Articles you may be interested inNew types of dose distributions for vertical sidewall minimizing total dose in 3-D electron-beam proximity effect correction of nanoscale features J. Vac. Sci. Technol. B 30, 06F307 (2012); 10.1116/1.4767446 Nanoscale geometry assisted proximity effect correction for electron beam direct write nanolithography Proximity effect correction using pattern shape modification and area density map for electron-beam projection lithography J.Proximity effect correction by dose modulation is widely practiced in electron-beam lithography. Optical proximity control is also possible using a combination of shape adjustment and phase control. Assigning "the right" dose ͑or fill factor and phase for optics͒ is a well known mathematical inverse problem. Linear programming, by definition, is the appropriate method for determining dose. In the past, the technique was too slow for full-scale implementation in mask making. Here, the authors discuss how recent developments in computer speed and architecture have improved the prospects for full-scale implementation. In addition, the authors discuss some numerical techniques, analogous to gridding and relaxation, that make linear programming more attractive in mask making.