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NASA NTRS1997

Simulation of Ultra-Small Electronic Devices: The Classical-Quantum Transition Region

Concern is increasing about how quantum effects will impact electronic device operation as down-scaling continues along the SIA Roadmap through 2010. This document describes part of a new semiconductor device modeling (SDM) program at NAS to investigate these concerns by utilizing advanced NAS and third-party numerical computation software to rapidly implement and investigate electronic device models including quantum effects. This SDM project will investigate quantum effects in devices in the classical-quantum transition region, especially sub-0.1 mm MOSFETs. Specific tasks planned for this project include the use of quantum corrections to the classical drift-diffusion and hydrodynamic models of electron transport, arid the use of nominally quantum models including significant scattering.

Biegel, Bryan A.↗

DOE OSTI2021

Trap-Assisted Dopant Compensation Prevents Shunting in poly-Si Passivating Interdigitated Back Contact Silicon Solar Cells

Interdigitated back contact (IBC) solar cells achieve the highest efficiencies of single-junction architectures, but complicated patterning of the rear fingers and spreading of dopants during processing inhibit their mainstream adoption due to concerns of shunting between the IBC fingers. One method of simplifying patterning at the rear is by using contact masks combined with plasma-enhanced chemical vapor deposition (PECVD) or ion implantation. However, the intrinsic isolation region becomes contaminated during high-temperature annealing by lateral diffusion of dopants and during masked PECVD by spreading of dopant radicals through region between the mask and the substrate. Despite this contamination, we show through scanning spreading resistance microscopy and Kelvin probe force microscopy that a ~20 µm wide compensating region exists with high enough resistivity to prevent shunting. We model this p-i-n poly-Si system using two simulation models: a simple resistor model considering only the capture of charge carriers by trap defects in poly-Si to reduce the conductivity, and a more refined 1-dimensional finite element model using Poisson’s equation, drift-diffusion equations, and recombination of carriers. Using this model, we show that high defect density significantly decreases the current across the region between the p- and n-type fingers, preventing shunting.

atom probe↗

DOE OSTI2023

Inertial and anisotropic pressure effects on cross-field electron transport in low-temperature magnetized plasmas

In this paper, a one-dimensional (1D) particle-in-cell Monte Carlo collision (PIC-MCC) model is developed to investigate the effects of anisotropic pressure and inertial terms due to non-Maxwellian velocity distribution functions on cross-field electron transport. The conservation of momentum is evaluated by taking the moments of the first-principles gas-kinetic equation. A steady-state discharge is obtained without any low-frequency ionization oscillations by considering an anomalous electron scattering profile. Further, the results obtained from the 1D PIC-MCC model are compared with fluid models, including the quasi-neutral drift-diffusion (DD), non-neutral DD, and full fluid moment models. The discharge current obtained from the PIC-MCC model is in good agreement with the fluid models. The cross-field electron transport due to the inertial terms, i.e. the gradient of axial and azimuthal drift, is evaluated. Moreover, PIC-MCC simulation results show non-zero, anisotropic, off-diagonal pressure tensor terms due to asymmetric non-Maxwellian electron velocity distribution function, potentially contributing to cross-field electron transport.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Modeling the Charge and Exciton Distributions in Phosphorescent White Organic Light-Emitting Diodes

A comprehensive numerical model is developed to quantitatively analyze the charge and exciton distributions in phosphorescent white organic light emitting diodes (WOLEDs). The model encompasses bipolar charge drift-diffusion transport with doping-dependent charge mobilities, field-dependent charge hopping across multiple interfaces, exciton generation, diffusion, energy transfer, radiative decay, and non-radiative exciton annihilation. The model is validated by direct measurement of the exciton distribution in monochromatic phosphorescent OLEDs. It is then applied to complex, multilayer WOLEDs where it is used to accurately predict their intensity and current-dependent spectral shifts. The magnitudes of different exciton loss channels in WOLEDs are calculated and quantitatively compared. This model provides an alternative for the many experimental iterations commonly used to optimize the color balance of complex OLEDs. In this context, the model inspired the addition of a hole blocking layer in the WOLED to balance the charge conduction and reduce spectral shifts – a design that is verified by experiment.

