Inelastic mean free path length

A parameter of fundamental importance in electron spectroscopy is the inelastic mean free path length (IMFP) for electrons of a given kinetic energy originating in solids. 

Both the absorption and the resonant tunneling experiments find quantization effects for layer thicknesses of 50 A or less. It is, however, not immediately obvious why the quantum states should be observed even in these thin layers. The discussion of the transport in Chapter 7 concludes that the inelastic mean free path length is about 10-15 A at the mobility edge. The rapid loss of phase coherence of the wavefunction should prevent the observation of quantum states even in a 50 A well, but there are some factors that may explain the observations. The mean free path increases at energies above the... 

Static defects scatter elastically the charge carriers. Electrons do not loose memory of the phase contained in their wave function and thus propagate through the sample in a coherent way. By contrast, electron-phonon or electron-electron collisions are inelastic and generally destroy the phase coherence. The resulting inelastic mean free path, Li , which is the distance that an electron travels between two inelastic collisions, is generally equal to the phase coherence length, the distance that an electron travels before its initial phase is destroyed ... 

It is not strictly correct to equate the inelastic mean free path with the attenuation length, as we do so essentially in Fig. 1. One would have to assume in the experiment that as many electrons are scattered elastically into as out of the direction of the analyser slits. Because of the net loss due to back scattering this can never be the case in practice. 

An entirely new situation arises for a semiconductor with NEA. Here the threshold for photoemission of electrons is the band gap energy, that is, a bulk rather than a surface property, and novel phenomena are to be expected. Tbis is indeed the case, and the most spectacular of these phenomena is certainly the contribution of bulk excitons to the photoelectron yield of diamond surfaces with NEA as first reported by Bandis and Pate [73, 107]. In addition, the depth from which electrons contribute to the yield is no longer limited by the inelastic mean free path of some tens of Angstroms but by the diffusion length of electrons and excitons of the order of micrometers, a fact that is responsible for the near 100% quantum efficiency of NEA diamond surfaces alluded to earlier (Section 10.3). 

In order to derive a composition or thickness from peak intensities, certain parameters characterizing the sample are typically needed. They enter the particular equation used for analysis [5, 6]. Examples of such parameters are the inelastic mean free path (IMEP) or the effective attenuation length (EAL) (defined below). Clearly, the uncertainty of the final result will depend on the validity of the model and the equation used for the particular specimen morphology, uncertainties of the measured peak intensities [6], and uncertainties of the sample-parameter data. 

The XPS spectra are strongly affected by the orientation of the sample, the source, and the spectrometer. Almost all (about 95%) of the signal emerges from the distance 3 A within the solid, where A is the inelastic mean free path of the electron, also called the attenuation length of the emerging electron. The sampling depth, d, of the subsurface analyzed by XPS is given by... 

The question may arise whether the self-energy effects are important in the normal state. These are known to be smaller than the inelastic backscattering nonlinearities in the ballistic regime [18]. If we decrease the contact size d or the elastic mean free path li in order to make the inelastic contribution negligible, the latter parameters become comparable to the Fermi wave length of charge carriers and the strong nonlinearities connected with localization occur, which masks the desired phonon structure [19]. 

Fig. 1. Mean free path for inelastic scattering, A, for aluminium [after Refs. (6) and (7)]. Experimental points measured mean attenuation lengths taken from the compilation by Powell (5)...

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