Abstract
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.
Highlights
Introduction and MotivationFor the past 450 years, the one thousand or so surviving instruments made by the Cremonese master luthiers such as Andrea Amati (1505–1577), Antonio Stradivari (1644–1737) and BartolomeoGuiseppe Guarneri del Gesù (1698–1749) have entertained listeners worldwide
We focus on the subject of chemical mechanical planarization (CMP) and how the mechanical and kinematic aspects of the process may analytically and functionally relate to the Micromachines 2018, 9, 37; doi:10.3390/mi9010037
The mobility plot of arguably one of the greatest surviving violins, the “Plowden” Guarneri del Gesù (1735) is shown in Figure 1a as replotted by us using raw data provided by Zygmuntowicz [38] and based on tests performed by Bissinger and Oliver [16]
Summary
For the past 450 years, the one thousand or so surviving instruments made by the Cremonese master luthiers such as Andrea Amati (1505–1577), Antonio Stradivari (1644–1737) and Bartolomeo. Fabricating each layer causes severe topography, which in order to achieve the needed depth for focus requirements, has to be made more or less optically flat prior to forming any subsequent layers above it To achieve such planarized wafer surfaces, CMP was invented and used in manufacturing by International Business Machines (IBM) in the mid-1980s [24]. In a CMP process, much like violin playing, as the wafer, the slurry nano-particles and the pad make physical contact with one another, multiple high-frequency stick-slip events are created that cause vibrations within the wafer-slurry-pad-polisher system. These vibrations are manifested in the form of fluctuations of shear and normal forces during polishing. Our present study continues to explore a combination of the unique spectral fingerprinting methods noted above, to demonstrate that certain well-established violin characteristics and test methods have counterparts in CMP
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