42 ENGINEERING↗

DOE OSTI2023

High-Fidelity Simulations of Plasma-Assisted Oxidation of Hydrocarbon Fuels Using Nanosecond Pulsed Discharges

Next, a robust and efficient framework for simulating NSPD in multiple dimensions is developed. The reactive Navier-Stokes equations are extended to include a drift-diffusion plasma-fluid model with a local field approximation (LFA) in a finite-volume solver, which uses an adaptive mesh refinement (AMR) strategy to address the wide separation of length scales in the problem. A two-way coupling strategy is used whereby the plasma-fluid model and reactive Navier-Stokes equations are integrated simultaneously. The oxidation of ethylene/air mixtures mediated by NSPD is simulated in a pin-to-pin configuration. All phases of the plasma discharge are simulated explicitly (including streamer ignition, propagation, and connection, as well as the subsequent spark phase), along with the evolution of the plasma during the inter-pulse period. Temporally and spatially-resolved results are presented, with an emphasis on the analysis of heating and energy deposition, as well as of the evolution of the concentration of active particles generated during the NSPD and their influence on ignition.

adaptive mesh refinement↗

NASA NTRS2007

Hypersonic Magneto-Fluid-Dynamic Compression in Cylindrical Inlet

Hypersonic magneto-fluid-dynamic interaction has been successfully performed as a virtual leading-edge strake and a virtual cowl of a cylindrical inlet. In a side-by-side experimental and computational study, the magnitude of the induced compression was found to be depended on configuration and electrode placement. To better understand the interacting phenomenon the present investigation is focused on a direct current discharge at the leading edge of a cylindrical inlet for which validating experimental data is available. The present computational result is obtained by solving the magneto-fluid-dynamics equations at the low magnetic Reynolds number limit and using a nonequilibrium weakly ionized gas model based on the drift-diffusion theory. The numerical simulation provides a detailed description of the intriguing physics. After validation with experimental measurements, the computed results further quantify the effectiveness of a magnet-fluid-dynamic compression for a hypersonic cylindrical inlet. At a minuscule power input to a direct current surface discharge of 8.14 watts per square centimeter of electrode area produces an additional compression of 6.7 percent for a constant cross-section cylindrical inlet.

Shang, Joseph S.↗

NASA NTRS1996

A Parallel Multilevel Spectral Element Scheme

A parallel multilevel strategy is developed using spectral (p) finite elements. Hierarchic bases are particularly well suited since the element matrices and vectors are nested and the multilevel projections easiliy performed. Since the basis degree is used to specify the multigrid level, an EBE strategy is natural br the multilevel technique. Results are presented for two candidate nonlinear elliptic transport problems: the augmented drift-diffusion equations of semiconductor device modeling and the stream function-vorticity equations of incompressible fluid dynamics.

Davis, M. B.↗

DOE OSTI2022

Protein drift-diffusion dynamics and phase separation in curved cell membranes and dendritic spines: Hybrid discrete-continuum methods

We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic strength, protein kinetics, and self-assembly of clusters. We perform simulation studies for model spine geometries varying the neck size to investigate how phase-separation and protein organization is influenced by different shapes. We also show how our methods can be used to study the roles of geometry in reaction-diffusion systems including Turing instabilities. Furthermore, our methods provide general approaches for investigating protein kinetics and drift-diffusion dynamics within curved membrane structures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Efficiency and Forward Voltage of Blue and Green Lateral LEDs with V-shaped Defects and Random Alloy Fluctuation in Quantum Wells

For nitride-based blue and green light-emitting diodes (LEDs), the forward voltage V for is larger than expected, especially for green LEDs. This is mainly due to the large barriers to vertical carrier transport caused by the total polarization discontinuity at multiple quantum well and quantum barrier interfaces. The natural random alloy fluctuation in quantum wells has proven to be an important factor reducing V for . However, this does not suffice in the case of green LEDs because of their larger polarization-induced barrier. V-shaped defects (V-defects) have been proposed as another key factor in reducing V for to allow lateral injection into multiple quantum wells, thus bypassing the multiple energy barriers incurred by vertical transport. In this paper, to model carrier transport in the whole LED, we consider both random-alloy and V-defect effects. A fully two-dimensional drift-diffusion charge-control solver is used to model both effects. The results indicate that the turn-on voltages for blue and green LEDs are both affected by random alloy fluctuations and the V-defect density. For green LEDs, V for decreases more due to V-defects, where the smaller polarization barrier at the V-defect sidewall is the major path for lateral carrier injection. Then, we discuss how the V-defect density and size affects the results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2001

Electro-Thermal Simulation Studies of SiC Junction Diodes Containing Screw Dislocations Under High Reverse-Bias Operation

