Predictions of range distributions

An essential first step in the consideration of ion implantation effects is to understand how energy is coupled into the target material. We will first present examples of energy transfer and ion range, and then indicate how these features have been calculated. In practice there has been a continuous interaction between the theoretical and experimental assessments of ion ranges. This has resulted in modifications to the theories so that there are now tabulations and computer codes which predict ion ranges in virtually any ion/target combination. These computations are accurate to within 5–15%. Consequently, although it is useful to know the underlying assumptions of the range theories, and hence their limitations, the majority of the profiles for the distributions of implanted ions are calculated from standard computer simulations. Since knowledge of the ion range, damage distribution or surface sputtering involves many factors in addition to the initial ion range, the existing level of accuracy is perfectly acceptable. Indeed, divergence between measured and computed ranges is frequently not a result of a failure of the computation, but, rather, it results from the fact that such computer codes do not allow for subsequent migration and secondary processes. As has already been mentioned briefly in Chapter 1, there are two main processes which slow down the incoming ion. These are electronic excitations and nuclear collisions. The rate of energy transfer for each process is a function of the nuclear charge and mass of the incoming ion (Z1, M1), and the target (Z2, M2), as well as the energy.

Ion implantation may be used to change the optical properties of insulators, either because of the chemical presence of the dopant ions, or more generally because of the radiation damage caused during their implantation. The latter effect produces a significant change in the refractive indices of most materials, and consequently He+ implantation has been used to define optical waveguides in a wide variety of substrates. These include electro-optic, non-linear and laser host materials, with key successes in quartz, LiNbO3, KNbO3, KTiOPO4 (KTP), Bi4Ge3O12 (BGO), garnets such as Y3Al5O12 (YAG), and amorphous glasses such as silica and lead germanate.

Although this technique has wide applicability, the refractive index profiles vary considerably between materials, and even between different indices of the same material. The index change may vary in degree, and even in sign, for both the nuclear collision and the electronic ionisation regions. These effects are discussed in this chapter, together with their applicability in the formation of optical waveguides, and more complex structures. Of particular interest are the three detailed examples of quartz, LiNbO3 and Bi4Ge3O12 since between them they embody most of the features so far observed in ion implanted waveguides in insulating materials. The performance of the implanted waveguides is considered in terms of their thermal stability and their attenuation due to absorption, scattering and tunnelling losses. The He+ guides are first compared with those produced by conventional chemical diffusion methods. At the end of the chapter, waveguides formed by implantation of chemically active components are discussed.

Spectroscopy is concerned with the interaction of light with matter. This monograph deals with collision-induced absorption of radiation in gases, especially in the infrared region of the spectrum. Contrary to the more familiar molecular spectroscopy which has been treated in a number of well-known volumes, this monograph focuses on the supermolecular spectra observable in dense gases; it is the first monograph on the subject.

For the present purpose, it is useful to distinguish molecular from supermolecular spectra. In ordinary spectroscopy, the dipole moments responsible for absorption and emission are those of individual atoms and molecules. Ordinary (or allowed) spectra are caused by intra-atomic and intra molecular dynamics. Collisions may shift and broaden the observable lines, but in ordinary spectroscopy collisional interactions are generally not thought of as a source of spectral intensity. In other words, the integrated intensities of ordinary spectral lines are basically given by the square of the dipole transition matrix elements of individual molecules, regardless of intermolecular interactions that might or might not take place. Supermolecular spectra, on the other hand, arise from interaction-induced dipole moments, that is dipole moments which do not exist in the individual (i.e., non-interacting) molecules. Interaction-induced dipole moments may arise, for example, by polarization of the collisional partner in the electric multipole field surrounding a molecule, or by intermolecular exchange and dispersion forces, which cause a temporary rearrangement of electronic charge for the duration of the interaction.

In Chapter 5 the absorption spectra of complexes of interacting atoms were considered. If some or all of the interacting members of a complex are molecular, additional degrees of freedom exist and may be excited in the presence of radiation. As a result, besides the translational profiles discussed in Chapter 5, new spectral bands appear at the rotovibrational transition frequencies of the molecules involved, and at sums and differences of such frequencies – even if the non-interacting molecules are infrared inactive. The theory of absorption by small complexes involving molecules is considered in the present Chapter.

