Non-uniformity of wafer and pad in CMP: kinematic aspects of view

In this paper, we analyze the non-uniformity of sliding distance on both wafer and polishing pad from kinematic point of view. Using the Fourier series expansion, we can show that in steady state the non-uniformity is determined by the ratio between rotary speeds of platen and wafer carrier (m), and the ratio of wafer radius to the distance between the center of platen and wafer (R_c/d). In general, the non-uniformity of wafer increases with |m| and R_c/d. An important observation for polishing pad is that in two particular ranges of the ratio m, the larger R_c/d produces the smaller non-uniformity. Then a ring type polishing pad is proposed for the purpose of improving the non-uniformity of both wafer and pad. However, it turns out that the result is much worse than we expected.