Light Matter Interaction - Optical Properties of Materials - Exam 2 | OSE 5312, Exams of Chemistry

Download Light Matter Interaction - Optical Properties of Materials - Exam 2 | OSE 5312 and more Exams Chemistry in PDF only on Docsity! OSE 5312 OPTICAL PROPERTIES OF MATERIALS Summer 2001 Exam 2 (Open book, open notes) Friday, July 13, 1:30 p.m. - 6:30 p.m. Useful parameters: electron mass = 9.11 x 10-31 kg, e = 1.6 x 10-19 C o = 8.85 * 10-12 F/m,  = 1.05 x 10-34 Js 1. (a) Sketch the interband absorption vs. photon energy for a bulk (3-D) semiconductor. On the same graph, make a qualitative sketch of the refractive index vs. photon energy. (Explain your rational by graphically applying Kramers Kroenig relations.) (b) Repeat part (a) for a semiconductor where the electron motion is confined in 1 dimension ("a quantum well"). (c) Repeat part (a) for a semiconductor where the electron motion is confined in 2 dimensions ("a quantum wire"). (15 points) 2. Far from linear absorption regions, the wavelength dependence of the refractive index is often expressed in terms of a "Sellmeier equation" of the form:         B An 2 2 2 1 , where  is the vacuum wavelength. If the susceptibility can be modeled using the lorentz model where there are several electronic modes:          )( 2 D p , where p is the plasma frequency and   iD  22)( for mode , find expressions for A and B. (10 points) You may look at any notes, texts, etc., but not at old exam solutions from previous years. Also, you can not discuss this exam or its content with anyone other than the instructor. I declare I have completed this exam in accordance with the above rules and with the UCF codes of academic conduct. Signed____________________________________ Date________________ 3. Below is the data for a Sellmeier equation for Fused Silica (SiO2). Use this to determine the group velocity of a pulse of light at a wavelength of 532 nm. (10 points) 4. A diatomic molecule has atomic masses 4 amu and 10 amu. The atoms are spaced by distance x and the potential they sit in is found to be adequately described by: V(x) = {1(Å5)/x10-1/x5} · 2 (kg Å7/s2) where x is in Å. Find the equilibrium spacing, xo. Determine the range over which the potential approximates a harmonic potential, and find the natural vibrational frequency of the molecule in this range. (15 points) 5. The potential experienced by an electron in a linear organic molecule may be approximated by an infinite one dimensional potential well of width a = 14 Å. That is: V(x) = 0, for |x| < a/2, V(x) = , for |x| > a/2. (a) Find the energy eigenvalues and eigenfunctions for the first few electronic states. (b) Assuming the electron initially sits in the lowest energy state, find the wavelengths of the first three nonzero absorption lines. (c) Find the oscillator strengths, f1n, of these three absorption lines. Does it appear that the TRK sum rule (  n nf 11 ) is valid for this system? (20 points) 6. Show that the Kramer-Kroenig relations for dielectric constant  lead to the sum rule: f1   0.6961663 2   2 0.0684043( ) 2   f3   0.8774794 2   2 9.896161 2   c 3 10 14  m/s f2   0.4079426 2   2 0.1162414 2   f4   0 FUSED SILICA n   1 f1   f2   f3   f4   Reference: Handbook of Optics (OSA) (valid 0.21 - 3.71 m) f1 ( ) f2 ( ) f3 ( ) f4 ( ) 