QUANTITATIVE EXAMINATION OF THE THERMOELECTRIC-POWER OF N-TYPE SI IN THE PHONON DRAG REGIME

A quantitative comparison between theory and experiment is presented for the thermoelectric power of n-type Si at low temperatures, where crystal boundary scattering of phonons is predominant. The expression for the Seebeck coefficient is obtained by simultaneously solving the coupled Boltzmann equations for electrons and phonons. The thermoelectric power is measured from samples of two different donor concentrations (ND=8×10 14 cm-3 and 7×1015 cm-3) at temperatures ranging from 25 to 200 K, where the thickness is varied by etching the samples (370-73 μm). The phonon mean free path for crystal boundary scattering, determined from experimental thermopower, agrees well with that gained from the theory of thermal conductivity corrected for the phonon velocities of interest. An additional measurement of the thermal conductivity yields the mean free path for phonon-phonon scattering, which is about two orders of magnitude less than that obtained from thermopower. This difference confirms the influence of the different parts of the phonon spectrum involved in the calculation of the appropriate transport parameters.