Study of the band-gap energy of radiation-damaged silicon

Abstract

The transmission of silicon crystals irradiated by 24 GeV/c protons and reactor neutrons has been measured for photon energies, $E{\hat{I}}^3$, between 0.95 and 1.3 eV. From the transmission data the absorption coefficient $\hat{I}\pm$ is calculated, and from $\hat{I}\pm (E_{\hat{I}}^3)$ 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 $\sqrt{\hat{I}\pm (E{\hat{I}}^3)}$ smoothed with a Gaussian kernel has been used.

11 pages, 7 figures