Microelectronic Engineering 70 (2003) 478–488 www.elsevier.com / locate / mee Inverse analysis of material removal data using a multiscale CMP model a, b a c a * Jongwon Seok , Andrew T. Kim , Cyriaque P. Sukam , Anurag Jindal , John A. Tichy , c c Ronald J. Gutmann , Timothy S. Cale a Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180-3590, USA b Texas Instruments Inc., Dallas, TX 75243, USA c Focus Center - New York, Rensselaer: Interconnections for Gigascale Integration, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA Abstract This paper describes a mechanical model for a representative dual axis rotational chemical mechanical planarization (CMP) tool. The model is three-dimensional, multiscale and includes sub-models for bulk pad deformation, asperity deformation, lubrication based slurry flow, carrier film deformation, wafer compliance and material removal by abrasive particles in the slurry. With the model, material removal rate (MRR) can be determined as a function of stress applied to the wafer, relative sliding speed, and material and geometric parameters of the pad and slurry. Experimental material removal rate profiles obtained from Cu polishing experiments performed on a wafer without rotation are analyzed as an inverse problem. We use MRR data to predict local CMP conditions such as fluid film thickness, fluid pressure and contact pressure. The results are consistent with available experimental and analytical information. This inverse technique offers promise as an improved method of CMP model verification.  2003 Elsevier B.V. All rights reserved. Keywords: Chemical mechanical planarization; Elastohydrodynamics; Multiscale modeling; Contact stress analysis; Inverse problem 1. Introduction load, wafer and pad velocities, pad and slurry physical properties, and operating conditions affect In commonly used chemical mechanical planariza- the global and local polishing (material removal) tion (CMP) processes, material removal is accom- rates and uniformities. MRR is also affected by the plished by pressing a rotating wafer into a relatively chemical reactivity of the slurry [1], the materials to soft, porous, rotating pad, while an abrasive slurry is be polished [2], and various details such as patterns continuously fed onto the pad. Material removal rate on the wafer surface [3]. (MRR) during CMP depends on mechanical effects Though widely used in industry, and with a large (abrasion) and chemical effects. The applied normal body of empirical results, the CMP process has not been well modelled. This is largely because it involves complicated solid–solid and solid–fluid *Corresponding author. Tel.: 11-518-276-8003; fax: 11-518- interactions [4] that induce boundary lubrication [5], 276-8761. E-mail address: seokj@alum.rpi.edu (J. Seok). accompanied by unclarified wear mechanisms [6] at 0167-9317 / 03 / $ – see front matter  2003 Elsevier B.V. All rights reserved. doi:10.1016 / S0167-9317(03)00365-4