Nonuniformity of Wafer and Pad in CMP: Kinematic Aspects of View

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we analyze the nonuniformity of sliding distance on both the wafer and polishing pad from a kinematic point of view. Using the Fourier series expansion, it can be shown that in steady state the nonuniformity caused by contact relative velocity is determined by rotational speed ratio between platen and wafer carrier <formula formulatype="inline"><tex>$(m)$</tex></formula> and the ratio of wafer radius to the distance between the platen center and wafer center <formula formulatype="inline"><tex>$({R_c/d})$</tex></formula>. In general, the nonuniformity of wafer increases with <formula formulatype="inline"> <tex>$\vert m\vert$</tex></formula> and <formula formulatype="inline"><tex>$({R_c/d})$</tex> </formula>. An important observation for the polishing pad is that in two particular ranges of the ratio <formula formulatype="inline"><tex>$m$</tex> </formula>, larger <formula formulatype="inline"><tex>$({R_c/d})$</tex></formula> on the contrary yields smaller nonuniformity. Then, a ring-type polishing pad is proposed for the purpose of improving the nonuniformity of both wafer and pad. However, it turns out the result for the pad of large size is worse than the traditional shape, unless the rotational speed of the pad is much slower than that of the wafer. </para>