Critical angles and minimum yields for planar channeling

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 χ_min 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 χ_min 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 χ_min 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.