Advanced Solid State Physics

Linear response theory

Outline
• Linear response theory
• Fourier transforms
• Discrete Fourier Transforms
• Causality and the Kramers-Kronig relations     W
• Impulse response function, Green's function
• Generalized susceptibility
• Causality     W
• Kramer-Kronig relations     W
• Fluctuation-dissipation theorem
• Dielectric function
• Insulators and semiconductors
• Breakdown field     W
• Low-k dielectrics     W
• High-k dielectrics     W
• Loss tangent     W
• Polarizability     W
• Inter- and Intraband transitions
• Joint density of states
• Metals
• Collisionless metals
• Diffusive metals
• Microwave engineering
• Experimental techniques
• Reflection electron energy loss spectroscopy (REELS)
• Ellipsometry      W     6:24 
• Optical properties of selected materials

Reading

Kittel: Discussion of the dielectric function at the first part of chapter 14 and the discussion of the Kramers-Kronig relations at the first part of chapter 15

Student presentations
• Optical properties of Materials  9:09 
• Ellipsometry measurements
• Elipsometery video   6:24 

References
• A book that describes the propagation of electromagnetic waves through media in more detail is Electromagnetic Waves and Antennas by Sophocles J. Orfanidis.
• Plots of the dielectric functions for various materials can be found at http://refractiveindex.info
• An article that illustrates many of the topics discussed in this section is P. Lautenschlager, M. Garriga, L. Vina, and M. Cardona, Temperature dependence of the dielectric function and interband critical points in silicon, Phys. Rev. B 36, 4821–4830 (1987)