Drift-diffusion Transport Research Articles

Ultra-wide Bandgap AlGaN Channel HEMTs for Portable Power Electronics Applications

AlGaN channel (Eg>3.4 eV) is the most effective method for enhancing the breakdown field of the group III-nitride based HEMTs. This work demonstrates the potential of AlGaN double channel HEMTs on Silicon carbide substrate. The device DC characteristics are investigated using numerical simulator by using drift-diffusion transport model. The AlGaN double channel HEMTs enhances the total 2DEG density due to double potential well and shows better current driving capability (IDS) of 0.714 A/mm, transconductance (gm) of 116 mS/mm, and low specific ON-resistance (Ron) of 3.262 Ω.mm. The AlGaN double channel HEMT on Silicon carbide substrate exhibited 680 V blocking voltage (VBR) and gate field plate HEMT shows 532 V. The effective reduction in electric field at the gate edge is the major source for elevated breakdown voltage in field plate HEMTs. The superior DC characteristics indicates the proposed wide bandgap channel HEMT is suitable device for future portable power converters.

Carrier transport simulation methods for electronic devices with coexistence of quantum transport and diffusive transport

In this manuscript, carrier transport simulation methods are proposed for devices with the coexistence of quantum transport and diffusive transport by combining the nonequilibrium Green's function method with the drift-diffusion transport simulation method. Current continuity between quantum transport and drift-diffusion transport is ensured by setting quantum transport current as the connection boundary condition of drift-diffusion simulation or by introducing quantum transport-induced carrier generation rates to drift-diffusion simulation. A comprehensive study of our method and the method combining the Wentzel–Kramers–Brillouin (WKB) method with the drift-diffusion transport simulation method is performed for n-type tunnel oxide passivating contact solar cell to investigate their applicable conditions and balance the accuracy and computational cost. As the oxide barrier width, barrier height, and electron effective mass increase, or the doping concentration in the electron transport layer decreases to the extent that the blocking effect of the oxide barrier on light-generated electrons becomes significant, method I is more accurate since the transmission coefficient near the conduction band edge calculated by WKB is overestimated; otherwise, method II is more suitable due to its low computational cost without the loss of accuracy. In addition, the differences between current densities, carrier densities, and Shockley–Read–Hall recombination rates simulated under the two current continuity conditions for the solar cell with different carrier mobilities are also further explored and analyzed.

Effective gate length determination of AlGaN/GaN HEMTs from direct measurements of thermal signatures

Determining junction temperature and two-dimensional temperature profile is critical for high-power GaN-based high electron mobility transistors to optimize performance, improve device reliability, and better thermal management. Here, we have demonstrated that resistance temperature detectors of the same material as the gate contact delineated between gate-to-source and gate-to-drain regions can accurately profile the temperature along the channel. The temperature profile is asymmetric and skewed toward the drain side, and the degree of asymmetry is used to determine the effective gate length experimentally. A two-dimensional thermodynamic model along with drift-diffusion transport matches well with the experimental data, validating the temperature profile and effective channel length extraction under bias. The vertical depth profiling of the temperature is also determined by identifying the isothermal profile through the resistance temperature detectors. The isothermal lines are largely circular in the GaN region from isotropic two-dimensional heat diffusion, with the pinch-off region acting as a heating filament. The isothermal circular profile turns elliptical in the SiC substrate due to its higher thermal conductivity.

Artificial neural network models for metal-ferroelectric-insulator-semiconductor ferroelectric tunnel junction memristor

Metal-Ferroelectric-Insulator-Semiconductor (MFIS) structure ferroelectric tunnel junction (FTJ) memristor becomes one of the most promising candidates for next-generation memories. Two numerical simulation methods have been developed and analyzed previously to calculate the tunneling current in the MFIS-FTJ, one by using the Wentzel–Kramers–Brillouin (WKB) method with the band profile obtained from Poisson's equation, the other by self-consistently solving Poisson's equation and the drift-diffusion transport equations with a tunneling-induced carrier generation rate. However, numerical methods can be computationally expensive, especially for device design with various parameters. In this work, an artificial neural network (ANN) model that can predict the device performance is proposed, the model can reduce computational cost while maintaining good accuracy. In addition, to further investigate the applicable conditions of the two simulation methods mentioned above, we also develop an ANN model to predict the relative differences between the two methods' results under different conditions, and the prediction results show good agreement with numerical results.

