Scattering Fundamentals

It is difficult to observe tliese surface processes directly in CVD and MOCVD apparatus because tliey operate at pressures incompatible witli most teclmiques for surface analysis. Consequently, most fundamental studies have selected one or more of tliese steps for examination by molecular beam scattering, or in simplified model reactors from which samples can be transferred into UHV surface spectrometers witliout air exposure. Reference [4] describes many such studies. Additional tliemes and examples, illustrating botli progress achieved and remaining questions, are presented in section C2.18.4. 

The normal distribution of measurements (or the normal law of error) is the fundamental starting point for analysis of data. When a large number of measurements are made, the individual measurements are not all identical and equal to the accepted value /x, which is the mean of an infinite population or universe of data, but are scattered about /x, owing to random error. If the magnitude of any single measurement is the abscissa and the relative frequencies (i.e., the probability) of occurrence of different-sized measurements are the ordinate, the smooth curve drawn through the points (Fig. 2.10) is the normal or Gaussian distribution curve (also the error curve or probability curve). The term error curve arises when one considers the distribution of errors (x — /x) about the true value. 

Table 9 shows the classification system for blacks most commonly used in mbber. The ASTM numbering system is based on the fundamental particle si2e of the black. Particle si2e is deterrnined by several methods, including iodine absorption, nitrogen absorption, and light scattering. 

It is a fundamental principle of quantum mechanics that electrons bound in an atom can have only discrete energy values. Thus, when an electron strikes an atom its electrons can absorb energy from the incident electron in specific, discrete amounts. As a result the scattered incident electron can lose energy only in specific amounts. In EELS an incident electron beam of energy Eq bombards an atom or collection of atoms. After the interaction the energy loss E of the scattered electron beam is measured. Since the electronic energy states of different elements, and of a single element in different chemical environments, are unique, the emitted beam will contain information about the composition and chemistry of the specimen. 

Band gaps in semiconductors can be investigated by other optical methods, such as photoluminescence, cathodoluminescence, photoluminescence excitation spectroscopy, absorption, spectral ellipsometry, photocurrent spectroscopy, and resonant Raman spectroscopy. Photoluminescence and cathodoluminescence involve an emission process and hence can be used to evaluate only features near the fundamental band gap. The other methods are related to the absorption process or its derivative (resonant Raman scattering). Most of these methods require cryogenic temperatures. 

P. Schattschneideh Fundamentals of Inelastie Electron Scattering, Springer-Verlag, Wien - New York 1986. 

The reflection 7 of x-rays by a crystal (x-ray diffraction) results fundamentally from the unmodified scattering of x-rays by the atoms or ions in the different planes of the crystal. For many purposes, it suffices to regard the atoms or ions as the scattering centers, but a complete description of the process requires that the electrons be considered. 

The simplicity mentioned above exists for various kinds of samples that meet the fundamental requirements laid down in Chapters 6 and 7. Examples are a thin film on a suitable substrate, a sample dissolved at low concentration in a solvent transparent to x-rays, or a sample uniformly dispersed in a similarly transparent medium. In all cases, scattered x-rays should be at a minimum to keep the background low. From the point of view taken here, a trace is thus regarded as a major constituent in a sample if sensible absorption and enhancement effects are absent—if, that is, Equation 7-3 is valid. 

A modern laser Raman spectrometer consists of four fundamental components a laser source, an optical system for focusing the laser beam on to the sample and for directing the Raman scattered light to the monochromator entrance slit, a double or triple monochromator to disperse the scattered light, and a photoelectric detection system to measure the intensity of the light passing through the monochromator exit slit (Fig. 7). 

At a fundamental level, it has been shown that PECD stems from interference between electric dipole operator matrix elements of adjacent continuum f values, and that consequently the chiral parameters depend on the sine rather than the cosine of the relative scattering phases. Generally, this provides a unique probe of the photoionization dynamics in chiral species. More than that, this sine dependence invests the hj parameter with a greatly enhanced response to small changes in scattering phase, and it is believed that this accounts for an extraordinary sensitivity to small conformational changes, or indeed to molecular substitutions, that have only a minimal impact on the other photoionization parameters. 

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