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Franz X. Bronold

Publications and source records attributed to Franz X. Bronold.

At least 19 recordsLinked to original sources
arXiv2025

Microphysical boundary condition for the electron kinetics of a plasma

We derive and implement a suitable boundary condition for the kinetic description of the electrons inside a plasma, which takes into account microphysical processes inside the wall. It is based on the surface scattering kernel, which describes the scattering cascade of the electron in the solid and the excitation of secondary electrons. The resulting boundary condition is inelastic, angle- and energy-dependent. The implementation for a Boltzmann equation solved by a Legendre polynomial expansion method is presented, elucidating the modest additional computational cost of the new boundary condition. Results, indicating the influence of the inelasticity, are shown for the example of a silicon wall facing argon, helium and oxygen plasmas, but the described construction is also valid for other materials. An effective reflection coefficient is defined to compare the results with previously used boundary conditions.

physics.plasm-ph↗
arXiv2017

Kinetic modeling of the electronic response of a dielectric plasma-facing solid

We present a self-consistent kinetic theory for the electronic response of a plasma-facing dielectric solid. Based on the Poisson equation and two sets of spatially separated Boltzmann equations, one for electrons and ions in the plasma and one for conduction band electrons and valence band holes in the dielectric, the approach gives the quasi-stationary density and potential profiles of the electric double layer forming at the interface due to the permanent influx of electrons and ions from the plasma. The two sets of Boltzmann equations are connected by quantum-mechanical matching conditions for the electron distribution functions and a semi-empirical model for hole injection mimicking the neutralization of ions at the surface. Essential for the kinetic modeling is the ambipolarity inside the wall, leading to an electron-hole recombination condition, and the merging of the double layer with the quasi-neutral, field-free regions deep inside the wall and the plasma. To indicate the feasibility as well as the potential of the approach we apply it to a collisionless, perfectly absorbing interface using intrinsic and extrinsic silicon dioxide and silicon surfaces in contact with a two-temperature hydrogen plasma as an example.

physics.plasm-ph↗
arXiv2016

Microscopic theory of electron absorption by plasma-facing surfaces

We describe a method for calculating the probability with which the wall of a plasma absorbs an electron at low energy. The method, based on an invariant embedding principle, expresses the electron absorption probability as the probability for transmission through the wall's long-range surface potential times the probability to stay inside the wall despite of internal backscattering. To illustrate the approach we apply it to a \SiOTwo\ surface. Besides emission of optical phonons inside the wall we take elastic scattering at imperfections of the plasma-wall interface into account and obtain absorption probabilities significantly less than unity in accordance with available electron-beam scattering data but in disagreement with the widely used perfect absorber model.

physics.plasm-ph↗
arXiv2015

Absorption of an electron by a dielectric wall

We introduce a method for calculating the probability with which a low-energy electron hitting the wall of a plasma gets stuck in it and apply the method to a dielectric wall with positive electron affinity smaller than the bandgap using MgO as an example. In accordance with electron beam scattering data we obtain energy-dependent sticking probabilities significantly less than unity and question thereby for electrons the perfect absorber assumption unisono used in plasma modeling.

physics.plasm-ph↗
arXiv2014

Infrared light extinction by charged dielectric core-coat particles

We study the effect of surplus electrons on the infrared extinction of dielectric particles with a core-coat structure and propose to use it for an optical measurement of the particle charge in a dusty plasma. The particles consist of an inner core with negative and an outer coat with positive electron affinity. Both the core and the coat give rise to strong transverse optical phonon resonances, leading to anomalous light scattering in the infrared. Due to the radial profile of the electron affinity electrons accumulate in the coat region making the infrared extinction of this type of particles very charge-sensitive, in particular, the extinction due to a resonance arising solely due to the core-coat structure. The maximum of this resonance is in the far-infrared and responds to particle charges realizable in ordinary dusty laboratory plasmas.

physics.plasm-ph↗
arXiv2013

Surface electrons at plasma walls

In this chapter we introduce a microscopic modelling of the surplus electrons on the plasma wall which complements the classical description of the plasma sheath. First we introduce a model for the electron surface layer to study the quasistationary electron distribution and the potential at an unbiased plasma wall. Then we calculate sticking coefficients and desorption times for electron trapping in the image states. Finally we study how surplus electrons affect light scattering and how charge signatures offer the possibility of a novel charge measurement for dust grains.

