Darken's equation and other diffusion relations in the light of atomistic kinetic concepts

Maser, K.

doi:10.1007/s100080050186

Cited by 9 publications

(9 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here means the jump distance of the dopant particles. Provided that their probability distribution is only a function of but is independent of position, concentration, and so forth, it leads to [34] ( ,…”

Section: Einstein's Deduction Of Fick's Lawmentioning

confidence: 99%

“…Non-Fickian phenomena of dopant transport in solids have to be considered on the base of a more generic approach like the concept of occupiable sites for dopant species (dopantoccupiable or DOCC-sites concept, resp.) [34]. This atomistic kinetic framework considers dopant migration in solids as discrete jumps of dopant particles via distinct sites instead of assuming a continuous course of solid-state diffusion.…”

Section: Non-fickian Migration Of Dopants In Solidsmentioning

confidence: 99%

“…In [34,37] the transport of dopant particles via point defects in a cubic lattice is considered in detail. The relationship for the dopant particle flux density comprises four components:…”

Section: Non-fickian Migration Of Dopants In Solidsmentioning

confidence: 99%

“…Although silicon oxide is not crystalline in the narrower sense, [38] presents results showing that a transition from the crystalline into the amorphous phase proceeds at the SiO 2 /Si interface via the crystalline or ordered phase of SiO 2 . is the dopant DOCCsite neighborhood constant, which is designated as in original papers [34,37]. The dopant jump rate describes the probability of the jumping process for a preferential dopant particle to jump into the neighboring lattice plane within a considered time interval.…”

Section: Non-fickian Migration Of Dopants In Solidsmentioning

confidence: 99%

See 3 more Smart Citations

A Self-Consistent Model for Thermal Oxidation of Silicon at Low Oxide Thickness

Gerlach

Maser²

2016

Advances in Condensed Matter Physics

View full text Add to dashboard Cite

Thermal oxidation of silicon belongs to the most decisive steps in microelectronic fabrication because it allows creating electrically insulating areas which enclose electrically conductive devices and device areas, respectively. Deal and Grove developed the first model (DG-model) for the thermal oxidation of silicon describing the oxide thickness versus oxidation time relationship with very good agreement for oxide thicknesses of more than 23 nm. Their approach named as general relationship is the basis of many similar investigations. However, measurement results show that the DG-model does not apply to very thin oxides in the range of a few nm. Additionally, it is inherently not self-consistent. The aim of this paper is to develop a self-consistent model that is based on the continuity equation instead of Fick’s law as the DG-model is. As literature data show, the relationship between silicon oxide thickness and oxidation time is governed—down to oxide thicknesses of just a few nm—by a power-of-time law. Given by the time-independent surface concentration of oxidants at the oxide surface, Fickian diffusion seems to be neglectable for oxidant migration. The oxidant flux has been revealed to be carried by non-Fickian flux processes depending on sites being able to lodge dopants (oxidants), the so-called DOCC-sites, as well as on the dopant jump rate.

show abstract

Section: Einstein's Deduction Of Fick's Lawmentioning

confidence: 99%

Section: Non-fickian Migration Of Dopants In Solidsmentioning

confidence: 99%

“…In [34,37] the transport of dopant particles via point defects in a cubic lattice is considered in detail. The relationship for the dopant particle flux density comprises four components:…”

Section: Non-fickian Migration Of Dopants In Solidsmentioning

confidence: 99%

Section: Non-fickian Migration Of Dopants In Solidsmentioning

confidence: 99%

See 2 more Smart Citations

A Self-Consistent Model for Thermal Oxidation of Silicon at Low Oxide Thickness

Gerlach

Maser²

2016

Advances in Condensed Matter Physics

View full text Add to dashboard Cite

show abstract

“…3 Despite this effort, current knowledge of diffusion in liquid metals is limited and far from satisfactory. [4][5][6] One of the main reasons for this situation is the lack of accurate and consistent diffusion data. 7 To briefly summarize, there are two common techniques to measure diffusion coefficients in liquid metals: the long capillary (LC) and shear cell (SC) methods.…”

Section: Introductionmentioning

confidence: 99%

A sliding cell technique for diffusion measurements in liquid metals

Geng¹,

Zhu²,

Zhang³

2014

AIP Advances

View full text Add to dashboard Cite

The long capillary and shear cell techniques are the usual methods for diffusion measurements in liquid metals. Here we present a new “sliding cell technique” to measure interdiffusion in liquid alloys, which combines the merits of these two methods. Instead of a number of shear cells, as used in the shear cell method, only one sliding cell is designed to separate and join the liquid diffusion samples. Using the sliding cell technique, the influence of the heating process (which affects liquid diffusion measurements in the conventional long capillary method) can be eliminated. Time-dependent diffusion measurements at the same isothermal temperature were carried out in Al-Cu liquids. Compared with the previous results measured by in-situ X-ray radiography, the obtained liquid diffusion coefficient in this work is believed to be influenced by convective flow. The present work further supports the idea that to obtain accurate diffusion constants in liquid metals, the measurement conditions must be well controlled, and there should be no temperature gradients or other disturbances.

show abstract

Voltammetry of Electroactive Oil Droplets. Part II: Comparison of Experimental and Simulation Data for Coupled Ion and Electron Insertion Processes and Evidence for Microscale Convection

et al. 2000

View full text Add to dashboard Cite

Modelling electrochemical processes at the three phase junction between electrode–aqueous electrolyte–oil droplet presents a considerable challenge due to the complexity of simultaneous electron transfer between electrode and droplet, ion uptake or expulsion between droplet and aqueous phase, the interaction of redox centers at high concentration, and transport processes accompanying the electrochemical process. For the case of oxidation of para‐tetrahexylphenylenediamine (THPD) microdroplet deposits on basal plane pyrolytic graphite electrodes or random arrrays of microelectrodes (RAM) three models may be envisaged which proceed via A) exchange of ions between droplet and aqueous electrolyte with the electrochemical process commencing at the electrode–oil interface, B) rapid electron transport over the oil–aqueous electrolyte interface and the electrochemical process commencing from the oil–aqueous electrolyte interface inwards, and C) slow electron transport across the oil–aqueous electrolyte interface and the electrochemical process commencing solely from the triple interface. Numerical simulation procedures for these three models, which allow for interaction of redox centers via a regular solution theory approach, are compared with experimental data. A positive interaction parameter, Z=1.4, consistent with a dominant ionic liquid–ionic liquid and neutral oil–neutral oil type interaction is determined from experimental data recorded at sufficiently slow scan rates. The overall mechanism, which governs the voltammetric characteristics at higher scan rates, is shown to be apparently consistent with the triple interface model C). However, the rate of diffusional transport determined by comparison of experimental with simulation data is orders of magnitudes too high. Additional convection processes, possibly of the Marangoni type, appear to be responsible for the fast rate observed for the redox process. The significance of the models presented in the context of microdroplet deposits for other related electrochemical systems is discussed.

show abstract

Darken's equation and other diffusion relations in the light of atomistic kinetic concepts

Cited by 9 publications

References 3 publications

A Self-Consistent Model for Thermal Oxidation of Silicon at Low Oxide Thickness

A Self-Consistent Model for Thermal Oxidation of Silicon at Low Oxide Thickness

A sliding cell technique for diffusion measurements in liquid metals

Voltammetry of Electroactive Oil Droplets. Part II: Comparison of Experimental and Simulation Data for Coupled Ion and Electron Insertion Processes and Evidence for Microscale Convection

Contact Info

Product

Resources

About