Theory of the F-centers of Coloured Alkali Halide Crystals. Part I

Abstract

As is well-known, the various physical properties of semiconductors are essentially determined by the existence of the so-called quasi-atomic states in the forbidden region of energy band system characteristic for the body crystal. Since the lattice imperfections due to the inclusion of foreign atoms and stoichiometric excess-atoms, the internal cracks within the crystals or other mechanism may be considered to become possible origins which give rise to the mentioned quasi-atomic states, the consistent, theoretical attack of semiconductors will be necessarily confronted with a difficult problem of treating mathematically the imperfect crystals, while in the perfect crystals the method of solution of Schrödinger wave equation is well known to be much simplified owing to the periodicity and symmetry valid within the perfect crystals. In addition to the mentioned theoretical difficulty in solving the wave equation of the imperfect crystal, the vast experimental investigations of the physical properties of semiconductors reveal that even the experimental data of the same kind of semiconductors are always at variance with each other, showing the sensitive dependencies of the materials upon the experimental method of preparations. Such experimental difficulties to get the precise reproduction of the materials with consistent physical properties will become serious obstacles for proceeding the reliable physical considerations of the semiconductors. In view of the above situations both theoretical and experimental, therefore, it seems to be more enlightened at the present stage of the theory that the particularly simple semiconductors with reliable and systematic experimental data shall be thoroughly worked out theoretically in order to find a suitable method of approximation for solving the quasi-atomic states characteristic for semiconductors and then the theoretical method obtained shall be extended to those of the more complicated semiconductors accessible in both pure and applied fields of atomic physics. From the standpoint mentioned above, we shall here take the coloured alkali halide crystals which have been worked out experimentally by the systematic observations of Pohl and his coworkers, von Hippel and others. According to the experimental investigaions the colour-center, i.e., F-center responsible for the selective absorption of light and the colouration of the crystals may be considered to be typical ones of the mentioned quasi-atomic states whithin semiconductors. In Part I we shall work theoretically the detailed structure of F-absorption band peculiar to the alkali-halide crystals in connection with its temperature effect, and in Part II the general theory of trapped electrons within the quasi-atomic states of semiconductors shall be developed. The quasitative application of the general theory to the F-centers of NaCl crystal shall be attempted to do in comparison with the experimental observations in Part III.