Ballistic-electron-emission spectroscopy of Au/Si and Au/GaAs interfaces: Low-temperature measurements and ballistic models

Low-temperature ballistic-electron-emission spectroscopy measurements are presented for Au/Si(100), Au/Si(111), and Au/GaAs(100) interfaces. Spectra were acquired at 77 K for the Au/Si systems and at 7 K for Au/GaAs(100). The results show that in the near-threshold region, the experimental spectra cannot be adequately described by ballistic models based only on kinematical constraints. In this work, a dynamical ballistic model is formulated incorporating the quantum transmittance and elastic scattering. The model includes all kinematically allowed semiconductor states, i.e., both zone-centered energy-band minima and non-zone-centered minima. Appropriate expressions for the quantum transmittance and reflectance functions are derived for non-zone-centered minima within a semiclassical model. Additionally, the effect of nonparabolic bands on the model is analyzed. For Au/Si(111), fits to experimental spectra show that substantial scattering must occur to account for both the observed magnitude and shape of the spectrum. For all interfaces, excellent agreement between model and experiment was obtained over a range from well below threshold up to 0.25 V above threshold, depending on the interface. The addition of an energy-dependent effective mass did not change these results. Model fits also were consistently better than previously used power-law approximations. {} 1996 The American Physical Society.