Impurity and free-carrier effects on the far-infrared dispersion spectrum of silicon.
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.
Karstens
William
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Saint Michael's College, Colchester, Vermont 05439, USA. wkarstens@smcvt.edu
Bobela
David C
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Smith
D Y
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