Penetration depth, phase transitions

If the penetration depth of the light is much smaller than the film thickness, illumination of the nanocrystalline electrode from the electrolyte side is expected to give a characteristic spiral in the high frequency IMPS response (Fig. 8.29). This spiral is typical for a constant time lag (i.e., frequency dependent phase shift), and it arises simply from the transit time required for carriers to move from the front face to the rear contact. By contrast, if the electrode is illuminated through the substrate, electrons are generated close to the contact and the transit time is much smaller (Fig. 8.29). This is reflected in the high value of o)min. 

Ultraviolet Raman spectroscopy has emerged as a powerful technique for characterization of nanoscale materials, in particular, wide-bandgap semiconductors and dielectrics. The advantages of ultraviolet excitation for Raman measurements of ferroelectric thin films and heterostructures, such as reduced penetration depth and enhanced scattering intensity, are discussed. Recent results of application of ultraviolet Raman spectroscopy for studies of the lattice dynamics and phase transitions in nanoscale ferroelectric structures, such as superlattices based on BaTiOs, SrTiOs, and CaTiOs, as well as ultrathin films of BaTiOs and SrTi03 are reviewed. 

Next came the likewise phenomenological Ginzburg-Landau theory of superconductivity, based on the Landau theory of a second-order phase transition (see also Appendix B) that predicted the coherence length and penetration depth as two characteristic parameters of a superconductor (Ginzburg and Landau, 1950). Based on this theory, Abrikosov derived the notion that the magnetic field penetrates type II superconductors in quantized flux tubes, commonly in the form of a hexagonal network (Abrikosov, 1957). The existence of this vortex lattice was... 

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