Toward Optimal Design of Compound Semiconductor Nanocrystals: First-Principles Analysis, Monte Carlo Simulations, and Experimental Synthesis and Characterization

Crystalline semiconductor nanocrystals with dimensions over the range from 2 to 10 nm (quantum dots) exhibit size-dependent luminescence due to quantum confinement of excitons. This leads to unprecedented tunability in band gap, which can be controlled by varying the composition, morphology, and size of the nanocrystals. Based on optimization of band gap by such controlled variables, nanocrystals can be designed for pertinent photovoltaic applications, light-emitting devices, and as luminescent biological labels. Synthesis of core/shell quantum-dot structures produces materials that are more stable against photo-oxidation and have improved photoluminescence (PL) efficiencies. Various colloidal synthesis routes to core/shell structures exist, including the coating of a wider-band-gap semiconductor core with a shell of a narrower-band-gap material in a two-step process.  However, one-step processes for synthesizing such core/shell structures remain elusive.

In this presentation, we report theoretical and experimental results toward understanding the underlying physics that governs such core/shell structure formation and can lead to one-step synthesis strategies. Specifically, we address the problem of equilibrium surface segregation in ternary II-VI and III-V semiconductor nanocrystals using Monte Carlo (MC) and conjugate gradient (CG) methods based on classical force fields in conjunction with first-principles density functional theory (DFT) calculations.  We have conducted MC/CG simulations for structural and compositional relaxation of In_xGa_1-xAs and ZnSe_1-xS_x slab supercells exposing two free surfaces with either [001] or [110] crystallographic orientation. For the simulations, we have used properly modified/extended parameterizations of the valence-force-field (VFF) description of directional bond stretching and bending. The parameterizations were validated by comparisons with DFT calculations of energy differences for various configurations of In_xGa_1-xAs and ZnSe_1-xS_x unreconstructed slabs at different values of the compositional parameter x. The VFF models were then used to analyze surface segregation phenomena and determine the resulting equilibrium concentration profiles in ternary crystalline nanoparticles with well-defined facets and diameters d > 1.7 nm. Our relaxation method consists of a multi-stage sequence that includes MC sweeps employing exchanges between In and Ga atoms in In_xGa_1-xAs structures and between Se and S atoms in ZnSe_1-xS_x structures, followed by many continuous-space MC sweeps over all atoms for structural relaxation with an MC step for strain/volume relaxation of the slabs/particles after each such sweep; in all of the above stages, trials are accepted or rejected according to the Metropolis criterion. The MC simulation is preceded and followed by energy minimization according to a CG scheme to account for local structural relaxation. Our DFT calculations were carried out within the generalized gradient approximation (GGA) and the local density approximation (LDA) and employed the projector-augmented-wave method and slab supercell models. We calculated surface energies, model surfactant binding energies, and segregation tendencies for the passivated and unpassivated In_xGa_1-xAs and ZnSe_1-xS_x slabs with [001] and [110] crystallographic orientations. In our experiments, we synthesized nanocrystals using injection of organometallic precursors into hot coordinating solvents. The nanocrystal synthesis was carried out under vacuum and in the presence of argon to avoid reaction with oxygen. The synthesized nanocrystals were then dispersed in butanol.

We present simulation results for the equilibrium concentration distributions in slabs of In_xGa_1-xAs and ZnSe_1-xS_x as a function of composition, x, slab thickness, and slab surface crystallographic orientation, as well as in In_xGa_1-xAs and ZnSe_1-xS_x nanocrystals with well-defined [001] and [110] surface facets as a function of x and nanocrystal size. The results identify the parameter range for the assembly of core/shell structures, such as an In-deficient core surrounded by an In-rich shell in In_xGa_1-xAs nanocrystals. We also report PL spectra, transmission-electron-microscopy (TEM) images, and X-ray photoelectron spectra (XPS) of our experimentally synthesized nanocrystals. The underlying surface segregation is analyzed in particle-size and composition space and its impact on the experimental one-step synthesis of core/shell nanocrystal structures is discussed.