Estimating the optimum dose for arbitrary substrate materials based on Monte Carlo simulated point spread functions

摘要

In electron beam lithography (EBL), determining the optimum exposure dose is a key factor for a successful exposure when using a new substrate or changing the acceleration voltage. It is well known that the optimum dose in EBL depends on the exposed material stack as well as the energy of the injected electrons. An experimental dose calibration is usually necessary to establish the optimum process conditions for new materials. In this study we will calculate the optimum dose employing simulations and attempt to verify the results experimentally. Monte Carlo simulations were performed in order to determine the point-spread function (PSF) for a set of commonly used substrate materials. The optimum dose for each of the material stacks was calculated by comparing the simulated PSFs. Numeric integration of the individual PSFs was used to determine the total energy deposited in a specific layer of the resist. The ratio of the total energies is equal to the ratio of the optimum doses. To verify our calculation results experimentally, we exposed dose calibration tests using contrast curves and device patterns. The tests were repeated on different substrates with different material properties to determine the range of validity of our method. A comparison of the calculated and measured optimum doses is presented, showing a good agreement in the range of 10% except for samples suffering from heavy charging. This limitation might be explained by the neglect of charging effects in the simulation model. It was shown that Monte Carlo simulations can be used to calculate the optimum doses for new substrate materials which reduces the need for extensive experimental dose calibration, saving time and cost. (C) 2016 Elsevier B.V. All rights reserved.