Answer Happy

Only (e) and (f) are needed to be answered. Thank you.
1. (a) Derive the relationship between the absorption coefficient a and the extinction coefficient x for light travelling through an absorbing material. [4 marks] (b) Derive the dispersion relationship for the dielectric constant of a material as a function of applied frequency where the symbols have their usual meaning: Ne? 1 E,(6)=1+x+ io. 0 (5 marks] (c) Determine the high and low frequency limits of the real part of the dielectric constant. [3 marks] (d) In a measurement of the frequency response of a material, the low frequency dielectric constant was found to be 14, the high frequency value 10. Use this information to determine the resonant frequency of the material. The number of atoms per unit volume N, is 1 x 1097m? [3 marks) (e) Give an explanation of the optical absorption measurement technique and indicate how it can be used to determine whether a semiconductor has a direct or indirect bandgap. [5 marks] (f) Sketch the reflectivity and the absorption coefficient of SiO2 and Al in the range 100 nm to 1000 nm and explain these spectra. (5 marks]