Estimation of Kinetic Parameters of Additives By Semi-Analytical Solution

Abstract

The electrodeposition of Cu and other metals is an essential step in the interconnect fabrication, 3-D integration, and various packaging technologies. Such electrodeposition processes are enabled by a group of organic additives. Furthermore, strong agitation is often used to expedite the electrodeposition rate when the processing time becomes critical for large features, which however introduces non-uniform mass transport within a single feature and between different features. A numerical description of how organic additives behave in conjunction with external flow at various feature geometry and dimensions is a challenging task, but much needed for chemistry and process development. Among the various requirements, the additive behavior or their electrochemical impacts on Cu deposition needs to be precisely described.This talk reports an effort to obtain the numerical parameters that describe the additive behaviors during Cu deposition on rotating disc electrodes (RDE). A one-dimensional semi-analytical model is developed for Cu electrodeposition from a two-component additive system. The steady-state mass transport differential equations of each chemical species, including diffusion and convection, are solved analytically at different potentials, while the boundary conditions at the RDE surface are coupled with each other through the surface coverages of adsorbed species. The steady state of such surface coverage results from a dynamic equilibrium between three co-existing processes, adsorption, desorption and incorporation (consumption), namely, Adsorption Rate – Desorption Rate – Consumption Rate = 0 A set of solutions, including the concentration profile of each species in electrolyte as well as the surface coverage of each adsorbate, can be obtained at a fixed potential. The equations are first solved considering only the suppressor for a range of over-potential. It was found that, for a specific range of voltages and kinetic parameters, multiple non-trivial solutions of surface coverage exist. In other words, multiple steady states exist at a same applied potential. As shown in Figure 1, this translates to a S-shaped negative differential resistance (NDR) feature in cyclic voltammogram (CV), consistent with experimental observation reported in literature. The numerically calculated NDR region was found sensitive to the additive concentration and therefore extremely useful in determining the electrochemical parameters using multiple experimental datasets with different concentrations. The swarm optimization algorithm used for parameter fitting and the correlation between multiple numerical solutions with the NDR region will be discussed in details in the talk. Figure 1