Detailed Study of theΓ15Conduction-Band Minimum in Germanium by Photoemission and Transverse Electroreflectance

Direct transitions occurring at the center of the Brillouin zone can be unambiguously identified by photoemission and transverse electroreflectance methods. In a material whose valenceband maximum lies at $\Gamma$, such transitions produce structure on the leading edge of the energy distribution curve (EDC) of photoemitted electrons. In transverse electroreflectance (TER), the absence of polarization dependence associated with multivalley effects provides a signature of transitions having $\Gamma$ symmetry. In this paper we report three independent studies of direct transitions near 3 eV in germanium; namely, photoemission EDC, energy-derivative EDC, and polarization-dependent TER. Both photoemission experiments yield a value 2.92 ± 0.05 eV for the minimum separation ${\Gamma }_6^{-}-{\Gamma }_8^{+}$ at 300°K. The TER experiment can only be performed at 80°K or below, and gives 3.00 ± 0.05 eV for the same gap at 80°K. The agreement among all three is perfect, assuming a temperature coefficient of -4 × ${10}^{-4\mathrm{}}$ eV/°K. The spin-orbit splitting of the conduction band is observed directly in the TER spectra; we find $\Delta \left({\Gamma }_{15}\right)\equiv {\Gamma }_8^{-}-{\Gamma }_6^{-}=0.\mathrm{}191+0.005$ eV. The present results are compared with recent band calculations and previous experiments.