Quantum-mechanical simulations of photon-stimulated field emission by transfer matrices and Green's functions

For the purpose of simulating photon-stimulated field emission by taking account of three-dimensional aspects, a specific formulation of electronic scattering is developed. This formulation relies on both the transfer-matrix and Green’s-functions formalisms. It is combined with a Floquet expansion of the wave function for taking account of quanta exchanges between the electrons and the electromagnetic radiation. With specific techniques to preserve numerical stability, this methodology is well suited to compute the transmission of the field-emitted/photon-stimulated electrons between two electrodes and their propagation to a distant screen. The theory is applied to the computation of photon-stimulated field emission from a tungsten plane emitter (described by z<~0), which supports a 1-nm-long hemispherical protrusion. The extraction bias ranges from 12 to 24 V (the interelectrode distance is 4 nm). The electromagnetic radiation has a wavelength ranging from 0.1 to 10μ and a power flux density ranging from 5.96×1010 to 5.96×1012W/m2. Current-relative-increase curves, total-energy distributions (TED), and Fowler-Nordheim plots are provided. The results point out a resonance in the current enhancement at a radiation wavelength of approximately 0.3μ. Taking advantage of this resonance and working at low extraction bias leads to a better sensitivity of the emision current to the radiation power flux density.