Impact of photomasks on linewidth variation

In modern logic processes, variation of linewidths, rather than resolution, often sets the practical lower limit to dimensions. In this context, it is useful to understand how linewidth errors on photomasks contribute to linewidth errors on silicon. It is generally impossible to express the total linewidth variance as the sum of terms that depend only on the photomask or only on other factors. This follows partly because linewidth errors from several sources, such as non- uniform illumination or aberrations of the projection optics, combine with photomask errors to yield significant covariance. In this regard, photomask errors characterized by low spatial frequencies, such as those arising from resist and Cr processing, are more significant than the errors mask writers produce with higher spatial frequencies. A further complication at dimensions of interest, is that printed linewidth is a non-linear function of photomask linewidth, the effect being to amplify the consequences of linewidth errors on photomasks. Closely related to non-linearity are line shortening and proximity effects. When photomasks are compensated to mitigate these problems, round-off to minimum address increments becomes another source of linewidth errors.