Modified Preston Equation- Revisited
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"Centerfor Advanced Materials Processing, Clarkson University, Potsdam, NY-13699. ABSTRACT The effect of pressure and velocity on the polish rates of copper was determined in DI water and in the presence of ferric nitrate, H 20 2/glycine, and NH 4 OH with alumina particles as the abrasives. The polish rate shows a stronger dependence on velocity than that predicted by the Preston equation in the case of ferric nitrate, a highly reactive chemical. The velocity dependence is weaker for the other two less reactive chemicals, and is the same as that predicted by Preston equation for DI water. Our earlier empirical model, R = KPV + BV + Rc, where K, B, and Rc are constants, describes all the polish rate data satisfactorily. INTRODUCTION The effect of pressure and velocity on the removal rate of oxide and metal films in a chemical-mechanical polish process has been widely investigated. Yet, there is no consensus and several different theoretical models have been proposed. Most of them take the form R = KPaVb (-2), where R denotes the polish rate, K is a proportionality constant, P is the applied downward pressure, V is the velocity, and a and b are constants that take fractional values between 1/3-1. When a and b are both equal to 1, this equation becomes the Preston equation3 , well known in optical glass polishing industry. Liu et. al., 4 modeled the wear mechanism during chemical-mechanical polishing (CMP) and reported the Preston equation to be valid for polishing of Si0 2 films. However, Zhao and Shi5 reviewed the polish rate dependence on pressure and velocity and argued that the relative hardness of the pad with respect to the wafer and the abrasive particles plays a crucial role. It is suggested that Preston's equation, with its linear dependence on pressure and velocity, is applicable only when the hardness of the polishing pad is similar to or higher than that of the
abrasives or the surface being polished. They show how the rate dependence on pressure can become sub-linear if the pads are softer and derive a value of 2/3 for the exponent a based on the contact area between an asperity and the wafer surface. Furthermore, according to them, while polishing with such soft pads, the abrasive particle can slide and cause appreciable material removal only when the applied pressure exceeds a threshold value. Since in a typical CMP process in silicon device manufacturing, the pads are always softer than the films being planarized, they argued that Preston equation needs to be modified for describing the polish rate dependence on pressure. Indeed, they were able to fit the pressure dependence of the measured polish rates for Si0 2, Cu and Al reported by several authors using a non-zero threshold pressure and a value of a = 2/3. In all these derivations, the role of the slurry chemicals during the polish process is not apparent. Even under static conditions, some of the chemicals can dissolve the material as in the case of ferric nitrate and copper or even H 20 2/glycine and copper. This effect can, in principle, be ea
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