Marius Chemla

Vacancy pairs and correlation effects in kCl and NaCl single crystals

Abstract We compare the self-diffusion coefficients, respectively determined with radioactive tracers and from the ionic conductivity, in the intrinsic range of pure KCl and NaCl single crystals. The correlation effect and the vacancy pair effect originate deviations between both values. The vacancy pair effect is successfully measured by studying the influence of divalent anions and divalent cations on the self-diffusion coefficients in KCl. We derive the value of the correlation factor f = 0.75 ±0.04, which provides a direct experimental verification of the correlation theory ( f = 0.78). The whole set of the recent measurements of transport processes and isotope effects in NaCl are reexamined by considering this value for the correlation factor. We derive the whole set of properties of the free and associated vacancies in NaCl and KCl.

Transport, Relaxation, and Kinetic Processes in Electrolyte Solutions

I: Basic Concepts.- 1.1 Introduction.- 1.1.1 Ions in solution.- 1.1.2 Diffusion current.- 1.1.3 Electric current.- 1.2 Systems in Thermodynamic Equilibrium.- 1.2.1 Equilibrium conditions.- 1.2.2 Chemical potential.- 1.2.3 Chemical equilibrium.- 1.3 Electrolyte Solutions.- 1.3.1 Mean concentration and mean activity coefficient.- 1.3.2 Electrochemical potential.- 1.3.3 Ionic equilibria in solutions.- 1.4 Preliminary Remarks on Transport Processes.- II: Coupled Processes and Chemical Reactions in Solutions.- 2.1 Continuity Equations.- 2.2 Mass Conservation.- 2.3 Constitutive Equations.- 2.4 Solutions of the Basic Transport Equations.- 2.5 Normal Modes.- 2.5.1 Relaxation modes.- 2.5.2 Migration modes.- 2.5.3 Diffusion modes.- 2.5.4 Series expansion of normal modes.- 2.5.5 Mutual diffusion.- 2.6 Coupled Diffusion.- 2.6.1 Diffusion coefficients.- 2.6.2 Coupled diffusion.- 2.6.3 Normal mode analysis without ion pairing.- III: Hydrodynamic Properties.- 3.1 Introduction.- 3.2 General Aspects of Hydrodynamics.- 3.3 Inviscid Fluids.- 3.3.1 Time derivative of velocity.- 3.3.2 Eulers equation.- 3.3.3 Bernoullis relation.- 3.3.4 Vorticity.- 3.4 Viscous Incompressible Fluids.- 3.4.1 Preliminary remarks.- 3.4.2 Microscopic origin of viscosity.- 3.4.3 Equation of motion of a viscous liquid.- 3.4.4 Dynamic similarity and Reynolds number.- 3.5 Stokes Approximation.- 3.5.1 Flow due to a moving sphere at small Reynolds numbers.- 3.5.2 Velocity field around a sphere.- 3.6 Hydrodynamic Interactions of Moving Spheres.- IV: Excess Quantities.- 4.1 Distribution and Correlation Functions.- 4.2 Debye-Huckel Limiting Law.- 4.3 Activity Coefficients.- 4.3.1 System of hard spheres.- 4.3.2 Ions in solution.- 4.4 Chemical Model.- 4.5 Electrolyte Solutions at Moderate to High Concentrations.- 4.5.1 Cluster expansion of the pair-correlation function.- 4.5.2 Ornstein-Zernike equation.- 4.5.3 Integral equation methods.- 4.5.4 Mean spherical approximation.- 4.6 Hydrodynamic Interactions.- V: The Role of Ion Aggregation and Micelle Formation Kinetics in Diffusional Transport of Binary Solutions.- 5.1 Diffusional Transport of Symmetrical Electrolytes.- 5.2 Some Remarks on the Diffusional Transport of Symmetrical Electrolytes.- 5.2.1 Role of activity coefficients.- 5.2.2 Relaxation to local equilibrium.- 5.2.3 Relaxation to local electroneutrality.- 5.2.4 Relaxation of an electroneutral fluctuation of electrolyte concentration.- 5.3 Diffusional Transport of Unsymmetrical Electrolytes.- 5.3.1 Continuity equations and their transformations.- 5.3.2 Case of one ionic complex and no solvation-desolvation process.- 5.3.3 Case of two ionic complexes and one solvation-desolvation process.- 5.3.4 Three ionic complexes and two solvation-desolvation processes.- 5.4 Monomer-Micelle Exchange in Micelle Diffusion.- 5.5 Concluding Remarks.- VI: Diffusion, Migration and Chemical Reactions in Electrolyte Solutions beyond Ideality.- 6.1 Introduction.- 6.2 Electrolyte Conductance.- 6.3 Apparent Ionic Charge.- 6.3.1 Electrolyte conductance and self-diffusion.- 6.3.2 Relaxation effect.- 6.3.3 Electrophoretic effect.- 6.3.4 Apparent charge at Debye-Huckel and CM level.- 6.3.5 Apparent charge at MSA level.- 6.4 Experimental Contributions to the Apparent Charge Concept.- 6.4.1 Solutions of completely dissociated electrolytes.- 6.4.2 Solutions of associated electrolytes.- 6.4.3 Polyelectrolyte solutions.- 6.4.4 Coupled diffusion of polyelectrolytes.- 6.5 Solutions of Complex Electrolytes.- 6.5.1 Fast exchange reactions.- 6.5.2 Slow exchange reactions.- 6.6 Electrophoretic Transport and Exchange Reactions.- 6.6.1 Transport equations.- 6.6.2 Data analysis.- 6.6.3 Electrophoretic transport pattern.- VII: Relaxation. Processes in High Frequency Electromagnetic Fields.- 7.1 Fundamental Equations.- 7.2 Electric Polarization.- 7.2.1 Electric polarization of nonconducting liquids at low frequencies.- 7.2.2 Electric polarization of nonconducting liquids at high frequencies.- 7.2.3 Polarization at optical frequencies.- 7.3 Response Functions and Relaxation Times.- 7.3.1 Step-response function and pulse-response function.- 7.3.2 Molecular response function.- 7.3.3 Relaxation times and relaxation time distributions.- 7.4 Relaxation Processes in Solvents and Their Electrolyte Solutions.- 7.4.1 Relaxation processes in pure solvents and solvent mixtures.- 7.4.2 Influence of ions on solvent relaxation times.- 7.4.3 Relaxation processes of ion pairs.

