Size dependence of refractive index of gold nanoparticles

Abstract

The extinction spectra of spherical gold nanoparticles suspended in a homogeneous media were measured and the results were adjusted with Mie’s theory together with an appropriate modification of the optical properties of bulk material considering the limitation that introduces the size of nanoparticles on the dielectric function. Usually, the contribution of free electrons to the dielectric function is modified for particle size, while the contribution of bound electrons is assumed to be independent of size. This work discusses the separated contribution of free and bound electrons on the optical properties of particles and their variation with size for gold nanoparticles. The effects of dielectric function and its changes with size on extinction spectra near plasmon resonance are considered. The damping constant for free electrons was changed with size as usual and a scattering constant of <i>C</i> = 0.8 was used. For the bound electron contribution, two different models were analysed to fit the extinction spectra: on the one hand, the damping constant for interband transitions and the gap energy were used as fitting parameters and on the other, the electronic density of states in the conduction band was made size dependent. For the first model, extinction spectra corresponding to particles with radius <i>R</i> = 0.7 nm were fitted using two sets of values of the energy gap and damping constant: <i>E_g</i> = 2.3 eV and γ_b = 158 meV/h or <i>E_g</i> =2 .1 eV and γ_b = 200 meV/ h . For the second model, a simple assumption for the electronic density of states and its contribution to the dielectric function in terms of size allowed to adjust extinction spectra for all samples explored (from 0.3 to 1.6 nm radius). This last model uses only one parameter, a scale factor R₀ 0.35 nm, that controls the contribution of the bound electrons in nanoparticles. Contrast between the maximum and the minimum in the extinction spectra near the resonance at 520 nm or alternatively the broadening of the plasmon band can be used to determine the size of gold nanoparticles with radius smaller than 2 nm.