Best focus shift mechanism for thick masks
The best focus shift due to thick mask effects is well known, both in ArF, and more importantly in EUV, where the shorter wavelength is small compared to both mask openings and absorber height. While the effect is stronger in opaque features in clear field masks, the best focus shift is visible in dark field masks as well, and it becomes even more pronounced when scattering bars are added to non-dense features. This pattern dependent focus variation can be predicted in both exact EMF simulations and fast image calculations that are used for optical proximity correction (OPC). Even though this focus shift can be predicted and patterns can be corrected in OPC, we would like to understand the mechanism that causes this focus shift. This can help us understand if, in addition to best focus shift, the image quality is further deteriorated due to the thick mask effects. The best focus shift is found to be an interplay of the complex diffraction coefficient due to thick mask effects and the direction of the light that is incident on the mask, or coherence value σ. A change in focus adds a phase term to each of the complex diffraction coefficients, causing their rotation in a phasor diagram. Best focus is found when the phasors have an angle of 0 or 180 degrees to each other and depending on which diffracted orders are caught in the pupil and contribute to imaging. We investigate the effect of partial coherence, mask thickness, and assist feature placement on best focus shift. We observe a waveguide effect in the absorber gaps because of the reduced real index of refraction in the absorber layer, making vacuum the optically dense medium. We suggest ways to lessen the best focus shifts through assist feature placement or the use of alternative absorbers that are closer matched to the dielectric index of vacuum.