SiGe superlattice nanocrystal infrared and Raman spectra: A density functional theory study

Abstract

Infrared and Raman vibrational spectrum are calculated using ab initio density functional theory for SiGe superlattice nanocrystal of approximately 1.6 nm length. After obtaining the optimum positions of atoms via geometrical optimization using density functional theory, coupled perturbed Hartree-Fock equations are solved iteratively to obtain vibrational spectrum. Frequencies of vibrations are analyzed against intensities, reduced masses, and vibrational force constants. A scale factor of 0.81 is suggested to correct the frequencies of the present calculations that are obtained using STO-3 G basis functions. Results show that SiGe nanocrystals have complex and rich vibrational spectrum that can be generally divided into three regions. The highest reduced masses are in the first region where Si and Ge atoms are the main contributors to vibrations with a smaller number of vibrations attributed to hydrogen atoms. The highest intensity lines in SiGe superlattice nanocrystals are in the middle region where most of the modes of vibration can be excited. The third region is characterized by high force constants. The first region shows a redshift of the original Ge-Si bond vibration from the calculated bulk 418 cm−1 to the present nanocrystal 395 cm−1. Hydrogen vibrations interferences are found in the same redshift region that might induce uncertainties in the experimentally measured redshift. Si-H and Ge-H vibrations are observed mainly in the second and third region and less frequently in the first region. These vibrations include modes of vibration such as symmetric, asymmetric, wagging, scissor, rocking, and twisting modes.