Phys560Notes-15 - Infrared Properties (of Ionic Crystals)...

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Infrared Properties (of Ionic Crystals) Assume the system is nonmagnetic, 1 . Optical properties determined by the dielectric function, D ε E . Assume cubic symmetry. DE DEP  Assume no free charges. 0  D 0 i kE 4 i  Ek E ( = bound charge density) Longitudinal (plasmon) waves ,, EDP k 0  0 0 Transverse waves 0  0 0 in general 1 ct   H E 1 HD  2 11 ctct         EE E D 2 2 22 1  2 2 2 k c kN cc  N = complex refractive index ni  Experimental determination of n and : Reflection Reflectivity =   2 2 2 2 1 1 r o n I I n   Absorption d to I Ie (ignore reflections) absorption coefficient 2 c Calculation of in Terms of Microscopic Quantities Consider insulators only (no conduction electrons). Assume cubic symmetry. Exampes: NaCl, GaAs, Si, Ge, Ne, …
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loc pE p = dipole moment of a unit cell (or an ion or an atom); loc E = local field; = unit cell (or ionic/atomic) polarizability , a microscopic quantity that can be calculated quantum mechanically or measured from gas phase data. = a macroscopic quantity of interest; to be determined from 3 1 macro micro V dr V  EE E , where 1 3 aV  ( = wavelength of interest) Caution: macro E is well defined only for a . From classical E&M (J. D. Jackson), 4 3 loc  P for cubic systems (Lorentz relation). 4 DE E P 2 3 loc v p P dipole moment in each unit cell / cell volume 2 3 loc vv  E E 4 EP E 2 4 3 v  E 14 23 v  Clausius-Mossotti relation If 1 (for example, dilute systems), 4 11 4 v  . = susceptibility. This approximation corresponds to ignoring the local field correction. Calculation of Contributions to include: electronic: valence, a few eV; core, 10 eV ionic: ionic displacements (phonons), infrared; ionic reorientation, 0 infrared Will focus on phonon contributions here; infrared response.  0. infrared ee a    Electronic contributions are ~ a constant (negligible frequency dependence) For simplicity, consider cubic diatomic "ionic" solids, like GaAs, NaCl, etc. Dipole moment each unit cell: qq   pu u w q = infrared charge With a (infrared), mode of interest is ~ at zone center. w is ~ the same for all nearby unit cells.   loc Mk q  uu u E    loc q  u E Unit cell + ion – ion
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k = effective force constant, including contributions from possibly several shells The forces on the two ions are equal and opposite because of Neuton's third law.
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This note was uploaded on 03/21/2012 for the course PHYS 560 taught by Professor Flynn during the Spring '08 term at University of Illinois, Urbana Champaign.

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Phys560Notes-15 - Infrared Properties (of Ionic Crystals)...

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