Effect of Additives on Shape Evolution during Electrodeposition: II. Parameter Estimation from Roughness Evolution Experiments

Abstract

Numerical analysis procedures are used to identify the most sensitive parameters and estimate their values based on experimental measurements and a hypothesized mechanism for the effect of additives on copper electrodeposition. The electrolysis system consists of an acid copper sulfate bath containing accelerator, suppressor, and leveler additives in the range of concentrations typically used for deposition of on-chip wiring interconnections. Experimental measurements, obtained with an impinging jet apparatus, included surface roughness evolution and potential-time curves under constant current deposition in a set of 36 electrolyte compositions, selected by a D-optimal design procedure. The hypothesized additive mechanism consisted of a set of 15 surface reactions and 3 homogeneous chemical reactions. A mathematical model was composed that couples kinetic Monte Carlo simulation (for roughness evolution) with a finite volume method (for computing surface concentrations and potential). After identifying the most sensitive parameters and estimating their values, the surface concentrations of key species associated with the additive mechanism were simulated. The methods reported here are reusable and may be applied to other applications beyond the copper electrodeposition used here for its initial development.