Cryogenic MOSFET Subthreshold Current: From Resistive Networks to Percolation Transport in 1-D Systems

Small area MOSFETs are known to exhibit oscillations in subthreshold current at deep cryogenic temperatures. This feature becomes more pronounced as the drain bias is lowered down, even if its footprint is still recognizable in saturation regime. In this article, we restrict the analysis to the linear operation of cryogenic MOSFETs, where transistors can be regarded as simple resistors. In order to reproduce the main aspects of the experimental behavior, we first propose a model based on the concept of “resistive networks.” The resistors’ conductivity is initially described by drift–diffusion transport. Afterward, this model is provided with a physical background, given by the so-called “percolation transport theory.” In this context, the inversion channel conductivity is affected by the potential fluctuations induced by the presence of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{Si--\text{Si}}\text{O}_{\text{2}}$</tex-math> </inline-formula> interface trap charges. An example of such percolative current is simulated for a Gaussian-like potential. Finally, the negative transconductance often observed in the experimental curves is modeled by introducing a more advanced model for resistors’ conductivity, which relies on the Kubo–Greenwood integral.

Theoretical Study of Carrier Transport in Metal–Ferroelectric–Insulator–Semiconductor Ferroelectric Tunnel Junction Memristor

Ferroelectric tunnel junction (FTJ) based on the metal–ferroelectric–insulator–semiconductor (MFIS) stacks shows great potential in neuromorphic and in-memory computing. Tunneling current in the MFIS-FTJ can be calculated by the Wentzel–Kramers–Brillouin (WKB) method with the band profile solved from Poisson’s equation or by self-consistently solving Poisson’s equation and the drift-diffusion transport equations with a tunneling-induced carrier generation rate. The carrier redistribution in the semiconductor is neglected in the former method, which reduces the complexity and saves the computational cost but may or may not lead to significant errors. In this article, a comprehensive study of the two simulation methods mentioned above is performed to investigate their applicable conditions and balance the accuracy and computational cost. The current densities of the MFIS-FTJs with different material parameters, including the barrier width, barrier height, carrier mobility, and polarization charge density simulated by the two methods, are compared and analyzed. As the voltage drop across the semiconductor cannot be neglected, method II is required to take the carrier transport in the semiconductor into account and method I is not accurate; otherwise, method I is more suitable due to its low computational cost without loss of accuracy.

Hexahedron-Based Control Volume Finite Element Method for Fully Coupled Nonlinear Drift-Diffusion Transport Equations in Semiconductor Devices

We present a new stabilized 3-D control volume finite element method (FEM) for massively parallel simulation of drift-diffusion transport in semiconductor devices. This new solver employs unstructured hexahedral elements, thus leading to a very efficient scheme; both Poisson and current continuity equations are discretized with control volume FEM, and thus, the accuracy and stability are improved. Furthermore, a fully coupled Newton’s method is applied to solve these nonlinear equations, thus remarkably increasing the numerical stability. Then, we apply this new solver to simulate diode, MOSFET, and multifinger MOSFET devices. Numerical results indicate that the hexahedron-based method requires fewer iterative numbers, and its computing speed is 3.44–4.61 times faster than the tetrahedron-based counterpart. Moreover, our fully coupled Newton’s method permits constant iterative numbers, showing strong numerical stability even when the drain voltage is 160 V.

(Digital Presentation) Finite Element Modeling of Thermoelectric Effects in Phase Change Memory Cells

We model the current density in a semiconductor based on the drift-diffusion transport of the charge carriers to accurately determine the thermoelectric effects in the bulk material (Thomson effect) and material junctions (Peltier effect). We utilize the model to perform 2-D finite element simulations of mushroom phase change memory cell with a critical dimension of 20 nm using temperature and electric field dependent material parameters and analyze the contributions of symmetric Joule heating and asymmetric thermoelectric heats during reset and set operations. We investigate the effect of altering the direction of current flow by changing the connection point between the cell and the access device and observe that, corresponding change in thermoelectric effects cause significant difference in operation dynamics, temperature distribution profiles, amorphous volume, energy requirement and resistance contrast between reset and set states.

