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DOE OSTI2024

Full-torus impurity transport simulation in boron powder injection experiments in the Large Helical Device

The toroidal distribution of boron deposition on plasma-facing components (PFCs) in boron powder injection using an impurity power dropper (IPD) was investigated by full-torus simulation and observations in a systematic plasma density-scan experiment. The images of the ablation of dropped boron powders observed with a visible CCD camera were consistently explained by the simulations of the ablation positions of the boron powders considering the size distribution. Simulations assuming full-torus boron deposition on the PFCs did not reproduce the observed intensity profile of boron emission lines for higher plasma densities. It indicated that the density of boron deposited on PFCs installed toroidally far from the IPD was low for higher plasma densities due to the change in the ablation positions of the boron powders toward the outboard side. The experimental results verified the previous full-torus simulation of the toroidal distribution of the boron deposition in both lower and higher plasma densities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Low-loss superconducting titanium nitride grown using plasma-assisted molecular beam epitaxy

Titanium nitride (TiN) is a known superconducting material that is attractive for use as passive components in superconducting circuits for both conventional and quantum information devices. In contrast to conventional synthesis techniques, here, plasma-assisted molecular beam epitaxy is reported to produce high-quality TiN on bare silicon wafers. Using a rf-plasma source to crack the nitrogen molecules and a conventional high-temperature effusion cell for titanium, TiN growth is completed under nitrogen-rich conditions. The growth and nucleation is monitored in situ, while the structure and composition are characterized using x-ray diffraction, atomic force microscopy, x-ray photoelectron spectroscopy, secondary ion mass spectroscopy, and scanning transmission electron microscopy. The stoichiometric TiN (111) films sit on an amorphous nitride layer with low impurity concentrations. The films superconduct with Tc=5.4 K, and coplanar waveguide resonators are fabricated with a small center width of 6 μm that demonstrate single-photon quality factors approaching 1M and high-power quality factors over 5M without observing saturation.

Richardson, C. J. K. (ORCID:0000000188175347)↗

DOE OSTI2025

Amorphization and siliconization of silicon carbide as a first wall material

The understanding and prediction of silicon carbide (SiC) material evolution exposed to SOL plasma conditions is of prime interest because SiC represents a promising main chamber wall plasma-facing material for next-step fusion devices (low hydrogenic diffusion, good mechanical and thermal properties under neutron irradiation). Gross and net Si erosion rates from SiC surfaces in contact with a well-diagnosed L-mode plasma in the DIII-D tokamak have been simulated and the surface concentrations of impurities have been tracked as a function of time. Coupled simulation of surface model and impurity transport demonstrates amorphization of crystalline SiC exposed to L-mode plasma due to the accumulation of displacement damages under ion irradiation. This affects the lifetime of SiC plasma facing components. Surface evolution is tightly coupled to impurity transport in the plasma and therefore needs to be integrated with impurity transport simulations to effectively predict Si erosion rates and sub-surface concentrations as a function of time. The simulation workflow couples a semi-analytical surface model to the impurity transport code GITR. The surface model is a homogeneous mixed-material model that tracks physical & chemical sputtering and reflection of impurities. Gross erosion is primarily influenced by the background plasma parameters and redeposition patterns are mainly influenced by the prompt redeposition due to the gyro-orbits of impurity ions. Although crystalline form of SiC is preferable for fusion wall applications because of resistance to neutron irradiation, this work indicates that crystalline SiC will undergo amorphization under D plasma contact with implications of higher sputtering and fuel retention. These results direct us to explore the effects of amorphization on crystalline SiC and further the physics basis of SiC usage as first wall material for fusion environments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Radiative divertor detachment and impurity transport with nitrogen and neon seeding in KSTAR H-mode plasmas

