Thermal motion of atoms in crystalline silicon: Beyond the Debye theory

Evidence is presented for nonrigid thermal vibrations of crystal-bound silicon atoms, using an extensive set of measured structure factors $F_m$ accurate to 0.1%. A model allowing for a different Debye-Waller factor (DWF) for each electronic shell is found to fit all $F_m$ well with four such factors. DWF’s refined from $F_m$ using calculated shell-by-shell partial structure factors yield good agreement with earlier results derived from low-order reflections but not with ab initio shell-model calculations. Also, no evidence is found for an anharmonic term in the atomic potential.