Parameter Sensitivity Analysis of Monte Carlo Simulations of Copper Electrodeposition with Multiple Additives

Monte Carlo simulations are typically characterized by a large number of unknown parameters, many of which are difficult to obtain experimentally. Parameter sensitivity analysis can be used to quantify the effect of the unknown parameters. This information can be used to decide which parameters should be optimized or determined more accurately through further experimental or simulation studies. The parameter sensitivity analysis for Monte Carlo simulations is complicated by the stochastic nature of the simulations, making it difficult to isolate responses from background noise. In the present study, a stochastic optimization problem was formulated and solved, which produced a first-order accurate equation for computing the sensitivities that optimally accounts for the simulation noise. This new approach for computing sensitivities for stochastic simulations significantly increases the accuracy over existing methods. The approach is illustrated by application to a Monte Carlo code that simulates copper electrodeposition from a sulfate bath onto a flat copper substrate in the presence of a three-additive system of chloride, polyethylene glycol, and mercapto propane sulfonic acid.