Abstract
Spin-on processing is used in many industries to deposit very thin coatings on flat substrates, including silicon wafers, flat-panel displays, and precision optical components. A liquid precursor solution is first dispensed onto the surface of the substrate; this fluid then spreads out very evenly over the surface due to large rotational forces caused by spinning of the substrate. When looking for an optimum coating procedure process engineers can adjust many variables including the peak spin speed, the ramping rate to reach that speed, the spinning time, as well as allowing for dynamic solution dispense before ramping up, though most protocols focus on the peak spin speed as the primary controlling variable. Engineers often construct spin-speed versus thickness correlations that enable predictable adjustment of spin-speed to achieve a desired thickness. Yet, rather little attention has been paid to the importance of the acceleration rate used to reach the desired peak speed. We show here that ramping rate is also important in helping establish the final coating thickness. We present a numerical model of the fluid flow on a spinning wafer when the spin-speed is ramping linearly up to a desired peak speed and then held constant. It is shown that the coating may “set” into its final thickness before the spin-speed reaches its peak value. In these cases then the peak spin-speed parameter is no longer the primary variable that defines the final coating thickness. This also impacts the interpretation of critical exponents found when fitting spin-speed vs. thickness data. We perform parallel experimental measurements for different ramping-up times and confirm the results from the numerical model. Both experimental and theoretical results support use of the simplified model put forth by Meyerhofer over 25 years ago (J. Appl. Phys. 49 (1978) 3993-3997).