Diffusion layer thickness reduction

Figure 2.86 Schematic representation of variation in the diffusion layer thickness, 6, as a function of time for the reduction of an oxidant O at a fixed planar electrode. [O ] is the concentration of O in the bulk of the solution, [O]0, is the concentration at the electrode surface, x is the distance into the solution from the electrode surface, and du etc, are the diffusion layer thickness at various times etc.

Figure 2.IW The variation in the concentrations of O and R with distance, x, from the electrode surface for the electrochemical reduction O + e " -+ R, EO]0 and [RJt) are the concentrations of the species at the electrode surface and is the diffusion layer thickness.

Although electroless deposition seems to offer greater prospects for deposit thickness and composition uniformity than electrodeposition, the achievement of such uniformity is a challenge. An understanding of catalysis and deposition mechanisms, as in Section 3, is inadequate to describe the operation of a practical electroless solution. Solution factors, such as the presence of stabilizers, dissolved O2 gas, and partially-diffusion-controlled, metal ion reduction reactions, often can strongly influence deposit uniformity. In the field of microelectronics, backend-of-line (BEOL) linewidths are approaching 0.1 pm, which is much less than the diffusion layer thickness for a... 

The metal ion in electroless solutions may be significantly complexed as discussed earlier. Not all of the metal ion species in solution will be active for electroless deposition, possibly only the uncomplexed, or aquo-ions hexaquo in the case of Ni2+, and perhaps the ML or M2L2 type complexes. Hence, the concentration of active metal ions may be much less than the overall concentration of metal ions. This raises the possibility that diffusion of metal ions active for the reduction reaction could be a significant factor in the electroless reaction in cases where the patterned elements undergoing deposition are smaller than the linear, or planar, diffusion layer thickness of these ions. In such instances, due to nonlinear diffusion, there is more efficient mass transport of metal ion to the smaller features than to large area (relative to the diffusion layer thickness) features. Thus, neglecting for the moment the opposite effects of additives and dissolved 02, the deposit thickness will tend to be greater on the smaller features, and deposit composition may be nonuniform in the case of alloy deposition. 

Figure 14 shows a schematic representation of a mixed potential diagram for the electroless deposition reaction. Oxidation of the reductant, in this case hypophos-phite, is considered to be under 100% kinetic control. A mixed kinetic-diffusion curve is shown for the reduction of the metal ion, in our case Co2+, in the region close to the mixed potential, Em. Thus, since Co deposition occurs under a condition of mixed kinetic and diffusion control, features small relative to the diffusion layer thickness for Co2+ will experience a higher concentration of the metal ion, and hence... 

Adsorbed additives also tend to undergo reduction during the electroless process, and become incorporated as impurities into deposits, most likely via a mechanism similar to that involved in ternary alloy deposition. In a manner similar to that discussed below in greater detail for dissolved 02, electroless deposition rates will be lower for features smaller than the stabilizer diffusion layer thickness. The edges of larger features, which experience higher stabilizer levels due to enhanced nonplanar... 

As discussed earlier, it is generally observed that reductant oxidation occurs under kinetic control at least over the potential range of interest to electroless deposition. This indicates that the kinetics, or more specifically, the equivalent partial current densities for this reaction, should be the same for any catalytically active feature. On the other hand, it is well established that the O2 electroreduction reaction may proceed under conditions of diffusion control at a few hundred millivolts potential cathodic of the EIX value for this reaction even for relatively smooth electrocatalysts. This is particularly true for the classic Pd initiation catalyst used for electroless deposition, and is probably also likely for freshly-electrolessly-deposited catalysts such as Ni-P, Co-P and Cu. Thus, when O2 reduction becomes diffusion controlled at a large feature, i.e., one whose dimensions exceed the O2 diffusion layer thickness, the transport of O2 occurs under planar diffusion conditions (except for feature edges). 

