Evolution of metal-compound residues on the walls of plasma etching reactor and their effect on critical dimensions of high-k/metal gate

It was found that critical dimensions of high-k/metal gates obey the multivariate linear approximation with the precision of 3σ=±0.86nm, whose explanatory variables are amounts of metal compounds remaining on the plasma reactor walls. To measure their amounts, the authors assumed they are proportional to amounts of atoms sputtered out by Ar plasma and falling onto a Si wafers placed on a wafer stage. In this study, effects of metal compounds of W, Ti, Ta, and Hf, which are used to construct full-metal/high-k gates, were measured. It was found that Ti and Ta compounds dominate the fluctuation of critical dimensions and the dependency of their amount on wafer numbers being etched obeys a simple difference equation. From these results, they can estimate and minimize the fluctuations of critical dimensions in mass fabrications.