Stable Growth and Kinetic Roughening in Electrochemical Deposition

Abstract

We studied kinetic roughening of copper which was electrodeposited at slow rates. The surfaces showed a unique scaling. In the shorter length regime, the interface width scaled with the length scale L as L (u = 0.87~0.05). In the longer length regime, the width scaled with the deposition time t as t~( P = 0.45~0.05). The value of a + a/P, 2.8, is much larger than 2 predicted for the case where the growing direction is normal to the surface everywhere.The scaling behavior is interpreted as the result of enhanced growth of the protrusions owing to nonlocal Laplacian growth effect. PACS numbers: 68.55.Jk, 05.70.Ln, 68.70.+w, 82.65.Dp Surface roughness of growing films on Aat substrates has been shown to exhibit scaling behavior over large variations of length scales, and thus considerable interest [1,2] has been recently directed to the physics of dynamic scaling. Theory [1,3) predicts that the interface width (the mean surface height fluctuation) W(L, t) for length scale L and growth time t scales as W(L, t)~L, for L (( L, ,Z = cr/P. (4) The scaling behavior is equivalent to scale invariance of the surface height deviation from the average plane at point x and t, h(x, t): The statistical properties of h(x, t) coincides with those of b h(bx, b't), where b is an arbitrary rescaling factor [2].In many growth processes, growth is determined solely by the local conditions at the growing site such as reaction rates, surface relaxation rates, and stochastic noise. Kardar, Parisi, and Zhang (KPZ) [3] studied such growing surfaces based on a nonlinear Langevin continuum equation using renormalization-group techniques. The ballistic deposition model [4, 5] and Eden growth model [6] are believed to belong to the same universality class as the KPZ growth, and many theoretical and numerical simulation studies have been done [1,2]. For the KPZ type local growth model, the value of a is predicted to be 0.4 (Ref. [2]) for a planar substrate and the surface is compact and self-affine. On the other hand, in a nonlocal growth process called Laplacian growth, the motion of the growing interface is controlled by a fieldlike quantity (e.g., concentration of a diffusing particle and electric potential) which satisfies the Laplace equation. In this case, deposition occurs preferentially on protrusions. This causes an instability, known as the Mullins-Sekerka instability [7], which can often lead to much rougher bulk-fractal (self-similar) structures where a -1. Surface growth in physical systems is likely to have both local and nonlocal growth effects.Electrochemical deposition is an ideal system for studying the competition between these growth processes because the local and the nonlocal growth effects can be controlled by changing the growth conditions [8,9]. Deposition near the mass-transfer-limited current condition [10] corresponds to diffusion limited growth and leads to unstable morphologies such as fractal and densebranching morphologies, which have been studied extensively [9, 11, 12]. At slow growth rates, the growth is control...

Growth equation with a conservation law

“…Furthermore, one can speculate whether some growth experiments, which yield exponents that do not agree with the KPZ exponents, may contain nonlocal growth effects such as, e.g., the experiments on electrochemical deposition reported in Refs. [8,9].…”

“…(a) Diagrammatic representation of the GKE equation (9). (b) The vertex λ which includes integration over (q, Ω).…”

Effect of Morphology and Hydrogen Evolution on Porosity of Electroplated Cobalt Hard Gold

“…Similar trends were observed in nickel hard gold plating onto copper substrate 19 and in other electroplated metal systems. 20 In a connector application, a surface with faceted features results in a substantial increase in the contact resistance, making it an unacceptable candidate for good connectors. Thus, the optimal plating condition must be able to avoid that.…”

“…A high atomic percentage of hydrogen, about 6.9%, 15 has been found in the deposit. The presence of hydrogen in gold deposit is in the form of hydrogen gas trapped in the voids due to the low solubility of hydrogen in the gold lattice.16 From these facts, the hypothesis that the pores are a result of hydrogen bubbles 8 seems reasonable.To elucidate key factors of porosity formation, we conducted a systematic study on deposits from constant current ͑dc͒ and pulse plating [16][17][18][19][20] conditions. We emphasize the impact of morphology and hydrogen evolution rate on porosity.…”

“…To elucidate key factors of porosity formation, we conducted a systematic study on deposits from constant current ͑dc͒ and pulse plating [16][17][18][19][20] conditions. We emphasize the impact of morphology and hydrogen evolution rate on porosity.…”