Achieving core-edge compatible divertor detachment is a critical requirement for stable operation in future fusion devices. This study compares nitrogen and neon seeding in KSTAR H-mode plasmas with carbon walls, combining experiments and SOLPS-ITER modelling to evaluate their radiative dissipation and core-edge compatibility. Experimentally, N seeding achieved stronger divertor detachment, with larger reductions in target particle and heat fluxes, a higher divertor radiation fraction, and a lower core radiation fraction than Ne. In contrast, Ne seeding triggered a significant rise in core radiation followed by H–L back transitions, limiting the maximum total radiated power fraction to roughly half that of N. SOLPS-ITER simulations reproduced the experimental trends and revealed that the better core-edge compatibility of N arises from its higher divertor retention in addition to its higher cooling factor. The relative positions of the stagnation points of impurity poloidal velocity and ionization sources did not explain the different divertor compression. Instead, in the present modelling, the higher impurity parallel particle flux, resulting from the higher parallel impurity velocity, explains the stronger nitrogen impurity compression in the divertor region. The parallel temperature distribution with N was more favourable for achieving higher impurity parallel velocity than with Ne, because the impurity velocity is governed by modifications of the main ion flow due to friction and thermal forces, both of which strongly depend on the temperature. Ultimately, this behaviour is attributed to the strongly divertor-localized radiation of N. These results demonstrate that N is more effective than Ne in achieving radiative divertor detachment while maintaining low core contamination in KSTAR, consistent with observations in other present tokamaks.

KSTAR↗

NASA NTRS2008

Fast Electromechanical Switches Based on Carbon Nanotubes

Electrostatically actuated nanoelectromechanical switches based on carbon nanotubes have been fabricated and tested in a continuing effort to develop high-speed switches for a variety of stationary and portable electronic equipment. As explained below, these devices offer advantages over electrostatically actuated microelectromechanical switches, which, heretofore, have represented the state of the art of rapid, highly miniaturized electromechanical switches. Potential applications for these devices include computer memories, cellular telephones, communication networks, scientific instrumentation, and general radiation-hard electronic equipment. A representative device of the present type includes a single-wall carbon nanotube suspended over a trench about 130 nm wide and 20 nm deep in an electrically insulating material. The ends of the carbon nanotube are connected to metal electrodes, denoted the source and drain electrodes. At bottom of the trench is another metal electrode, denoted the pull electrode (see figure). In the off or open switch state, no voltage is applied, and the nanotube remains out of contact with the pull electrode. When a sufficiently large electric potential (switching potential) is applied between the pull electrode and either or both of the source and drain electrodes, the resulting electrostatic attraction bends and stretches the nanotube into contact with the pull electrode, thereby putting the switch into the "on" or "closed" state, in which substantial current (typically as much as hundreds of nanoamperes) is conducted. Devices of this type for use in initial experiments were fabricated on a thermally oxidized Si wafer, onto which Nb was sputter-deposited for use as the pull-electrode layer. Nb was chosen because its refractory nature would enable it to withstand the chemical and thermal conditions to be subsequently imposed for growing carbon nanotubes. A 200- nm-thick layer of SiO2 was formed on top of the Nb layer by plasma-enhanced chemical vapor deposition. In the device regions, the SiO2 layer was patterned to thin it to the 20-nm trench depth. The trenches were then patterned by electron- beam lithography and formed by reactive- ion etching of the pattern through the 20-nm-thick SiO2 to the Nb layer.

Kaul, Anupama↗

DOE OSTI2024

Autonomous hybrid optimization of a SiO 2 plasma etching mechanism

Computational modeling of plasma etching processes at the feature scale relevant to the fabrication of nanometer semiconductor devices is critically dependent on the reaction mechanism representing the physical processes occurring between plasma produced reactant fluxes and the surface, reaction probabilities, yields, rate coefficients, and threshold energies that characterize these processes. The increasing complexity of the structures being fabricated, new materials, and novel gas mixtures increase the complexity of the reaction mechanism used in feature scale models and increase the difficulty in developing the fundamental data required for the mechanism. This challenge is further exacerbated by the fact that acquiring these fundamental data through more complex computational models or experiments is often limited by cost, technical complexity, or inadequate models. In this paper, we discuss a method to automate the selection of fundamental data in a reduced reaction mechanism for feature scale plasma etching of SiO 2 using a fluorocarbon gas mixture by matching predictions of etch profiles to experimental data using a gradient descent (GD)/Nelder–Mead (NM) method hybrid optimization scheme. These methods produce a reaction mechanism that replicates the experimental training data as well as experimental data using related but different etch processes.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Helium bubble size effects on the surface morphological response of plasma-facing tungsten

