Origin of ringlike angular distributions observed in rainbow channeling in ultrathin crystals

Abstract

Using the theory of crystal rainbows, we prove that the well-known doughnut patterns observed in ion channeling in thin crystal membranes are manifestations of the rainbow effect. This is done by a detailed morphological study of the high-resolution experimental angular distributions of 2 MeV protons channeled in a 55-nm-thick (001) silicon crystal tilted away from the [001] direction. The inner side of the doughnut is the dark side of the rainbow, analogous to the Alexander's dark band, occurring between the primary and secondary meteorological rainbows.