Modeling of shot noise in x-ray photoresist exposure

Abstract

New photoresist technologies yielding higher resist sensitivities together with the greater photon energies inherent in x-ray lithography put lithography systems closer and closer to the shot noise limit. Thus there is a need to address the effects of shot noise on resist exposure. We will present the description of a stochastic model, and its implementation in a simulator, which emulates the exposure process by effecting what amounts to a photon-by-photon treatment of the problem, thereby taking into account the effects of shot noise. The model starts with an aerial image, computed using a deterministic model based on Fresnel diffraction, interprets it as the probability density function (pdf) for the distribution of the photons. The stochasticity of the process is taken into account by randomly generating a finite number of events (photons) whose distribution follows the pdf. The penetration depths are stochastically predicted according to the appropriate distribution. At the point predicted, the incident energy is redistributed according to a point spread function or a full Monte Carlo method. The superposition of all of the photons provides us with the latent image. The dissolution process is then modeled using a stochastic cell dissolution model. We will present results of practical importance for chemically amplified resist systems and correlate the results with observations made in the laboratory.