1 / 11

Optical Processes in Crystals and Excitons: Theory and Applications

Explore the dielectric function, reflectivity, and excitons in crystals through Kramers-Kronig relations and Raman spectroscopy. Learn about response functions and the behavior of charged oscillators in an electromagnetic field, along with sum rules and applications in semiconductor energy gaps.

mbarnes
Télécharger la présentation

Optical Processes in Crystals and Excitons: Theory and Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Dept of Phys M.C. Chang Optical processes and excitons • Dielectric functionand reflectance • Kramers-Kronig relations • Excitons • Frenkel exciton • Mott-Wannier exciton • Raman spectroscopy

  2. Dielectric function, reflectivity r, and reflectance R Response of a crystal to an EM field is characterized by (k,), (k0 compared to G/2) Experimentalists prefer to measure reflectivity r (normal incidence) Prob.3 It is easier to measure R than to measure   measure R() for   () (with the help of KK relations)  n()  ()

  3. Kramers-Kronig relations (1926) KK relation connects real part of the response function with the imaginary part examples of response function: • does not depend on any dynamic detail of the interaction • the necessary and sufficient condition for its validity is causality Ohm’s law polarization reflective EM wave Example: Response of charged (independent) oscillators For the j-th oscillator (atom or molecule with Z bound charges), steady state electric dipole

  4. Some properties of (): (1) () has no pole above (including) x-axis. (2) along (upper) infinite semi-circle (3) ’() is even in , ’’() is odd in . Collection of oscillators for identical oscillators Figs from http://www.physics.uc.edu/~sitko/LightColor/10-Optics1/optics1.htm

  5. ω and many more…, e.g., (4)+(5) (next page): By Ferrel and Glover (1958) From (1), (2), we have ( can be , or , or... ) property (3) used Also, A few sum rules: An example of the “fluctuation-dissipation” relation From (1) and (2), >>1 (Prob. 2): Thomas-Reiche-Kuhn sum rule From (3), >>1 (Prob. 4):

  6. KK relation for reflection Why take log? See Yu and Cardona for related discussion • constant R(s) doesn’t contribute • s>>, s<< don’t contribute ref: Cardona and Yu

  7. Conductivity of free electron gas (j=0, with little damping) (KK relations can be checked easily in this case) Recall that (chap 10) Real part of DC conductivity diverges (compare with ne2/m) Drude weight D Other sum rules (Mahan, p358): Related to the energy loss of a passing charged particle

  8. Dielectric function and the semiconductor energy gap (prob.5) band gap absorption (due to nonzero ’’) can be very roughly approximated by Si Ge GaAs InP GaP ’ 12.0 16.0 10.9 9.6 9.1 Eg (theo) 4.8 4.3 5.2 5.2 5.75 Ex (exp’t) 4.44 4.49 5.11 5.05 5.21 (ref: Cardona and Yu) Figs from Ibach and Luth

  9. Interband absorption for GaAs at 21 K Excitons (e-h pairs) in insulators • Tight bound Frenkel exciton: • (excited state of a single atom) • alkali halide crystals • crystalline inert gases

  10. Weakly bound Mott-Wannier excitons Similar to the impurity states in doped semiconductor: CuO2

  11. 1930 Raman effect in crystals

More Related