Estimating the performance of SOI FinFET transistor using electro-thermal formulation in conjunction with the quasi-ballistic effective electron mobility approach

Modeling and simulating FinFET based circuits, disentangled as Physics-based FinFET models, constitute predictive technology models for device and circuit simulations. The electrostatic properties as well as the electron and phonon transport are very responsive to the thermal effects in diffusive as well as in quasi-ballistic regimes suggesting thereby, the necessity of their consideration for effective device modeling and design particularly in nano FinFET devices. In this paper, we describe the calibration of the drift-diffusion (D-D) transport approach for simulating the quasi-ballistic effect in short channel occurring in nanoscale devices. A strong coupling of the calibrated D-D model with the enhanced Ballistic-Diffusive Equation (BDE), susceptive to prescribe the phonon and electron transports is introduced. The Finite Element Method (FEM) is used to produce results by numerical simulation of the electro-thermal model offered in Bulk and SOI FinFET devices. We have found that the proposed mobility model performs quite well and mainly infuences the drain current and the heat source by Joule effect. Our results extracted from the calibrated D-D model are compared and contrasted with those obtained experimentally and with those obtained with the numerically exact configuration. A decent agreement between the proposed model dealing with SOI FinFET as well as Bulk FinFET and the experimental data is obtained. Results obtained by using the enhanced electro-thermal model hold promise for thermal simulations of heat transport in Bulk and SOI FinFET devices, suggesting that the dopant concentration have a crucial role for the increasing of the temperature inside the Bulk/SOI FinFET.

Benchmarking of Analog/RF Performance of Fin-FET, NW-FET, and NS-FET in the Ultimate Scaling Limit

In this work, we examine and benchmark the analog/RF performance metrics of silicon-based multigate devices, such as Fin-FET, gate-all-around nanowire (NW)-FET, and gate-all-around nanosheet (NS)-FET, in the ultimate scaling limit of sub-5-nm technology node. The performance analysis of multigate devices is done using a fully calibrated 3-D technology computer-aided design (TCAD) simulation based on self-consistent solutions of Poisson’s equation, drift-diffusion transport equation, and carrier continuity equation with quantum correction terms for accounting band-to-band tunneling and confinement effects. Our performance benchmarking suggests that NS-FET with (100) surface orientation is a more favorable candidate over NW-FET and Fin-FET for analog/RF applications with higher voltage gain (32 V/V), higher peak cutoff frequency (373 GHz), and higher maximum oscillation frequency (389 GHz) at the 5-nm technology node. The performance benefits of NS-FET are found to be retained by decreasing the channel length, increasing the effective device width, and stacking the multichannel. Furthermore, our studies identify the proper directions to optimizations for achieving high-frequency and high-gain RF operations with multigate devices.

Picosecond-range switching of high-voltage Si diode due to the delayed impact-ionization breakdown: Experiments vs simulations

The effect of delayed impact ionization breakdown initiated in a high-voltage Si or GaAs p+nn+ diode by a steep voltage ramp leads to 100 ps avalanche transient from the blocking to conducting state. Here, measurements of the voltage and current dependences in the Si diode exhibiting 100-ps kilovolt switching are presented together with simulations with focus on comparison. Device voltage and current are measured simultaneously and independently in a high-quality matched coaxial circuit. In simulations, we account for wave propagation and reflection processes in the coaxial driving/measuring circuit and for the inhomogeneity of the avalanche switching over the device cross section. This makes quantitative comparison with measurements possible. An agreement in switching time and transient characteristics can be achieved only under the assumption that a smaller part of the cross section is avalanching. The 100-ps switching time is formed not during the passage of superfast ionizing front in the “active” part of the device, as it is widely believed, but by the discharge time of the “passive part” over the conducting “active” part. The inner circuital current that flows within the device along the closed loop plays a dominant role in this process. Sources of initial carriers, the temperature dependence of the effect, and the limits of drift-diffusion transport model in describing the phenomenon of delayed breakdown are discussed.

Multi-scale modeling of 2D GaSe FETs with strained channels

Electronic devices based on bidimensional materials (2DMs) are the subject of an intense experimental research, that demands a tantamount theoretical activity. The latter must be hold up by a varied set of tools able to rationalize, explain and predict the operation principles of the devices. However, in the broad context of multi-scale computational nanoelectronics, there is currently a lack of simulation tools connecting atomistic descriptions with semi-classical mesoscopic device-level simulations and able to properly explain the performance of many state-of-the-art devices. To contribute to filling this gap we present a multi-scale approach that combines fine-level material calculations with a semi-classical drift-diffusion transport model. Its use is exemplified by assessing 2DM field effect transistors with strained channels, showing excellent capabilities to capture the changes in the crystal structure and their impact into the device performance. Interestingly, we verify the capacity of strain in monolayer GaSe to enhance the conduction of one type of carrier, enabling the possibility to mimic the effect of chemical doping on 2D materials. These results illustrate the great potential of the proposed approach to bridge levels of abstraction rarely connected before and thus contribute to the theoretical modeling of state-of-the-art 2DM-based devices.

