Size distribution dependence of the dielectric function of Si quantum dots described by a modified Maxwell-Garnett formulation

作者：Keita A S^*; Naciri A En

来源：Physical Review B, 2011, 84(12): 125436.

DOI：10.1103/PhysRevB.84.125436

Numerical inversion of effective medium equations used in ellipsometry data analysis are carried out, without using any parameterized dispersion formula, in order to investigate on the influence of size distribution (SD) on the dielectric properties of silicon quantum dots (Si QDs) within a silica matrix over the energy range [0.65-6.5 eV]. To do so the dielectric DF) of the whole inhomogeneous layer is properly determined, and then a modified version of the Maxwell-Garnett (MG) formula, which is often used in the ellipsometric modeling of nanoscale Si, is set forth. This formula, which accounts for SD, was formerly introduced by Banyai and Koch. We show that a small change in the size dispersion value may induce a sensitive modification in the line shape of the DF. It is also pointed out that if only the filling factor f is accounted for as in the classical MG formula this may lead to the overestimation of the amplitude of the DF of the Si nanoclusters. Furthermore the use of f solely may induce an underevaluation of the optical-gap energy of the Si QDs but also of the broadening and transition energies associated to the E(1)-like and E(2)-like critical points of crystalline Si. Likewise it is shown that SD does have an impact on the static dielectric constant epsilon(0) at low frequency, contrary to what has been generally supposed. Indeed it is demonstrated that provided that either quantum confinement or surface polarization is considered, then the parameters describing the size dependence of epsilon(0) at 0.65 eV are subjected to sensitive changes as the size dispersion sigma increases.

• 出版日期2011-9-19