Channeling Effects in the Energy Loss of 3-11-MeV Protons in Silicon and Germanium Single Crystals

Planar and axial channeling effects of 3-11-MeV protons in 25-50-μ-thick silicon and germanium single crystals were investigated by studying the direction and energy distributions of the transmitted particles. The total energy distributions were investigated as function of crystal orientation using a large-acceptanceangle solid-state detector Limiting angles of incidence for channeling were obtained at several incident energies and crystal thicknesses. The energy and intensity as a function of emergence angles (for a fixed angle of incidence) were obtained by scanning the emergent proton distributions with a small-acceptanceangle detector (75.×${10}^{-7\mathrm{}}$ sr) or a masked lithium-drifted position-sensitive detector in a plane 102 cm from the crystal. The least energy loss for protons transmitted parallel to the $〈110〉$ and $〈111〉$ axes and the {111}, {110}. and {100} planes of silicon were investigated and it was found that the least energy loss for each axis was the same as that of the most open planes intersecting at that axis. Measurements of the least energy loss and its straggling were made for the {111} and {110} planes of silicon and germanium. A mechanism of least energy loss is presented for which it is assumed that the energy loss of the well-channeled protons is due to interactions with the weakly bound valence electrons only. The measurements agree well with the theory and are used to extract the local density of valence electrons sampled by the well-channeled protons. A theoretical model of channeling is presented and comparisons made with experiment. Average potentials for the atom rows and planes of silicon are calculated for the static lattice at different temperatures. Multiple Coulomb scattering into channels is considered, as well as the trajectories of the high-loss particles.