Finite element analysis of SCALPEL wafer heating

Abstract

A high-throughput scattering with angular limitation projection electron beam lithography ͑SCALPEL͒ tool will typically deliver up to 1.5ϫ10 Ϫ4 J to an area of 250 mϫ250 m over a time of 200 s, corresponding to a power input of 0.75 W. This heat deposition occurs in the upper 60 m of a wafer creating local thermal strain at the time of image formation, and depends on mask and tool conditions and specific boundary conditions. Initial modeling results indicate expansion-induced peak pattern placement errors of ϳ1 nm on a local scale ͑i.e., a 3 mm effective field size͒, several nanometers in a chip area, and a few microns overall. Since the use of a mainly predictive correction algorithm is anticipated, it is vital to conduct a rigorous investigation of the heat transfer and strain formation. Results are presented of such an analysis, illustrating the heating response for the fundamental building blocks of the SCALPEL writing strategy.