Spectroscopy of Kondo and Spin-Flip Scattering: High-Field Tunneling Studies of Schottky-Barrier Junctions

Abstract

A comprehensive study of the energy, temperature, and magnetic field dependence of the anomalous Kondo and spin-flip conductances $G^{\mathrm{}\left(3\right)\mathrm{}}\mathrm{}\left(V\right)\mathrm{}$ and $G^{\mathrm{}\left(2\right)\mathrm{}}\mathrm{}\left(V\right)\mathrm{}$, in vacuum-cleaved metal-semiconductor tunnel junctions is reported. Localized Anderson magnetic moments are characteristic of Schottky barriers at donor concentrations a few times the Mott critical concentration $N_c$. These moments, coupled to the conduction electrons in the semiconductor by the $s-d$ exchange interaction $-2J\overrightarrow{\mathrm{S}}·\overrightarrow{\sigma }$, are lightly screened neutral donors at the inner edge of the depletion region. The background conductance in vacuum-cleaved junctions on Si: (1.6×${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$ donors) agrees satisfactorily with the parabolic barrier model, extended to the thin-barrier limit. A detailed study shows the energy dependence of the zero-bias Kondo scattering peak $G^{\mathrm{}\left(3\right)\mathrm{}}\mathrm{}\left(V\right)\mathrm{}$ to be in good agreement with the third-order perturbation theory of Kondo and Appelbaum. High magnetic field studies confirm that a large negative $g$ shift $\Delta g=2J{\rho }_F\sim -1.\mathrm{}0$ and related broadening $\Gamma =\pi {\left(J{\rho }_F\right)}^{2}g{\mu }_{B}H$ of the Zeeman transition of the local moment occur via the exchange interaction. The broadening $\Gamma$ additionally produces, for $\Gamma \gg k_{B}T$, a quenching of the Kondo scattering peak from $-logT$ to $-log\left(\frac{\Gamma }{k_B}\right)$. The directly measured parameters $J{\rho }_F$ and $E_0$ determine a divergence temperature $T_K=\left(\frac{E_0}{k_B}\right)\times \exp \left(\frac{1}{J{\rho }_F}\right)=(2\mathrm{}\pm 1)$ °K, significantly higher than an upper bound ∼0.5 °K, indicated by the observed accurate $logT$ dependence of $G^{\mathrm{}\left(3\right)\mathrm{}}\mathrm{}\left(0\right)\mathrm{}$ to 0.4 °K. The discrepancy is removed by assuming simultaneous potential and exchange scattering in a ratio determined via Appelbaum's theory from the observed ratio $\frac{G^{\mathrm{}\left(3\right)\mathrm{}}}{G^{\mathrm{}\left(2\right)\mathrm{}}}$. In summary, the tunneling spectra and an extended Kondo-Appelbaum perturbation theory, including the implied $g$ shift, broadening $\Gamma$, and an added potential scattering, are in good agreement.