The Debye-Waller factor of disordered solids: The case for amorphous silicon
This paper presents a first-principles study of the Debye-Waller factor and the Debye temperature for amorphous silicon (α-Si) from lattice-dynamical calculations and direct molecular-dynamics simulations using density-functional theory (DFT). The effects of temperature and structural disorder on the intensity of the diffraction maxima and the vibrational mean-square displacement (MSD) of Si atoms are studied in the harmonic approximation, with particular emphasis on the bond-length disorder, the presence of coordination defects, and microvoids in α-Si networks. It has been observed that the MSDs associated with tetrahedrally bonded Si atoms are considerably lower than their dangling-bond counterparts—originating from isolated and vacancy-induced clustered defects—and those on the surface of microvoids, leading to an asymmetric non-Gaussian tail in the distribution of atomic displacements. An examination of the effect of anharmonicity on the MSD at high temperatures using direct ab initio molecular-dynamics simulations (without the harmonic approximation) suggests that the vibrational motion in α-Si is practically unaffected by anharmonic effects at temperatures below 400 K, as far as the present DFT calculations are concerned. The Debye temperature of α-Si is found to be in the range of 488–541 K from specific-heat and MSD calculations using first-principles lattice-dynamical calculations in the harmonic approximation, which matches closely with the experimental value of 487–528 K obtained from specific-heat measurements of α-Si at low temperatures.