Proximity correction for e-beam lithography

摘要

Abstract: As the critical dimensions required for masks and e-beam direct write become ever smaller, the correction of proximity effects becomes more necessary. Furthermore, the problem is beset by the fact that only a positive energy dose can be applied with the e-beam. We discuss here approaches such as chopping and dose shifting which have been proposed to meet the positivity requirement. An alternative approach is to treat proximity correction as an optimization problem. Two such methods, local area dose correction and optimization using a regularizer proportional to the informational entropy of the solution, are compared. A notable feature of the regularized proximity correction is the ability to correct for forward scattering by the generation of a 'firewall' set back from the edge of a feature. As the forward scattering width increases, the firewall is set back further from the feature edge. The regularized optimization algorithm is computationally time consuming using conventional techniques. However, the algorithm lends itself to a microelectronics integrated circuit coprocessor implementation which could perform the optimization much faster than even the fastest work stations. Scaling the circuit to larger number of pixels is best approached with a hybrid serial/parallel digital architecture which would correct for proximity effects over 10$+8$/ pixels about one hour. This time can be reduced by simply adding additional coprocessors. !26