Study of the Band-Gap Energy of Radiation-Damaged Silicon

The transmission of silicon crystals irradiated by 24 GeV/c protons and reactor neutrons has been measured for photon energies, E γ , between 0.95 and 1.3 eV. From the transmission data the absorption coefficient α is calculated, and from α(E γ ) the fluence dependence of the band-gap energy, E gap, and the energy of transverse optical phonons, E ph, determined. It is found that within the experimental uncertainties of about 1 meV neither E gap nor E ph depend on fluence up to the maximum fluence of 1 × 1017 cm−2 of the measurements. The value of E gap agrees within about 1 meV with the generally accepted value, if an exciton-binding energy of 15 meV is assumed. A similar agreement is found for E ph. For the extraction of E gap and E ph the second derivative of α(Eγ) smoothed with a Gaussian kernel has been used.