Optical Absorption and Dispersion in Solids by J. N. Hodgson (auth.)

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By J. N. Hodgson (auth.)

The electromagnetic thought of Maxwell and the electron thought of Lorentz and Drude encouraged loads of experimental paintings at the optical homes of solids within the overdue 19th and early 20th centuries. The time was once now not then ripe, even though, for common development during this box. The experimental ideas weren't on hand to supply compatible specimens for optical measurements with good­ outlined constitution and purity. at the theoretical facet, the classical electron concept supplied just a very incomplete account of the interplay of sunshine waves with topic. The centre of curiosity in optical study moved to atomic and molecular spectroscopy the place quantitative effects have been more uncomplicated to procure. The quantum concept, beginning with Bohr's conception of 1913, supplied a hugely winning foundation for the translation of the optical spectra of atoms and molecules. The present-day concept of the optical homes of solids is predicated at the quantum concept of electrons in solids, built from the early researches of Sommerfeld and Bloch, and the idea of lattice vibrations originating within the study by means of Born. The formal con­ nection among optical absorption and electron wave features in solids has been popular because the Thirties however it is barely lately that electron power band calculations have accomplished adequate accuracy to make ecocnomic a comparability of experimental and theoretical effects. with out a few tips from a theoretical band constitution calculation, it'd be tricky to make any development with the in­ terpretation of an optical absorption spectrum.

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6, has been. analysed in this way using the following characteristic energies: TO (0·0598 eV), LO (0·0513 eV), LA (0·0414 eV), TA (0·0158 eV). These values agree quite well with estimates from the calculated density of phonon states for silicon. 2. A more detailed comparison of theory and experiment has been made using the method of critical point analysis. The concept of critical points of a combined density of states will be discussed in Chapter 3 in connection with interband transitions. Similar calculations can be made for the difference bands, W = (Wl- wJ and three-phonon bands such as W = (WI + Wa + w 3).

6 An infra-red absorption band of quartz. 63) with Ao = (2nclw o) = 12'85 ,urn, (wo/Y) = 100, (Wp2/w0 2) = 0·10 (contribution to Reference: w. Experimental curve for normal reflectance Ro with E parallel to c-axis. 8 1 (0)). O. SPITZER and D. A. KLEINMAN, Phys. , 121, 1324-35 (1961). Kleinman have shown that the complicated infra-red absorption and dispersion spectrum of quartz can be represented by a sum of seven Lorentz terms for each polarization, c and E -'-= c. The experimental data consisted of normal reflectance values for wavelengths between 5 and 37 p,m.

Reference: W. COCHRAN and R. A. COWLEY, 'Handbuch der Physik', Vol. XXV/2a, pp. 59-156 (1967). The number of normal modes can be found by the application of boundary conditions for the displacement. The normal modes corresponding to a particular branch can be represented by points on q-space with position vectors equal to the wave vectors of each mode. The number of representative points in a volume Vq of q-space is (VqJ8:n: 3) for a non-degenerate branch. The total number of representative points in the Brillouin zone is N, the number of unit cells in the crystal.

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