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Adequate determination of micro and macro properties of optical nano-crystals

Šetrajčić J. P.

Opto-Electronics Review

2017

Vol. 25, No. 4

303--310

The main problem in theoretical analysis of structures with strong confinement is the fact that standard mathematical tools: differential equations and Fourier’s transformations are no longer applicable. In this paper we have demonstrated that the method of Green’s functions can be successfully used on low-dimension crystal samples, as a consequence of quantum size effects. We can illustrate a modified model through the prime cubic structure molecular crystal: bulk and ultrathin film. Our analysis starts with standard exciton Hamiltonian with definition of commutative Green’s function and equation of motion. We have presented a detailed procedure of calculations of Green’s functions, and further dispersion law, distribution of states and relative permittivity for bulk samples. After this, we have followed the same procedures for obtaining the properties of excitons in ultra-thin films. The results have been presented graphically. Besides the modified method of Green’s functions we have shown that the exciton energy spectrum is discrete in film structures (with a number of energy levels equal to the number of atomic planes of the film). Compared to the bulk structures, with a continual absorption zone, in film structures exist resonant absorption peaks. With increased film thickness differences between bulk and film vanish.