The Shear Force Law: A Guide to Modeling CMP Removal Rates

Abstract

A new theory is presented that generalizes the classical version of Preston’s Law in chemical-mechanical planarization (CMP). The approach is motivated by removal rate data that cannot be explained by the classical version. The theory begins by observing that when removal rates are plotted against the measured wafer frictional shear force, the data often lie on or near half-lines that emanate from a common intercept on the removal rate axis. The half-lines have slopes that are indexed by polishing speed. While the common intercept might be interpreted as a static etch rate, evidence suggests that it may be due mainly to compliant pad fragments generated by conditioning. An extension of the new model outside of the experimental design using a Stribeck curve is found to explain the puzzling non-Prestonian removal rate trends. It also suggests an explanation for some frequently observed removal rate pressure thresholds. Finally, the new theory predicts that it is possible to scale the pressure and speed in CMP to obtain a desired scaling of the removal rate without changing the friction coefficient. The approach has been successfully applied to several recent metal and dielectric polishing processes that use a variety of consumables.