Continuum time-delayed electron hopping in the extended dynamical molecules and entropy-ruled Einstein relation for organic semiconductors

Charge transport (CT) in dynamically disordered molecular systems is still unclear; though it is fundamentally important to understand the semiconducting properties of molecular devices. In this regard, we explore vibronically coupled polaron hopping transport in the extended hopping systems (N + 1 sites) of thiazolothiazole (TZTZ) based molecules. The molecular vibrations correlated charge transfer integral and site energy fluctuation effects on polaron transport are analyzed by kinetic Monte-Carlo simulations. In order to quantify the CT properties more precisely, we have proposed the continuum time delayed CT mechanism, which takes account of typical disordered (static or dynamic) effect via dispersion on each CT quantity (like charge transfer rate, diffusion coefficient, mobility, current density and etc) at each hopping. The charge compressibility analysis further addresses the electronic level understanding of all CT quantities, which originally relates the thermodynamic density of states with CT. Using differential entropy-dependent charge density and diffusion expressions, the drift-diffusion transport has been elucidated for different extended systems of TZTZ derivatives. Besides, we have mainly developed entropy-ruled diffusion-mobility relation for both degenerate and nondegenerate materials to study the validity and limitations of original Einstein relation, which directly pertain to the device performance. Here, the traversing chemical potential along the hopping sites is the deterministic parameter of diffusion-mobility ratio. Using our continuum time delayed model, we can categorize the typical disordered transport in the molecular semiconductors; whether is dynamic or static or intermediate disordered transport.

Physics based compact modeling of symmetric double gate MOS transistors with high mobility III-V channel material

In this work, we report a physics-based core model of surface potential, inversion charge, and drain current of a symmetric double-gate MOSFET with high mobility III-V channel material. The model efficiently captures all essential device physics of III-V MOSFETs. The carrier quantization effect inside the quantum well formed between oxide and channel region, is modeled by solving time-independent Schrödinger wave equation. The surface potential and inversion charge are obtained from the explicit solution of the Poisson and Schrödinger equation. A first-order correction has been applied to incorporate the modifications in sub-band energy due to applied gate bias voltages. The conduction band non-parabolicity effect is also included in our proposed model. The drain current has been derived using drift-diffusion transport including the velocity overshoot effect. The core model is free from any empirical parameters. The model predicted results have been validated with self-consistent Schrödinger-Poisson solver and commercial device simulator (TCAD) for different channel thicknesses, effective masses, a wide range of gate and drain bias voltages, and different non-parabolicity factor. The model predicted results are found to be in reasonable agreement with numerical simulation data.

1-D Drift-Diffusion Simulation of Two-Valley Semiconductors and Devices

A two-valley formulation of 1-D drift-diffusion transport is presented that takes the coupling between the valleys into account via a new approximation for the nonlocal electric field. The proposed formulation is suitable for the simulation of III-V heterojunction bipolar transistors as opposed to formulations that employ the single electron gas approximation with a modified velocity-field model, which also causes convergence problems. Based on Boltzmann transport equation simulations, model parameters of the proposed two-valley formulation are given for GaAs, InP, InAs, and GaSb at room temperature. Applications of the new formulation are also demonstrated.

Multiphysics simulation of plasma channel formation during micro-electrical discharge machining

A 2D axisymmetric plasma model for micro-electrical discharge machining (μEDM) is developed, and the discharge phenomenon is discussed in this paper. Variations in different plasma properties, such as density, temperature, and collisions of the electrons bombarding the anode and cathode electrodes, were simulated to comprehensively explain the discharge process. The said properties of the plasma channel will be extremely helpful in determining the heat flux available at the tool and workpiece of μEDM. The governing equations of electrostatics, drift-diffusion, and heavy species transport were coupled together and solved simultaneously for computing the properties of the plasma channel in water vapor. The simulation describes the movement of electrons and ions in the inter-electrode gap during the discharge initiation under the applied electric field. The anode spot responsible for the material removal was formed much earlier compared to the cathode spot formed at the tool. Both the temperature and the density of the electrons were observed to be higher near the workpiece, compared to the tool electrode. The temperature of the electrons and the current density of the plasma obtained during the simulation will be useful to determine the heat flux responsible for the material removal. The non-equilibrium nature of the plasma sheath is responsible for the steep changes in the collisional power loss and higher capacitive power deposition near the workpiece electrode.

