Crystalline nanoparticles, including semiconductor particles and nanodiamonds, are actively investigated nowadays for applications in novel materials, quantum computing, biology and medicine. One of the important methods of nanoparticles study is Raman spectroscopy. In comparison with bulk material the Raman peak frequency in nanoparticles is downshifted and the peak is asymmetrically broadened. These effects are straightly related with the finite particle size. This opens up a possibility to use Raman spectroscopy for measuring nanoparticles sizes.
The standard tool for crystalline nanoparticles Raman spectra (RS) theoretical analysis is semi phenomenological phonon confinement model (PCM). It is based on the assumption of Gaussian decay of vibrations from the particle center to its boundary. Further analysis of this model shows that it contains some important flaws.
We propose a new model free of PCM disadvantages using the system microscopical parameters. The only adjustable parameter of the theory is the phonon linewidth. In order to obtain the particle vibrational eigenmodes we use the dynamical matrix method. Then, the bond polarization model is utilized to calculate the particle RS. With the usage of some averaging procedure, we also formulate our method in analytical form. The latter does not require cumbersome calculations but loses some information about the spectrum. In the framework of our theory we successfully describe the recent experimental data on nanodiamonds powders with sizesvarying from 1 to 10 nm, while PCM is unable to fit them.
In the second part of the work we propose a simple method for obtaining nanoparticles RS. It is based on solving boundary value problem, which resembles Klein-Fock-Gordon equation. The results of this approach reproduce the numerical ones with the high accuracy. So, instead of solving dynamical matrix, one can solve simple Laplace equation. In the framework of this theory we investigate the question of particles shape influence on RS and we obtain some interesting results.
515 room (Birzhevaya line, 14)