Transfer efficiency in ballistic electron emission microscopy taking diffraction of emitted hot electrons into account

We have analyzed the transfer efficiency of ballistic electron emission microscopy (BEEM), taking the finite spot size of the emitted electron beam from scanning probes into account. Three-dimensional diffraction from an aperture at a surface-metal/air interface is introduced to model an effect caused by the finiteness of spot size. As a general trend, the diffraction decreases BEEM transfer efficiency. The diffraction effect increases as the spot size decreases and the air-gap distance increases. In a Au/GaAs sample, BEEM transfer efficiency markedly deteriorates down to 6% of the value derived from a conventional planar tunneling theory when a spot size of 0.2 nm, an air-gap distance of 0.6 nm, and an electron energy of 0.2 eV, measured from the bottom of the GaAs conduction band, are assumed. BEEM transfer efficiency is markedly dependent on the spot size of the emitted hot electron. This result indicates that the BEEM current depends on the spatial resolution of the scanning probe, that is, the condition of the tip apex.