Research On Pixel-based Mask Optimization Method In Optical Lithography

Mask optimization(MO) technique can enhance the resolution of optical lithography and enable that using the present lithography machine can manufacture chip with smaller feature size. Pixel-based MO method discretizes mask pattern as a raster image constituted by grids, and the light transmittance of each grid is characterized as a gray-scale pixel; it synthesizes mask pattern by optimizing each pixel's value. In practical applications, pixel-based MO method encounters many technical challenges, which can be categorized as follow:(1) Mask manufacturability problem, the synthesized mask pattern usually posses a lot of small, unwanted block objects which extremely increase the manufacture cost and some of are even unreachable during real manufacturing.(2) Robustness problem, with ever shrinking feature size, the printed feature of mask gets increasingly sensitive to the fluctuation of the process parameters, mainly defocus and exposure dose variation; this causes a narrow process window and limits the yield.(3) Computational efficiency problem, a state-of-the-art processor chip contains billions of transistors; the mask pattern is extremely dense and its optimization process is extraordinary time-consuming.In order to address these three problems, this dissertation carries out research on pixel-based MO method, and uses benchmark logic circuit patterns to test and verify the proposed methods. The main contents of this dissertation are as follow:A new criterion for judging mask imaging quality, named edge distance error(EDE), is defined. EDE has the dimension of length and has a closed-form formula with respect to mask; thus it is intuitive and efficeient to guide the mask synthesis.A filtering-based mask regularization method is proposed. This method interprets the gray-level transitions and small, unwanted block objects, as unwanted noises in mask, and employs a filter to remove these noises to satisfy manufacturing constraints. In optimization process, this filter is directly incorporated with mask in the cost function, and can result in a smooth and close-to-binary mask pattern effectively. Besides, the proposed method enhances the manufacturability of each intermediate mask.The impacts of process variations and their distribution on synthesized mask pattern are investigated. At first, a process variations-aware lithography forward model is derived; then the statistical model for robust MO is built, and the filtering-based mask regularization method is generalized for this robust optimization framework. From the simulation, the robustness of synthesized mask against the process parameters fluctuation is demonstrated, and the impacts of process variations distribution on synthesized mask pattern are analyzed.The numerical solution method for pixel-based MO is developed, and a cascadic multigrid(CMG) algorithm is proposed. The optimization direction and the iterative step size are sufficiently derived, and PRP conjugate gradient and quasi-optimal step are introduced. CMG algorithm achieves more than four times speedup compared to the conventional methods that synthesize mask on a fixed fine grid.In summary, this dissertation explores the difficulties of pixel-based MO faced in practical applications, and proposes corresponding solutions. These works enrich the mask synthesis theory in optical lithography, and potentially augment the current portfolio of techniques used for driving the limit of optical lithography.