Sub-pixel alignment for direct-write electron beam lithography

Abstract

We have developed a novel, sub-pixel alignment algorithm based on calculating a 3 × 3 array of residual values of the fit of an auto-correlation of an alignment mark template with the cross-correlation of the template with an imaged mark. The residual array is then fit by a second order polynomial, and the location having the minimum residual – the optimum alignment location – is determined analytically from the polynomial. This method naturally interpolates between the discrete pixels of the alignment mark and template images. The method is robust and can be used effectively with signal-to-noise ratios as low as −4 dB. Its performance is enhanced by appropriate choice of mark material, with Au marks with a signal-to-noise ratio of 0.48 dB yielding a factor of two. Alignment repeatabilities of ±2 nm were obtained using 5 nm Cr/50 nm Au marks with a 5 nm pixel. Using a 10 nm pixel, accuracies of 4.3 nm, 3 σ were achieved with Au/Cr marks while 360 nm of Si topography yielded repeatabilities of 14.8 nm, 3 σ or 19.7 nm, 3 σ with a 100 nm resist coating. The technique was employed in the fabrication of a zone plate using two aligned exposures. Overlay values better than 5 nm were observed.