Microscopic Theory of Cation Exchange in CdSe Nanocrystals

Although poorly understood, cation-exchange reactions are increasingly used to dope or transform colloidal semiconductor nanocrystals (quantum dots). We use density-functional theory and kinetic Monte Carlo simulations to develop a microscopic theory that explains structural, optical, and electronic changes observed experimentally in Ag-cation-exchanged CdSe nanocrystals. We find that Coulomb interactions, both between ionized impurities and with the polarized nanocrystal surface, play a key role in cation exchange. Our theory also resolves several experimental puzzles related to photoluminescence and electrical behavior in CdSe nanocrystals doped with Ag.

Figure 1

Electrostatic reduction of the activation barrier for cation exchange. For cation exchange to occur, Ag ions must replace Cd ions on the CdSe lattice. (a) The pathway with the lowest activation barrier (0.68 eV in DFT) is the Cd kick-out reaction, in which an interstitial ${\mathrm{Ag}}_{\text{int}}^{+}$ displaces a Cd, creating an interstitial ${\mathrm{Cd}}_{\text{int}}^{2+}$ and a substitutional ${\mathrm{Ag}}_{\text{Cd}}^{-}$. (b) The barrier for the Cd kick-out reaction is reduced (to 0.42 eV) if a substitutional ${\mathrm{Ag}}_{\text{Cd}}^{-}$ already occupies a neighboring site, because the arrangement of charges in the final state is then electrostatically favorable.

Figure 2

Microscopic model of Ag doping and cation exchange of CdSe NCs. (a) At low concentration, Ag are highly mobile interstitial ions, ${\mathrm{Ag}}_{\mathrm{int}}^{+}$. As their number increases, their mutual repulsion pushes them toward the NC surface (top) where a Cd kick-out reaction can occur [step (i)]. The substitutional ${\mathrm{Ag}}_{\mathrm{Cd}}^{-}$ created by the kick-out reaction attracts the remaining ${\mathrm{Ag}}_{\mathrm{int}}^{+}$ [step (ii)]. (b) An electrostatically bound complex is then formed by two Ag at the surface, forming a nucleus of ${\mathrm{Ag}}_2\mathrm{Se}$. (c) At even higher Ag concentrations, all interstitial and Cd sites at the surface become occupied with Ag. This fully substituted CdSe closely resembles the naumannite crystal structure of ${\mathrm{Ag}}_2\mathrm{Se}$.

Figure 3

Four stages of cation exchange, depicted by snapshots from KMC simulations at 300 K. Red and blue spheres denote ${\mathrm{Ag}}_{\mathrm{int}}^{+}$ and ${\mathrm{Ag}}_{\mathrm{Cd}}^{-}$, respectively. (a) With only one ${\mathrm{Ag}}_{\mathrm{int}}^{+}$, the impurity stays near the NC center. (b) With additional ${\mathrm{Ag}}_{\mathrm{int}}^{+}$, they repel each other toward the surface, where kick out of Cd by Ag can occur. (c) If no further Ag is added, the impurities eventually cluster at the surface, mostly as ${\mathrm{Ag}}_{\mathrm{Cd}}^{-}$. (d) Additional Ag leads to the growth of ${\mathrm{Ag}}_2\mathrm{Se}$ at the surface.

Figure 4

Site occupancy at 300 K of ${\mathrm{Ag}}_{\mathrm{int}}$ (red) and ${\mathrm{Ag}}_{\mathrm{Cd}}$ (blue) versus radial distance from the center of the NC. The distributions are averages over 100 KMC simulations for (a) one, (b) two, and (c) 150 Ag impurities per NC. The black curve in (a) shows the Boltzmann distribution at 300 K based on the energy from dielectric polarization.