and “antineurons” connect to a layer of mushroom body output neurons (MBONs) which bias behavioral intent in opposite ways. All-to-all connectivity between the competing integrators and their MBON partners allows for correct and erroneous decisions; dopaminergic reinforcement sets choice probabilities via reciprocal changes to the efficacies of on and off KC synapses; and pooled inhibition between αβc KCs can establish equivalence with the drift-diffusion formalism known to describe behavioral performance. The response competition network gives tangible form to many features envisioned in theoretical models of mammalian decision making, but it differs from these models in one respect: the principal variables—the fill levels of the integrators and the strength of inhibition between them—are represented by graded potentials rather than spikes. In pursuit of similar computational goals, a small brain may thus prioritize the large information capacity of analog signals over the robustness and temporal processing span of pulsatile codes.

Interplay of Photons and Charge Carriers in Thin-Film Devices

Thin films are gaining ground in photonics and optoelectronics, promising improvements in their efficiency and functionality as well as decreased material usage as compared to bulk technologies. However, proliferation of thin films would benefit not only from continuous improvements in their fabrication, but also from a unified and accurate theoretical framework of the interplay of photons and charge carriers. In particular, such a framework would need to account quantitatively and self-consistently for photon recycling and interference effects. To this end, here we combine the drift-diffusion formalism of charge carrier dynamics and the fluctuational electrodynamics of photon transport self-consistently using the recently introduced interference-extended radiative transfer equations. The resulting equation system can be solved numerically using standard simulation tools, and as an example, here we apply it to study well-known GaAs thin-film solar cells. In addition to obtaining the expected device characteristics, we analyze the underlying complex photon transport and recombination-generation processes, demonstrating the physical insight provided for unevenly excited structures through the direct and self-consistent description of photons and charge carriers. The methodology proposed in this work is general and can be used to obtain accurate physical insight into a wide range of planar optoelectronic devices, of which the thin-film single-junction solar cells studied here are only one example.

Effect of the spin-orbit interaction at insulator/ferromagnet interfaces on spin-orbit torques

We theoretically investigate spin-orbit torques in insulator/ferromagnet/normal-metal structures with a focus on interfacial spin-orbit coupling effect at an insulator/ferromagnet interface. Based on the spin drift-diffusion formalism generalized to consider transverse spin currents in a ferromagnet and the boundary condition to consider transverse spin currents leaving from a ferromagnet, we find that interfacial spin-orbit coupling at the insulator/ferromagnet interface contributes to dampinglike spin-orbit torque, which is important for current-driven magnetization dynamics, even when the interfacial spin-orbit coupling generates the only fieldlike component. We also calculate spin-orbit torques in a single ferromagnet sandwiched by two dissimilar insulators, which provides additional information about interfacial spin-orbit interaction at insulator/ferromagnet interfaces.

Analytical modeling of graphene oxide based memristor

Nowadays, carbon–based materials like graphene and its derivatives consume great nano-technological applications worldwide. Graphene, due to its attractive properties such as its unusual charge transport, mechanical and thermal capabilities, is in the nano-scaling research spotlight. Additionally, to overcome the scaling limitations of large-scale charge-storage-based memories, the Memristor is focused upon as a nonvolatile memory. In the present work, the modeling of a Memristor based on graphene oxide as an active layer is considered. The drift-diffusion formalism as an electron transport mechanism, derived from ion immigration, is explored. It is concluded that by increasing the voltage between two metalelectrodes, the carrier concentration is increased, and the carrier mobility on the sandwiched layer (graphene oxide) is decreased. The conductive path by the redox of graphene oxide (GO) atoms, due to the conversion of sp3 to sp2 oxygen functionalities, is formed, which can be modeled by degenerate mode (the low resistance switching or ON state). This path is ruptured by decreasing the voltage into the reset voltage, which is modeled by the non-degenerate mode (the high resistance switching or OFF state). Finally, the model in comparison with the experimental data numerically is simulated, and acceptable results for metal and graphene–like path formation are observed.

