About this note
A plain-language summary of the 3 publications listed under this topic on Academic Publications (Topic-wise). Full citations are under References.
Why this matters
Microlithography is the process used to print circuit patterns onto silicon wafers when making microchips and MEMS devices (micro-electro-mechanical systems such as tiny sensors and actuators). A wafer is coated with a light-sensitive polymer film called a photoresist, exposed to a pattern of ultraviolet light, and then baked so that a chemical reaction fixes the pattern before the unwanted resist is washed away. Several bake steps occur along the way, each followed by chilling the wafer back to room temperature.
The modern resists used in this process are chemically amplified: the reaction speeds up only beyond a threshold temperature, so they are very sensitive to how fast the wafer heats and to how uniform its temperature is. Small temperature differences across a 300 mm wafer show up as variations in the critical dimension, the width of the smallest feature printed, and so in the quality of the chips. Heat transfer design of the bake equipment is therefore a manufacturing problem with tight tolerances.
What we did
This line of work began in industry. While at the Microlithography Division of FSI International in Texas, we worked with Natarajan Ramanan on a new combination bake-chill station (Narasimhan and Ramanan, 2004). Conventional stations bake wafers on a heavy aluminium hotplate and then move them by robot to a separate chill plate. The new design used a thin, low thermal mass bake plate to hold the wafer during both steps. To bake, the bake plate is separated from a massive chill plate below it; to chill, the two are brought into contact, a switch that takes from a fraction of a second to a couple of seconds. We built an axisymmetric model and a three-dimensional model of the station and solved the flow and energy equations with the commercial software Fluent, then compared the predictions with measurements from a wafer carrying 42 temperature sensors. A companion paper presented the full thermal analysis of the station, including how mechanical features of the bake plate disturb the wafer temperature and how to correct for them (Narasimhan, 2005).
At IIT Madras, with Satish Karra, we took up a question these studies had only touched on: how to make the heater surface itself nearly isothermal (of uniform temperature) during the post-exposure bake (Narasimhan and Karra, 2006). Heat leaks away from the top and sides of a disc heater by convection, so a uniform heat input from below leaves a temperature difference across the top surface, an imprint of which passes to the wafer. Rather than asking what temperatures a given heat input produces, we asked the inverse question: what distribution of heat input produces the most uniform surface temperature? This is an inverse heat transfer problem. To keep it affordable, we split the bottom of a 300 mm heater into just two zones, an inner and an outer ring, each with its own heat flux, and studied the effect of where the split is placed. We solved the problem numerically and also with a scale analysis from first principles.
What we found
Thermal agility. The simulations and experiments confirmed that the combination station can switch quickly between bake set points. For a 120 °C bake, the wafer reached the set point in about 30 s, and even at 250 °C it did so within 30 to 40 s of a 90 s bake, which the low thermal mass of the bake plate makes possible (Narasimhan and Ramanan, 2004).
Uniformity. The temperature difference across the wafer fell below 0.2 °C after about 60 s of baking and approached 0.1 °C by the end of the bake, meeting the industry standard. The three-dimensional model showed that protruding “ears” of the bake plate acted as heat sinks and caused circumferential non-uniformity, which could be removed by varying the heat load around the bake plate (Narasimhan, 2005). In experiments, the controller held the bake set point within 0.02 °C (Narasimhan and Ramanan, 2004).
Productivity. Because three robot moves per wafer were eliminated, handler capacity rose by more than 15%, and at high throughput (150 wafers per hour) cluster productivity improved by about 7 to 9% (Narasimhan and Ramanan, 2004).
Two-zone heating. The smallest achievable surface temperature difference decreases as the split between the zones moves outward. There is a critical split radius below which the inner zone needs no power at all, and the scale analysis predicted this radius in excellent agreement with the simulations. The critical radius does not depend on the set point temperature, only on the convection heat loss at the heater edge. When the edge heat transfer coefficient exceeds about 100 W/m²K, the critical radius approaches the heater edge, and two zones are no longer enough; several radial zones would then be needed (Narasimhan and Karra, 2006).
Related
References
- Narasimhan, A and Karra, S., (2006), “An Inverse Heat Transfer Method to Provide Near-Isothermal Surface for Disc Heaters used in Microlithography”, Int. J. Heat and Mass Transfer, 49, 4624 – 4632. [DOI 10.1016/j.ijheatmasstransfer.2006.04.019]
- Narasimhan, A., (2005), “Thermal Analysis of a Silicon Wafer Processing Combination Bake-Chill Station used in Microlithography”, Materials and Manufacturing Processes, 20, 1-14. [DOI 10.1081/AMP-200042048]
- Narasimhan, A. and Ramanan, N., (2004), “Simulation Studies and Experimental Verification of the Performance of a Combination Bake-Chill Station”, J. Microlithography, Microfabrication and Microsystems, 3(2), 1537-1646. [DOI 10.1117/1.1668269]