Multiple scattering, of electrons

In any of the steps 1, 3 and 4, multiple scattering of electrons can play an important role in the techniques of interest here. On the one hand, multiple scattering provides a greater sensitivity to various aspects of structure on the other hand, it complicates the theoretical treatment, i.e. it complicates the extraction of the structural information. For the following discussion it will be useful to first describe in more detail a couple of important features of electron scattering by individual atoms in a surface. 

The background derives mainly from the multiple scattering of electron and ihe extension of adsorption edges. The background to be subtracted from the EELS spectrum is empirically described as... 

A second powerful use of diffraction is in atomic-scale structure determination, which is especially well known for LEED [127, 163-166]. There the experimental and calculated intensity-voltage (I-V) curves are compared for various surface structures, taking multiple scattering of electrons into account (see Chapter 3.2.1 in Volume 1). However, there is a complication in performing the calculations for QCs because periodic boundary conditions cannot be applied (the same problem noted earlier for DFT). 

Affected by multiple scattering are, in particular, porous materials with high electron density (e.g., graphite, carbon fibers). The multiple scattering of isotropic two-phase materials is treated by Luzatti [81] based on the Fourier transform theory. Perret and Ruland [31,82] generalize his theory and describe how to quantify the effect. For the simple structural model of Debye and Bueche [17], Ruland and Tompa [83] compute the effect of the inevitable multiple scattering on determined structural parameters of the studied material. 

In high-mobility liquids, the quasi-free electron is often visualized as having an effective mass m different fron the usual electron mass m. It arises due to multiple scattering of the electron while the mean free path remains long. The ratio of mean acceleration to an external force can be defined as the inverse effective mass. Often, the effective mass is equated to the electron mass m when its value is unknown and difficult to determine. In LRGs values of mVm 0.3 to 0.5 have been estimated (Asaf and Steinberger,1974). Ascarelli (1986) uses mVm = 0.27 in LXe and a density-dependent value in LAr. 

Here P( R ) is the scattering potential for the ensemble of scatters at locations R G is the free-space electron propagator and T0 the f-matrix for multiple scattering of the electron by the surface. 

Due to the extremely short wavelengths of the accelerated electrons, the resolution of the instrument is not due to the radiation diffraction limits but to other effects such as multiple scattering of the electrons in the resist layer and substrate surface, and secondary electron emission [73,75,78]. These, mainly resist dependent, effects are hard to identify in detail but can be controlled to some extent during the exposure. However, it is not just the resolution of the resist which is the controlling factor in the ultimate particle size reached, rather it depends on exposure conditions (dose, beam intensity, etc.), the type of developer and processing technique used, and the way in which the hnal pattern is transferred to the substrate [79]. 

The sum in the right-hand side of equation (73) describes the perturbation of the scattering at atomic nucleus due to the multiple scattering on electrons. In the first approximation, the scattering matrix is determined as... 

Multiple scattering of the incident or primary electrons as they enter the specimen causes them to follow numerous trajectories. This diffusion of the electron beam is mainly dependent on the atomic number of the specimen and also on the energy of the primary electrons. A useful equation derived by Everhart and Hoff (.2) describes the electron beam energy dissipation range for low atomic number elements as ... 

Electronic transitions within the valence shell of atoms and molecules appear in the energy-loss spectrum from a few electron volts up to, and somewhat beyond, the first ionization energy. Valence-shell electron spectroscopy employs incident electron energies from the threshold required for excitation up to many kiloelectron volts. The energy resolution is usually sufficient to observe vibrational structure within the Franck-Condon envelope of an electronic transition. The sample in valence-shell electron energy-loss spectroscopy is most often in the gas phase at a sufficiently low pressure to avoid multiple scattering of the... 

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