Generalized Spin Drift-Diffusion Formalism in the Presence of Spin-Orbit Interaction of Ferromagnets.

We generalize the spin drift-diffusion formalism by considering spin-orbit interaction of a ferromagnet, which generates transverse spin currents in the ferromagnet. We consider quantum-mechanical transport of transverse spins in a spin-orbit coupled ferromagnet and develop a generalized drift-diffusion equation and boundary condition. By combining them, we identify previously unrecognized spin transport phenomena in heterostructures including ferromagnets. As representative examples, we show self-generated spin torque and self-generated charge pumping in ferromagnet-normal metal bilayers. The former is a torque exerting on a ferromagnet, originating from a transverse spin current leaving from the ferromagnet itself, whereas the latter is the Onsager reciprocity of the former. Our work not only provides a concise formalism for the effects of nondephased transverse spins in ferromagnets but also enables to design spintronic devices without an external spin source.

A Physics-Based Compact Model for Ultrathin Black Phosphorus FETs—Part I: Effect of Contacts, Temperature, Ambipolarity, and Traps

We report a physics-based surface-potential compact model to describe current–voltage ( $I$ – $V$ ) relationship in a few-layered ambipolar black phosphorus (BP) transistors. To model the device electrostatics, the 2-D density of states of carriers and Fermi–Dirac statistics are used, while carrier transport is described using the drift-diffusion formalism. The model also comprehends the effects of interface traps and voltage-dependent Schottky-type source/drain contact resistances. Compared with prior BP FET models that are mainly suited for near-equilibrium transport and room-temperature operation, the model developed here is applicable over broad bias and temperature range. Validation of the model against measurement data of BP transistors with gate lengths 300–1000 nm and operating temperature from 200–298 K is demonstrated in a companion article.

Machine Learning Approach for Predicting the Effect of Statistical Variability in Si Junctionless Nanowire Transistors

This letter investigates the possibility to replace numerical TCAD device simulations with a multi-layer neural network (NN). We explore if it is possible to train the NN with the required accuracy in order to predict device characteristics of thousands of transistors without executing TCAD simulations. Here, in order to answer this question, we present a hierarchical multi-scale simulation study of a silicon junctionless nanowire field-effect transistor (JL-NWT) with a gate length of 150 nm and diameter of an Si channel of 8 nm. All device simulations are based on the drift-diffusion (DD) formalism with activated density gradient (DG) quantum corrections. For the purpose of this letter, we perform statistical numerical experiments of a set of 1380 automictically different JL-NWTs. Each device has a unique random distribution of discrete dopants (RDD) within the silicon body. From those statistical simulations, we extract important figures of merit (FoM) such as OFF-current (IOFF) and ON-current (ION), subthreshold slope (SS), and voltage threshold (VTH). Based on those statistical simulations, we train a multi-layer NN and we compare the obtained results with a general linear model (GLM). This shows the potential of using NN in the field of device modeling and simulation with a potential application to significantly reduce the computational cost.

Spin transparency for the interface of an ultrathin magnet within the spin dephasing length

We examine a modified drift-diffusion formalism to describe spin transport near an ultrathin magnet whose thickness is similar to or less than the spin dephasing length. Most of the previous theories on spin torque assume the transverse component of a injected spin current dephases perfectly thus are fully absorbed into the ferromagnet. However, in the state-of-art multilayer systems under consideration of recent studies, the thicknesses of ferromagnets are on the order of or less than a nanometer, thus one cannot safely assume the spin dephasing to be perfect. To describe the effects of a finite dephasing rate, we adopt the concept of transmitted mixing conductance, whose application to the drift-diffusion formalism has been limited. For a concise description of physical consequences, we introduce an effective spin transparency. Interestingly, for an ultrathin magnet with a finite dephasing rate, the spin transparency can be even enhanced and there arises a non-negligible field-like spin-orbit torque even in the absence of the imaginary part of the spin mixing conductance. The effective spin transparency provides a simple extension of the drift-diffusion formalism, which is accessible to experimentalists analyzing their results.

