The spectroscopic properties of crystalline silicon wafers are investigated experimentally as a function of the temperature. To this goal, samples of phosphorus-doped silicon are characterized using Terahertz Time-Domain Spectroscopy (THz-TDS) in reflection. Four different samples span resistivities from ∼0.04 − 50Ω cm, for temperatures ranging from room temperature to 200 C. The measurements confirm that the widely used Drude's theory is adequate also to model the dispersion of silicon at higher temperatures. When comparing the corresponding scattering times obtained here using THz TDS pulses with the scattering time derived from the well accepted DC based empirical model of the mobility, differences emerge depending on the doping level. The scattering times predicted and measured are on the same order of magnitude and the anticipated reduction of the scattering time with increasing temperature has also been confirmed by the high frequency measurements. The absorptivity of the samples is also estimated accurately as a function of the frequency up to 1 THz.

According to our recent modal representation, the origin of thermal radiation can be associated to the distribution of a finite number of current sources, independent one from the other (the Degrees of Freedom). In a companion paper we have also shown that, if one is only interested in the energy radiated, the current sources can be mathematically replaced by a much larger number of equivalent sources, that are unphysical, as they are imposed to be uncorrelated at any distance and are distributed all over the volume. A classic procedure for estimating the electromagnetic energy emitted by such ensemble of energetically equivalent currents is presented. The derivation presented here can just as well be applied to another set of energetically equivalent currents, the Quantum born Rytov currents. To arrive to a final analytical expression for the radiation, multiple simplifying approximations are used. Treating the problem in transmission rather than in reception provides useful insights on their limits and applicability.

The thermal energy radiated by silicon wafers with different conductivities is characterized experimentally in the mm and sub-mm wave ranges. These samples are heated up, and the energy that they radiate thermally is captured by different horn antennas covering the frequency band between 75 and 500 GHz. The energy radiated (in the order of pW) and collected by the horn antennas is subsequently detected by zero bias Schottky diodes. The measured thermal radiated power agrees with the prediction from Planck's law for the highly doped wafers, corresponding to high conductivities. However, for low conductivities, the measurements show a descending pattern as a function of the frequency, which is not in line with expectations from Planck's law. Parallelly, we have developed a theoretical model providing a classical explanation of these results [1].