Changes in Optical Properties of Molecular Nanostructures

Abstract

This paper represents an overview about exciton systems in the molecular nanostructures (ultra thin films and superlattices) and their implications on optical properties, primarily on absorption coefficient, which is given in the form of dielectric permittivity. With utilization of Green's function method, we have calculated dispersion law, spectral weight of exciton states and dielectric permittivity for every type of nanostructures. All obtained results are compared with optical properties in bulk crystals. Dielectric permittivity in all types of nanostructures shows very narrow and discrete dependence of external electromagnetic field frequency, which is a consequence of the expressed quantum effects, very thin thickness in these structures (or at least one dimension confinement) and boundary conditions. PACS numbers: 77.55.+f, 78.20.−e, 78.66.−w, 78.67.−n Excitons in nanostructuresIn this theoretical research of optical properties of nanostructure materials we have to start from the assumption that excitons are generated in materials as response on the external electromagnetic field [1]. Although excitons are not the only (quasi) particles that can be find in the nanostructures when external electromagnetic field is turned on, this statement is satisfactorily correct if we use the molecular crystals [2]. Following this fact, we would restrict our research on dielectric (non-conductive) molecular crystalline materials, where standard excitons Hamiltonian include Pauli-operators with unsuitable statistic and therefore we would have to cross onto Bose statistics [1][2][3]. In further calculus we would use Green's function method [4] and corresponding equation of motion in approximation of nearest neighbor, but including dimensional restrictions related to configuration and internal organization of nanostructure, in particular we would observe ultra thin films and superlattices. The next step is transition from direct space to k-space, i.e. performing the time and space Fourier transformations [3,5]. The advantage of this transition is direct and elegant calculation of energy dispersion law. To obtain the dielectric permittivity (which is related with optical properties of the materials through the absorption coefficient), we would have to calculate Green's functions * corresponding author; e-mail: bora@df.uns.ac.rs exactly [5], with implicit spectral weights, i.e. probability of exciton creation with particular energy and position in nanostructures. Dispersion lawWe have calculated energy dispersion law for two class nanostructures: ultra thin films and superlattices. The ultra thin film consist of up to 20 parallel layers of atomic (or molecular) crystalline planes, with significant influence of boundaries, which are represented trough two kind of exciton perturbations -one is localized on the site of the atom (or molecule), and the second is energy transfer between boundary plane and the first internal neighbor plane. We will indicate with ∆ exciton energy on the site of the atom, and with ε 0/N perturbation ...

Research of properties of nanoscopic structures

“…Based on the formed models of ultrathin films, super-lattices, quantum wires and dots, as well as monitored microscopic and macroscopic features of such crystalline systems, we showed an extremely large influence of the decrease of spatial dimensions and boundary conditions to the change of physically relevant (optics, thermodynamics and electro transporting) characteristics of crystal substances [86][87][88][89][90][91][92][93][94][95][96][97][98][99][100]. Critical temperatures up to 100 K are explained here: although the effects of electron-phonon interaction (as in BSC-theory) are still not calculated.…”

Influence of symmetric perturbations on optical properties of molecular nanofilms

“…Veza između dielektrične permitivnosti, indeksa prelamanja i koeficijenta apsorpcije je data izrazom:  1/2 = n + κ. Ukoliko se uvede kompleksna frekvnecija ( →  + i) u izraz za dielektričnu permitivnost, tada i dielektrična permitivnost postaje kompleksna:  = ' + i'', te na osnovu ovoga možemo izračunati koeficijent apsorpcije i indeks prelamanja [12,20] pomoću: 21,22]. Vidljivo je da su navedene optičke veličine zavisne od sloja, pa samim tim i od perturbacionih parametara koji vladaju na graničnim slojevima.…”