Transport Phenomena in Chemical Mechanical Polishing

Chemical mechanical polishing (CMP) is currently being used in the fabrication of integrated circuits and has been identified as an enabling technology for the semiconductor industry in its drive toward gigabit chips and subquartermicron feature sizes in the near future. At the present time, it appears that the global planarization necessary for establishing reliable multilevel interconnects can only be achieved by using CMP. As with any process with such potential commercial impact, the technology has moved forward into production even though a complete model based on first principles is nonexistent. In the long run, the availability of such models will help optimize the operation of CMP and permit the user to define the best operating conditions for each specific application. Our objective in this article is to present a model which deals with some crucial transport phenomena issues in CMP. In a typical CMP tool, the wafer is mounted on a suitable device and is held above a polishing pad made of a porous polymeric material. In the case of smaller wafers, it is common to mount more than one wafer on a holder called a polishing head. The pad and the wafer holder can be rotated at specified rates while pressing the wafer against the pad surface by applying a load which can be varied. A liquid is distributed over the pad and occupies the space between the wafer and the pad when the equipment is operated. The liquid contains a colloidal suspension of abrasive particles such as alumina or silica as well as specific chemicals chosen for polishing. In another type of tool, the pad moves linearly on a belt while the wafer is pressed against it, but the idea is the same, namely, that relative motion occurs between the wafer and the pad in the presence of a liquid containing abrasive particles. The state of the literature on the modeling of CMP in the semiconductor field is reviewed by Nanz and Camilletti. 1 A review of CMP in glass polishing is provided by Cook, 2 who discusses the mechanism by which material is removed. Cook suggests that polishing occurs due to softening of the glass surface by the chemicals with subsequent removal of this softened layer by the particles through abrasion. The abrasive process is described using a model of a sphere imbedded to a certain depth into a surface by the application of a load, with the particle gouging out material from the surface in proportion to this depth. One key aspect of this picture is that the rate of removal is proportional to the product of the relative velocity between the two surfaces and the applied pressure, leading to an equation which is traced to Preston 3 and which is currently used in the industry for describing the rate of removal of silicon dioxide. Also, the amount removed is independent of the size of the abrasive particles in this picture. The Preston equation is used to describe overall removal rates, but cannot account for higher removal rates from elevated surfaces, which is the basis of planarization. Also, it is seen from the present work that when transport