The objective of this work was to conduct a modeling study of SiC P-N junction diodes operating under high reverse biased conditions. Analytical models and numerical simulation capabilities were to be developed for self-consistent electro-thermal analysis of the diode current-voltage (I-V) characteristics. Data from GRC indicate that screw dislocations are unavoidable in large area SiC devices, and lead to changes in the SiC diode electrical response characteristics under high field conditions. For example, device instability and failures linked to internal current filamentation have been observed. The physical origin of these processes is not well understood, and quantitative projections of the electrical behavior under high field and temperature conditions are lacking. Thermal calculations for SiC devices have not been reported in the literature either. So estimates or projections of peak device temperatures and power limitations do not exist. This numerical study and simulation analysis was aimed at resolving some of the above issues. The following tasks were successfully accomplished: (1) Development of physically based models using one- and two-dimensional drift-diffusion theory for the transport behavior and I-V characteristics; (2) One- and two-dimensional heat flow to account for internal device heating. This led to calculations of the internal temperature profiles, which in turn, were used to update the electrical transport parameters for a self-consistent analysis. The temperature profiles and the peak values were thus obtainable for a given device operating condition; (3) Inclusion of traps assumed to model the presence of internal screw dislocations running along the longitudinal direction; (4) Predictions of the operating characteristics with and without heating as a function of applied bias with and without traps. Both one and two-dimensional cases were implemented; (5) Assessment of device stability based on the operating characteristics. The presence of internal non-uniformities, particularly filamentary structures, was probed and demonstrated; (6) Cause and physical origins of filamentary behavior and unstable I-V characteristics were made transparent; (7) It was demonstrated that diodes containing defects would be more prone to thermal breakdown associated with the temperature dependent decrease in the thermal conductivity; and (8) Finally, negative differential resistance (S-shaped NDR) which can potential lead to device instability and filamentary behavior was shown to occur for diodes containing a line of defects such as could be associated with a screw dislocation line.

Joshi, R. P.↗

DOE OSTI2021

On the Equilibrium Electrostatic Potential and Light-Induced Charge Redistribution in Halide Perovskite Structures

Lead halide perovskites are semiconductor materials which are employed as nonintentionally doped absorbers inserted between two selective carrier transport layers (SCTL), realizing a p-i-n or n-i-p heterojunction. In our study, we have developed and investigated a lateral device, based on methylammonium lead iodide (MAPbI3) in which the p-i-n heterojunction develops in the horizontal direction. Our research suggests that the effective doping level in the MAPbI3 film should be very low, below 1012 cm-3. Along the vertical direction, this doping level is not enough to screen the electric field of the buried heterojunction with the SCTL. The perovskite work function is therefore affected by the work function of the SCTL underneath. From drift-diffusion simulations, we show that intrinsic perovskite-SCTL structures develop mV range surface photovoltages (SPVs) under continuous illumination. However, perovskite-SCTL structures can develop SPVs of hundreds of mV, as confirmed by our measurements. We therefore analyzed the compatibility between low doping and low defect densities in the perovskite layer and such high SPV values using numerical modeling. It is shown that these high SPV values could originate from electronic processes due to large band offsets in the buried perovskite-SCTL heterojunctions, or at the SCTL-transparent conductive oxide (TCO) buried heterojunction. However, such electronic processes can hardly explain the long SPV persistence after switching off the illumination.

defects↗

DOE OSTI2024

An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model

A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density $f$ = $f$ ($x, v, t$) converges to an isotropic function $M (v)$$ρ$$(x, t)$, called the drift-diffusion limit, where $M$ is a Maxwellian and the physical density $ρ$ satisfies a second-order parabolic PDE known as the drift-diffusion equation. Numerical approximations that mirror this property are said to be asymptotic preserving. In this paper we build a discontinuous Galerkin method to the semiconductor model, and we show this scheme is both uniformly stable in $ε$, where 1/$ε$ is the scale of the collision frequency, and asymptotic preserving. Here in particular, we discuss what properties the discrete Maxwellian must satisfy in order for the schemes to converge in $ε$ to an accurate $h$-approximation of the drift-diffusion limit. Discrete versions of the drift-diffusion equation and error estimates in several norms with respect to $ε$ and the spacial resolution are also included.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Massively parallel axisymmetric fluid model for streamer discharges

A highly parallelizable fluid plasma simulation tool based upon the first-order drift-diffusion equations is discussed. Atmospheric pressure plasmas have densities and gradients that require small element sizes in order to accurately simulate the plasm resulting in computational meshes on the order of millions to tens of millions of elements for realistic size plasma reactors. To enable simulations of this nature, parallel computing is required and must be optimized for the particular problem. Here, a finite-volume, electrostatic drift-diffusion implementation for low-temperature plasma is discussed. The implementation is built upon the Message Passing Interface (MPI) library in C++ using Object Oriented Programming. The underlying numerical method is outlined in detail and benchmarked against simple streamer formation from other streamer codes. Electron densities, electric field, and propagation speeds are compared with the reference case and show good agreement. Convergence studies are also performed showing a minimal space step of approximately 4 μm required to reduce relative error to below 1% during early streamer simulation times and even finer space steps are required for longer times. Additionally, strong and weak scaling of the implementation are studied and demonstrate the excellent performance behavior of the implementation up to 100 million elements on 1024 processors. Lastly, different advection schemes are compared for the simple streamer problem to analyze the influence of numerical diffusion on the resulting quantities of interest.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Ionization waves in low-current dc discharges in noble gases obtained with a hybrid kinetic-fluid model

