Chemical Mechanical Planarization and Old Italian Violins

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.

Real-Time Shear and Normal Force Trends in Copper Chemical Mechanical Planarization with Different Conditioning Discs

“…With the following equation, frequency becomes order (p). [28][29][30] The order is then the number of events or vibrations per revolution. Since we are normalizing to the speed of the platen, an order of one corresponds to the frequency from the platen.…”

Tribological, Thermal, Kinetic, and Pad Micro-Textural Studies Using Polyphenylene Sulfide Retaining Rings in Interlayer Dielectric Chemical Mechanical Planarization

“…We have coined this companion curve as the "Delta" curve which is represented by plotting directivity (Δ) vs the pseudo-Sommerfeld number on a linear scale. 44 Directivity itself (taken from the science of characterizing old Italian violins, which believe it or not, have many similarities to CMP tools) [45][46][47][48][49][50] is defined as the ratio of measured variances in shear force to variances of normal force at a given polishing PV condition. 44,[51][52][53][54][55] Here, the fluctuating components of shear and normal forces are the key factors and not their absolute values.…”

“…44 Directivity itself (taken from the science of characterizing old Italian violins, which believe it or not, have many similarities to CMP tools) [45][46][47][48][49][50] is defined as the ratio of measured variances in shear force to variances of normal force at a given polishing PV condition. 44,[51][52][53][54][55] Here, the fluctuating components of shear and normal forces are the key factors and not their absolute values. In this case, the ordinate and the abscissa are independent of one another, and because we use linear scales, there are no distortions or optical illusions that would have been caused by the logarithmic scales.…”

Correlating Removal Rate to Directivity in Copper Chemical Mechanical Planarization

“…(12)(13)(14)(15)(16)(17) Previous work has focused on the vibrations that occur in various CMP processes. (12)(13)(14)(15)(16)(17)(18)(19)(20)(21) Fukuroda et al, Hetherington et al, Kojima et al and Rao et al studied vibrations in CMP and found that they could be used as an end-point detection technique for polishing different materials. (18)(19)(20)(21) However, the authors did not correlate the vibrations to RR.…”

“…Of the works that have studied vibrations in CMP, several have focused on Δ's role in the process. (12)(13)(14)(15)(16)(17) Philipossian et al…”