Monte Carlo simulation of spatially distributed beams in electron-beam lithography

The spatial distribution of energy deposited in a thin polymer film of polymethyl methacrylate (PMMA) by a laterally distributed electron beam is simulated with Monte Carlo calculations. The Monte Carlo simulation includes the significant contribution from electrons that are backscattered from the substrate (Si) into the film. Equienergy density contours (eV/cm3) are calculated for specific cases of beam voltage, film thickness, beam width, and beam‐edge slope. A time‐dependent solubility model is also incorporated to simulate the time evolution of the developed contours. A size effect is observed; i.e., the development time for a line depends on the line width. This intraproximity effect is ascribed to electrons backscattered from the substrate.