Drift-diffusion Current Research Articles

Modeling thermoelectric effects in piezoelectric semiconductors: New fully coupled mechanisms for mechanically manipulated heat flux and refrigeration

We present a continuum theory for analyzing the interaction between the thermoelectric and mechanical fields in piezoelectric semiconductors. The balance laws and dissipation inequality are formulated in the reference configuration. Thermodynamically consistent constitutive equations are derived, including the drift-diffusion current, Fourier's law for thermal flux, Seebeck effect, and Peltier effect, by introducing a generalized Fick's law. The heat conduction equation and Joule heating generation with the semiconducting effect are derived by combing the energy balance and the second Gibbs relation. The framework is then geometrically linearized for applications in small deformation of crystal solids. Based on the newly developed framework, two new coupling mechanisms between thermoelectric and mechanical fields in crystals of class of 6mm are identified. 1) A mechanical load can block both electron and thermal fluxes in the loading area via the mechanically induced potential well. At a strain level of 1%, the current and heat flow can be reduced by as much as 80%. This effect facilitates the design of new switching devices. 2) The mechanical load can surprisingly act as a current amplifier through the induced potential barrier. Furthermore, making use of the new and unusual Joule heating generation, thermal dipoles can be created, indicating that mechanical loading can lead to local refrigeration. Via a simple numerical model, we demonstrate that the mechanical deformation can produce a temperature difference of 0.06 K at the strain level of around 1%. Based on this new and exciting cooling mechanism, we further propose a novel multi-stage pyramidal cascade device for refrigeration. The framework in this paper provides a foundation for analyzing multiple physics problems in semiconductor structures and also potential ideas for switching and refrigeration devices. Since it is based on finite deformation theory, the present framework would be helpful in analyzing the behavior of emerging flexible semiconductor materials or developing the corresponding computational methods.

A SPICE Compact Model for Ambipolar 2-D-Material FETs Aiming at Circuit Design

We report a charge-based analytic and explicit compact model for field-effect transistors (FETs) based on 2-D materials (2DMs), for the simulation of 2DM-based analog and digital circuits. The device electrostatics is handled by invoking 2-D density of states and Fermi-Dirac statistics that are later combined with the Lambert-W function and Halley's correction to eventually obtain explicit expressions for the electron and hole charges, which are exploited in the calculation of drift-diffusion currents for both carriers. Furthermore, the charge model is extended to obtain characteristics of 2DM-based negative capacitance FETs. The model is benchmarked against experimental MoS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> FET measurements and experimental ambipolar characteristics of narrowband-gap materials, such as black phosphorus. Its soundness for SPICE circuit-level simulations is also demonstrated.

Modeling Photocatalysts and Reactors for Solar Hydrogen Production through Particle-Based Water Splitting

Hydrogen as an energy carrier has by far the highest gravimetric energy density, which, when produced by a renewable pathway would go a long in achieving the goal of carbon neutral and responsible economy. Photocatalytic water splitting is a promising approach for the production of solar hydrogen. The technological potential of this approach is unclear and it is not known how the choice of the components (semiconducting particles, electrolyte, mediator, etc.), the design of the system, and the operating conditions affect the performance of the system.Firstly, we present a steady 1-dimensional model of a single photocatalyst particle which couples semiconductor physics to account for the charge carrier generation and transport with the electrochemical kinetics governed by the butler-volmer equation. We account for the solar absorption and the charge carrier generation with Lambert-Beer’s law. We then solve for the carrier transport and conservation with Poisson’s equations and the hole and electron transport by drift diffusion currents. We assume the recombination in the particle to be a Shockley-Reed-Hall trap recombination. The semiconductor electrolyte interface is treated as an ideal Schottky contact. We show the effect of intrinsic parameters like doping concentration, electron affinity (band positions), relative permittivity on the operating current density. We also present the effect of particle size on the operating current density.Secondly, we present a transient 0-dimensional model, which accounts for ideal solar absorption, ideal charge generation and transport, and the kinetic characteristics at the catalytic sites for two sets of photocatalyst semiconductor particles. We solve for species transport (mediator species and protons) and conservation in the one or two reactor compartments separated by a semipermeable membrane. We evaluate this 0-dimensional model on a reactor level as well, comparing three different reactor types, these three types include: i) a single photocatalyst reactor, ii) a membrane-separated dual compartment reactor and iii) a membrane-separated dual compartment reactor with wire and two auxiliary electrodes. We put forth a theoretically limiting efficiency which considers no overpotentials and a realistic case which accounts for losses for each type of reactor. For these reactor designs, we establish a link between the thermodynamic limits and materials requirements, changes in material requirements when more realistic operation and losses are considered, and compare the three reactor designs.Conclusively, the steady 1-dimensional particle model allows us to evaluate the effect of intrinsic material properties of a single photocatalyst on the operating current density, and the transient 0-dimensional model giving us a broader evaluation on a reactor design level with respect to the employed photocatalysts and redox mediators.