Refined drift-diffusion model for the simulation of charge transport across layer interfaces in organic semiconductor devices

We present a new approach to simulate the transport of charges across organic/organic layer interfaces in organic semiconductor devices. This approach combines the drift-diffusion formalism away from the interface with a hopping description of the charge transport in the vicinity of the interface. It has been implemented in the commercial software SETFOS allowing for fast simulations of the complete device. This new model takes into account both recombination and generation mechanisms across the interface enabling the modeling of charge-generation/recombination interfaces for the numerical simulation of tandem devices. Using this approach, it is also possible to simulate devices using 1,4,5,8,9,11-Hexaazatriphenylenehexacarbonitrile as a hole-injection layer. This particular material has a very deep HOMO level (approximately 9.5 eV), which would seemingly prevent such a layer to be used as a hole-injection material in the framework of traditional drift-diffusion models.

Impact of Randomly Distributed Dopants on $\Omega$ -Gate Junctionless Silicon Nanowire Transistors

This paper presents experimental and simulation analysis of an Q-shaped silicon junctionless nanowire field-effect transistor (JL-NWT) with gate lengths of 150 nm and diameter of the Si channel of 8 nm. Our experimental measurements reveal that the ON-currents up to 1.15 mA/μm for 1.0 V and 2.52 mA/μm for the 1.8-V gate overdrive with an OFF-current set at 100 nA/μm. Also, the experiment data reveal more than eight orders of magnitude ON-current to OFF-current ratios and an excellent subthreshold slope of 66 mV/dec recorded at room temperature. The obtained experimental current-voltage characteristics are used as a reference point to calibrate the simulations models used in this paper. Our simulation data show good agreement with the experimental results. All simulations are based on drift-diffusion formalism with activated density gradient quantum corrections. Once the simulations methodology is established, the simulations are calibrated to the experimental data. After this, we have performed statistical numerical experiments of a set of 500 different JL-NWTs. Each device has a unique random distribution of the discrete dopants within the silicon body. From those statistical simulations, we extracted important figures of merit, such as OFF-current and ON-current, subthreshold slope, and voltage threshold. The performed statistical analysis, on samples of those 500 JL-NWTs, shows that the mean I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> -V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gs</sub> characteristic is in excellent agreement with the experimental measurements. Moreover, the mean I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> -V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gs</sub> characteristic reproduces better the subthreshold slope data obtained from the experiment in comparison to the continuous model simulation. Finally, performance predictions for the JL transistor with shorter gate lengths and thinner oxide regions are carried out. Among the simulated JL transistors, the configuration with 25-nm gate length and 2-nm oxide thickness shows the most promising characteristics offering scalable designs.

Unified computational model of transport in metal-insulating oxide-metal systems

A unified physics-based model of electron transport in metal-insulator-metal (MIM) systems is presented. In this model, transport through metal-oxide interfaces occurs by electron tunneling between the metal electrodes and oxide defect states. Transport in the oxide bulk is dominated by hopping, modeled as a series of tunneling events that alter the electron occupancy of defect states. Electron transport in the oxide conduction band is treated by the drift–diffusion formalism and defect chemistry reactions link all the various transport mechanisms. It is shown that the current-limiting effect of the interface band offsets is a function of the defect vacancy concentration. These results provide insight into the underlying physical mechanisms of leakage currents in oxide-based capacitors and steady-state electron transport in resistive random access memory (ReRAM) MIM devices. Finally, an explanation of ReRAM bipolar switching behavior based on these results is proposed.

Compact Model for Low Effective Mass Channel Common Double-Gate MOSFET

In the spirit of quantum drift-diffusion formalism, we propose a core compact model for low-effective mass channel common double-gate MOSFET. In contrast to the existing models, carriers in each subband are treated to be in locally thermal equilibrium within that subband, but not with the carriers in a different subband. We observe quasi-linear relationship between energy eigenvalue, quasi-Fermi level, and carrier density in each subband and exploit it to obtain closed-form expressions for drain current and terminal charges. Proposed model, which is free from any unphysical model parameter or interpolating function, captures the essential device physics (strong transverse confinement, wave function penetration, multisubband occupancy, bias-dependent diffusivity, and Fermi–Dirac distribution of the carriers) while preserving the mathematical simplicity of industry standard Silicon MOSFET models. Drain current, conductance, and capacitances calculated from the proposed model are found to be in good agreement with numerical device simulation for a wide range of channel thickness, effective mass, oxide thickness asymmetry, and bias voltages.

