DebyeWaller Factors and the PbTe BandGap Temperature Dependence
Abstract
Measurements of the temperature variation of xray diffraction peak intensities have been used to show that the meansquare thermal displacement of Pb in PbTe is approximately twice that of Te. This phenomenon is explained, using a calculation of the meansquare displacements from vibrational eigenvalues and eigenvectors, in terms of the heavy thermal weighting of the acoustic modes relative to the optical. The Pb motion dominates in the acoustic modes, whereas the Te motion dominates in the optic modes. DebyeWaller factors obtained from the calculated meansquare displacements have been associated with a modified LinKleinman pseudopotential to obtain a theoretical estimate of the temperature dependence of the band gap. The modifications are necessary because of errors associated with their treatment of spinorbit interaction. The calculated bandgap increase of 0.008 Ry between 100 and 300 °K is in fair agreement with an experimental estimate of the explicit increase. It is shown that the magnitude of the shift is quite sensitive to adjustable parameters in the gap calculation as well as to the DebyeWaller factors. The sign of the shift is dependent on the relative ordering of levels and the relative meansquare displacements of the ions but not, otherwise, on the details of the calculation.
 Publication:

Physical Review B
 Pub Date:
 September 1970
 DOI:
 10.1103/PhysRevB.2.1966
 Bibcode:
 1970PhRvB...2.1966K