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Band mapping, in condensed matter physics refers to the process which allows for detection (and measurement) of photoelectrons emitted from an observed surface at different emission angles. This process is employed in a spectroscopy technique formally known as ARPES --Angle-resolved photoemission spectroscopy. ARPES is used to investigate the electronic structure of solids, solid surfaces and interfaces.

By employing the band mapping process, several fundamental physical properties of a solid can be determined. The properties which can be determined using this process include (but are not limited to) the following:

Kinetic energy of the electron(s);
Elasticity;
Electrical/Magnetic properties; and
Optical properties.

The electronic states in the solid are described by energy bands, which have associated energy band dispersions E(k) — energy eigenvalues for delocalized electrons in a crystalline medium according to Bloch's theorem.

Band mapping has an advantage over optical spectroscopy. In the latter, only the energy-band separations at various optical critical points in k-space — entropy between the initial and final states — are determined. ARPES, on the other hand, provides information about the absolute location of energy bands at different values of k relative to the Fermi level (EF).
References

Park, Jongik. "Photoemission study of the rare earth intermetallic compounds: RNi2Ge2 (R = Eu, Gd)." 2004, Iowa State University, Ames, Iowa


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