We will be concerned with the spectral bands in the microwave and infrared regions. The translational and the purely rotational bands appear both at low frequencies and form in general one composite band, especially at the higher temperatures where individual lines tend to overlap (‘rototranslational band’). Moreover, various rotovibrational bands in the near infrared will be considered, such as the fundamental and the overtone bands. Even high overtone bands in the visible are of interest, e.g., of H2. We have seen in Chapter 3 that induced spectra of the kind are readily discernible in gases whose (non-interacting) molecules are infrared inactive, but evidence exists that suggests the presence of induced absorption in the allowed molecular bands as well. Induced absorption involving electronic transitions will be briefly considered in Chapter 7.

The existing bibliographies on collision-induced absorption (CIA) list more than 800 original papers published in the 45 years of history of the field. Furthermore, a number of review articles focusing on one aspect of CIA or another are listed, along with compilations of lectures given at summer schools, advanced research seminars or scientific conferences. A monograph which attempts to review the experimental and theoretical foundations of CIA, however, cannot be found in these carefully compiled listings.

Yet the field is of great significance and continues to attract numerous specialists from various disciplines. CIA is a basic science dealing with the interaction of supermolecular systems with light. It has important applications, for example in the atmospheric sciences. CIA exists in all molecular fluids and mixtures. It is ubiquitous in dense, neutral matter and is especially striking in matter composed of infrared-inactive molecules. As a science, CIA has long since acquired a state of maturity. Not only do we have a wealth of experimental observations and data for virtually all common gases and liquids, but rigorous theory based on first principles exists and explains nearly all experimental results in considerable detail. Ab initio calculations of most aspects of CIA are possible which show a high degree of consistency with observation, especially in the low-density limit.

In this Chapter, we will briefly look at a number of topics related to collision-induced absorption of infrared radiation in gases. Specifically, in Section 7.1, we consider collision-induced spectra involving electronic transitions in one or more of the interacting molecules. In Section 7.2, we focus on collision-induced light scattering, which is related to collision-induced absorption in the same way that Raman and infrared spectra of ordinary molecules are related. The collision-induced Raman process arises from the fact that the polarizability of interacting atoms/molecules differs from the sum of polarizabilities of the non-interacting species. Closely related to the collision-induced Raman and infrared spectroscopies are the second (and higher) virial coefficients of the dielectric properties of gases, which provide independent measurements of the collision-induced dipole moments, Section 7.3. Finally, we look at the astrophysical and other applications of collision-induced absorption in Sections 7.4 and 7.5.

Collision-induced electronic spectra

Collision-induced electronic spectra have many features in common with rovibrotranslational induced absorption. In this Section, we take a look at the electronic spectra. We start with a historical note on the famous forbidden oxygen absorption bands in the infrared, visible and ultraviolet. We proceed with a brief study of the common features, as well as of the differences, of electronic and rovibrotranslational induced absorption.

In this Appendix we attempt to briefly review developments since the early 1990ies in the field of collision-induced absorption in gases. Many of the new contributions were announced, and numerous references to current literature were given in the proceedings of periodic conferences and special workshops. We mention especially the Proceedings of the biennial International Conferences on Spectral Line Shapes and the annual Symposia on Molecular Spectroscopy. New work in collision-induced absorption in gases has been reviewed in the Proceedings of a NATO Advanced Study Institute, a NATO Advanced Research Workshops, and in a recent monograph Molecular Complexes in Earth's, Planetary, Cometary, and Interstellar Atmospheres. A multi-authored volume, a significantly augmented treatment of bremsstrahlung, is also of interest here, for example when electrically charged particles exist in dense, largely neutral and hot environments, e.g., in shock waves, in the atmospheres of “cool” white dwarf stars, in sonoluminescence studies, etc.

Binary Interaction-Induced Dipoles.Ab initio quantum chemical calculations of interaction-induced dipole surfaces are known for some time (Section 4.4, pp. 159 ff.) Such calculations were recently extended for the H2—He and H2—H2 systems, to account more closely for the dependencies of such data on the rotovibrational states of the H2 molecules.

The theory of collision-induced absorption developed by van Kranendonk and coworkers and other authors has emphasized spectral moments (sum formulae) of low order. These are given in closed form by relatively simple expressions which are readily evaluated. Moments can also be obtained from spectroscopic measurements by integrations over the profile so that theory and measurement may be compared. A high degree of understanding of the observations could thus be achieved at a fundamental level. Moments characterize spectral profiles in important ways. The zeroth and first moments, for example, represent in essence total intensity and mean width, the most striking parameters of a spectral profile.

