Range-energy relation of hot electrons in gold

The range L( E) of hot electrons is defined in respect to a set of specific experimental measurements. Monochromatic light of frequency ν is incident upon a surface of thin gold film of thickness W. It is found both experimentally and theoretically that the number of electrons that escape over a fixed barrier at the opposite surface per absorbed photon is proportional to exp[- W/ L( E)]. The range L( E) as a function of the electron energy E measured from the Fermi level is determined by photoexcitation vacuum-collection experiments in a high-vacuum phototube and by photoexcitation internal-collection measurements across the Schottky barriers of AuGaP and AuSi devices. To correlate the electron-phonon ( l_p) and electron-electron mean free path ( l_e) with the experimental range L, an analytical expression of the form L = ( {l _el _p}/{3}) ^{1}/{2} is obtained for the case of scattering with weak absorption; and L = l_e for the case of ballistic transport. A range measurement performed at liquid nitrogen temperature confirms that L is a combined mean free path of l_e and l_p, and the calculated l_e for the above two cases agrees with the computer result based on the Monte Carlo method. The range decreases from 700 Å for electrons with energy 1 eV above the Fermi level to 200 Å for 2 eV, and gradually lessens to about 70 Å for 5 eV. On the other hand, l_e decreases from about 3000 to 100 Å in the same energy region. This extremely strong dependence of l_e on initial energy agrees qualitatively with theoretical calculations based on the self-energy approach and the screened potential formulation.