Here F is the Faraday constant C = concentration of dissolved O2, in air-saturated water C = 2.7 x 10-7 mol cm 3 (C will be appreciably less in relatively concentrated heated solutions) the diffusion coefficient D = 2 x 10-5 cm2/s t is the time (s) r is the radius (cm). Figure 16 shows various plots of zm(02) vs. log t for various values of the microdisk electrode radius r. For large values of r, the transport of O2 to the surface follows a linear type of profile for finite times in the absence of stirring. In the case of small values of r, however, steady-state type diffusion conditions apply at shorter times due to the nonplanar nature of the diffusion process involved. Thus, the partial current density for O2 reduction in electroless deposition will tend to be more governed by kinetic factors at small features, while it will tend to be determined by the diffusion layer thickness in the case of large features. 

Although separate determination of the kinetic and thermodynamic parameters of electron transfer to transient radicals is certainly important from a fundamental point of view, the cyclic voltammetric determination of the reduction potentials and dimerization parameters may be useful to devise preparative-scale strategies. In preparative-scale electrolysis (Section 2.3) these parameters are the same as in cyclic voltammetry after replacement in equations (2.39) and (2.40) of Fv/IZT by D/52. For example, a diffusion layer thickness S = 5 x 10-2 cm is equivalent to v = 0.01 V/s. The parameters thus adapted, with no necessity of separating the kinetic and thermodynamic parameters of electron transfer, may thus be used to defined optimized preparative-scale strategies according to the principles defined and illustrated in Section 2.4. 

Reduction of the solution temperature allows transition from steady-state to peak-shaped response simply by way of the marked diminution of D at low temperatures. Figure 16.5 shows slow-scan cyclic voltammograms obtained at two microdisk electrodes as a function of solution temperature. Between -120 and -140°C there is a particularly clear transition for the 25-pm-diameter electrode as the diffusion-layer thickness becomes less than the disk radius. Also illustrated here is the immense decrease in the limiting currents that is seen over this range of temperatures due to the 100-fold decrease in D. 

The cathodic reaction during corrosion of iron in sea water is oxygen reduction. Solubility of 02 from the air in sea water is 0.189 mol m 3 and the diffusion coefficient of 02 is 2.75 x 10 9 m2 s 1. The diffusion layer thickness in an unstirred solution is about 0.5 mm. (a) Estimate the corrosion current density of iron in sea water, (b) If iron is connected to the negative pole of an external... 

If the potential applied to the electrode is sufficiently negative (reduction) or positive (oxidation), all the electroactive species that reach the electrode will react and we obtain the limiting current, /L, whatever the value of the standard rate constant, k0. The relation between the limiting current and the diffusion layer thickness, <5, is... 

In the general case, the logarithmic analysis of the wave is a curve with two asymptotes. For the reduction, the slope of the asymptote at higher potential is 0.059/n V, while the slope of the asymptote at lower potentials is 0.059/an V. The half-wave potential depends on the drop life-time, or the diffusion layer thickness. The electrode reactions with these characteristics are called - quasireversible. 

Fig. 38 The reduction of 0.5 mM 3-bromobenzophenone in DMF/0.1 M (C4H9)4NC104 solution at a 3-mm diameter glassy carbon disc electrode, (a) Cyclic voltammogram measured under silent conditions at a scan rate of 50 mV s . (b)-(d) Sonovoltam-mograms obtained with 25 W cm" intensity ultrasound at 27, 15 and 8 mm horn-to-electrode separations respectively, (e) Plot of sonovoltammetric limiting currents vs the reciprocal diffusion layer thickness. The solid lines show the theoretical expected behaviour for simple one- and two-electron processes respectively whilst the dotted line corresponds to that for an ECE mechanism with a rate constant of 600 s . ...

Figure 4-7 Concept of electrochemical reaction increasing the diffusion layer thickness (concentration polarization) of analyte via a reduction (or oxidation) at the surface of the working electrode. As time (t) increases, the diffusion layer thickness grows quickly to a value that is determined by degree of convection in the sample solution.