While spectral moments permit significant comparisons between measurements and theory, it is clear that some information is lost if a spectroscopic measurement is reduced to just one or two numbers. Furthermore, for the determination of experimental moments, substantial extrapolations of the measured spectra to low and high frequencies are usually necessary which introduce some uncertainty, even if large parts of the spectra are known accurately. For these reasons, line shape computations are indispensible for detailed analyses of measured spectra, especially where the complete absorption spectra cannot be measured. Moreover, one might expect that the line shape of the induced spectra, with its ‘differential’ features like logarithmic slopes and curvatures and the dimer structures, depend to a greater degree on the details of the intermolecular interactions than the spectral moments.

In this chapter we summarize some background information concerning molecular collisions, dipoles and radiation, spectroscopy, and statistical mechanics that will be needed later. This Chapter should be skipped in a first reading. It is hoped that a reader who comes back to this Chapter later with specific questions will find the answers here — or, at least, some useful reference for further study.

Intermolecular potentials

The ideal gas law, Eq. 1.1 with B = C = … = 0, may be derived with the assumption of non-interacting ‘point particles’. While in the case of rarefied gases at high temperatures this assumption is successful in that it predicts the relationship between pressure, density and temperature of a gas in close agreement with actual measurement, it was clear that important features of gaseous matter, such as condensation, the incompressibility of liquids and solids, etc., could not be modeled on that basis. As early as in 1857, Clausius argued convincingly that intermolecular forces must be repulsive at short range and attractive at long range. When in 1873 van der Waals developed his famous equation of state, a significant improvement over the ideal gas law, he assumed a repulsion like that of hard spheres at near range, and attraction at a more distant range.

Our general understanding of molecular collisions and energy transfer rests mainly upon classical mechanics. Except for particular quantum mechanical processes, such as transitions between different electronic states, and quantum mechanical features like resonances or interferences classical mechanics is a very useful tool for the study of molecular encounters (Porter and Raff 1976; Pattengill 1979; Truhlar and Muckerman 1979; Schatz 1983; Raff and Thompson 1985; Levine and Bernstein 1987:ch.4). This holds true for photodissociation as well (Goursaud, Sizun, and Fiquet-Fayard 1976; Heller 1978a; Brown and Heller 1981; Schinke 1986c; Goldfield, Houston, and Ezra 1986; Schinke 1988b; Guo and Murrell 1988a,b).

Classical mechanics is the limit of quantum mechanics as the de Broglie wavelength λB = 2πħ/(2mE)½ becomes small. The total energy released as translational and internal energy in UV photodissociation often exceeds 1 eV and therefore λB is of the order of 0.1 Å or shorter. On the other hand, the range of the potential is typically much larger so that the quantum mechanical wavefunction performs many oscillations over the entire interaction region (see Figures 2.3 and 3.2, for example). Furthermore, in many cases the fragments are produced with high internal excitation (Figure 3.3) which additionally favors a classical description.

The classical picture of photodissociation closely resembles the timedependent view. The electronic transition from the ground to the excited electronic state is assumed to take place instantaneously so that the internal coordinates and corresponding momenta of the parent molecule remain unchanged during the excitation step (vertical transition).

Rotational excitation of photofragments is a wide field with many subtleties. In the foregoing chapters we have considered exclusively the scalar properties of rotational excitation, i.e., the distributions of final rotational states of the products and the forces that control them. For this purpose, it was sufficient to study the case that the total angular momentum of the entire molecular system is zero, J = 0. This restriction drastically facilitated the theoretical formulation and allowed us to concentrate on the main effects without being intimidated by complicated angular momentum coupling. In Section 11.1 we will extend the theory of rotational excitation to general total angular momentum states J ≠ 0. Our aim is the investigation of final rotational product states following the photodissociation of single rotational states of the parent molecule (Section 11.3). Before doing so, however, we discuss in Section 11.2 the distribution of the various electronic fine-structure states (Λ-doublet states) if the fragment possesses a nonzero electronic angular momentum which couples with the angular momentum of the nuclear motion. Important examples are OH and NO.

The vector of the electromagnetic field defines a well specified direction in the laboratory frame relative to which all other vectors relevant in photodissociation can be measured. This includes the transition dipole moment, μ, the recoil velocity of the fragments, v, and the angular momentum vector of the products, j. Vector correlations in photodissociation contain a wealth of information about the symmetry of the excited electronic state as well as the dynamics of the fragmentation. Section 11.4 gives a short introduction.