Phonon scattering and quantum mechanical reflection at the Schottky barrier

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Abstract
Motivated by the recently developed experimental capability of ballistic‐electron‐emission microscopy (BEEM), we study the effect of phononscattering and quantum mechanical reflection on the ballistic transport across the Schottky barrier from the metal into the semiconductor. We argue that, for the Schottky barrier formed by a metal overlayer on a semiconductor substrate, one can typically expect the quantum mechanical transmission probability to have an E 1/2 dependence, where E is the electron kinetic energy in the final state. We make a distinction between the metallurgical metal/semiconductor interface and the Schottky barrier energy maximum resulting from image potential, and calculate the optical phononscattering rate between the interface and the maximum. We compute the combined effect of optical phononscattering and quantum mechanical scattering on the ballistic transport for an initially isotropic velocity distribution of electrons in the metal, and we show that the two scattering processes combine to give a much weaker energy dependence than for either effect alone for cases of the Au/Si and Au/GaAs at both 300 K and 77 K. We use our model to show that the magnitude of the BEEM current for Au/Si should be roughly 5 times larger than for Au/GaAs and that decreasing the temperature from 300 K to 77 K should increase the magnitude of the BEEM current for Au/GaAs by a factor of about 3. There is fairly good agreement between our predictions and the available experimental evidence.