Mean free path of the electrons

The strong point of AES is that it provides a quick measurement of elements in the surface region of conducting samples. For elements having Auger electrons with energies hr the range of 100-300 eV where the mean free path of the electrons is close to its minimum, AES is considerably more surface sensitive than XPS. 

As is to be expected, inherent disorder has an effect on electronic and optical properties of amorphous semiconductors providing for distinct differences between them and the crystalline semiconductors. The inherent disorder provides for localized as well as nonlocalized states within the same band such that a critical energy, can be defined by distinguishing the two types of states (4). At E = E, the mean free path of the electron is on the order of the interatomic distance and the wave function fluctuates randomly such that the quantum number, k, is no longer vaHd. For E < E the wave functions are localized and for E > E they are nonlocalized. For E > E the motion of the electron is diffusive and the extended state mobiHty is approximately 10 cm /sV. For U <, conduction takes place by hopping from one localized site to the next. Hence, at U =, )J. goes through a... 

When the electron beam enters the sample, it penetrates a small volume, typically about one cubic micron (10-18m3 ). X-rays are emitted from most of this volume, but Auger signals arise from much smaller volumes, down to about 3 x 10 25m3. The Auger analytical volume depends on the beam diameter and on the escape depth of the Auger electrons. The mean free paths of the electrons depend on their energies and on the sample material, with values up to 25 nm under practical analytical conditions. 

The high density of states found in the 3c/bands of Fe, Co, and Ni leads to a reduction of the mean free path of the electrons in this band. This causes a decrease in their mobility and hence in the electrical conductivity of these elements compared to simple metals and copper where the conduction electrons are in s/p bands. 

Here we will summarize, from the previous subsections as well as from literature, some typical properties and representative parameters (see table 6) of the superconducting state of YNi2B2C and LuNi2B2C where completeness is not attempted. These materials are usually clean-limit type II superconductors. However by substitutional disorder on the rare earth site in (Y,Lu)Ni2B2C or on the transition-metal site in Lu(Ni,Co)2B2C the residual resistance ratio RRR = p(300 K)/p(Tc), where p(T) is the normal state resistivity, and the mean free path / of the electrons in the normal state can be considerably reduced... 

Equation (5.4) is valid as long as the skin depth is large in comparison to the mean free path of the electrons in the metal. This holds true in the microwave range at room temperature, for cryogenic temperature the surface resistance lies above the values predicted by Equation (5.4) and exhibits a f2 3 rather than a f1 2 frequency dependence (anomalous skin effect [7]). 

X is the inelastic mean free path of the electron (see Fig. 3.1) a1 is the mean-squared displacement of atoms in the sample ... 

Auger electron spectroscopy (AES) — When an electron is removed from a level of energy E of a surface atom, the hole is filled by an electron from a higher electronic level E2. The energy difference between the two involved orbitals is transferred to a third electron of level /i3 which then leaves the atom and may be measured as an Auger electron. Due to the mean free path of the electrons AES is a surface analytical method with a depth resolution of some few nm as in the case of XPS. The excitation of electrons and the primary ionization process... 

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. 

For the majority of industrial catalysts, the sizes of supported metal particles arc less than the mean free path of the electrons analysed. All the metal in the particles is effectively analysed. For highly dispersed systems, XPS surface analysis and bulk X-ray nuorcsccncc analysis therefore give similar results. Comparing information from these two techniques can be used to show a change in the distribution of metals on the surface due, for example, to sintering or to the inclusion of one of the metals into the carrier structure. 

X-ray photoelectron diffraction is the coherent superposition of a directly photo-emitted electron wave with the elastically scattered waves from near-neighboring atoms. This gives element-specific structural information about the near surface atoms in a single crystal [8-10]. The short inelastic mean free path of the electron waves at the kinetic energies of interest (15 to 1000 eV) leads to surface sensitivity and determination of the atomic geometry of the emitting atom. The known energies of narrow XPS core-level peaks lead to element specificity. The resolution of surface peaks and chemical shifts may even sometimes lead to a chemical state-specific structure determination. 

Instead of this we must regard the electrons as not entirely free but as colliding from time to time with the atoms of the lattice. Thus the electrons describe zig-zag paths, and the paths described in the magnetic field will exhibit only slight deviations from these if the motion is approximately rectilinear between two collisions, i.e. if the radius of curvature is large compared with the mean free path of the electrons. As we know, the angular velocity of the electrons is... 

F is the bulk collision constant, A is a positive dimensionless factor, Vf is the Fermi velocity and R the particle radius. From a classical point of view, this modification is supported by the fact that, when the radius is smaller than the bulk mean free path of the electrons, there is an additional scattering factor at the particle surface. This phenomenon, known as the mean free path effect, is abundantly discussed in [19]. In a quantum approach, the boundary conditions imposed to the electron wave functions lead to the appearance of individual electron-hole excitations (Fandau damping) [21] resulting in the broadening of the SPR band proportional to the inverse of the particle radius as in Eq. (8) [22]. A chemical interface damping mechanism has also been considered, leading to the l/R dependence of F [23]. 

The phase shift of the Friedel oscillations by k/2 from a cosine-function to a minus sine-function was recently reported as a common effect of the short mean-free path of the electrons [5.126], an interpretation quite similar to that argued by Kaneyoshi for the effective exchange interaction described in the review. Structure-induced pseudo gaps at EF in amorphous Mg-Zn alloys mentioned above, were confirmed and were also found in the mean time for Ca-Zn [5.127]. 

One possible explanation of this observation lies in the fact that the energy distribution of the electrons changes with benzene partial pressure. (The rare gas probably has little effect compared with benzene because of the much lower ionization potential of the latter.) At higher partial pressures of benzene, the electron-benzene collision rate increases and the mean free path of the electrons decreases. These changes would cause a limitation of the energy which electrons could gain in the alternating... 

Electron transport in the nanoparticles may be influenced by bulk and surface scattering and trapping. If the mean free path of the electron is much smaller than the particle radius, additional surface scattering will not have much effect on the movement of electrons from particle to particle. However, if the mean free path of the electrons is larger than the particle radius, scattering at the surface becomes important. The geometry of the junction between particles is also likely to influence carrier... 

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