Lowest mean transverse energy obtainable from a photocathode

The intrinsic normalized emittance of a photoemission source is eps_n = $\sigma_x$ sqrt(MTE/(m c^2)), with sigma_x the rms source size and MTE the mean transverse energy of emitted electrons. Values of approximately $5\,\mathrm{meV}$ were reported around 2020 from near-threshold photoemission of cryogenically cooled single-crystal Cu(100). Determine the lowest achievable MTE at quantum efficiency $\ge 1e-5$ and the physics that sets it (lattice temperature, surface roughness and work-function variation, electron-phonon and electron-electron scattering, multiphoton emission).

MTE measurements versus temperature, photon energy and surface preparation on candidate cathodes, matched by a photoemission model including the surface.