The Cramer–Rao accuracy bound for optimum processing of the edge registration mark signal in electron beam lithography

Abstract

Experimental data from the IBM direct‐write electron beam lithography machine EL‐3 are used to evaluate a lower bound on the estimation error resulting from the application of optimal signal processing in determining the mark edge position for registration. The e‐beam is swept using a 20 kV accelerating voltage in a raster fashion across a bare rectangular groove of dimensions 5 μm wide×100 μm long×0.5 μm deep. Waveforms for backscattered electrons detected by diodes are processed statistically. The mathematical and numerical techniques are developed to handle a large but sparse noise correlation matrix. The bound obtained decreases exponentially with the sampling rate (at least throughout the range of measurement explored), and it represents the ultimate accuracy achievable with any signal processing technique. The implications of having multiple records of a waveform are included. Comparisons with other approaches are discussed.