Optical analyses of radiation effects in ion-implanted Si: Fractional-derivative-spectrum methods

Abstract

Fractional-derivative spectra (FDS) have been developed for studying radiation effects in crystals by monitoring the optical interband transitions at critical points. Optical spectra of ${\mathit{E}}_1$ structure of ${\mathrm{As}}^{+}$-implanted Si, at doses from 3×${10}^{12}$ to 1×${10}^{16}$ ions ${\mathrm{cm}}^{\mathrm{-}2}$, have been analyzed with use of 3/2th-derivative spectra. Symmetric line shapes in the ${\mathit{E}}_1$ region near 3.4 eV were found in the FDS both for crystalline and ion-implanted samples until the critical dose, above which the spectra became structureless. No change was determined, within the experimental errors, either in the line-shape symmetry or in the ${\mathit{E}}_1$ critical-point threshold for the implanted samples, compared with those of crystal Si, but a sharp increase in linewidth was observed. The FDS peak-to-peak height, which describes the crystal damage in the implanted region, is related to the fractional number of dangling bonds, found to vary with 1-(${\mathrm{\Phi }}_{\mathit{d}}$/Φ${)}^{\mathrm{\beta }}$, where β≊0.33 initially followed by a transfer to 0.78 until saturation, Φ is the total dose, and ${\mathrm{\Phi }}_{\mathit{d}}$ is a constant. Both of the sharp changes in linewidth and in dependence of the number of dangling bonds take place at the dose of 3×${10}^{13}$ ions ${\mathrm{cm}}^{\mathrm{-}2}$, attributed to the accumulated stresses in the damaged region. The relationship between dangling bonds and structural disorder is discussed. For annealed samples, FDS directly yielded a shrinking of the ${\mathit{E}}_1$ threshold, together with a decrease in the optical response. They were found to be logarithmically dependent on impurity concentration.