Size dependent properties of Au particles: Coherent excitation and dephasing of acoustic vibrational modes

Ultrafast laser spectroscopy has been used to characterize the low frequency acoustic breathing modes of Au particles, with diameters between 8 and 120 nm. It is shown that these modes are impulsively excited by the rapid heating of the particle lattice that occurs after laser excitation. This excitation mechanism is a two step process; the pump laser deposits energy into the electron distribution, and this energy is subsequently transferred to the lattice via electron–phonon coupling. The measured frequencies of the acoustic modes are inversely proportional to the particle radius; a fit to the data for the different sized particles yields ${\mathrm{v̄}}_R{\text{=0.47c}}_l\mathrm{/Rc,}$ where R is the particle radius, $c_l$ is the longitudinal speed of sound in Au, and c is the speed of light. This functional relationship exactly matches the prediction of classical mechanics calculations for the lowest frequency radial (breathing) mode of a free, spherical particle. The inverse dependence of the frequency on the radius means that the modulations are damped for polydisperse samples. Analysis of our data shows that this inhomogeneous decay dominates the damping, even for our high quality samples (8%–10% dispersion in the size distribution). The size dependence of the electron–phonon coupling constant was also examined for these particles. The results show that, to within the signal to noise of our measurements, the electron–phonon coupling constant does not vary with size for particles with diameters between 4 and 120 nm. Furthermore, the value obtained is the same as that measured for bulk gold.