## Abstract

We investigate a generalized Cauchy power-series expansion for the index of refraction of an *n*-type elemental semiconductor in the region of IR transparency. A plot of index versus photon energy squared should be very nearly linear if all absorptions lie above the transparent region. However, free carriers produce far-IR absorption, and the dispersive signature of this is a deviation from linearity in the mid- to far-IR. By retaining terms with negative exponents in the index expansion, we find a substantially improved fit to index measurements. Moreover, the free-carrier density may be determined from the coefficients in the regression fit. The method has been used to evaluate several extensive index measurements for doped silicon found in the literature.

© 2006 Optical Society of America

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