Optical Constants of Silicon in the Region 1 to 10 ev

Abstract

The reflectance, ${|r(\ensuremath{\lambda})|}^{2}$, of single crystal silicon was measured in the range 1 to 11.3 ev. The phase, $\ensuremath{\theta}(\ensuremath{\lambda})$, was computed from these data using the Kramers-Kronig relation between the real and imaginary parts of the complex function $\mathrm{ln}r=\mathrm{ln}|r|+i\ensuremath{\theta}$. The optical constants, $n$ and $k$, were then determined from the Fresnel reflectivity equation. The real part of the refractive index, $n$, shows a sharp maximum of magnitude 6.9 at 3.3 ev. The extinction coefficient, $k$, shows maxima of magnitude 3.1 at 3.5 ev and 5.1 at 4.3 ev; optical absorption above 3 ev is associated with the onset of strong direct transitions. The results indicate that much useful information, applicable to band structure calculations for both silicon and germanium, could be obtained from limited reflectance studies (2 to 5 ev) on Ge-Si alloys.