Optimization in the Photolithography Bay: Scheduling and the Traveling Salesman Problem

In a semiconductor factory, integrated circuits (or chips) are constructed on top of slabs of silicon, called wafers. The construction of these wafers is complicated and many different processing steps are needed to gradually building the chip layer by layer. Of these steps, photolithography uses the most expensive equipment. Therefore, the photolithography equipment is often the bottleneck of the factory. Photolithography is used to transfer the geometric pattern of a chip on a wafer. First a light-sensitive photoresist is put on the wafer. ThenUV light is sent through a photomask on the photoresist. The exposed parts of the photoresist will chemically react, creating the pattern. After the exposure, chemical reactions and metal depositions make a layer of circuits on the wafer. In this thesis, we try to increase the production of the semiconductor factory by reducing the time needed for the photolithography. In the first part, we look at themachine level. The time to process a wafer on a lithography steppermachine is determined by different elements of the process (Chapter 2). It turns out that the blade movement required in the exposure step has a significant impact total time required to process a wafer. The blade movement in turn depends on the order in which the different images are processed. Hence we want to find an ordering of the images, such that the blade movement is minimized. This problem turns out to be equivalent to the a priori traveling salesmen problem in the scenario model. The practical problem instances found are solved a limited amount of time using an integer linear programming solver and the average blade movement is reduced by approximately 20%, which reduces the average exposure time 1.6%.