RESUMEN
Quantifying the optical extinction cross section of a plasmonic nanoparticle has recently emerged as a powerful means to characterize the nanoparticle morphologically, i.e., to determine its size and shape with a precision comparable to electron microscopy while using a simple optical microscope. In this context, a critical piece of information to solve the inverse problem, namely, calculating the particle geometry from the measured cross section, is the material permittivity. For bulk gold, many datasets have been reported in the literature, raising the question of which one is more adequate to describe specific systems at the nanoscale. Another question is how the nanoparticle interface, not present in the bulk material, affects its permittivity. In this work, we have investigated the role of the material permittivities on the morphometric characterization of defect-free ultra-uniform gold nanospheres with diameters of 10 nm and 30 nm, following a quantitative analysis of the polarization- and spectrally-resolved extinction cross section on hundreds of individual nanoparticles. The measured cross sections were fitted using an ellipsoid model. By minimizing the fit error or the variation of the fitted dimensions with color channel selection, the material permittivity dataset and the surface damping parameter g best describing the nanoparticles are found to be the single crystal dataset by Olmon et al. [Phys. Rev. B 86, 235147 (2012)] and g ≈ 1, respectively. The resulting nanoparticle geometries are in good agreement with transmission electron microscopy of the same sample batches, including both 2D projection and tomography.
RESUMEN
Nanoparticles are widely utilised for a range of applications, from catalysis to medicine, requiring accurate knowledge of their size and shape. Current techniques for particle characterisation are either not very accurate or time consuming and expensive. Here we demonstrate a rapid and quantitative method for particle analysis based on measuring the polarisation-resolved optical extinction cross-section of hundreds of individual nanoparticles using wide-field microscopy, and determining the particle size and shape from the optical properties. We show measurements on three samples consisting of nominally spherical gold nanoparticles of 20 nm and 30 nm diameter, and gold nanorods of 30 nm length and 10 nm diameter. Nanoparticle sizes and shapes in three dimensions are deduced from the measured optical cross-sections at different wavelengths and light polarisation, by solving the inverse problem, using an ellipsoid model of the particle polarisability in the dipole limit. The sensitivity of the method depends on the experimental noise and the choice of wavelengths. We show an uncertainty down to about 1 nm in mean diameter, and 10% in aspect ratio when using two or three color channels, for a noise of about 50 nm2 in the measured cross-section. The results are in good agreement with transmission electron microscopy, both 2D projection and tomography, of the same sample batches. Owing to its combination of experimental simplicity, ease of access to statistics over many particles, accuracy, and geometrical particle characterisation in 3D, this "optical nanosizer" method has the potential to become the technique of choice for quality control in next-generation particle manufacturing.