Exploring the fundamental limit of CD control: a model for shot noise in lithography

We have made measurements with our Quadra raster shaped beam lithography system to evaluate the shot-noise-induced critical dimension uniformity (CDU). We found that at the isofocal dose, the shot-noise-induced CDU is directly proportional to the edge blur, and is linear with the rate of CD change with dose. Here we propose a phenomenological model which permits an experimentalist to relate the CDU to controllable lithographic parameters. The model considers both the counting statistics of the incident electrons and the noise from the electron induced chemistry. The model suggested that the shot-noise induced CDU may be minimized by reducing the beam blur, forward scattering, through the optimization of the resist smoothing distance and maximizing the number of acid molecules created in the resist by an incident electron. With the proper parameters, this model matches the experimental observations well. It also predicts the limit of the improvements and suggests guides for future resist development. Shot-noise induced line edge roughness is also discussed.