Electron transfer through semiconductor-vacuum interfaces with negative and positive electron affinity: effect of jump in mass

The effect of jump in electron mass at the crystal-vacuum interface on photoemission from semiconductors is considered. In the effective mass approximation, the angular and energy dependences of the electron transmission coefficient through interfaces with jump in mass and potential steps of different signs, corresponding to negative and positive electron affinities, are considered. It is shown that due to jump in mass, there are a critical energy and a critical angle of incidence of electrons, which separate qualitatively different angular and energy dependences of the transmission coefficient, respectively. Jump in mass makes it possible for electrons to transfer (up to complete transmission) through a positive potential step with a normal component of kinetic energy below the height of the step. The calculated dependences of the emission quantum yield of thermalized electrons on the affinity value are compared with the experimental data on photoemission from $p$-GaAs(Cs,O). Possible reasons for the significant differences between the experiment and the calculation are analyzed: a complex potential profile, including the near-surface band bending in the semiconductor and the image charge potential in vacuum, scattering in the (Cs,O) layer, and the need to go beyond the effective mass approximation and to take into account full Bloch nature of electron wave functions in semiconductors.