Model-based compensation for thermal position drifts

Variations in environmental temperature conditions during the mask writing process are recognized for their potential to adversely impact the achievable placement precision. A laser writer sequentially exposes the mask area along a stripe-by-stripe writing trajectory. Any time-dependent position drift between the mask coordinate system and the write field centre is recorded along this trajectory. Depending on the inherent time scale of the drift process, the effect on the mask can manifest as a deformation of the stripe itself, a stripe displacement, or a global grid error. In this study, we present a model-based compensation method that predicts thermal position drifts based on temperature sensor readings. The approach has been implemented in a proof-of-concept study on an ULTRA mask writer system, leveraging two essential hardware features. Firstly, the common capability of laser mask writers to function as a placement metrology tool through the same lens as in exposure mode. Secondly, the standard system has been equipped with additional, suitably positioned precision temperature sensors. By combining these features, we create a time series database of synchronous placement error and temperature readings that allows us to train a predictive drift model. Once the model is trained, it can be operated in real-time compensation mode during placement metrology or exposure to counteract thermal drifts.