Non-linear dose- and blur-dependent edge placement correction

Method for calculating a pattern to be exposed on a target by means of a charged-particle multi-beam writing apparatus, said apparatus exposing a multitude of pixels (px) within an exposure region (r1) on the target to generate said pattern by means of a scanning stripe exposure, wherein the pattern is realized as a pixel graphic composed of a plurality of pixels defined in accordance with a raster grid on the exposure region (r1), wherein each of said pixels is represented by a geometric pixel shape located at a respective pixel position and is assigned an intensity value corresponding to a value of exposure dose to be exposed for the respective pixel, the method comprising the steps of:

• (i) providing a vector pattern as a number of pattern elements, wherein each pattern element has a respective geometric shape comprising a boundary and an interior, and wherein each pattern element is associated with an assigned dose (D), which defines a value of exposure dose to be exposed for each of said pixels within the interior of the respective geometric shape of the pattern element, and
• (ii) rasterizing the vector pattern into the pattern by calculating, for each of the plurality of pixels, respective intensity values based on the vector pattern,
• wherein a position correction for at least one edge position of a pattern element boundary is performed during one of steps (i) and (ii), said position correction including the steps of:
• determining a position value describing said edge position,
• determining a corrected position value based on the position value using a predefined non-linear function, said predefined non-linear function (ƒξ(Φ)−1) describing the inverse of the relationship between a nominal position value (d, dx), said nominal position value being used as input value during exposure of the pattern, and position (d, dx) of the pattern element boundary generated when exposed with said nominal position value, wherein said predefined non-linear function is further dependent on at least one parameter including at least one of the assigned dose of the pattern element involved and a blur of the pixels, and
• modifying the pattern to effectively shift the pattern element boundary in accordance with the corrected position value.