Temperature-Dependence of Debye-Waller Factors of Semiconductors Presented in Terms of Cumulant Expansion

This work studies temperature-dependence of Debye-Waller factors of semiconductors presented in terms of cumulant expansion in extended X-ray absorption fine structure (EXAFS). The advances in these studies are succeeded based on further development of the anharmonic correlated Einstein model derived primary for fcc crystals into the one for applying to semiconductors and for creating a method having the advantage that all considered quantities are provided based on only the calculation or measurement of second cumulants. Analytical expressions of three first EXAFS cumulants have been derived. They describe the thermodynamic and anharmonic properties and contribute to accurate structural determination of semiconductors. The theory simplifies the many-body task into the one of one-dimensional model with taking the many-body effects into account based on the first shell near neighbor contributions to the vibration between absorber and backscattered atoms. Morse potential is assumed to describe single-pair atomic interaction. The results calculated using the present theory and those obtained by the created method for Ge having diamond structure are found to be in good agreement with experiment and with those of other theorie.

Keywords: Temperature dependence; Debye-Waller factor; Cumulant expansion; Anharmonic correlated einstein model; Semiconductor