Abstract We report a simulation study on the effects of helium (He) bubble size on the morphological evolution and pattern formation on the surface of tungsten used as a plasma-facing component (PFC) in nuclear fusion devices. We have carried out a systematic investigation based on self-consistent dynamical simulations of surface morphological evolution according to an atomistically-informed, 3D continuum-scale model that captures well the relevant length and time scales of surface nanostructure formation in PFC tungsten. The model accounts for PFC surface diffusion, driven by the biaxial compressive stress originating from the over-pressurized He bubbles in the near-surface region of PFC tungsten as a result of He plasma exposure, combined with the formation of self-interstitial atoms in tungsten that diffuse toward the PFC surface and the flux of surface adatoms generated as a result of surface vacancy-adatom pair formation upon He implantation; this transport of surface adatoms contributes to the anisotropic growth of surface nanostructural features due to the different rates of adatom diffusion along and across step edges of islands on the tungsten surface. Our detailed analysis reveals that varying the average He bubble size plays an important role in the PFC surface growth kinetics as well as the resulting surface topography. Specifically, we find that an increase in the He bubble size leads to a deceleration in the growth rate of the tungsten nanotendrils that emanate from the PFC surface. We also find that the separation distance between the resulting surface features increases with increasing He bubble size, as well as over time. This coarsening effect is a thermally activated process resulting in an accurate description of the temperature dependence of the average surface feature separation by an Arrhenius relation.

36 MATERIALS SCIENCE↗

NASA NTRS2004

High Power Light Gas Helicon Plasma Source For VASMIR

The VASIMR space propulsion development effort relies on a high power (greater than 10kW) helicon source to produce a dense flowing plasma (H, D and He) target for ion cyclotron resonance (ICR) acceleration of the ions. Subsequent expansion in an expanding magnetic field (magnetic nozzle) converts ion lunetic energy to directed momentum. This plasma source must have critical features to enable an effective propulsion device. First, it must ionize most of the input neutral flux of gas, thus producing a plasma stream with a high degree of ionization for application of ICR power. This avoids propellant waste and potential power losses due to charge exchange. Next, the plasma stream must flow into a region of high magnetic field (approximately 0.5 T) for efficient ICR acceleration. Third, the ratio of input power to plasma flux must be low, providing an energy per ion-electron pair approaching 100 eV. Lastly, the source must be robust and capable of very long life-times (years). In our helicon experiment (VX-10) we have measured a ratio of input gas to plasma flux near 100%. The plasma flows from the helicon region (B approximately 0.1 T) into a region with a peak magnetic field of 0.8 T. The energy input per ion-electron pair has been measured at 300 plus or minus 100 eV. Recent results at Oak Ridge National Laboratory (ORNL) show an enhanced efficiency mode of operation with a high power density, over 5 kW in a 5 cm diameter tube. Our helicon is presently 9 cm in diameter and operates up to 3.5 kW of input power. An upgrade to a power level of 10 kW is underway. Much of our recent work has been with a Boswell double-saddle antenna design. We are also converting the antenna design to a helical type. With these modifications, we anticipate an improvement in the ionization efficiency. This paper presents the results from scaling the helicon in the VX-10 device from 3.5 to 10 kW. We also compare the operation with a double-saddle to a helical antenna design. Finally, we discuss modeling of these configurations using ORNL's EMIR code.

Squire, J. P.↗

DOE OSTI2020

Hydrodynamic conditions in laser irradiated buried layer experiments

The calculation of open shell ionization level and radiative properties of materials in Non-Local Thermal Equilibrium (NLTE) is currently still a major challenge for any atomic model. The predictions of various NLTE atomic codes at these conditions still differ significantly. In recent years, a new buried layer platform was developed at the Lawrence Livermore National Laboratory and the Laboratory for Laser Energetics. This platform is used to measure ionization distribution and emission of open L-shell, mid-Z ions and open M-shell, high-Z ions at NLTE conditions that are relevant in many laser plasma applications. These experiments offer a unique chance for benchmarking the atomic models. In order to perform these experiments, a uniform well characterized plasma source is required. In this work, we present one-dimensional (1D) and two-dimensional simulations of the experimental platform. These simulations were used for both the design and the analysis of the experiments. The simulations demonstrate the different phases of hydrodynamic evolution of the target and identify the time windows in which uniform conditions can be achieved. A 1D expansion of the target was found to be adequate to describe the target's evolution for most of the experiment duration. The fast 1D simulations were compared with recent experimental results from the Omega laser facility. The sensitivity of the results to several modeling parameters such as the electron flux limiter and laser resonant absorption is reported.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1997

