The silicon optical absorption coefficient revisited

The optical absorption coefficient, alpha(lambda), in silicon in the visible part of the spectrum is an important performance parameter of integrated photodiodes, as it largely determines the responsivity and the wavelength dependence thereof. Absorption is coupled to refraction, n*(lambda)= n(lambda)-jk(lambda), via the extinction coefficient, alpha(lambda)= 4 pi .k(lambda)/lambda. Accurate data on the complex index of refraction in silicon has been available for a long time, which also provides a database of the absorption coefficient and its dispersion. On the other hand is the absorption fully determined by the magnitude and shape of the silicon bandgap. Optical measurements, therefore, also enabled the analysis of the bandgap structure. A square relation was found, alpha(lambda)=(h nu -E-g)(2). This paper shows that the E-2-relation only applies to photon energies close to the indirect bandgap and that the E-5/2- function is a better approximation to describe the optical absorption at visible wavelengths.