A Comprehensive Physics-Based Current–Voltage SPICE Compact Model for 2-D-Material-Based Top-Contact Bottom-Gated Schottky-Barrier FETs

In this article, we report the development of a novel physics-based analytical model for explaining the current-voltage relationship in Schottky barrier (SB) 2-D-material field effect transistors (FETs). The model has at its core the calculation of the surface-potential (SP) which is accomplished by invoking 2-D density of states in conjunction with Fermi-Dirac (FD) distribution for electron and hole statistics. The explicit computation for the SP, carried out using the Lambert-W function together with Halley's method, is used to construct the SP-based band-diagram for realizing the transparency of the SBs. Thereafter, the ambipolar current is derived in terms of the electron and hole injection phenomena-the thermionic emission and Fowler-Nordheim tunneling mechanisms-at the SB contacts. Furthermore, drift-diffusion current is derived in terms of the SP and incorporated in the model to account for the scattering in the intrinsic 2-D channel. Finally, the Verilog-A model is validated against experimental I-V data reported in the literature for two different 2-D-material systems. This is the first demonstration of an explicit SP-based SPICE model for ambipolar SB-2-D-FETs that is simultaneously built on tunneling-emission and drift-diffusion formalisms.

Inflection Phenomenon in Cryogenic MOSFET Behavior

This brief reports the analytical modeling and measurements of the inflection in the MOSFET transfer characteristics at cryogenic temperatures. Inflection is the inward bending of the drain current versus gate voltage, which reduces the current in weak and moderate inversion at a given gate voltage compared to the drift-diffusion current. This phenomenon is explained by introducing a Gaussian distribution of localized states centered around the band edge. The localized states are attributed to disorder and interface traps. The proposed model allows to extract the density of localized states at the interface from the dc current measurements.

Comparison between proton irradiated triple gate SOI TFETS and finfets from a TID point of view

This paper compares, for the first time, the total ionizing dose degradation of 600 keV proton-irradiated silicon triple gate SOI tunnel FETs (TFETs) with SOI FinFETs fabricated with the same structure on the same wafer. This work is based on electrical measurements and TCAD simulations. Devices with different dimensions were exposed up to 10 Mrad(Si) dose of proton radiation. For transistors with narrow fin width, the radiation influence is negligible in both devices types. For WFIN = 250 nm and a proton radiation dose up to 10 Mrad(Si), on the other hand, a severe influence is observed in nFinFETs and pFinFETs present on the same die as the p-type TFETs. In the TFETs, no marked influence is observed. Only for a TFET of WFIN = 500 nm and 10 Mrad(Si) one can observe some radiation influence. The main degradation is caused by the buried oxide positive fixed charges and the interface traps which was also confirmed by TCAD simulations. The tunneling current of Tunnel-FETs presents a much better radiation hardness compared to the drift-diffusion current of SOI FinFETs.

