Temperature Dependence of Indirect Interband Tunneling in Germanium

Abstract

The temperature dependence of the tunneling current in antimony-doped germanium tunnel diodes has been measured between 1.2 and 360°K at a number of bias voltages. The results have been compared with theory of Kane in a manner which is insensitive to the lack of agreement between the observed $I-V$ characteristic and the theoretically predicted shape. All important effects have been taken into account including the explicit temperature dependences of the band gap, the effective masses, the phonon densities, the Fermi functions, and of the Fermi level positions with respect to the band edges. Excellent agreement was obtained both as to the temperature dependence itself and also to its bias dependence. The magnitude of the tunneling exponent could be determined from the measurements. This value agrees with that obtained from the effect of stress on the same tunnel diodes. Using the value 4×${10}^{-49\mathrm{}}$ ${\mathrm{erg}}^2$ ${\mathrm{cm}}^3$ for the electron-phonon coupling constant which has been estimated from other experiments, the absolute magnitude of Kane's expression is found to be too small by a factor of about 20. Some difficulty is noted with respect to the phonon energy terms in the tunneling exponents of the theoretical expression.