physics.plasm-ph↗
arXiv2012

Electron surface layer at the interface of a plasma and a dielectric wall

We study the potential and the charge distribution across the interface of a plasma and a dielectric wall. For this purpose, the charge bound to the wall is modelled as a quasi-stationary electron surface layer which satisfies Poisson's equation and minimizes the grand canonical potential of the wall-thermalized excess electrons constituting the wall charge. Based on an effective model for a graded interface taking into account the image potential and the offset of the conduction band to the potential just outside the dielectric, we specifically calculate the potential and the electron distribution for magnesium oxide, silicon dioxide and sapphire surfaces in contact with a helium discharge. Depending on the electron affinity of the surface, we find two vastly different behaviors. For negative electron affinity, electrons do not penetrate into the wall and an external surface charge is formed in the image potential, while for positive electron affinity, electrons penetrate into the wall and a space charge layer develops in the interior of the dielectric. We also investigate how the electron surface layer merges with the bulk of the dielectric.

physics.plasm-ph↗
arXiv2011

Plasma walls beyond the perfect absorber approximation for electrons

Plasma walls accumulate electrons more efficiently than ions leading to wall potentials which are negative with respect to the plasma potential. Theoretically, walls are usually treated as perfect absorber for electrons and ions implying perfect sticking of the particles to the wall and infinitely long desorption times for particles stuck to the wall. For electrons we question the perfect absorber model and calculate, specifically for a planar dielectric wall, the electron sticking coefficient $s_e$ and the electron desorption time $τ_e$. For the uncharged wall we find $s_e\ll 1$ and $τ_e\approx 10^{-4}s$. Thus, in the early stage of the build-up of the wall potential, when the wall is essentially uncharged, the wall is not a perfect absorber for electrons. For the charged wall we find $τ_e^{-1}\approx 0$. Thus, $τ_e$ approaches the perfect absorber value. But $s_e$ is still only of the order of $10^{-1}$. Calculating $s_e$ as a function of the wall potential and combining this expression with the quasi-stationary balance equations for the electron and ion surface densities we find the selfconsistent wall potential, including surface effects, to be 30% of the perfect absorber value.

physics.plasm-ph↗
arXiv2009

Physisorption kinetics of electrons at plasma boundaries

Plasma-boundaries floating in an ionized gas are usually negatively charged. They accumulate electrons more efficiently than ions which leads to the formation of a quasi-stationary electron film at the boundaries. We propose, in a colloquial manner, a physisorption-inspired quantum-kinetic description of the build-up of surface charges at inert plasma boundaries and calculate the electron sticking coefficient and the electron desorption time, which play an important role in determining the quasi-stationary surface charge, and about which little is empirically and theoretically known, from a microscopic model for the electron-wall interaction. In an exploratory calculation we specifically consider a metallic boundary. But thereby we identify quite generally what we believe are the key issues of the electronic microphysics at inert plasma boundaries in the hope to inspire other groups to join us on our journey.

physics.plasm-ph↗
arXiv2009

Towards a microscopic theory of particle charging

We recently questioned the treatment of a dust particle as a perfect absorber for electrons and ions and proposed a surface model for the charge of a dust particle in a quiescent plasma which combines the microscopic physics at the grain boundary (sticking into and desorption from external surface states) with the macrophysics of the discharge (plasma collection fluxes). Within this model the charge and partial screening of the particle can be calculated without relying on the condition that the total electron collection flux balances on the grain surface the total ion collection flux. Grain charges obtained from our approach compared favorably with experimental data. The purpose of this paper is to describe our model in more detail, in particular, the hypotheses on which it is built, contrast it with the standard charging models based on flux balancing on the grain surface, and to analyze additional experimental data.

physics.plasm-ph↗
arXiv2008

Elementary processes in gas discharges

This chapter presents, from a quantum-mechanical point of view, a tutorial discussion of elementary collision processes in the bulk of a gas discharge. Instead of merely listing kitchen-made cross section formulae and unrelated cross section data, emphasis has been given on an unified description of elementary processes based on general principles of quantum-mechanical multi-channel scattering theory. By necessity, the presentation is rather dense. Technical details left out, as well as cross section data, can be found, respectively, in the quoted original papers and the review articles, monographs, and web-sites mentioned in the introductory remarks to this chapter.

physics.plasm-ph↗
arXiv2006

Excitonic versus electron-hole liquid phases in Tm[Se,Te] compounds

We discuss, from a theoretical point of view, excitonic phases at the pressure induced semiconductor-semimetal transition in $\rm TmSe_{0.45}Te_{0.55}$,focusing, in particular, on the stability against an electron-hole liquid. The electron-hole pair density parameter $r_s(E_g,T)$ is calculated within the quasi-static plasmon pole approximation as a function of temperature $T$ and energy gap $E_g$ and converted into $-E_g(r_s,T)$. A comparison of this quantity, which is the electron-hole pair chemical potential, with the exciton binding energy reveals that excitons should be suppressed in contrast to experimental evidence for excitonic phases. We suspect therefore inter-valley exciton scattering and exciton-phonon scattering to substantially stabilise excitons in $\rm TmSe_{0.45}Te_{0.55}$.