Quantum theory of terahertz conductivity of semiconductor nanostructures

Efficient and controlled charge carrier transport through nanoelements is currently a primordial question in the research of nanoelectronic materials and structures. We develop a quantum-mechanical theory of the conductivity spectra of confined charge carriers responding to an electric field from dc regime up to optical frequencies. The broken translation symmetry induces a broadband drift-diffusion current, which is not taken into account in the analysis based on Kubo formula and relaxation time approximation. We show that this current is required to ensure that the dc conductivity of isolated nanostructures correctly attains zero. It causes a significant reshaping of the conductivity spectra up to terahertz or multiterahertz spectral ranges, where the electron scattering rate is typically comparable to or larger than the probing frequency.

Two-dimensional analytical model for asymmetric dual-gate tunnel FETs

An analytical model for asymmetric dual-gate (ADG) tunnel field-effect transistors (TFETs) combining a TFET with a junctionless field-effect transistor (JL FET) is presented and investigated extensively for the first time in this paper, with the aim of addressing the challenges of conventional DG TFETs. The drain current is composed of the tunneling current of TFET and the drift-diffusion current of JL FET, which leads to high drain current. The model also predicts the impacts of the lengths of the source and intrinsic regions on the potential and drain current. The results show that ADG TFET can generate optimum results (in terms of on-state current Ion and on-to-off current ratio Ion/Ioff) compared with the conventional DG TFET, higher Ion of 129 µA/µm and a larger Ion/Ioff of 2.1 × 1010 are obtained when the optimized lengths of the source and intrinsic regions are almost 14 nm. Very good agreements for both the potential and the drain current are observed between the model calculations and the simulated results.

Spice-compatible modeling of high injection and propagation of minority carriers in the substrate of Smart Power ICs

Classical substrate noise analysis considers the silicon resistivity of an integrated circuit only as doping dependent besides neglecting diffusion currents as well. In power circuits minority carriers are injected into the substrate and propagate by drift–diffusion. In this case the conductivity of the substrate is spatially modulated and this effect is particularly important in high injection regime. In this work a description of the coupling between majority and minority drift–diffusion currents is presented. A distributed model of the substrate is then proposed to take into account the conductivity modulation and its feedback on diffusion processes. The model is expressed in terms of equivalent circuits in order to be fully compatible with circuit simulators. The simulation results are then discussed for diodes and bipolar transistors and compared to the ones obtained from physical device simulations and measurements.

Screening and interaction of conductive grains charged by drift-diffusion currents in plasma

The problem of interaction between two ideally conductive spherical charged macroparticles is solved numerically for strongly collisional weakly ionized plasma. The potential and charge density spatial distributions as well as the interaction force are studied and compared with the analytical solution. The electron and ion fluxes that arise due to the absorption of plasma particles by the grain are described using the drift-diffusion approach. The results are obtained for the stationary state, in which the net current through the grain surface is zero.

Elucidating the Photoresponse of Ultrathin MoS2 Field-Effect Transistors by Scanning Photocurrent Microscopy

The mechanisms underlying the intrinsic photoresponse of few-layer (FL) molybdenum disulphide (MoS2) field-effect transistors are investigated via scanning photocurrent microscopy. We attribute the locally enhanced photocurrent to band-bending assisted separation of photoexcited carriers at the MoS2/Au interface. The wavelength-dependent photocurrents of few layer MoS2 transistors qualitatively follow the optical absorption spectra of MoS2, providing direct evidence of interband photoexcitation. Time and spectrally resolved photocurrent measurements at varying external electric fields and carrier concentrations establish that drift-diffusion currents dominate photothermoelectric currents in devices under bias.

Parameter determination from current–voltage characteristics of HgCdTe photodiodes in forward bias region

Current–voltage characteristics of HgCdTe photodiodes in the forward bias region have been modeled considering mechanisms including drift-diffusion current, recombination current, metal-semiconductor contact and constant series resistance. Moreover, a fitting method based on the genetic algorithm has been developed to obtain values of related physical parameters from the measured dynamic resistance–voltage curves. Fitting results of \(n^+\)-on-\(p\) planar devices with different cutoff wavelengths are presented to illustrate the model and method, which are available and promising in acquiring device parameter values and evaluating the electrode contact quality.

