Prediction of surface topography due to finite pixel spacing in focused ion beam milling of circular holes and trenches

Abstract

Successful implementation of focused ion beam technologies in fabrication of practically important structures, including circular holes and trenches requires evaluating the ion dose delivered to the specimen by the beam and subsequently predicting the formed topography. In this article, the analytical expressions for the ion dose are obtained in polar coordinates using Bessel functions. These expressions can be transformed into relatively straightforward formulas useful in many applications. On the basis of the expressions derived, the surface shape of structures under consideration is analytically described if constant sputtering yield conditions are realized throughout the milling process. For practically relevant structure preparation, when the distance between neighboring beam stops is less than approximately two beam diameters, it was established that the mean depth and the peak-to-valley surface roughness can be evaluated by simple formulas. The outcomes of theoretical findings are confirmed by the comparison with the numerically obtained results and experimental data retrieved from the fabricated circular holes.