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Summary for Chapter 2
                                           3 Dimer Atom
                    1 Intermediate layer atom
                                             4 Rest Atom    2  1              3
                    2 Adatom                                                     4

                                                                                   (b)


                                                                             3
                                                             1
                                                                              4

                                                            2
                                                    (a)
                                                                              (c)
                Figure 2.30. (a) The Si  111〈  〉 7 ×  7  -reconstructed surface imaged with a scanning tun-
                neling microscope. The overlay indicates the various atomic positions in the DAS layer.
                The pictures (b) and (c) to the right are for comparison purposes, and show the first four
                silicon atom layers. (c) Shows a 3-dimensional view of the first four atom layers of the lat-
                tice.



                             quantum-well semiconductor lasers also represent superlattices.  We
                             expect the superlattice to have a local influence on the dispersion curve
                             because additional waves are admitted with another wavelength [2.2],
                             [2.16].




                             2.6 Summary for Chapter 2

                             The forces between the constituent atoms of a crystal lead to the
                             pseudoparticle of lattice vibrational energy: the phonon. From this view,
                             we obtain the dispersion curves for a solid with its different phonon
                             branches. The acoustic phonons, in the long wavelength limit, are the
                             elastic waves we know from a macroscopic viewpoint, and we com-
                             pletely recover the classical theory of elasticity. The high frequency opti-



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