Fig. 4: Trajectory of the threshold photoelectrons.
From: Work function seen with sub-meV precision through laser photoemission
a The refraction and reflection of the photoelectrons and the definition of the threshold photoelectrons. Red, blue and black lines indicate the trajectory of the electrons. \({{\bf{k}}}\) is the photoelectron momentum before incident on the surface; \({{\bf{k}}}_{{\rm{s}}}\) and \({{\bf{k}}}{\!}_{{\rm{s}}}^{{\rm{th}}}\) are those after the incidence. b The energy diagram for the threshold photoelectrons. Ef, \({E}_{{\rm{PE}}}^{{\rm{th}}}\) and Es are the energy levels of the fastest, threshold and slowest photoelectron, respectively, and EF is the Fermi level. ϕs and ϕa are the work functions of the sample and analyser, respectively. The lower section shows the electric field existing between the sample and e-lens separated with the working distance of za − zs ~ 32 mm (Supplementary Note 1), where zs and za are the locus of the sample surface and e-lens entrance on the z axis, respectively. The vacuum level (Vvac) is the solution to the Poisson equation. \({\varepsilon }_{{\rm{s}}}^{\rm{th}}\) and \({\varepsilon }_{{\rm{a}}}^{{\rm{th}}}\) are the kinetic energy of the threshold photoelectron at z = zs and za, respectively. c The trajectory (black lines) of the threshold photoelectrons dragged by the electric field. The threshold photoelectron emitted normal to the surface has the smallest momentum (shortest black arrow) when entering the e-lens, and hence, is the slowest and forms the slowest-end cutoff. \({k}_{{\rm{a}}}^{\perp }\) is the z component of the threshold-photoelectron momentum at z = za and θ is the emission angle seen by the analyser.
