Defining and measuring development rates for a stochastic resist: a simulation study

Abstract

Photoresist development rate can be defined microscopically (the development rate at a point) or macroscopically (the propagation rate of an average resist height). In the presence of stochastic noise, these two rates will be different. In order to properly calibrate lithography simulators, the difference between these two definitions of development rate should be quantified. Using theoretical derivations and a stochastic (Monte Carlo) development simulator, the propagation rate of a resist surface is characterized in the presence of stochastic variation in the resist deprotection concentration and a nonlinear development rate response. The resulting propagation rate (macroscopic development rate) can be more than an order of magnitude higher than for the case of no stochastic noise. Correlation in the development rate creates an effective surface inhibition over a depth into the resist proportional to the correlation length, with results that are qualitatively different for two-dimensional versus three-dimensional simulations. The differences between microscopic and macroscopic dissolution rate can have an important effect on how development rate models should be calibrated, depending on their use in continuum or stochastic lithography simulators.