The Monte Carlo method is widely used to simulate the signal from a scanning electron microscope. Although the results closely match the actual signal, the method is inherently slow due to the repeated calculation of random trajectories. The authors re-examine the alternative approach of using an approximate model to describe the signal. The authors develop a progressive approximate model which describes the spatial probability distribution of an electron along its entire path. The model also includes information about the angular and energy distribution of the electron. The model is compared to the Monte Carlo method by determining the yield of backscattered electrons as the beam is scanned across a step feature. For this simple feature the model-based approach computes the signal approximately two orders of magnitude faster. (C) 2007 American Vacuum Society.