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, $E{\gamma}$, between 0.95 and 1.3 eV. From the transmission data the absorption coefficient ${\alpha}$ is calculated, and from ${\alpha}(E_{\gamma})$ 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 $1 \times 10^{17}$ 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 $\sqrt{{\alpha}(E{\gamma} )}$ smoothed with a Gaussian kernel has been used.