Spot size predictions of a focused ion beam based on laser cooling

The Atomic Beam Laser Cooled Ion Source (ABLIS) is a new source for focused ion beam instruments, which are used in the semiconductor industry, to image and modify structures on the nanometer length scale. The ABLIS employs laser cooling and compression of an atomic beam of rubidium to increase its brightness significantly. By photo-ionization in an accelerator structure, ions are then created and accelerated immediately. The bottleneck for retaining a high brightness, is disorder-induced heating: ions, created at random initial positions, heat up due to relaxation of the potential energy associated with these positions. This effect is counteracted by the applied electric field to quickly reduce the ion density. However, since ionization takes place over a finite distance, a larger electric field implies a larger energy spread of the beam and therefore larger chromatic aberrations of the lens system. Here we report on analytical and numerical investigations of the conditions under which the smallest spot sizes can be reached. With particle tracking simulations, a relation was found between the current and the minimum electric field needed to suppress disorder-induced heating. This relation was used to account for chromatic aberration of the lens system. An analytical calculation was performed of the possible spot size of the ABLIS setup, including the finite brightness of the beam and spherical and chromatic aberration of a realistic lens system. The results show that sub-nanometer spot sizes are possible for currents up till 10pA. The calculation was verified with particle tracking simulations of the whole beam line.