Three-state lithography model: An enhanced mathematical approach to predict resist characteristics in grayscale lithography processes
Background: Physical modeling of grayscale lithography processes for the prediction of photoresist heights leads to complex mathematical algorithms. A promiment example is the numerical simulation of the photoresist shape after development through Dills equations. These grayscale lithography models exhibit accurate prediction quality but can not directly implemented into mask layout tools to simplify the layout procedure. Limited process windows, changes in the mask design, variations of the used materials or manufacturing tools lead to time-consuming and cost-intensive test procedures to adjust the photoresist model for sufficient results. Aim: The focus of this work is to enhance current grayscale lithography models for a straightforward method with the same precise prediction of remaining photoresist heights to simplify the mask layout process. Moreover, we aim for an uncomplicated optimization of the model to minimize the empirical analysis necessary for its use. Approach: Based on experimental results, we deploy a sectionally defined mathematical expression that includes the theory of Fraunhofer diffraction and illumination-dependent activation of the photo-sensitive component and its solubility in developer. Results: We produced pyramidal, spherical and chess field structures with exposure doses of 3000 and 15,000 J/m2 on bare silicon substrates with 100-nm resolution and on silicon substrates with antireflective coatings, with accuracy as fine as 20 nm. Conclusion: The proposed three-state lithography model has been verified by experimental evaluation. It is able to operate in a wide process window and can be directly implemented in existing mask layout software. This model ensures a cost-efficient and precisely controlled production of three-dimensional topographies using grayscale lithography processes.