Method for compensating pattern placement errors caused by variation of pattern exposure density in a multi-beam writer

A method for compensating pattern placement errors during writing a pattern on a target in a charged-particle multi-beam exposure apparatus including a layout generated by exposing a plurality of beam field frames using a beam of electrically charged particles, wherein each beam field frame has a respective local pattern density, corresponding to exposure doses imparted to the target when exposing the respective beam field frames. During writing the beam field frames, the positions deviate from respective nominal positions because of build-up effects within said exposure apparatus, depending on the local pattern density evolution during writing the beam field frames. To compensate, a displacement behavior model is employed to predict displacements; a local pattern density evolution is determined, displacements of the beam field frames are predicted based on the local pattern density evolution and the displacement behavior model, and the beam field frames are repositioned accordingly based on the predicted values.