Thermal modeling of photomask precision baking system

Baking processes are widely acknowledged as being crucial steps in Photomask manufacture, and in particular, the Post-Exposure Bake (PEB) is regarded as the most critical. For 45nm-node Photomasks, and subsequent technology generations, the performance requirements for baking systems significantly exceed those of currently-available equipment. In comparison with Silicon Wafers, Photomask substrates, (typically 6inch square quartz), exhibit markedly different thermal properties. These differences conspire to make Photomask precision baking far more difficult than is the case for wafers. Multi-zone heating systems have been developed, and in principle offer a practical tuning method allowing better surface temperature uniformity of Photomasks during critical bake steps to be achieved. The best of these systems compensate, to some extent, for multiple causes of temperature non-uniformity within the baking system. Generally however, the root causes of temperature non-uniformity in the baking process have not all been identified, still less eliminated, and thus there remains a limit to the degree of control of Photomask surface temperature which can be achieved. In this study, we devised a "Thermal model" of the Photomask baking process. This model has enabled us to identify root causes of non-uniformity of Photomask surface temperatures, as well as providing a quantitative way of assessing how Photomask baking systems may be improved. We present simulation results from the model, as well as actual test data measured by sensor array plate.