In electroanalysis, electrodes of millimeter dimensions are termed millielec-trodes, while the more recently developed very small area electrodes of micron dimensions are termed microelectrodes there are differences in properties beyond simply the change of dimension. Thus in millielectrode-scale experiments the enhancement of the diffusion-limited current plateau has been observed by a number of other workers—for example, in the reduction of methylviologen in aqueous acetonitrile [32], in the oxidation of bis(cyclopentadienyl) molybdenum dichloride in acetonitrile [33], as well as in several other studies on the aqueous ferrocyanide/ferricyanide couple using wire or disc millielectrodes to study diffu-sional phenomena [34—36], Typical values of the diffusion layer thickness of approximately 5 pm are found under ultrasound [35] in contrast to the normal value of approximately 500 pm in silent conditions. 

The effect of various ultrasonic fields on the yield and rate of electrochemical processes in the oxidation of Fe2+ to Fe3+, Fe(CN)g to Fe(Cn)g, and Cr3+ to Cr4+ are also reported [141]. Percentage yields and current efficiencies for these reactions were studied at a cd of 0.25 A/mm2 with and without ultrasound at frequencies of 15,25, and 200 kHz. It was found that ultrasound always accelerated the process and increased current efficiencies dramatically. The authors found the optimum ultrasonic frequency to be 25 KHz, and also confirmed that ultrasound raised the limiting-current density considerably, causing a reduction of the diffusion layer thickness and therefore increasing the efficiency of the electrolytic reaction. 

The droplet height varied between 400 and 1100 pm. The local corrosion rates were determined by EIS and electrochemical polarization measurements. An increase in corrosion rate was observed with decreasing electrolyte thickness below 800 pm. The increase of the corrosion rate was due to the decrease of the diffusion layer thickness, resulting in an increase in oxygen reduction rate. 

E3.10. Calculate the limiting current density for oxygen reduction in an alkahne solution if the oxygen concentration is 0.4 mol/m, the diffusion coefficient, D02, is equal to 5.0 x 10 vc /s, and the diffusion layer thickness is 195.3pm. 

Consider the reduction of a species O at a cathode O + ne R. Once electrolysis of species O begins, its concentration at the electrode surface, Cq(x = 0) becomes smaller than the value Cq in the bulk solution (far from the electrode). This simplified treatment is based on the idea that a stagnant layer of thickness Sq exists at the electrode surface (Nernst diffusion layer), with stirring maintaining the concentration of O at Cq beyond x = 5q as shown Fig. 2.8. In the figure, x = 0 corresponds to the electrode surface and 8q is the diffusion layer thickness, and concentration profiles are shown at two different electrode potentials. The rate of mass transfer is proportional to the concentration gradient at the electrode surface and can be expressed as ... 

The changes of electrolyte concentration cause the changes of surface charge and consequently the thickness of diffusion layer. The reduction of this layer favours the coagulation (Fig. 5.17). 

Figure 5.3 Current-potential dependence of a diffusion limited reduction process (deposition of Ag, c = 10 mol-dm D = 1.6 X 10 cm s ), diffusion limited currents on a rotating-disc electrode, corresponding diffusion layer thicknesses...

The principal way to eliminate the diffusion term is reduction of the diffusion layer thickness. Under stationary condition this is achieved by enforced convection. For non-stationary conditions one can describe the increasing diffusion contribution by a time-dependent diffusion layer thickness. 

A great many model systems that have been studied by electroanalytical methods are available for comparison with sono-voltammetric measurements. The reduction of halogenated aromatic compounds is known to cause in many cases the cleavage of the carbon halide bond with a first-order rate constant determined by the properties of the molecule. From the known range of accessible diffusion layer thicknesses in sonovoltammetry, ca. 1-15 xm, unimolecular rate constants ranging from 10 to 10" s are accessible. The reduction of 3-bromobenzophenone and ortho-bromonitrobenzene in DMF [66] may be described by the ECE type mechanism given in Eqs. 7(a-d). 

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