Same ion channel populations and different excitabilities: beyond the conductance-based model

Multicellular organisms rely on electrical signaling to communicate messages within and between different tissues. Channel-mediated ionic transport is typically modeled with conductance-based formulations that assume currents are the result of ionic electrical drift, without taking diffusion into consideration [1]. In contrast, formulations of current that assume ionic flux depends on electrical drift and diffusion are not as widely used in the literature [3-5]. These representations are more realistic and display experimentally observable phenomena that conductance-based models cannot reproduce (e.g. rectification). The two formulations are, however, mathematically related because conductance-based currents are linear approximations of drift-diffusion currents. Importantly, conductance-based models of membrane potential are not first order approximations of drift-diffusion models. The two approaches predict qualitatively and quantitatively different behaviors in the dynamics of membrane potential. For instance, two neuronal membrane models with identical populations of ion channels, one written with conductance-based currents, the other with driftdiffusion currents, undergo transitions into and out of repetitive oscillations through different mechanisms and for different levels of stimulation. These differences in excitability are observed across different levels of ion channel expression in response to excitatory synaptic input. The electrophysiological profiles of drift-diffusion and conductance-based models having identical ion channel populations are different. As a consequence, the inputoutput and computational properties of networks constructed with conductance-based and electrodiffusion models should be different as well. The drift-diffusion formulation is proposed as a theoretical improvement over conductance-based models that may lead to more accurate predictions and interpretations of experimental data at the single cell and network levels.

Membranes with the same ion channel populations but different excitabilities.

Electrical signaling allows communication within and between different tissues and is necessary for the survival of multicellular organisms. The ionic transport that underlies transmembrane currents in cells is mediated by transporters and channels. Fast ionic transport through channels is typically modeled with a conductance-based formulation that describes current in terms of electrical drift without diffusion. In contrast, currents written in terms of drift and diffusion are not as widely used in the literature in spite of being more realistic and capable of displaying experimentally observable phenomena that conductance-based models cannot reproduce (e.g. rectification). The two formulations are mathematically related: conductance-based currents are linear approximations of drift-diffusion currents. However, conductance-based models of membrane potential are not first-order approximations of drift-diffusion models. Bifurcation analysis and numerical simulations show that the two approaches predict qualitatively and quantitatively different behaviors in the dynamics of membrane potential. For instance, two neuronal membrane models with identical populations of ion channels, one written with conductance-based currents, the other with drift-diffusion currents, undergo transitions into and out of repetitive oscillations through different mechanisms and for different levels of stimulation. These differences in excitability are observed in response to excitatory synaptic input, and across different levels of ion channel expression. In general, the electrophysiological profiles of membranes modeled with drift-diffusion and conductance-based models having identical ion channel populations are different, potentially causing the input-output and computational properties of networks constructed with these models to be different as well. The drift-diffusion formulation is thus proposed as a theoretical improvement over conductance-based models that may lead to more accurate predictions and interpretations of experimental data at the single cell and network levels.

Two-dimensional model of space charge limited electron injection into a diode with Schottky contact

We present an analytical two-dimensional (2D) model of a high current space charge limited (SCL) electron injection into a solid through a Schottky contact for a n+–i–n+ diode with constant mobility and no velocity overshoot effect. The amount of electron injection is limited by the barrier at the contact, which includes the effect of electron tunnelling through the Schottky barrier. For a given barrier height, the SCL current condition can be reached if the tunnelling current becomes dominant over the drift–diffusion current. An analytical scaling is present to show the enhancement of the SCL current due to finite contact size, which is verified by a 2D device simulator over a wide range of parameters.

Numerical Calculation of the Drift Diffusion Current for Elastically Interacting Point Defects

AbstractFor long range interactions the probability of defect encounter is determined by the drift diffusion current of one defect to the other. This current is calculated numerically for iso‐tropic point defects in an anisotropio elastic continuum. The diffusion current is found to be a fixed fraction of that caused by a spherical potential for which the current can bewritten by a simple analytical expression.