Characteristic Energies and Shifts in Optical Spectra of Colloidal IVVI Semiconductor Nanocrystals R. Leitsmann †,‡, * and F. Bechstedt † † European Theoretical Spectroscopy Facility (ETSF) and Institut fu ¨r Festko ¨rpertheorie und -optik, Friedrich-Schiller-Universita ¨t Jena, Max-Wien-Platz 1, 07743 Jena, Germany, and ‡ GWT-TUD GmbH, Material Calculations, Annabergerstr. 240, 09125 Chemnitz, Germany T he efficient multiple-exciton genera- tion discovered in lead chalco- genide nanocrystals (NCs) 1-3 opens the possibility of generating sev- eral electron-hole pairs from a single, high-energy photon. This mechanism po- tentially increases the optical efficiency of these nanosystems and makes them promising candidates for light sources in the mid-infrared spectral region or for light absorbers in third-generation solar- cell devices. Recent progress has been made in synthesizing colloidal NCs made of narrow-gap semiconductors such as PbS, PbSe, and PbTe. 4-6 Typically, the band gaps of these materials can be tuned between 0.5 and 1.5 eV, which cov- ers the entire near-infrared spectral re- gion. On the other hand, the synthesis of NCs with band gaps smaller than 0.5 eV is still a challenging task. 7 The theoretical ab initio description of IV-VI materials is also ambitious for dif- ferent reasons. There is a remarkable ionic contribution to the chemical bond- ing. As a consequence, most of the com- mon IV-VI semiconductors crystallize in rocksalt (rs) structure with the space group Fm3m (O h 5 ). In addition, PbTe and SnTe exhibit shallow cation-derived d states. 8 Therefore, one has to treat (be- side the s,p states) the outermost d elec- trons of the group IV elements as valence electrons. On the other hand, for a pre- cise description of heavy elements like Pb, the inclusion of relativistic effects (e.g., spin-orbit coupling, SOC) is necessary. 9,10 One question, which arises, is whether the replacement of Pb with the lighter atom Sn may reduce these ef- fects. Furthermore, to be able to com- pare theoretical results to experimental findings for realistic NC sizes, one has to use huge supercells. This increases the computational cost of the calculations considerably. In the present article, we focus on the description of rhombo-cuboctahedral IV-VI semiconductor quantum dots (QDs) with a pseudohydrogen passiva- tion shell. Pseudohydrogen atoms with 1/3 (H) or 5/3 (H*) electrons are used. 8,11 In the center of these structures can be either an anion or a cation, which leads to different surface terminations due to the shellwise construction. The differ- ently sized NCs are denoted as QD-da and QD-dc, were d is the diameter in units of the bulk lattice constant a 0 and a/c de- scribe the ionic character (anion/cation) of the central atom. RESULTS AND DISCUSSION Structural Properties. Independent of the character of the central ion, the struc- tural optimization of the IV-VI semicon- ductor quantum dots almost conserves the six-fold coordinated rs structure of the bulk phase of these compounds. This is illustrated in Figure 1, where we show the optimized structure of 0.64 nm (QD- 1a), 1.28 nm (QD-2a), and 1.92 nm *Address correspondence to roman@ifto.physik.uni-jena.de. Received for review August 11, 2009 and accepted October 23, 2009. Published online October 29, 2009. 10.1021/nn900987j CCC: $40.75 © 2009 American Chemical Society ABSTRACT We investigate structural, electronic, and optical properties of colloidal IVVI semiconductor quantum dots (QDs) using an ab initio pseudopotential method and a repeated supercell approximation. In particular, rhombo-cuboctahedral quantum dots consisting of PbSe, PbTe, and SnTe with a pseudohydrogen passivation shell are investigated for different QD sizes. The obtained dependence of the confinement energy on the QD size questions the use of three-dimensional spherical potential well models for small QD structures. The predicted band gaps are almost in agreement with measured values. The calculated FranckCondon shifts vary significantly with the QD size. Only for PbSe they may explain the Stokes shift between optical absorption and emission. For the tellurides, spectral properties such as the oscillator strength are more important. KEYWORDS: ab initio · nanocrystals · lead salts · photoluminescence · confinement energy ARTICLE www.acsnano.org VOL. 3 ▪ NO. 11 ▪ 3505–3512 ▪ 2009 3505