Self-consistency and sum-rule tests in the Kramers-Kronig analysis of optical data: Applications to aluminum

Journal Article · Fri Aug 15 00:00:00 EDT 1980 · Phys. Rev., B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.22.1612· OSTI ID:5053729

Shiles, E; Sasaki, T; Inokuti, M; Smith, D Y

An iterative, self-consistent procedure for the Kramers-Kronig analysis of data from reflectance, ellipsometric, transmission, and electron-energy-loss measurements is presented. This procedure has been developed for practical dispersion analysis since experimentally no single optical function can be readily measured over the entire range of frequencies as required by the Kramers-Kronig relations. The present technique is applied to metallic aluminum as an example. The results are then examined for internal consistency and for systematic errors by various optical sum rules. The present procedure affords a systematic means of preparing a self-consistent set of optical functions provided some optical or energy-loss data are available in all important spectral regions. The analysis of aluminum discloses that currently available data exhibit an excess oscillator strength, apparently in the vicinity of the L edge. A possible explanation is a systematic experimental error in the absorption-coefficient measurements resulting from surface layers: possibly oxides: present in thin-film transmission samples. A revised set of optical functions has been prepared by an ad hoc reduction of the reported absorption coefficient above the L edge by 14%. These revised data lead to a total oscillator strength consistent with the known electron density and are in agreement with dc-conductivity and stopping-power measurements as well as with absorption coefficients inferred from the cross sections of neighboring elements in the periodic table. The optical functions resulting from this study show evidence for both the redistribution of oscillator strength between energy levels and the effects on real transitions of the shielding of conduction electrons by virtual processes in the core states.

• Research Organization: Argonne National Laboratory, Argonne, Illinois 60439
• OSTI ID: 5053729
• Journal Information: Phys. Rev., B: Condens. Matter; (United States), Vol. 22:4
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
ALUMINIUM
OPTICAL PROPERTIES
ELECTRONS
ENERGY LOSSES
KRAMERS-KRONIG CORRELATION
OSCILLATOR STRENGTHS
REFLECTIVITY
SUM RULES
CORRELATIONS
ELEMENTARY PARTICLES
ELEMENTS
EQUATIONS
FERMIONS
LEPTONS
LOSSES
METALS
PHYSICAL PROPERTIES
SURFACE PROPERTIES
360104* - Metals & Alloys- Physical Properties