cond-mat.str-el↗
arXiv2006

On the possibility of an excitonic insulator at the semiconductor-semimetal transition

We calculate the critical temperature below which an excitonic insulator exists at the pressure-induced semiconductor-semimetal transition. Our approach is based on an effective-mass model for valence and conduction band electrons interacting via a statically screened Coulomb potential. Assuming pressure to control the energy gap, we derive, in the spirit of a BEC-BCS crossover scenario, a set of equations which determines, as a function of the energy gap (pressure), the chemical potentials for the two bands, the screening wave number, and the critical temperature. We (i) show that in leading order the chemical potentials are not affected by the exciton states, (ii) verify that on the strong coupling (semiconductor) side the critical temperatures obtained from the linearized gap equation coincide with the transition temperatures for BEC of non-interacting bosons, (iii) demonstrate that mass asymmetry strongly suppresses BCS-type pairing, and (iv) discuss in the context of our theory recent experimental claims for exciton condensation in ${\rm TmSe_{0.45}Te_{0.55}}$.

cond-mat.str-el↗
arXiv2005

Semiclassical kinetic theory of electron spin relaxation in semiconductors

We develop a semiclassical kinetic theory for electron spin relaxation in semiconductors. Our approach accounts for elastic as well as inelastic scattering and treats Elliott-Yafet and motional-narrowing processes, such as D'yakonov-Perel' and variable g-factor processes, on an equal footing. Focusing on small spin polarizations and small momentum transfer scattering, we derive, starting from the full quantum kinetic equations, a Fokker-Planck equation for the electron spin polarization. We then construct, using a rigorous multiple time scale approach, a Bloch equation for the macroscopic ($\vec{k}$-averaged) spin polarization on the long time scale, where the spin polarization decays. Spin-conserving energy relaxation and diffusion, which occur on a fast time scale, after the initial spin polarization has been injected, are incorporated and shown to give rise to a weight function which defines the energy averages required for the calculation of the spin relaxation tensor in the Bloch equation. Our approach provides an intuitive way to conceptualize the dynamics of the spin polarization in terms of a ``test'' spin polarization which scatters off ``field'' particles (electrons, impurities, phonons). To illustrate our approach, we calculate for a quantum well the spin lifetime at temperatures and densities where electron-electron and electron-impurity scattering dominate. The spin lifetimes are non-monotonic functions of temperature and density. Our results show that at electron densities and temperatures, where the cross-over from the non-degenerate to the degenerate regime occurs, spin lifetimes are particularly long.

cond-mat.mtrl-sci↗
arXiv2004

Anderson localization in strongly coupled disordered electron-phonon systems

Based on the statistical dynamical mean field theory, we investigate, in a generic model for a strongly coupled disordered electron-phonon system, the competition between polaron formation and Anderson localization. The statistical dynamical mean field approximation maps the lattice problem to an ensemble of self-consistently embedded impurity problems. It is a probabilistic approach, focusing on the distribution instead of the average values for observables of interest. We solve the self-consistent equations of the theory with a Monte-Carlo sampling technique, representing distributions for random variables by random samples, and discuss various ways to determine mobility edges from the random sample for the local Green function. Specifically, we give, as a function of the `polaron parameters', such as adiabaticity and electron-phonon coupling constants, a detailed discussion of the localization properties of a single polaron, using a bare electron as a reference system.

cond-mat.str-el↗
arXiv2003

Cluster meanfield approximation for the optical response of weakly doped semiconductor quantum wells

The calculation of the optical properties of doped semiconductor quantum wells is an intricate many-body problem because of the dynamical response of the excess carriers to the photogenerated valence band hole. At low densities, however, where the main effect of the dynamical response is the formation of trions, a simple cluster meanfield approximation can be effectively employed to calculate the optical susceptibility.

cond-mat.str-el↗
arXiv2002

Magnetic-field dependence of electron spin relaxation in n-type semiconductors

We present a theoretical investigation of the magnetic field dependence of the longitudinal ($T_1$) and transverse ($T_2$) spin relaxation times of conduction band electrons in n-type III-V semiconductors. In particular, we find that the interplay between the Dyakonov-Perel process and an additional spin relaxation channel, which originates from the electron wave vector dependence of the electron $g$-factor, yields a maximal $T_2$ at a finite magnetic field. We compare our results with existing experimental data on n-type GaAs and make specific additional predictions for the magnetic field dependence of electron spin lifetimes.

cond-mat.mtrl-sci↗