Temperature and Energy Dependence of Proton Dechanneling in Silicon

The dechanneled fractions of protons impinging along the $〈111〉$ and $〈110〉$ axial directions of Si have been measured for ion energies between 0.3 and 1.5 MeV and for target temperatures ranging between 80 and 423 °K. The dechanneled fraction is a linear function of the penetration depth $z$. Its dependence on beam energy $E$ and the target temperature $T$ can be described simply through the parameter $\frac{z{\rho }^2}{E}$, ${\rho }^2$ being the mean-square vibrational amplitude normal to the row. All the experimental points follow a unique linear trend if plotted vs $\frac{z{\rho }^2}{E}$. The dechanneled fraction for the $〈110〉$ axis is a factor of 2 lower than that for the $〈111〉$. A theoretical model has been developed to describe the dechanneling in terms of a steady increase in the transverse energy, accounting for both electronic and nuclear reduced multiple scattering. The initial transverse-energy distribution of the particle just beneath the crystal surface has been computed including the experimental angular spread, and both scatterings produced by the amorphous layers covering the surface and by the atomic string potential. The limiting transverse energy for the channeled-to-random transition has been taken from the experimental ${\psi }_{\frac{1}{2}}\mathrm{}\left(T\right)\mathrm{}$ values. The computed dechanneled fractions agree reasonably well with the experimental ones and justify their temperature and energy dependence. The calculated fractions differ from the experimental ones in their having an upward curvature; the significance of this disagreement is briefly discussed together with the approximations involved.