  Previous studies have shown that positron-annihilation spectroscopy is a
highly sensitive probe of the electronic structure and surface composition of
ligand-capped semiconductor Quantum Dots (QDs) embedded in thin films. Nature
of the associated positron state, however, whether the positron is confined
inside the QDs or localized at their surfaces, has so far remained unresolved.
Our positron-annihilation lifetime spectroscopy (PALS) studies of CdSe QDs
reveal the presence of a strong lifetime component in the narrow range of
358-371 ps, indicating abundant trapping and annihilation of positrons at the
surfaces of the QDs. Furthermore, our ab-initio calculations of the positron
wave function and lifetime employing a recent formulation of the Weighted
Density Approximation (WDA) demonstrate the presence of a positron surface
state and predict positron lifetimes close to experimental values. Our study
thus resolves the longstanding question regarding the nature of the positron
state in semiconductor QDs, and opens the way to extract quantitative
information on surface composition and ligand-surface interactions of colloidal
semiconductor QDs through highly sensitive positron-annihilation techniques.
