(Solved): 1. (a) Show that the dispersion of the dielectric constant resulting from the interaction of light ...

1. (a) Show that the dispersion of the dielectric constant resulting from the interaction of light with TO-phonons is given by: N1 1 &()=1+X+ SOM (1920 –w?_0%) T where N is the number of unit cells per unit volume, 1 is the effective charge per ion, u is the reduced mass and to is the TO phonon angular frequency. [7 marks] (b) From the expression above, derive the Lyddane-Sachs-Teller relationship NŽO _ EST 20 ??? [6 marks] (c) The reflectance spectrum of AlSb in the infra-red region is shown below. Explain why there is a region of large reflectance around 30 microns and explain why the value of reflectivity is less than 1. Determine the frequencies of the TO and LO phonon modes and determine est if &o= 11. [7 marks] 1.0 0.8 AISb 0.6 Reflectivity 0.4 0.2 0.0 16 20 24 28 32 36 40 Wavelength (um) (d) At short wavelengths, the reflectance of AISb reaches a value of about 0.25. Explain how this value arises. [5 marks)