A Performance Comparison of Pulsed Plasma Thruster Electrode Configurations

Pulsed plasma thrusters are currently planned on two small satellite missions and proposed for a third. In these missions, the pulsed plasma thruster's unique characteristics will be used variously to provide propulsive attitude control, orbit raising, translation, and precision positioning. Pulsed plasma thrusters are attractive for small satellite applications because they are essentially stand alone devices which eliminate the need for toxic and/or distributed propellant systems. Pulsed plasma thrusters also operate at low power and over a wide power range without loss of performance. As part of the technical development required for the noted missions, an experimental program to optimize performance with respect to electrode configuration was undertaken. One of the planned missions will use pulsed plasma thrusters for orbit raising requiring relatively high thrust and previously tested configurations did not provide this. Also, higher capacitor energies were tested than previously tried for this mission. Multiple configurations were tested and a final configuration was selected for flight hardware development. This paper describes the results of the electrode optimization in detail.

Arrington, Lynn A.↗

NASA NTRS2013

Inductive Pulsed Plasma Thruster Development and Testing at NASA-MSFC

THE inductive pulsed plasma thruster (IPPT) is an electrodeless space propulsion device where a capacitor is charged to an initial voltage and then discharged producing a high current pulse through a coil. The field produced by this pulse ionizes propellant, inductively driving current in a plasma located near the face of the coil. Once the plasma is formed it can be accelerated and expelled at a high exhaust velocity by the electromagnetic Lorentz body force arising from the interaction of the induced plasma current and the magnetic field produced by the current in the coil. In the present work, we present a summary of the IPPT research and development conducted at NASA's Marshall Space Flight Center (MSFC). As a higher-power, still relatively low readiness level system, there are many issues associated with the eventual deployment and use of the IPPT as a primary propulsion system on spacecraft that remain to be addressed. The present program aimed to fabricate and test hardware to explore how these issues could be addressed. The following specific areas were addressed within the program and will be discussed within this paper. a) Conical theta-pinch IPPT geometry thruster configuration. b) Repetition-rate multi-kW thruster pulsing. c) Long-lifetime pulsed gas valve. d) Fast pulsed gas valve driver and controller. e) High-voltage, repetitive capacitor charging power processing unit. During the course of testing, a number of specific tests were conducted, including several that, to our knowledge, have either never been previously conducted (such as multi-KW repetition-rate operation) or have not been performed since the early 1990s (direct IPPT thrust measurements).2 Conical theta-pinch IPPT thrust stand measurements are presented in Fig. 1 while various time-integrated and time

Polzin, Kurt A.↗

DOE OSTI2021

A boundary value “reservoir problem” and boundary conditions for multi-moment multifluid simulations of sheaths

Multifluid simulations of plasma sheaths are increasingly used to model a wide variety of problems in plasma physics ranging from global magnetospheric flows around celestial bodies to plasma–wall interactions in thrusters and fusion devices. For multifluid problems, accurate boundary conditions to model an absorbing wall that resolves a classical sheath remain an open research area. This work justifies the use of vacuum boundary conditions for absorbing walls to show comparable accuracy between a multifluid sheath and lower moments of a continuum-kinetic sheath.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Data and Code for Atomic Scale Etching of Diamond: Insights from Molecular Dynamics Simulations

This work investigates the effects of argon ions, hydrogen atoms, and hydrogen ions on the diamond (100) surface using classical molecular dynamics simulations. The purpose of this investigation was to asses plasma processing techniques for applications in quantum device manufacturing. The simulations suggest that combining argon ion smoothing with selective, near threshold energy H removal of amorphous C could be an effective strategy for diamond surface engineering, leading to more reliable and sensitive diamond color center devices. Results were found to differ significantly with interatomic potential, and an analysis of these differences was also carried out. Included in this repository are LAMMPS source files, input scripts, and plotting scripts required to reproduce the data. Also included are the output data required to make all the plots included in the associated publication.

