Development of a precision pre-aligner using the complete elliptic integral of the second kind to compute an eccentricity

Abstract

This paper proposes an eccentricity computation algorithm using the complete elliptic integral of the second kind for a pre-aligner. A CD-SEM is an inspection tool of the semiconductor device using the electron beam. Highly precision CD-SEM is required by the high integration of the semiconductor device progressing. Also, high throughput CD-SEM is required by the increased production of semiconductor devices which are smaller and thinner, because they are required by growing of smartphones and tablet PCs. A pre-aligner which is installed to improve throughput is a part of CD-SEM. The pre-aligner computes eccentricity of a Si wafer, and transfers it to inside the CD-SEM precisely. It is a non-contact type which can prevent contamination using a line image sensor to compute eccentricity. However, it is difficult for a conventional method to be highly precise, because it depends on an approximation and an experience even though it computes eccentricity using derivative and statistics calculation. At first, this paper shows that a wave pattern of the line image sensor is proportional to the complete eccentric integral of the second kind based on geometry analysis. Then, it proposes highly precise eccentricity calculation algorithm based on an analytical result. Finally it shows high precision pre-aligner by an experimental result.