Observation of a Cole–Davidson type complex conductivity in the limit of very low carrier densities in doped silicon

Using THz time-domain spectroscopy to measure the complex conductivity of doped silicon from low frequencies to frequencies higher than the THz plasma frequency and the carrier damping rate, we were able to show in the limit of extremely low carrier densities ${\text{N<10}}^{13}/{\mathrm{cm}}^{\mathrm{3}},$ that the Cole–Davidson $\mathrm{(C–D)}$ type complex conductivity accurately describes the conductivity of doped silicon. In the low N limit the $\mathrm{C–D}$ parameter β converges to 0.83 for $n$ -type and 0.70 for $p$ -type silicon. In addition, we have observed a new absorption line at 1.9 THz from an unidentified defect in some of our Czochralski, single-crystal, low-N silicon samples.