Comprehensive modeling of the lithographic errors in laser direct write

Patterns written by laser direct write have a critical dimension (CD) bias dependence on the dose similar to other direct write methods, such as electron beam lithography, which can be explained by the exposure intensity distribution (EID) of the laser beam. In this study, a comprehensive model based on the EID is proposed to understand the pattern CD bias dependence on the dose, which is known as the exposure latitude. This model was supported by the results of the exposure tests on MicroChem S1800 resist on an Si wafer using the Heidelberg DWL66+ laser writer. The exposure latitudes of the patterns at both micrometer and submicrometer scale were measured. At the micrometer scale, the exposure latitudes were found to have no measurable dependence on the pattern size and the local pattern density. This conclusion does not hold at the submicrometer scale where the length scale is comparable to the width of the laser beam. This study proposes a way to convert the experimental exposure latitude data into the EID functions and fit these functions by assuming a Gaussian laser beam intensity distribution. All empirical observations are found to agree with the predictions made by the EID model. The authors also show that this model can help achieve dimensional accuracy, especially when there is a change in the exposure process. Moreover, it can be used to analyze and minimize the CD inconsistency between different runs found in the experiments. To reduce such inconsistency, overexposing combined with a negative bias applied to the pattern is suggested.