Title: Primitive embeddings for generative modeling in inverse lithography
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: feature embeddings, inverse lithography, generative modeling, primitives, bayesian inference

Abstract: During the manufacturing process of integrated circuits, we require a mask in order to print a certain wafer design. Predicting this mask design is a complex task in the field of inverse lithography. The mapping from wafer to the mask design is ill-posed and requires solving a non-convex optimization task, having multiple potential solutions. Any difference in the setup of the problem (e.g. initialization, patching, or a different discretization scheme) tends to generate inconsistencies. The designed wafer features generally consist of a defined set of basic objects (primitives). Larger features can be built by transforming and aggregating these primitives. Following these observations, we propose a holistic generative approach that utilizes primitive embeddings. We use a model that encodes primitives per type, embeds positional information and then aggregates the feature information. A variational inference approach is then used to take samples of these encodings in the latent space. The samples are transformed by normalizing flows that try to recover the postulated distribution before constructing a mask design. A generative model predicts one of the best mask designs, avoiding inconsistencies and thus allowing for a flexible design approach. Finally we introduce a novel scoring method to fit this probabilistic setup. We assess the performance of this approach for a simplified inverse lithography setup. The main purpose of this study is to investigate the use of primitive modeling in inverse lithography tasks. Although we are not yet able to reach benchmark accuracy within this new setup, results are promising from an application point of view.