Modeling and Analysis of Double Channel GaN HEMTs Using a Physics-Based Analytical Model

In this work, we report the development of a new physics-based analytical model for current and charge characteristics of Double Channel (DC) Gallium Nitride High Electron Mobility Transistors (GaN-HEMTs). The model has at its core the self-consistent calculation of the charge densities, for both upper and lower channels, obtained from a solution of the Schrodinger and Poisson equations. Fermi-Dirac (FD) distribution together with 2D density of states is used for mobile carrier statistics in both the channels. Furthermore, drift-diffusion transport is used to compute the channel current using charge densities at channel extremities. Finally, the model is validated against TCAD simulation and experimental data for a DC-GaN-HEMT. The model, by virtue of its fully physics-based nature, precisely captures the charge screening effect in the lower channel without invoking any empirical clamping functions, unlike prior models, and also possesses the feature of being geometrically scalable.

A Fractional Drift Diffusion Model for Organic Semiconductor Devices

Because charge carriers of many organic semiconductors (OSCs) exhibit fractional drift diffusion (Fr-DD) transport properties, the need to develop a Fr-DD model solver becomes more apparent. However, the current research on solving the governing equations of the Fr-DD model is practically nonexistent. In this paper, an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices. The Fr-DD model is composed of two fractional-order carriers (i.e., electrons and holes) continuity equations coupled with Poisson’s equation. By treating the current density as constants within each pair of consecutive grid nodes, a linear Caputo’s fractional-order ordinary differential equation (FrODE) can be produced, and its analytic solution gives an approximation to the carrier concentration. The convergence of the solver is guaranteed by implementing a successive over-relaxation (SOR) mechanism on each loop of Gummel’s iteration. Based on our derivations, it can be shown that the Scharfetter–Gummel discretization method is essentially a special case of our scheme. In addition, the consistency and convergence of the two core algorithms are proved, with three numerical examples designed to demonstrate the accuracy and computational performance of this solver. Finally, we validate the Fr-DD model for a steady-state organic field effect transistor (OFET) by fitting the simulated transconductance and output curves to the experimental data.

Quasi-Ballistic Drift-Diffusion Simulation of SiGe Nanowire MOSFETs Using the Kinetic Velocity Model

This paper presents the calibration of the novel kinetic velocity model (KVM) in the drift-diffusion (DD) transport approach, which can account for the ballistic effect in short-channel devices. The KVM considers a thermionic emission limit and a free carrier acceleration limit for the mobility. We develop a methodology to extract the parameters for the KVM and for the high-field saturation velocity model for SiGe nanowires over the whole mole fraction range. The calibrated DD simulations with KVM show good agreement with Boltzmann transport equation results in terms of on-state current and carrier-weighted velocity distribution over a wide range of gate lengths for both linear and saturation regimes.

Effect of carrier drift-diffusion transport process on thermal quenching of photoluminescence in GaN

Thermal quenching of the defect-related photoluminescence (PL) has been widely used to determine the fundamental properties of point defects in GaN such as the activation energy (E t ) and capture cross section. However, in the present work, we have shown using drift-diffusion modeling and experimental analysis that the thermal quenching of defect-related PL from GaN does not only depend of the defect parameters but also is strongly governed by the carrier drift and diffusion in the depletion region. In particular, we have found that these processes significantly influence the slope of PL thermal quenching and temperature T 0 at which the quenching begins. As a result, E t obtained from the Arrhenius plot of the defect-related PL intensity in GaN provides the correct values of the defect activation energy only in the case of low surface state density ( cm−2eV−1) corresponding to the weak surface band bending. However, in the case of high D 0 giving rise to the significant surface band bending, the E t value should be cautiously interpreted because it may not correspond entirely to the real defect activation energy due to the drift-diffusion process. Finally, we have shown that our finding can explain in a coherent manner various anomalous behaviors of PL thermal quenching reported in the literature, such as tunable, abrupt or sample dependent thermal quenching. We believe that our findings can be very interesting for nitride growth technology community and optoelectronic device applications.