Calculation of the emission depth distribution function for electrons emitted from a crystal by the Bloch wave method

The quantum mechanical Bloch-wave method combined with the reciprocity principle has been used to describe electron transport in crystalline solids for determining the emission depth distribution function (EMDDF) of signal electrons in surface electron spectroscopy. The crystal structure and electron coherent scattering are explicitly taken into account; these are neglected in classical Monte Carlo methods. While electron inelastic scattering is treated with an optical potential, the EMDDF for Auger-electron emission from an Au (001) surface is calculated by the quantum method. The dependence of the EMDDF on emission angle and crystal structure has indicated that this quantum EMDDF strongly depends on the emission direction of Auger electrons and is sensitive to crystal structure. Comparisons made between the present results and classical Monte Carlo simulation results show pronounced differences due to electron-diffraction effects. The mean escape depth (MED) which describes the surface sensitivity of Auger electron spectroscopy, is also evaluated; the present calculation shows that the MED for a crystalline solid is about half that for an amorphous solid from a Monte Carlo calculation.