Cross-sections photoemission

Cross sections for photoemission from Zr 3d and Si 2s core levels,... 

For metal/semiconductor interfaces the limitations coming from 1) are not very severe since the cross sections for photoemission and the lifetime broadening of such deep state photopeaks along with the poor energy resolution of the photon source... 

From the experimental viewpoint 1. the analysis of the variation of photoionization cross sections (affecting the intensities of photoelectron spectroscopy), gives an insight into the orbital composition of the bands of the solid 2. the combination of direct and inverse photoemission provides a powerful tool to assess the structure of occupied and of empty states, and, in the case of localized 5 f states, permits the determination of a fundamental quantity, the Coulomb correlation energy, governing the physical properties of narrow bands. 

In Fig. 2, the two methods (XPS and UPS) are illustrated. Very often, a combination of the two methods is employed (XPSAJPS) the advantages of this combination will be illustrated later when the properties of photoemission cross-sections will be discussed. 

Photoemission cross-sections are different for different orbital states of an atom. Furthermore, for a given orbital state, the photoemission cross-section depends strongly on the energy of the exciting photon. This provides a very useful tool in photoemission as we shall discuss later. 

In the Koopmans theorem Umit the photoemission of one-electron from an atom or a core in a solid is given by a single Une, positioned at the eigenvalue of the electron in the initial state. The intensity of this line depends on the cross-section for the event, which is determined by the one-electron atomic wavefunctions Wi ( j m)(-Eb) and Pfln(nM, m )(Ekin) (where the atomic quantum numbers are indicated as well as the eigenvalues En,i,m = Eb and E dn of the initial and final state) (the overlap integral of (13)... 

The total cross-section for a photoemission event occuring in an (nl) initial state is given by ... 

It must be emphasized that these cross sections are only valid for an electron excitation into free-electron like final states (conduction band states with parabolic band shape) and not for resonance transitions as f — d or p - d excitations. If too low excitation energies (< 10 eV, see Table 1) are used in UPS, the final states are not free-electron like. Thus the photoemission process is not simply determined by cross-sections as discussed above but by cross-sections for optical transitions as well as a joint density of states, i.e. a combination of occupied initial and empty final states. 

The 5 f cross-section is particularly sensitive to the photon energy variation. This is a fortunate fact that has allowed a great deal of experimental and theoretical results to be obtained in actinides solids photoemission. In fact, due to it, 5 f states and 5 f character in bands are easily identified. 

The possible contribution of 5 f states to the BIS intensity at Ep suggests that some 5 f character may exist (even in Th, with a 5 f configuration) in the composition of the occupied valence band. In fact a small tail of occupied 5f states (0.5 states per atom. Ref. 57) is supposed to contribute to the intensity of the XPS experimental spectrum the rather high intensity of which may be due to the high cross-section for 5 f excitation. Energy dependent photoemission should then be able to identify this contribution. 

The other possible assignment of the 2.3 eV structure to 6d excitation (line II, Ref. 56, 66) cannot be ruled out. Resonant photoemission on Ce compounds ° shows indeed that a resonant enhancement at the 4 d 4 f threshold is not only present for 4f but also for 5 d emission. Thus an easy identification of 4f emission is not possible. Theoretical calculations of the cross section due to resonant enhancement result in a 2 eV shift to lower photon energy for the maximum 5d enhancement compared with the 4f enhancement ... 

In conclusion, the partial localization effects in the valence band spectra of the light actinides, although extremely important if convincingly verified, still need much experimental and theoretical investigation. It is expected that the situation will improve considerably when resonant photoemission studies become available for actinide compounds in which the 5 f and 6 d emissions do not overlap. In addition, theoretical calculations of 5 f and 6 d cross sections near the 5 d threshold will be very helpful. 

Figure 4 shows the combined XPS/BIS results for UO2. The main peak in inverse photoemission, centered at approximately 5 eV above Ep is attributed to a 5 f state, in part because of its dominating intensity (high cross section of states at 1500 eV electron excitation energy), in part by a comparison with the measured spectrum of Th (see Fig. 9), in which the 5 f states are well separated from s and d states. Thus, the peak... 

Fig. 2 Valence band photoemission profiles of empty C82 and Gd C82, recorded at room temperature with He Ia (21.22 eV) radiation. The inset shows the region close to the Fermi level on an expanded scale. For this photon energy, the photoionisation cross sections of the C 2s and C 2p levels dominate that of the Gd 4f levels...

Experimental information on the valence levels comes essentially from photoemission XPS and UPS measure densities of states (DOSs) convoluted with absorption cross sections, and these DOS values can be compared with those computed from VEH valence-band structures [195]. This has now been done for several CPs and the agreement is good. It would be more instructive to compare the actual band structure to angle-resolved (ARUPS) measurements, but this has never been done. What comes nearest is an ARUPS study of a series of long alkanes taken as models for polyethylene, a nonconjugated polymer [196]. 

Figure 8.12 Cross section in the (kx, ky) plane of the calculated Fermi surface in Y 1 2 3. The experimental results from angle-resolved photoemission (ARPES), de Haas van Alphen measurements (dHvA), and angular correlation of annihilation radiations (ACAR) are indicated. From Pickett etal. [61].

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