Electron Mean Free Paths

As we have seen, the electron is the easiest probe to make surface sensitive. For that reason, a number of hybrid teclmiques have been designed that combine the virtues of electrons and of other probes. In particular, electrons and photons (x-rays) have been used together in teclmiques like PD [10] and SEXAFS (or EXAFS, which is the high-energy limit of XAES) [2, Hj. Both of these rely on diffraction by electrons, which have been excited by photons. In the case of PD, the electrons themselves are detected after emission out of the surface, limiting the depth of sampling to that given by the electron mean free path. 

Kriebig U and Fragstein C V 1969 The limitation of electron mean free path in small silver particles Z. Physik 224 307... 

The above measurements all rely on force and displacement data to evaluate adhesion and mechanical properties. As mentioned in the introduction, a very useful piece of information to have about a nanoscale contact would be its area (or radius). Since the scale of the contacts is below the optical limit, the techniques available are somewhat limited. Electrical resistance has been used in early contact studies on clean metal surfaces [62], but is limited to conducting interfaces. Recently, Enachescu et al. [63] used conductance measurements to examine adhesion in an ideally hard contact (diamond vs. tungsten carbide). In the limit of contact size below the electronic mean free path, but above that of quantized conductance, the contact area scales linearly with contact conductance. They used these measurements to demonstrate that friction was proportional to contact area, and the area vs. load data were best-fit to a DMT model. 

Two mechanisms which contribute to GMR have been identified, a "non-local" mechanism and a "quantum" mechanism. To understand the first or non-local, mechanism it is necessary to understand that on the scale of the electron mean free path (possibly 10 to 20 nanometers at room temperature) electrical conduction is a non-local phenomenon. Electrons may be accelerated by an electric field in one region and contribute to the current in other regions. To a good approximation they may viewed as contributing to the current until they are scattered. 

When the size of metals is comparable or smaller than the electron mean free path, for example in metal nanoparticles, then the motion of electrons becomes limited by the size of the nanoparticle and interactions are expected to be mostly with the surface. This gives rise to surface plasmon resonance effects, in which the optical properties are determined by the collective oscillation of conduction electrons resulting from the interaction with light. Plasmonic metal nanoparticles and nanostructures are known to absorb light strongly, but they typically are not or only weakly luminescent [22-24]. 

Informations on the vibrational and electron mean free path properties. Such analysis is possible only if the interface phase is very well defined, and if temperature dependent measurements are done and compared. Debye Waller effects can be tangled with ordering transformation of the interface phase as a function of temperature and so on. If a single phase interface with order at least to the second nearest neighbour is recognised, then a temperature dependent Debye Waller, and mean free path analysis can be attempted. 

The breakdown of the diffusion theory of bulk ion recombination in high-mobility systems has been clearly demonstrated by the results of the computer simulations by Tachiya [39]. In his method, it was assumed that the electron motion may be described by the Smoluchowski equation only at distances from the cation, which are much larger than the electron mean free path. At shorter distances, individual trajectories of electrons were simulated, and the probability that an electron recombines with the positive ion before separating again to a large distance from the cation was determined. The value of the recombination rate constant was calculated by matching the net inward current of electrons... 

The simulation results of the electron ion recombination rate constant obtained in Ref. 39 are plotted in Fig. 5. The figure shows that the rate constant becomes lower than the Debye-Smoluchowski value when the electron mean free path exceeds —O.Olrc. At higher values of X, the ratio kjk further decreases with increasing mean free path. The simulation results are found to be in good agreement with the experimental data on the electron ion recombination rate constant in liquid methane, which are also plotted in Fig. 5. 

Figure 5 The rate constant of bulk electron-ion recombination, relative to the Debye-Smoluchowski value [Eq. (36)], as a function of the electron mean free path X. The solid line represents the simulation results, and the circles show the experimental data for liquid methane [49]. (From Ref. 39.)...

For UPS, the access to bulk properties can be gained by using several radiation sources as e.g. Hel and Hell (hv = 21.22 and 40.82 eV, respectively), and taking advantage of the electron mean free path variation. As can be seen by inspection of Fig. 8, the mean free paths of He I and AlKj(-excited photoelectrons are quite similar. 

The curves of Fig. 12.17 nicely illustrate the varied optical effects exhibited by small metallic particles in the surface mode region, both those explained by Mie theory with bulk optical constants and those requiring modification of the electron mean free path (see Section 12.1). Absorption by particles with radii between about 26 and 100 A peaks near the Frohlich frequency (XF — 5200 A), which is independent of size. Absorption decreases markedly at longer... 

Fig, 4.1. The universal curve for the electron mean free path as a function of electron kinetic energy. Dots show individual measurements... 

For bulk homogeneous material A of thickness essentially infinite compared with the typical electron mean free paths the intensity of the elastic peak. Ia is given by Eq. (1). 

The range of coherence follows naturally from the BCS theory, and we see now why it becomes short in alloys. The electron mean free path is much shorter in an alloy than in a pure metal, and electron scattering tends to break up the correlated pairs, so dial for very short mean free paths one would expect die coherence length to become comparable to the mean free path. Then the ratio k i/f (called the Ginzburg-Landau order parameter) becomes greater than unity, and the observed magnetic properties of alloy superconductors can be derived. The two kinds of superconductors, namely those with k < 1/-/(2T and those with k > l/,/(2j (the inequalities follow from the detailed theory) are called respectively type I and type II superconductors. 

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