Ge-Aqueous-Electrolyte Interface: Electrical Properties and Electroreflectance at the Fundamental Direct Threshold

Abstract

Electroreflectance (ER) measurements at the ${\ensuremath{\Gamma}}_{8+}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{7\ensuremath{-}}$ (fundamental direct) threshold are combined with electrical measurements in a detailed investigation of the nearly intrinsic Ge---neutral-aqueous-electrolyte interface. Capacitance and photovoltage (PV) measurements are combined to determine the flat-band potential and the impurity concentration of the space-charge region. These measurements show that no fast surface states are present for moderate modulating voltages for which the surface remains nondegenerate, and they allow the surface field to be calculated accurately over this range of surface potential. The instantaneous PV response shows that the Dember potential obeys quasiequilibrium equations for time intervals as short as 4 \ensuremath{\mu}sec. ER spectra are taken concurrently with measurements of the semiconductor surface field, yielding spectra suitable for quantitative interpretation. The very good agreement between these electrolyte and previously measured field-effect ER spectra indicates that the electrolyte ER spectra originate in the semiconductor, and demonstrates the equivalence of the two measurement techniques for this interface. By direct observation of the instantaneous reflectivity response, it is shown that surface states, generated electrochemically if intrinsic Ge is modulated beyond near-degeneracy (${\ensuremath{\phi}}_{s}\ensuremath{\gtrsim}300$ mV), seriously influence observed ER spectra. The low-field measurements possible with the electrolyte technique indicate that the ER spectra do not vanish identically at flat band (zero surface potential and field) for symmetric modulation of intrinsic material, as expected, but rather reach a minimum for slightly $p$-type surfaces (${\ensuremath{\phi}}_{s}=17$ mV, $\mathcal{E}\ensuremath{\cong}260$ V/cm). The amplitudes of the observed ER spectra exceed the predictions of the Franz-Keldysh theory by over an order of magnitude at all fields, providing strong evidence of enhancement by the electron-hole Coulomb attraction and substantiating previous conclusions obtained primarily on the basis of line-shape arguments. It is shown that sufficient strength to produce the observed low-field ER spectra can come only from the $n=1$ exciton absorption lines which lose their discrete nature at room temperature and behave as continuous states. The qualitative success of the inhomogeneous perturbation theory in describing line-shape evolution with increasing field appears to be due to the similarity of Franz-Keldysh and modulated continuum-exciton line shapes, together with a common dependence on the characteristic energy $\ensuremath{\hbar}\ensuremath{\Omega}$. A lifetime broadening of 1.8 \ifmmode\pm\else\textpm\fi{} 0.5 meV is deduced for this transition.