Brenner↗

NASA NTRS2000

Research Activities at Plasma Research Laboratory at NASA Ames Research Center

In order to meet NASA's requirements for the rapid development and validation of future generation electronic devices as well as associated materials and processes, enabling technologies are being developed at NASA-Ames Research Center using a multi-discipline approach. The first step is to understand the basic physics of the chemical reactions in the area of plasma reactors and processes. Low pressure glow discharges are indispensable in the fabrication of microelectronic circuits. These plasmas are used to deposit materials and also etch fine features in device fabrication. However, many plasma-based processes suffer from stability and reliability problems leading to a compromise in performance and a potentially increased cost for the semiconductor manufacturing industry. Although a great deal of laboratory-scale research has been performed on many of these processing plasmas, little is known about the gas-phase and surface chemical reactions that are critical in many etch and deposition processes, and how these reactions are influenced by the variation in operating conditions. Such a lack of understanding has hindered the development of process models that can aid in the scaling and improvement of plasma etch and deposition systems. Our present research involves the study of such plasmas. An inductively-coupled plasma (ICP) source in place of the standard upper electrode assembly of the Gaseous Electronics Conference (GEC) radio-frequency (RF) Reference Cell is used to investigate the discharge characteristics. This ICP source generates plasmas with higher electron densities and lower operating pressures than obtainable with the original parallel-plate version of the GEC Cell. This expanded operating regime is more relevant to new generations of industrial plasma systems being used by the microelectronics industry. The research goal is to develop an understanding of the physical phenomena involved in plasma processing and to measure much needed fundamental parameters, such as gas phase and surface reaction rates, species concentration, temperature, ion energy distribution, and electron number density.

Sharma, S. P.↗

DOE OSTI2022

Linear simulation of magnetohydrodynamic plasma response to three-dimensional magnetic perturbations in high-β P plasmas

In this work, we report the numerical analyses of linear magnetohydrodynamics (MHD) plasma response to applied three-dimensional magnetic perturbations (MPs) in a joint DIII-D/EAST collaboration on high-β P (poloidal beta) plasmas, utilizing the extended-MHD code M3D-C1, with the purpose of realizing a better understanding of the existing experiment in which the n=3 MPs were applied to such high-β P plasmas attempting to control large amplitude type-I ELMs. Such high-β P plasmas obtained at the DIII-D tokamak feature an upper-biased double null configuration, a high edge safety factor q 95 ~6.4, and a stable internal transport barrier (ITB) leading to relatively high core pressures. Single-fluid simulations show that the plasma response to n=3 MPs, including both non-resonant/kinking and resonant components, is significantly weaker than that to n=1 or 2 MPs. To survey the impact of q 95 on plasma response to applied MPs, the SEGWAY (Self-consistent Equilibrium Generating Workflow for AnalYsis) module, developed in the OMFIT integrated modelling framework, is employed to generate a series of equilibria with a wide range of q 95 while other key parameters including the normalized beta, electron density at pedestal top, and plasma shape are kept fixed. Compared to the vacuum response, single-fluid M3D-C1 simulations predict a much more significant decrease of resonant plasma response to the applied n=3 MPs at the maximum penetration radii as q 95 increases. In contrast to single-fluid simulation results showing resonant penetration occurs only near the pedestal top where the E×B toroidal rotation frequency is zero, two-fluid simulations show two comparable resonant penetrations locating near the pedestal top and the ITB foot, where the perpendicular electron rotation frequency is zero. Such resonant field penetration near the ITB foot may be responsible for the observed formation of a staircase structure in both electron density and temperature profiles and thereby a considerable deterioration of global plasma performance when MPs are applied in high-β P plasmas. Motivated by this numerical work, we provide some ideas for the future research, with the purpose of realizing effective ELM control in such high-β P plasmas on the DIII-D and EAST devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Variability of MHD instabilities in benign termination of high-current runaway electron beams in the JET and DIII-D tokamaks

