Atomistic origin and temperature dependence of Raman optical redshift in nanostructures: A broken bond rule

Consistent insight is presented into the atomistic origin and temperature (T) dependence of the redshift of Raman optical modes in nanostructures from the perspective of surface bond unsaturation and the bond-order-length-strength (BOLS) correlation [Sun et al., Phys Rev B 72, 134301 (2005)]. It turns out that: (1) the size-induced redshift of Raman optical modes results from the effect of bond order deficiency of atoms on the surface and its consequences on the force constants of bonds between the under-coordinated surface atoms; (2) the temperature-induced redshift arises from thermally induced bond expansion and bond weakening and (3) the magnitude of vibration of atoms in the surface or surrounding defects is always greater than the fully coordinated bulk atoms, while the frequency of such under-coordinated atoms are relatively lower. It is demonstrated that a combination of the freedoms of solid size and temperature of testing with Raman spectroscopy could lead to information about the vibrational frequency of a monatomic chain and single-bond energy, which is beyond the scope of the traditional size- and temperature-independent approaches.