Electroluminescent cooling in intracavity light emitters: modeling and experiments

We develop a coupled electronic charge and photon transport simulation model to allow for deeper analysis of our recent experimental studies of intracavity double diode structures (DDSs). The studied structures consist of optically coupled AlGaAs/GaAs double heterojunction light emitting diode (LED) and GaAs p–n-homojunction photodiode (PD) structure, integrated as a single semiconductor device. The drift–diffusion formalism for charge transport and an optical model, coupling the LED and the PD, are self-consistently applied to complement our experimental work on the evaluation of the efficiency of these DDSs. This is to understand better their suitability for electroluminescent cooling (ELC) demonstration, and shed further light on electroluminescence and optical energy transfer in the structures. The presented results emphasize the adverse effect of non-radiative recombination on device efficiency, which is the main obstacle for achieving ELC in III-V semiconductors.

Simulation of OLEDs with a polar electron transport layer

Organic light-emitting diodes (OLEDs) rely on the use of functional materials with suitable energy levels and mobilities for selective charge carrier injection and transport of one species only at the respective electrode. Until recently, however, the dipolar nature of many organic semiconductors has been largely ignored in this context. In particular, electron transports layers (ETLs) often exhibit spontaneous orientation polarization leading to interfacial charges that modify the electrical potential landscape inside a hetero-layer device.Here we demonstrate that the effect of polar ETLs can be simulated using the well-established Poisson and drift-diffusion formalism, if these interfacial charges are taken into account. Impedance spectroscopy is used in order to validate our approach and to characterize the polarity of the material. Finally, simulations allow to quantify the impact of polar ETLs on device performance.

Impact of carrier dynamics on the photovoltaic performance of quantum dot solar cells

The study presents a theoretical investigation of the impact of individual electron and hole dynamics on the photovoltaic characteristics of InAs/GaAs quantum dot solar cells. The analysis is carried out by exploiting a model which includes a detailed description of quantum dots (QD) kinetics within a drift-diffusion formalism. Steady-state and transient simulations show that hole thermal spreading across the closely spaced QD valence band states allows to extract the maximum achievable photocurrent from the QDs; on the other hand, slow hole dynamics turns QDs into efficient traps, impairing the short circuit current despite the extended light harvesting provided by the QDs.

Incorporating photon recycling into the analytical drift-diffusion model of high efficiency solar cells

The analytical drift-diffusion formalism is able to accurately simulate a wide range of solar cell architectures and was recently extended to include those with back surface reflectors. However, as solar cells approach the limits of material quality, photon recycling effects become increasingly important in predicting the behavior of these cells. In particular, the minority carrier diffusion length is significantly affected by the photon recycling, with consequences for the solar cell performance. In this paper, we outline an approach to account for photon recycling in the analytical Hovel model and compare analytical model predictions to GaAs-based experimental devices operating close to the fundamental efficiency limit.

Comprehensive numerical simulation of threshold-voltage transients in nitride memories

This paper presents a comprehensive numerical modeling for the threshold-voltage transients of nitride-based memory devices during programming, erasing and data retention. The developed numerical tool self-consistently solves the Poisson, continuity and trapping equations in the nitride layer using a drift-diffusion formalism. The continuity equation has been discretized using the Scharfetter–Gummel scheme and a modified Gummel-map has been optimized to ensure fully convergence of the equations. The numerical model is able to describe the memory device operation for different gate bias regimes, therefore addressing both the program/erase and the retention conditions. Finally, numerical results are shown to carefully reproduce experimental data on template devices with different gate stack compositions, validating the physical assumptions and making the model a valuable tool for nitride memories investigation and design.