Metals electron inelastic mean free path

Depending on the energy tico of the incident photons, valence band states and even core level electrons can be excited. UPS is a surface-sensitive technique since electrons have a very short inelastic mean free path, Xi, which depends on the kinetic energy Ek, and has a minimum value of 0.5 nm for T k 100 eV. The leading edge of the valence band is taken as the VBM or HOMO maximum and has to be referred to which has to be determined from a clean inorganic metal surface. Those electrons with k > 0 are removed from the sample and transmitted to the detector. The fundamental equation of the photoemission process is (Einstein, 1905) ... 

Photoelectron spectroscopy of valence and core electrons in solids has been useful in the study of the surface properties of transition metals and other solid-phase materials. When photoelectron spectroscopy is performed on a solid sample, an additional step that must be considered is the escape of the resultant photoelectron from the bulk. The analysis can only be performed as deep as the electrons can escape from the bulk and then be detected. The escape depth is dependent upon the inelastic mean free path of the electrons, determined by electron-electron and electron-phonon collisions, which varies with photoelectron kinetic energy. The depth that can be probed is on the order of about 5-50 A, which makes this spectroscopy actually a surface-sensitive technique rather than a probe of the bulk properties of a material. Because photoelectron spectroscopy only probes such a thin layer, analysis of bulk materials, absorbed molecules, or thin films must be performed in ultrahigh vacuum (<10 torr) to prevent interference from contaminants that may adhere to the surface. 

XPS or AES is extensively used not only to indicate the cleanliness of the sample before transfer, but also to indicate the presence of adsorbates and their oxidation states following electrochemical experiments and transfer back into the UHV environment. In the case of model platinum-based electrocatalysts, the electron spectroscopies have been used to estimate the coverage of the adsorbate metal atoms or the alloy composition. In the case of alloys, or the nucleation and growth of metal adsorbate structures, the techniques give only the mean concentrations averaged over a depth determined by the inelastic mean free path of the emitted electrons. Adsorption and reaction at surfaces often depend on the... 

Fig. 22. L3 palladium edge of Pd metal (dotted line) compared with one-electron band theory (solid line) taking account of the partial (1 = 2) local density of states, of the inelastic mean free path and of the core-hole lifetime. The dashed line shows the total density of states of palladium metal, which is quite different from the absorption spectrum. The zero of the energy scale is fixed at the Fermi energy...

The structural and electronic properties of the top few atomic layers of metals and semiconductors play a dominant role in the chemical (catalysis, corrosion) and electronic (semiconductor device interface) properties of a range of materials. For the study of electronic structure, surface analytical techniques typically employ particles such as photons, electrons, atoms, molecules, or ions. These particles must have just enough energy to probe only a few tenths of a nanometer into the solid, thereby investigating the surface atoms rather than the bulk atoms. Since low-energy electrons have inelastic mean free paths of only a few tenths of a nanometer in solids, they are made use of in many techniques, either as the incident projectile or as a particle emitted from the surface region. 

The information depth of both electron spectroscopies is determined by the inelastic mean-free path of the emitted electrons, which depends on the kinetic energy of the electron in the solid matrix. This dependence is known and has a minimum of about two atomic layers around 25 eV (53). The electron mean-free path is typically larger in oxides than in metals at equal energy, and it is particularly large for zeolites because of their low density. Together with reported ionization cross sections and in the case of AES, Auger decay probabilities, quantitative surface analysis is possible. Compilations of standard spectra are available from which peak energies and sensitivity factors can be obtained (53). 

These carbon films are considered as dirty metals whose temperature dependence of conductivity would depend on the inelastic mean free path 1 T) [76]. Now, when electron-phonon scattering is dominant, the mean free path will follow the relationship of 1, T) T. At low temperatures (for T < where 0 is the Debye temperature of the material) for both electron-electron scattering and electron-phonon scattering. 

Figure 3.1.11 Inelastic mean free path of electrons in metals. see e.g. G. ErtI and j. Ktippers, Low Energy Electrons and Surface Chemistry" (Verlag Chemie, Weinheim, 1974).

The inelastic point-contact spectra of phonons in metals are based on expansion of the nonlinear I — V characteristic in terms proportional to d/l , where d is the characteristic size of metallic nanoconstriction connecting two bulk metal half-spaces and Zt is the inelastic electron mean free path [1, 2]. 

Photoelectron spectroscopy is an inherently surface-sensitive technique. The electron inelastic scattering mean-free path (MFP) in solids depends on electron KE, and is very small, typically 0.5-2 nm, at the KE values of interest (10-10 eV). For metal particles and large MMC, particle diameters can be close to the MFP for bulk metals. 

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