Surfaces of colloidal PbSe nanocrystals probed by thin-film positron annihilation spectroscopy

Positron annihilation lifetime spectroscopy (PALS) and positron-electron momentum density (PEMD) studies on multilayers of PbSe nanocrystals (NCs), supported by transmission electron microscopy (TEM), show that positrons are strongly trapped at NC surfaces, where they provide insight into the surface composition and electronic structure of PbSe NCs. Our analysis indicates abundant annihilation of positrons with Se electrons at the NC surfaces and with O electrons of the oleic ligands bound to Pb ad-atoms at the NC surfaces, which demonstrates that positrons can be used as a sensitive probe to investigate the surface physics and chemistry of nanocrystals inside multilayers. Ab-initio electronic structure calculations provide detailed insight in the valence and semi-core electron contributions to the positron-electron momentum density of PbSe. Both lifetime and PEMD are found to correlate with changes in the particle morphology characteristic of partial ligand removal.

properties of colloidal semiconductor NCs are in general largely affected by the surface structure and composition including the passivation of surface states by ligand molecules attached to their surfaces. These surface properties depend, in turn, on sample preparation. 4,[11][12][13] For example, the morphology and surface composition of PbSe or CdSe NCs depend strongly on the method of synthesis and capping material used. 5,11,12,14 Several groups have found non-stoichiometric ratios of Pb to Se atoms in PbSe NCs in solution, which leads to the hypothesis that the NCs are enclosed by a monolayer of Pb atoms. [15][16][17][18] On the other hand, synchrotron X-ray Photoelectron Spectroscopy studies on PbSe NC layers have indicated the formation of a Pb-deficient sub-surface layer terminated by Se-atoms at the surface. 19 Recent experimental studies indicate that the positron is a sensitive probe of the electronic structure of colloidal NCs [20][21][22] and of the chemical composition at their surfaces, based on preferential trapping and annihilation of positrons at the surfaces. [21][22][23] In this paper we show that positrons are strongly trapped at the surfaces of the PbSe NCs, where they annihilate mostly with the Se atoms and with the O atoms from the oleate (OA) ligands bound to Pb ad-atoms. The dominant trend in the variation in positron annihilation characteristics is induced by partial removal of oleate ligands together with the attached Pb ad-atoms, leaving Se-rich surfaces behind, which is consistent with the changes in morphology of the PbSe NCs observed by Transmission Electron Microscopy (TEM).

II. EXPERIMENT and CALCULATION
Samples of PbSe NCs with four different average sizes ranging between 2.8 nm and 9.7 nm were synthesized using the method of Talapin and Murray. 24 A mixture of 95% hexane and 5% octane was used as a solvent for drop-casting PbSe NCs onto indium-tinoxide (ITO) coated glass substrates. 25 Films were formed with thicknesses in the range from 200 nm to over 1000 nm, as determined from positron Doppler broadening depthprofiles. The particle sizes were determined by Optical Absorption Spectroscopy, X-ray Diffraction (XRD) and TEM using a FEI Titan high-resolution TEM at 300 kV. The drop-cast nanocrystal films were further examined using positron annihilation lifetime spectroscopy (PALS) on the pulsed low-energy positron lifetime spectrometer PLEPS at FRM-II in Garching and two-dimensional angular correlation of annihilation radiation (2D-ACAR) on the thin-film POSH-ACAR setup at the Reactor Institute Delft. For comparison, a PbSe single crystal was studied by 2D-ACAR using a 22 Na positron source. The positron lifetime spectra were fitted using the program POSWIN. [25][26][27] The 2D-ACAR data were analysed using the program ACAR2D. 28 Ab-initio calculations of the PEMD were performed using the Korringa-Kohn-Rostoker method 29,30 to extract robust electronic contributions to the PEMD of the PbSe NCs. To further understand the nature of divacancies in PbSe, we employed the ab initio method as implemented in the VASP code 31 supercell calculations of Schottky pair defects (V Pb V Se ) in PbSe. 25

