Modeling electron emission and surface effects from diamond cathodes

Abstract

We developed modeling capabilities, within the Vorpal particle-in-cell code, for three-dimensional simulations of surface effects and electron emission from semiconductor photocathodes. They include calculation of emission probabilities using general, piece-wise continuous, space-time dependent surface potentials, effective mass, and band bending field effects. We applied these models, in combination with previously implemented capabilities for modeling charge generation and transport in diamond, to investigate the emission dependence on applied electric field in the range from approximately 2 MV/m to 17 MV/m along the [100] direction. The simulation results were compared to experimental data. For the considered parameter regime, conservation of transverse electron momentum (in the plane of the emission surface) allows direct emission from only two (parallel to [100]) of the six equivalent lowest conduction band valleys. When the electron affinity χ is the only parameter varied in the simulations, the value χ = 0.31 eV leads to overall qualitative agreement with the probability of emission deduced from experiments. Including band bending in the simulations improves the agreement with the experimental data, particularly at low applied fields, but not significantly. Using surface potentials with different profiles further allows us to investigate the emission as a function of potential barrier height, width, and vacuum level position. However, adding surface patches with different levels of hydrogenation, modeled with position-dependent electron affinity, leads to the closest agreement with the experimental data.

Theory of electron transport and emission from a semiconductor nanotip

“…In the transverse direction, the effective mass is also set to its bulk value m * t = 0.36m e . 29 Notice that for the adopted radii of the NW segments, the anisotropy and nonparabolicity of the bulk conduction band can affect the values of the quantized subband effective masses. 35 For the proof of principle calculations discussed below it is enough to use the bulk values.…”

“…For the diamond surface terminating the NW at z 0 we set χ = 0.3 eV. 29 The external electric field values < l a t e x i t s h a 1 _ b a s e 6 4 = " K f…”

“…The effect of the effective mass mismatch has already been examined for the bulk-vacuum interface in relation with the transverse momentum conservation. 29 Below, we examine new consequences of this effect rising fomr the band quantization.…”

“…28 Subsequently, modeling of electron emission from a planar hydrogenated diamond surface accounting for associated band banding effect, effective mass anisotropy, and the inhomogeneity of electron affinity has been reported. 29 Photocathodes of III-V semiconductors can also be activated to negative electron affinity. 30 In accord with Spicer's 3-step photoemission model, 31 carrier photoexcitation, transport, and emission simulations, based on a Monte Carlo (MC) method, have been reported for doped GaAs bulk slab and layered structures.…”