Depth dependence of angular dips: Measurements and calculations for H+and D+in Si and Ge

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Abstract
The variation of shape of angular dips with penetration depth has been investigated by the backscattering technique for 0.3 to 1.5 MeV protons and deuterons impinging on Si and Ge single crystals at different temperatures. Since the depth dependence of the angular dips at small depths is unknown the comparison between the experimental critical angle ψ 1/2 determined at non zero penetration and the theoretical values obtained at zero depth is ambiguous. Yield profiles vs. penetration depth have thus been calculated accounting for the nuclear and electronic reduced multiple scattering. The obtained results justify quantitatively both the magnitude of the experimental data and their dependence on the target temperature, ion energy and penetration depth. The disagreement previously reported between the figures calculated at zero depth and the extrapolated experimental values results from the strong variation ψ1/2 of near the crystal surface.