Infrared-reflection characterization of sintered SiC thermoelectric semiconductors with the use of a four-component effective medium model

Abstract

Infrared (IR) reflection spectra of sintered SiC thermoelectric semiconductors are studied as a function of doping concentration as well as of sintering temperature. Attention is focused on the changes in the reststrahlen band. The peak and dip frequencies remain constant, implying we are probing stable optical phonon mode in the crystalline grains through the interaction with IR photons. In contrast, variation of spectral shape, including the peak and background reflectance seems to give valuable information regarding the quality of the sintered samples and dopant distribution within the crystal grains and grain boundaries. Measured spectra are analyzed by the use of a four-component effective medium model. In this model we assume the presence of: (1) pores, (2) intergranular materials, (3) crystalline grains, and (4) metallic inclusions (at higher doping levels of metallic impurities), with volume fractions fi(i=1–4), respectively. For frequency dependent complex dielectric functions we employed: (a) a single oscillator model appropriate to the single crystal for the crystalline grains, (b) a Drude model for the metallic inclusions, and assumed (c) another single oscillator model for the intergranular material. The parameters of the latter are determined to give a best fit to the spectrum of a low doping level sample. This model gives excellent overall fit to measured spectra with the ratio f2/f3 and the damping coefficients for the oscillators as adjustable parameters when the experimental estimates for the fraction of pores f1 and metallic inclusions f4 are used. This is remarkable in view of the situation that similar data could not, so far, be explained in terms of the simple Maxwell–Garnet model. The results suggest that careful analyses of spectral shape of IR reflection in the optical phonon resonance region can be used to get information on the intergranular to grain ratio or on the damping coefficients, which are related to the quality of sintered samples or to the distribution of doped impurities among grains and grain boundaries. The background reflectance also give information on the presence of metallic inclusions although the effects of scattering may affect the interpretation. These results combined with the possibility of local probing seems to imply that IR reflectance can offer a versatile means to check the quality of the sintered samples.