Wave optical calculations of electron probes

Abstract

Electron probes used in electron-beam lithography systems are pushing towards the 1 nm scale. This exceeds the limit of accuracy of conventional knife-edge measuring techniques and conventional modeling methods. The only true way to accurately model such probes as their dimensions approach the 1 nm level is to use a wave optical method. Probe sizes are commonly estimated using the root-sum-of-squares method; i.e., by summing in quadrature the individual effects of the geometrical aberrations and diffraction. This method is relatively accurate when the probe size is greater than ∼10–15 nm, but fails with probes of smaller dimensions due to the inherent erroneous assumption that the effect of individual aberrations on the probe size can be treated independently. In this article we present a method for modeling an electron probe both on and off axis using a wave optical method. This method is commonly used to calculated probe sizes in the electron microscopy community but has not been applied to e-beam lithography systems until now. The wave optical method combines the effects of all geometrical aberrations, diffraction, electron source size, and defocus while fully adhering to the physics of the probe formation process. The challenge with applying this method to an e-beam lithography system is the relatively large field size (0.1–10 mm); in electron microscopy 50 nm is considered a large field size for high-resolution work!