Simulation of 3D Electrochemical Phase Formation: Mixed Growth Control

Abstract

Processes of nucleation and growth largely determine the structure and properties of thin films obtained by electrodeposition on foreign substrates. Theoretical aspects of the initial stages of electrochemical phase formation under constant and variable overpotentials are considered in this work. Simulation of multiple nucleation with mixed (charge transfer, and diffusion) controlled growth was performed for three cases (cyclic voltammetry, potentiostatic electrodeposition, and galvanostatic electrodeposition). The influence of the bulk concentration of depositing ions and the exchange current density at the electrolyte/nucleus interface on cyclic voltammograms (CVs), transients of current and overpotential, as well as the number and size of non-interacting new-phase nuclei was analyzed. It is found that, under galvanostatic conditions, the number of nuclei decreases as the concentration of depositing ions increases due to a more rapid decrease in overpotential. The proposed model was applied to determine the diffusion coefficient, exchange current density, and transfer coefficient considering the experimental CV.

Simulation of Diffusion-Controlled Growth of Interdependent Nuclei under Potentiostatic Conditions

“…The electrocrystallization parameter values were close to those for silver electrodeposition from the AgNO 3 -KNO 3 -NaNO 3 melt ( c Ag+ = 0.0166 M) [ 53 ]: T = 523 K, z = 1, υ = 1.7 × 10 −23 cm 3 , σ = 1 × 10 −5 J cm −2 , D = 1 × 10 −5 cm 2 s −1 , c 0 = 1 × 10 19 cm −3 . It was shown experimentally [ 46 , 53 ] and theoretically [ 54 ] for this system that, in a wide range of overpotentials, the rate of the charge transfer stage affects the kinetics of the nucleus growth only at the very initial stage, when the nucleus size is close to the critical one. The contributions of side processes, including surface diffusion, are also negligible [ 53 , 55 ], so this system is the most suitable for studying diffusion-controlled growth.…”

Mechanism and Kinetics of the Phase Formation and Dissolution of NaxWO3 on a Pt Electrode in a Na2WO4–WO3 Melt

“…Comparison with works investigating the influence of various factors (multi-stage process and mixed growth control [59,60,62,63], growth controlled by diffusion in a layer of finite thickness [64][65][66], and the migration effect [67][68][69]) on the current response under potentiostatic or potentiodynamic conditions indicates the need to consider combinations of these effects. Therefore, we used numerical simulation for a more detailed study of the mechanism and kinetics of deposit formation/dissolution in this system.…”

Influence of Macroscale Dimension on the Electrocrystallization of Cu Pad and Redistributed Layer in Advanced Packaging

“…It is worth noting that the macroscale dimension inevitably affects the profile and microstructure when the characteristic size of pattern is decreased to a level comparable to grain size. [16,17] Likely, it has been reported that the fluid fields in the middle and top surface of through silicon vias with different aspect ratios were different even under the same electroplating condition, which eventually led to different filling performances. [18] The difference of filling profile and microstructure induced by the macroscopic dimensions of pattern is called the size effect of electrocrystallization, which has rarely been studied previously.…”