Incident dose modification for proximity effect correction

Abstract

Electron-beam lithography (EBL) suffers from the effects of scattering of the incident electron beam. For good control of the size of the developed features, particularly when the fraction of incident electrons that is backscattered is large, incident dose modification is essential. The self-consistent correction technique equalizes the exposure of the resist within the desired features in the pattern, and this algorithm provides good correction for a wide range of feature shapes and sizes using both positive and negative resist systems. For EBL at the limits of resolution, the effects of forward scattering must be considered. The incident dose must be increased to compensate for the forward scattering effects when writing features smaller than about five times the range of the forward scattering. In order to equalize the average dose within these features, the incident doses must be increased by factors of up to 2, and greater increases are required to extend the system to even smaller features. If the backscattered fraction is η, the incident dose to define an isolated feature must be increased by as much as 1+η. In combination with a correction for forward scattering, the range of incident doses required can easily become 3:1. Curves are shown exhibiting the dose modifications required for different feature sizes and types as the resolution limit is approached, and the exposure contrast available. Sufficient dynamic range must be accommodated in the design of the electron-beam pattern generator to give sufficiently fine dose variations over a wide enough range.