Photon-Single Phonon Coupling at Polar Crystal Surfaces: Infrared Optical Anisotropy Spectra
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PHOTON-SINGLE PHONON COUPLING AT POLAR CRYSTAL SURFACES: INFRARED OPTICAL ANISOTROPY SPECTRA
W. LUIS MOCHAN*, JOSE RECAMIER* , GUILLERMO MONSIVAIS**, AND LUCIA DIAZ BARRIGA*
*Laboratorio de Cuernavaca, Instituto de Fisica, Universidad Nacional Aut6noma de M6xico, Apartado Postal 139-B, 62191 Cuernavaca Morelos, Mexico **Instituto de Fisica, Universidad Nacional Aut6noma de M6xico, Apartado Postal 20364, 01000 Mexico Distrito Federal, M6xico
ABSTRACT We extend a formalism for the calculation of the surface-induced infrared anisotropy spectra of cubic polar crystals, in order to incorporate surface relaxation, reconstruction, and in general, surface modifications to the dynamic matrix. We calculate the reflectance anisotropy of a model (110) GaAs surface. The spectra have a rich structure which can be related to critical points of the phonon dispersion relation, and to coupling to surface states and surface resonances. The results display a very large sensitivity to the surface parameters, indicating that the surface induced anisotropy can be employed as an optical surface probe in the far IR.
INTRODUCTION From an optical point of view, a crystal with cubic symmetry is isotropic. Therefore any anisotropy in its optical properties such as its reflectance must originate from its surface. The measurement of the reflection anisotropy of cubic crystals has been developed recently and it has become an important tool for the investigation of surfaces[1-8]. Several contributions to the visible and UV anisotropy signal have been identified, including transitions to and from surface states[9,10], surface modifications to the bulk interband transitions[l1], surface-induced bulk-electrooptic effects[6,7], bulk spatial dispersion[121, and the surface local field effect[13]. In some systems one of the above-mentioned effects predominates. Such is the case of natural Si(110) whose anisotropy spectra can be explained by the surface local field effect alone[14]. However, in many systems, more than one effect is significant. An example is the competition between the local-field and the electro-optic effects in GaAs[7]. Another is that between the local-field effect and the surface-allowed non-vertical transitions among bulk states in Si(110):H[15]. A full microscopic theory capable of dealing with all the phenomena mentioned above has not yet been developed. In this paper we explore the optical anisotropy spectra of polar crystals in the far infrared region. There, the optical response of the system is determined by the ionic motions, instead of the electronic transitions which dominate the visible and ultraviolet regions. Therefore, starting from an interatomic harmonic Hamiltonian a classical calculation of the IR optical properties can be developed, and its results would be appropriate in the linear response regime. In a previous work[16], a model bulk-truncated crystal was considered and it was shown that a sizable anisotropy (• 10-) is to be expected in the far infrared reflectance spectra of polar crystals. This anisotropy i
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