Measurement of Debye-Waller factors of silicon as a function of temperature using energy-filtered CBED rocking-curve technique

Abstract

The advantages of quantitative Convergent Beam Electron Diffraction (CBED) method for x-ray structure factor determination have been reviewed by Spence. The CBED method requires accurate values of Debye-Waller (D-W) factors for the estimation of the coefficients of crystal potential of the higher order beams, Vg, the calculation of the absorption potential, V′gusing the Einstein model for phonons, and finally the conversion of the fitted values of the coefficients of crystal potential, V″, to x-ray structure factors. Debye-Waller factors are conventionally determined by neutron or x-ray diffraction methods. Because of the difficulties in conducting high temperature neutron and x-ray diffraction experiments, D-W factors are rarely measured at temperatures above room temperature. Debye-Waller factors at high temperatures can be determined by Convergent Beam Electron diffraction (CBED) method using Transmission Electron Microscopy (TEM) employed with a hot stage attachment. Recently Holmestad et al. have attempted to measure the D-W factors by matching the energy-filtered Higher Order Laue Zone (HOLZ) line intensities near liquid nitrogen temperature.