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.

THz time-domain reflection spectroscopy experiments of crystalline Si samples of different doping and heated to temperatures up to 475 K have been performed to measure their electric permittivity, absorptivity and resistivity dispersion spectra. Free charge carrier volume concentration and scattering time have also been extracted from the measurements, as a function of temperature, to best fit the Drude model to the complex resistivity spectra. The dependence of these microscopic parameters to the temperature resembles the curves from the unified model for the carriers mobility, based on past dc measurements. The high-frequency data acquired with these measurements constitute the fundamental information and parameters, necessary for the characterization of crystalline Si thermal radiation emission.

The mm and sub-mm wave propagation and absorption in n-type c-Si are investigated as a function of temperature by time-domain reflectivity measurements. The temperature range spans from 300 K to 475 K and the complex electric resistivity, extracted from the reflectivity spectra, shows the same free electrons mobility degradation with temperature as observed with previous dc conductivity measurements. The Drude theory of free charge carriers, based on the conduction electron concentration and effective scattering time, well fit the experimental data from 200 GHz to 1 THz. The dependence of the scattering time with respect to the doping concentration and sample temperature is consistent with the empirical unified model for the electron dc mobility, which is widely used in c-Si passive components and device simulations.

The thermal energy radiated by silicon wafers with different conductivities is characterized experimentally in the m m 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 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. A recently developed theoretical model provides a classical explanation of these results [1].