Nature of Conduction in Doped Silicon

Via ultrafast optoelectronic THz techniques, we are able to test alternative theories of conduction by precisely measuring the complex conductivity of doped silicon from low frequencies to frequencies higher than the plasma frequency and the carrier damping rate. These results, obtained for both $n$ and $p$-type samples, spanning a range of more than 2 orders of magnitude in the carrier density, do not fit any standard theory. We only find agreement over the full frequency range with the complex conductivity given by a Cole-Davidson type distribution applied here for the first time to a crystalline semiconductor, and thereby demonstrate that fractal conductivity is not just found in disordered material.