Axial ion channeling patterns from ultra-thin silicon membranes

We present channeling patterns produced by MeV protons transmitted through 55 nm thick [0 0 1] silicon membranes showing the early evolution of the axially channeled beam angular distribution for small tilts away from the [0 0 1], [0 1 1] and [1 1 1] axes. Instead of a ring-like "doughnut" distribution previously observed at small tilts to major axes in thicker membranes, geometric shapes such as squares and hexagons are observed along different axes in ultra-thin membranes. The different shapes arise because of the highly non-equilibrium transverse momentum distribution of the channeled beam during its initial propagation in the crystal and the reduced multiple scattering which allows the fine angular structure to be resolved. We describe a simple geometric construction of the intersecting planar channels at an axis to gain insight into the origin of the geometric shapes observed in such patterns and how they evolve into the 'doughnut' distributions in thicker crystals.