Chemical Mechanical Planarization and Old Italian Violins

Previous studies have shown that spectral analysis based on force data can elucidate fundamental physical phenomena during chemical mechanical planarization (CMP). While it has not been literally described elsewhere, such analysis was partly motivated by modern violinmakers and physicists studying Old Italian violins, who were trying to discover spectral relations to sound quality. In this paper, we draw parallels between violins and CMP as far as functionality and spectral characteristics are concerned. Inspired by the de facto standard of violin testing via hammer strikes on the base edge of a violin's bridge, we introduce for the first time, a mobility plot for the polisher by striking the wafer carrier head of a CMP polisher with a hammer. Results show three independent peaks that can indeed be attributed to the polisher's natural resonance. Extending our study to an actual CMP process, similar to hammered and bowed violin tests, at lower frequencies the hammered and polished mobility peaks are somewhat aligned. At higher frequencies, peak alignment becomes less obvious and the peaks become more isolated and defined in the case of the polished wafer spectrum. Lastly, we introduce another parameter from violin testing known as directivity, Δ, which in our case, we define as the ratio of shear force variance to normal force variance acquired during CMP. Results shows that under identical polishing conditions, Δ increases with the polishing removal rate.