Finite element analysis of SCALPEL wafer heating

Abstract

A high-throughput scattering with angular limitation projection electron beam lithography (SCALPEL) tool will typically deliver up to 1.5×10−4 J to an area of 250 μm×250 μm over a time of 200 μs, corresponding to a power input of 0.75 W. This heat deposition occurs in the upper 60 μm 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 ∼1 nm on a local scale (i.e., a 3 mm effective field size), 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.