Measurements and Calculations of Critical Angles for Planar Channeling

The backscattering yields as a function of crystal orientation for planar channeling have been measured for 250-keV to 2-MeV protons and He ions in silicon, and 1-MeV He ions in Ge and GaP. The angular distributions have also been calculated using an average-potential model. Comparison between measured and calculated critical angles ${\psi }_{\frac{1}{2}}$ for the {110}, {100}, and {112} planes in silicon shows that it is necessary to include the effects of surface transmission to account for the observed dependence of ${\psi }_{\frac{1}{2}}$ on planar spacing. A few typical measured angular distributions are compared to the calculated results. The angular widths are in fair agreement with the slightly smaller experimental values. The calculated minimum yield is significantly lower and the shoulder regions are higher and narrower than measured experimentally. Possible reasons for these discrepancies are discussed.