Diploma - Max Planck Institute for Solid State Research

2.2 Photoemission Process 13
Figure 2.5: (a) general scheme of the three step model, (1) the photo excitation of the electron
inside solid, (2) transport to the surface and (3) the transmittion to the vacuum [28, p. 12]; (b)
sketch of the third step: penetration through the surface, only the parallel component of k is
conserved [28, p. 249]
distinguish between the wave vector of the crystal states k f and the momentum
of the excited electron K f = k i + G inside the solid.
(ii) Transport to the surface
After the excitation (having overcome the atomic potential) the electron travels
arbitrarily through the solid whereat the scattering is dominated by electronelectron
interaction. The electronic inelastic mean free path reads
λ (E, k) = τ d E
d k
and is approximately 3-5 Å for an energy range of 30-150 eV. Hence, one has to
include inelastic scattering processes for an appropriate description but they will
be neglected here. For further information I refer to [30].
(iii) Transmission to the vacuum
All electrons for which the component of the kinetic energy perpendicular to the
surface is large enough to overcome the surface potential, will transmit to the
vacuum:
2
2m K ⊥ 2 ≥ (E F − E 0 ) + Φ (2.13)
whereat E F is the Fermi level, E 0 the binding energy of the electron state and the
work function is denoted by Φ. The transmission through the surface conserves
the parallel momentum (cf. fig. 2.5b) and using the energy dispersion of the free
electron yields
K ‖ =
( 2m
2 E kin
) 1/2
sin ϑ out =
( 2m
2 E f − E F
) 1/2
sin ϑ in (2.14)