Size-Dependent Lattice Dynamics of Atomically Precise Cadmium Selenide Quantum Dots

Material properties depend sensitively on the atomic arrangements and atomic bonding, but these are notoriously difficult to measure in nanosized atomic clusters due to the small size of the objects and the challenge of obtaining bulk samples of identical clusters. Here, we have combined the recent ability to make gram quantities of identical semiconductor quantum-dot nanoparticles with the ability to measure lattice dynamics on small sample quantities of hydrogenated materials using high energy resolution inelastic x-ray scattering, to measure the size dependence of the phonon density of states in CdSe quantum dots. The fact that we have atomically precise structural models for these nanoparticles allows the calculation of the phonon density of states using density functional theory, providing both experimental and theoretical confirmations of the important role that the inertia of the surface capping species plays on determining the lattice dynamics.

Figure 1

Structure representation of the cadmium selenide quantum dots in the current study. Their chemical compositions and surface capping ligands are shown.

Figure 2

PDOS of the cadmium selenide nanoparticles and ${\mathrm{CdSe}}_{(\mathrm{bulk})}$ from (a) HERIX measurements and (b) DFT calculations. The calculated PDOS curves are normalized with the number of Cd and Se atoms and convoluted with a Gaussian function with a FWHM of 1.709 meV. The dashed lines mark the peak positions at 6 and 22 meV from bulk PDOS. Curves are offset vertically for clarity.

Figure 3

(a) Experimental PDFs of the cadmium selenide nanoparticles and ${\mathrm{CdSe}}_{(\mathrm{bulk})}$ collected at 20 K. The dashed line marks the peak position of ${\mathrm{CdSe}}_{(\mathrm{bulk})}$. The solid lines are the fits with a Gaussian function. Curves are offset vertically for clarity. (b) The extracted bond strains as a function of the nanoparticle edge length from PDF (circle) and DFT (diamond).