Benign termination, in which magnetohydrodynamic (MHD) instabilities deconfine runaway electrons (REs) following hydrogenic injections, is a promising strategy for mitigating dangerous RE loads after disruptions. Recent experiments on the Joint European Torus (JET) have explored this scenario at higher pre-disruptive plasma currents than are achievable on other devices, revealing challenges in obtaining benign terminations at I p ≥2.5 MA. This work analyzes the evolution of these high-current RE beams and their terminating MHD events using fast magnetic sensor measurements and EFIT equilibrium reconstructions for approximately 40 JET and 20 DIII-D tokamak discharges. On JET, unsuccessful non-benign terminations occur at low edge safety factor (q edge ≈ 2), and are preceded by intermittent, non-terminating MHD events at higher rational qedge. Trends in the internal inductance I i indicate more peaked RE current profiles in the high-I p non-benign population, which may hinder successful recombination through re-ionization of the companion plasma. In contrast, benign terminations on JET typically occur at higher q edge ≥3 and exhibit less peaked RE current profiles. DIII-D displays a broader range of terminating edge safety factors, again correlated with the measured values. Across both tokamaks, the RE current peaking is therefore found to determine which MHD instability boundary is encountered, a result confirmed by linear resistive MHD modeling with the CASTOR3D code. Measured growth rates are similar for benign and non-benign cases, indicating that ideal MHD timescales at low density after hydrogenic injection do not alone explain efficient RE deconfinement. Instead, non-benign cases are most readily characterized by their comparably lower overall MHD perturbation amplitudes δB. These observations suggest that the interplay between ideal and resistive dynamics governs the termination process, with implications for extrapolating benign RE termination to high-I p reactor scenarios.

MHD instabilities↗

DOE OSTI2024

Enhanced plasma performance in C-2W advanced beam-driven field-reversed configuration experiments

TAE Technologies’ fifth-generation fusion device, C-2W (also called ‘Norman’), is the world’s largest compact-toroid device and has made significant progress in field-reversed configuration (FRC) plasma performance. C-2W produces record breaking, macroscopically stable, high-temperature advanced beam-driven FRC plasmas, dominated by injected fast particles and sustained in steady state, which is primarily limited by neutral-beam (NB) pulse duration. The NB power supply system has recently been upgraded to extend the pulse length from 30 ms to 40 ms, which allows for a longer plasma lifetime and thus better characterization and further enhancement of FRC performance. An active plasma control system is routinely used in C-2W to produce consistent FRC performance as well as for reliable machine operations using magnet coils, edge-biasing electrodes, gas injection and tunable-energy NBs. Google’s machine learning framework for experimental optimization has also been routinely used to enhance plasma performance. D

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2002

Microscopic Foundation and Simulation of Coupled Carrier-Temperature Diffusions in Semiconductor Lasers

A typical semiconductor-based optoelectronic device, such as a diode laser, consists of three subsystems: an optical field, an electron-hole plasma (EHP), and a host crystal lattice. The physics of such a device involves the interplay of optical, electrical and thermal processes. A proper description of such a device requires that all three processes are treated on equal footing and in a self-consistent fashion. Furthermore, since a semiconductor laser has intrinsic spatial inhomogeneity, such a self-consistency naturally leads to a set of partial differential equations in space and time. There is a significant lacking of research interest and results on the transport aspects of optical devices in the literature with only a few exceptions. Even the most important carrier diffusion coefficient has not been properly derived and studied so far for optically excited plasma, while most of the work adopted results from electronics community where heavily doped semiconductors with mainly one type of carriers are dealt with. The corresponding transport equation for plasma energy or temperature has received even less attention. In this talk we describe our recent results on such a self-consistent derivation of temperature and carrier-density diffusion equations coupled with the lasing process. Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field. The equations derived above are implemented in various limiting cases to a typical diode laser to study the consequences of nonlinear diffusion and the cross diffusion terms on laser behavior, especially the dynamic behavior of a diode laser under modulation. Detailed results will be presented by comparing with the standard rate equation results.

Li, J.↗