Structure of stochastic Coulomb interactions in electron beam columns

Abstract

The stochastic Coulomb interactions in a probe forming beam with a crossover show a strong symmetric structure with respect to the crossover region that can be utilized to reduce beam blur, especially in configurations in which all the beam angles are the same. The blur contribution is nearly constant with distance along the column even though the magnitude of the transverse forces increase nearly inversely with the distance from the crossover. A consequence is that to first order the blur only depends on the beam semiangle and column length. Simulations utilizing fast multipole accelerated techniques show that the blur is about 42 nm for 1 μA current in a 40 cm column with a 1.5 mR Gaussian semiangle. For beam projection systems such as SCAPEL simulation shows that an aperture near the crossover can increase the stochastic blur.