Electrochemical and Radiochemical Study of Copper Contamination Mechanism from HF Solutions onto Silicon Substrates

The mechanism of copper contamination of silicon wafers from dilute HF solutions containing ultratrace levels of metallic ion impurities, was investigated using a new electrochemical cell, which proved to act as a very efficient sensor for in situ characterization. Upon copper contamination, the open-circuit potential was observed to shift rapidly toward more positive values at a rate nearly proportional to the copper concentration. All potential/time curves tend to reach a plateau, while quantitative measurements using radioactive tracers revealed that during a few tens of minutes, copper ions were continuously reduced on the silicon surface. Results are interpreted in terms of the mixed-potential theory and lead to the conclusion that copper nuclei act as a catalyst which enhances the cathodic activity for proton reduction. The model was supported by atomic force microscopy observations which showed the initiation of corrosion pits around the nuclei.

p‐ and n‐Type Silicon Electrochemical Properties in Dilute Hydrofluoric Acid Solutions

After a systematic study of the factors influencing the electrochemical characteristics of the silicon/HF solution junction, we have obtained reproducible and reliable values of the electrochemical kinetic parameters of the interface. One of the features of this system is that the corrosion reaction. on anodic and cathodic sites is equivalent to two redox reactions, one at the energy level of the conduction band, the other at the level of the valence band. Then, we supported the assumption that the junction with Si can be treated by the electrochemical model. Data have been obtained using n- and p-type silicon with different doping levels, in contact with deoxygenated or oxygen-saturated 5% HF aqueous solution, in the dark and under illumination. The electrochemical reaction kinetics are expressed as a corrosion rate in atom cm -2 s -1 for different Si substrates.

Anion diffusion mechanism in strontium chloride single crystals

Abstract Simultaneous measurements of the anion self-diffusion coefficient and of the ionic conductivity have been carried out in the intrinsic range (440–630°C) of pure Sr Cl 2 single crystals. The microtome sectioning method using the radiotracer 36 Cl has been successfully applied to this difficult matrial. Accurate values of the correlation factor have thus been derived by applying the Nerst-Einstein relation. Results suggest that the Frenkel defects are predominant in the anion sub-lattice with the enthalpy and entropy of formation of 2.98 eV and 22 K, respectively. The chloride anions diffuse via the vacancy mechanism to which is added to a lesser extent an exchange mechanism where the ions successively occupy lattice and interstitial sites.

