Critical angles and minimum yields for planar channeling

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Abstract
Measurements of the planar channeling of 120, 160 and 190 keV protons in Si, for a variety of atomic planes are presented. The observed half-angles at half minimum Ψ 1/2 turn out to be proportional to E −1/2 in this restricted energy range and show an almost linear dependence on the planar spacing d p- The minimum yield χmin is found to be proportional to dd −1 p, whereas the dechanneling as a function of the depth of scattering shows a strong dependence on d p- Comparing our results with results of other authors no energy dependence of χmin is observed. An analytical model is developed, including the effects of surface transmission and thermal vibrations, in which the half-angles at half-minimum Ψ1/2 and the minimum yield χmin are treated in a consistent way. The results of this model agree well with our experimental data, as well as with results of other authors for a variety of projectile target combinations. In addition the stopping power near the planes is obtained yielding values 3 to 5 times higher than for random incidence.