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Electronic Structure and Optical Properties

Of Bulk Materials 

And Their Interfaces

The electronic structure of materials represents the interatomic ionic, covalent, and metallic bonds formed by electrons which form the solid. ^[i],[ii]  The electronic structure can be considered from two general perspectives: that which provides information on the density of states (DOS) of the valence and conduction bands, and that which supplies information on the joint density of states (JDOS) for electronic transitions from the occupied valence bands to the unoccupied conduction bands. ^[iii]  Experimental techniques which produce information on the DOS are x-ray and ultraviolet photoelectron spectroscopy (XPS and UPS), Inverse Photoemission Spectroscopy, and Energy Loss Near Edge Structure (ELNES).  The DOS can also be determined from first principles, using band structure techniques typically under the Local Density Approximation, where the full band diagram of the occupied and unoccupied electronic states is produced, and the density of these states per unit energy interval is determined.^{[iv], [v]} 

Consider the optical, interband, transitions in the electronic structure, where the occupied valence band states are the initial states and the unoccupied conduction band states are the final states.  The JDOS corresponds to the matrix element for optical transitions between the valence and conduction band states.  The matrix element is large for allowed transitions between bands with a large DOS at the transition energy, and is smaller if the relative DOS of the two bands is less.  The JDOS is zero if the transitions are not allowed or if no initial or final states are present at the transition energy.  Since the JDOS includes the optical matrix element, it corresponds to the optical properties of the material, and to optical transitions interband, i.e., from occupied to unoccupied states.  The optical properties can be determined from first principles band structure calculations, if, after completing the band structure calculation, the optical matrix elements are then calculated for all possible interband transitions, and these are then summed so as to produce the JDOS or a related optical property such as the imaginary part of the dielectric constant, e₂.  The optical properties can also be determined from analysis of experimental optical data such as reflectivity or energy loss. 

Comment: (c) 2010 Roger H. French , frenchrh@lrsm.upenn.edu
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