Isotope effect of diffusion of 22Na+24Na+ in NaCl, KCl and KBr single crystals

Abstract Accurate measurements of the diffusion coefficient and isotope effect for diffusion of Na + have been carried out in the intrinsic range of NaCl, KCl and KBr single crystals. The technique which led to the more reliable results is described. This is based on the simultaneous use of the differences between the half-life times and the energy spectra of γ-radiation of the isotopes 22 Na and 24 Na after diffusion into two adjacent samples. In NaCl, the isotope effect is found to vary very little with temperature around the mean value 0·75, while the isotope effect decreases from 0·68 at 772°C down to 0·44 at 574°C in KCl, and from 0·64 at 693°C down to 0·52 at 601°C in KBr. Comparison of the vacancy pair contributions to the self-diffusion of Na + and Cl − [1] in NaCl is attempted. Comparison of the isotope effect in the different matrixes shows an influence of the relative ion sizes in agreement with the theory of Le Claire[2].

Kinetics of electrochemical corrosion of silicon wafers in dilute HF solutions

Abstract An extensive experimental study of the factors influencing the electrochemical characteristics of the silicon/DHF junction has been undertaken, and leads to reproducible and reliable values of the electrochemical kinetics of the corrosion reactions. The usual model of electron and hole transfers between a semiconductor and an electrolyte solution should include an additional term due to the generation of h+ and e− charges resulting from the dual redox reactions on anodic and cathodic sites. Then, in a narrow range of potential near the corrosion conditions, the classical Butler-Volmer electrochemical equations apply. The values of open circuit voltage and corrosion current have been obtained using n- and p-type silicon with different doping levels, in contact with deoxygenated or oxygen-saturated DHF solution, in the dark and under illumination. These data were used to characterize the electrochemical reaction kinetics leading to the corrosion rate expressed in atoms per square centimeter per second of different Si substrates. In addition, we derived an estimation of the exchange current density of the hydrogen evolution reaction on the Si surface.

Corrosion Rate of n‐ and p‐Silicon Substrates in HF, HF + HCl, and HF + NH 4 F Aqueous Solutions

A research program was initiated in order to investigate the electrochemical corrosion of n- and p-type silicon substrates in 0.25 M dilute HF solutions, and the influence of fluoride ions or proton additives. All experiments were conducted in both the dark and under constant light flux, with solutions thoroughly degassed by high purity argon bubbling. Polarization resistance measurements near an open-circuit potential lead to the value of the corrosion current, while scanning the potential in the range of anodic and cathodic reactions permitted evaluation of the kinetics of charge transfer as a function of the majority carriers density in the semiconductor and the ionic composition of the solution. The influence of these parameters on the surface roughness of the silicon samples was also examined by ex situ atomic force microscopy profile measurements.

Diffusion of Impurity Ions in Ionic Crystals. Treatment of the Diffusion Equations for Concentration Dependent Diffusion Coefficients

The equations for the diffusion of divalent ions into alkali halide crystals have been investigated for the case where the thermally produced vacancies and the vacancies added by the impurity are both to be taken into account. The concentration dependence on the diffusion coefficient is then given by D(C)=Dsα C[1+(1+2β/C2)(1+4β/C2)−1/2, where Ds, α, and β are constants at constant temperature. Ficks second law is numerically treated for the initial conditions of the thin deposited layer. The diffusion profiles calculated for trial values of the specific activity of 45Ca are in good agreement with the experimental profiles of diffusion of Ca+ + into NaCl single crystals.

Electrochemical test for silicon surface contamination by copper traces in HF, HF+HCl and HF+NH4F dilute solutions

The electrochemical open circuit potential response described in a previous publication proved very efficient for the study of silicon wafer contamination by copper traces from HF solutions containing 20 to 800 ppb Cu2+ ions. In pure 0.5% DHF, copper nuclei were immediately generated at the silicon surface. In the same conditions, when the solutions contained 0.5% DHF+HCl 1 M, no electrochemical response was observed leading to the conclusion that silicon contamination was greatly inhibited. Upon NH4 F 1 M addition to the 0.5% DHF solution, the surface seems to be transiently contaminated and then tends to be partly cleaned. Further studies, of surface contamination, using radioactive 64 Cu as tracer, confirmed that HCl addition to HF solutions was efficient to generate an extremely passive silicon surface and supported the conclusions derived from the free potential measurements.