Seebeck Effect in Germanium

TLDR

An apparatus measuring the Seebeck effect from 20 K to 375 K on germanium crystals with varied acceptor and donor concentrations was described, and the Seebeck data were compared with concurrently obtained Hall data. Above 250 K the Seebeck and Hall effects correlate as predicted by existing theory, but below 250 K a pronounced discrepancy appears whose temperature and dopant‑concentration dependence matches Herring’s phonon‑electron interaction theory, including a sample‑size‑dependent Seebeck voltage below 50 K and a mass parameter of 0.75 ± 0.2 m for both holes and electrons.

Abstract

An apparatus for making measurements of the Seebeck effect between 20\ifmmode^\circ\else\textdegree\fi{}K and 375\ifmmode^\circ\else\textdegree\fi{}K is described.Experimental curves of the Seebeck effect are given for a series of germanium crystals in which various concentrations of acceptor and donor atoms have been incorporated. The Seebeck data are compared with Hall data obtained concurrently. Above 250\ifmmode^\circ\else\textdegree\fi{}K the two effects can be correlated by means of existing theory. Below 250\ifmmode^\circ\else\textdegree\fi{}K a marked discrepancy occurs between existing theory and experiment. The temperature dependence of this discrepancy and its dependence upon concentration of added atoms are given. The results are consistent with a new theory proposed by C. Herring which considers an interaction between the phonon and electron systems. A dependence of Seebeck voltage upon sample dimension which is predicted by Herring's theory has been found in the temperature region below 50\ifmmode^\circ\else\textdegree\fi{}K.A value of $(0.75\ifmmode\pm\else\textpm\fi{}0.2)m$ has been determined for the mass parameter of both holes and electrons which enters into the "density of states" equation.