A hybrid kinetic-fluid model is used to study ionization waves (striations) in a low-current plasma column of dc discharges in noble gases. Coupled solutions of a kinetic equation for electrons, a drift-diffusion equation for ions, and a Poisson equation for the electric field are obtained to clarify the nature of plasma stratification in the positive column. A simplified two-level excitation-ionization model is used for the conditions when the nonlinear effects due to stepwise ionization, gas heating, and Coulomb interactions among electrons are negligible. It is confirmed that the nonlocal effects are responsible for the formation of moving striations in dc discharges at low plasma densities and low values of pR (the product of gas pressure and tube radius). Here, the calculated properties of self-excited waves of S–, P–, and R types in neon and S type in argon agree with available experimental data. The reason for helium plasma stability to stratification is clarified. It is shown that sustaining stratified plasma is more efficient than striation-free plasma when the ionization rate is a nonlinear function of the electric field. However, the nonlinear dependence of the ionization rate on the electric field is not required for plasma stratification. Striations of S–, P–, and R types in neon exist with minimal or no ionization enhancement. Effects of the column length and plasma density on the wave properties are demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2000

A Self-Consistent Plasma-Sheath Model for the Inductively Coupled Plasma Reactor

Accurate determination of ion flux on a wafer requires a self-consistent, multidimensional modeling of plasma reactor that adequately resolves the sheath region adjoining the wafer. This level of modeling is difficult to achieve since non-collisional sheath lengths are usually 3-4 orders of magnitude smaller than the reactor scale. Also, the drift-diffusion equations used for ion transport becomes invalid in the sheath since the ion frictional force is no longer in equilibrium with drift and diffusion forces. The alternative is to use a full momentum equation for each ionic species. In this work we will present results from a self-consistent reactor scale-sheath scale model for 2D inductively coupled plasmas. The goal of this study is to improve the modeling capabilities and assess the importance of additional physics in determining important reactor performance features, such as the ion flux uniformity, coil frequency and configuration effects, etc. Effect of numerical dissipation on the solution quality will also be discussed.

Bose, Deepak↗

NASA NTRS2011

Extension of the ADC Charge-Collection Model to Include Multiple Junctions

The ADC model is a charge-collection model derived for simple p-n junction silicon diodes having a single reverse-biased p-n junction at one end and an ideal substrate contact at the other end. The present paper extends the model to include multiple junctions, and the goal is to estimate how collected charge is shared by the different junctions.

drift-diffusion↗

NASA NTRS2009

A theoretical analysis of steady-state charge collection in simple diodes under high-injection conditions

A previous rigorous mathematical analysis of drift-diffusion equations was used to investigate collected charge in a simple reverse-biased p-n junction diode exposed to an ionization source that liberates carriers (electron-hole pairs) in a quasi-neutral region within the diode. Each of two simple models was found to agree with the more rigorous analysis when carrier liberation is sufficiently intense. One is the sensitive volume (SV) model, and the other was called “ambipolar diffusion with a cutoff” (ADC). The earlier rigorous analysis was worked out in detail only for a localized source, i.e., a point source of carrier liberation, so it was able to validate the applicability of each simple model only for that case. The present paper treats an arbitrary spatial distribution of carrier generation and concludes that the ADC model remains valid for this more general case, but the SV model does

Edmonds, Larry D.↗

NASA NTRS1996

Comparison of Non-Parabolic Hydrodynamic Simulations for Semiconductor Devices

Parabolic drift-diffusion simulators are common engineering level design tools for semiconductor devices. Hydrodynamic simulators, based on the parabolic band approximation, are becoming more prevalent as device dimensions shrink and energy transport effects begin to dominate device characteristic. However, band structure effects present in state-of-the-art devices necessitate relaxing the parabolic band approximation. This paper presents simulations of ballistic diodes, a benchmark device, of Si and GaAs using two different non-parabolic hydrodynamic formulations. The first formulation uses the Kane dispersion relationship in the derivation of the conservation equations. The second model uses a power law dispersion relation {(hk)(exp 2)/2m = xW(exp Y)}. Current-voltage relations show that for the ballistic diodes considered. the non-parabolic formulations predict less current than the parabolic case. Explanations of this will be provided by examination of velocity and energy profiles. At low bias, the simulations based on the Kane formulation predict greater current flow than the power law formulation. As the bias is increased this trend changes and the power law predicts greater current than the Kane formulation. It will be shown that the non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation are limited due to the binomial approximation which was utilized in the derivation.

Smith, A. W.↗