Contrast limitations in electron-beam lithography

State-of-the-art proximity effect correction (PEC) schemes show a degradation in contrast when they are applied to small features. It seems impossible to achieve a contrast better than that of the uncorrected pattern. In this article we provide mathematical proof that it is impossible to improve the contrast for the class of linear PEC kernels. For this class, higher resolution can only be achieved at the expense of contrast. This fundamental limitation implies a trade-off between the desired minimum feature size (related to critical dimension linearity) and contrast (related to critical dimension uniformity).