In this chapter time resolution will be introduced to photoemission experiments. This means not just a series of regular photoemission measurements to monitor the changes of a sample with time. In two-photon photoemission the time delay between the two photons is an additional experimental parameter which can be controlled with femtosecond resolution, i.e., on a time scale relevant for electronic processes. At the same time, the introduction of the second photon leads to the participation of an additional electronic state in the energy diagram for photoemission.
Energy diagramIn Figure 8.1 the transition from initial state |1 to an intermediate state |2 after the absorption of the photon with energy hν a is shown. The second photon of energy hν b excites the electron out of the intermediate state into the final state |3 . If the final state energy E 3 is above the vacuum energy E vac , the electron might leave the surface and its kinetic energy E kin is measured with an electron energy analyzer. Obviously, the initial state has to be occupied, i.e., its energy E 1 should be below the Fermi energy E F . The intermediate state on the other hand has to be empty at first. In most cases it is desirable to keep the photon energy hν a below the work function Φ = E vac − E F , because this constitutes the threshold for one-photon photoemission. This applies also to the other photon, because processes with the role of the two photons interchanged are possible as well.
Energy-resolved spectroscopyThe spectrum sketched at the right of Fig. 8.1 shows a peak at the final state energy E 3 . The cutoff at kinetic energy zero corresponds to the vacuum level E vac of the sample. Electrons with the highest energy after the absorption of the photons with energies hν a and hν b appear at kinetic energy E max − E vac = hν a + hν b − Φ. These limits are familiar from regular photoemission spectroscopy and can be used to determine the work function from the width of the spectrum. Similarly, the momentum k of the electron parallel to the surface is conserved for single-crystal surfaces. For electrons emitted at an angle ϑ with respect to the surface normal one obtainshk = √ 2mE kin sin ϑ. Umklapp processes would add reciprocal lattice vectors of the surface to the momentum conservation, but play usually no role in twophoton photoemission. One has to keep in mind that the kinetic energies are generally quite