Gradient-based optimization for efficient exposure planning in maskless lithography

Scanning laser lithography is a maskless method for exposing photoresist during semiconductor manufacturing. In this method, the energy of a focused beam is controlled while scanning the beam or substrate. With a positive photoresist material, areas that receive an exposure dosage over the threshold energy are dissolved during development. The surface dosage is related to the exposure profile by a convolution and nonlinear function, so the optimal exposure profile is nontrivial. A gradient-based optimization method for determining an optimal exposure profile, given the desired pattern and models of the beam profile and photochemistry, is described. This approach is more numerically efficient than optimal barrier-function-based methods but provides near-identical results. This is demonstrated through simulation and experimental lithography.