III. RESULTS and DISCUSSION
The PALS spectra of nearly all thin layers of PbSe NCs were found to display a dominant positron lifetime component 2 with a lifetime of 340 to 380 ps using a three component lifetime analysis. Figure 1 presents the average lifetime 1  would be needed to explain the size of the observed effect, i.e. at least two orders of magnitude larger than Pb monovacancy concentrations observed in PbSe single crystals. 33 Indeed, the formation energy of a V Pb V Se divacancy of 1.47 eV was found from our VASP calculation. 25 This implies that even at the highest synthesis temperature, the equilibrium concentration of divacancies is less than 10 - In order to gain additional insight in the surface composition of the PbSe nanocrystals, we investigated the same set of films using the positron 2D-ACAR method.
The measured 2D-ACAR momentum distributions were found to be isotropic, consistent with the random orientation of the NCs obtained by XRD. In Figure 2, the evolution of the 1D-ACAR momentum distributions N(p) as a function of particle size of the PbSe NCs is presented as the ratio between N(p) and the directionally averaged 1D-ACAR momentum distribution for the PbSe single crystal. At low momenta, the ratio curves show a reduction in the momentum range below 0.6 a.u. and a corresponding peak at  ligand coverage and Se exposed areas at the NC surface as will be explained below.
Interestingly, in the CdSe case, the ligand effects were much smaller. 38 Interestingly, the dependence of I Pb on particle size is seen to correlate with that of the positron lifetime. 25   The confinement peak near p~1.0 a.u. is fitted by a Gaussian curve to extract the peak area as a function of particle size.

A. Synthesis and characterization
Samples of PbSe NCs with four different average sizes ranging between 2.8 nm and 9.7 nm were synthesized using the method of Talapin

D. 2D-ACAR and Doppler broadening experiments
The nanocrystal films were studied with a high-intensity slow positron beam (POSH) originating from pair production in the reactor at Delft, 8 while the bulk PbSe single crystal was studied using a 22 Na radioactive source, which emits a -spectrum of positrons up to ~0.54 MeV. The 2D-ACAR measurements were carried out using an Anger-camera-type setup. 8,9 In order to select the optimum positron implantation energies

E1. Positron-Electron Momentum Density (PEMD) of rock salt PbSe
PbSe has the NaCl structure with space group 3 Fm m (No. 225) with lattice parameter a = 0.6120 nm. 11 Our electronic structure calculations are based on the local density approximation of density functional theory. The crystal potential was obtained by means of an all-electron fully charge-self-consistent semi-relativistic electronic structure computation using the Korringa-Kohn-Rostoker (KKR) method 12,13 with Von Barth-Hedin exchange and correlation. 14 The positron band structure and ground-state wave function were computed the same way, using the inverted electronic Hartree potential and adding a positron-electron correlation potential. The WIEN2K package 15 was employed to carry out calculations using the full-potential linear augmented plane wave (FLAPW) scheme in order to ascertain that the KKR band structure and Fermi level are basically the same as the full-potential results.
The positron-electron momentum density (PEMD), 2 (p), is given in the independent particle model by 2 2 . N p dp dp p and is in practice obtained by projection of a calculated or measured 2D-ACAR distribution ( , ) x z N p p using ( ) ( , ) x z x z N p N p p dp . Figure S7 presents the calculated 1D-ACAR momentum distribution for defect-free bulk PbSe. The 1D-ACAR profile for PbSe provides an insight into the origin of the peak at ~1 a.u. in the ratio curves shown in Fig. 2. Following Weber et al. 16 Figure S8 shows the calculated positron-electron momentum distribution N(p) of atomic oxygen presented as a ratio to the calculated directionally averaged 1D-ACAR distribution of single crystal PbSe. The ratio curve for the case of 50% annihilations with atomic oxygen and 50% annihilations with PbSe is also presented. The latter implies a O(1s) contribution -responsible for the high momentum rise beyond p = 2 a.u. -of about 1%, which is of similar magnitude as the O(1s) contribution found in Positron Auger Electron Spectroscopy (PAES) measurements of surface oxidized Cu. 17 Previous studies have shown that PAES is an extremely surface sensitive analysis technique. 18

E3. Calculation of the formation energy of the Schottky pair defect (V Ps V Se ) in PbSe
In order to obtain an estimate for the concentration of divacancies, the formation energy of a Schottky cluster (adjacent Pb-Se vacancies) was calculated using the ab initio VASP code 19 (PAW-GGA-PBE potentials, 64-atom 2x2x2 supercell, 8x8x8 k-mesh, cut-off energies for the plane wave and augmentation functions of 450 and 750 eV, respectively).
A formation energy of 1.47 eV was found after full relaxation, which implies that even at the highest synthesis temperature of 165 o C, the equilibrium concentration of Schottky pair defects is less than 10 -16 per pair of Pb-Se atoms.
F. Variation of the confinement peak with particle size Figure S9 shows that the peak at p~1.0 a.u. in Fig. 2 varies approximately as 1/d on particle diameter d, as could be expected from the scaling law for the optical band gap E gap~1 /d for PbSe nanoparticles. 20 The small increase of area for the 9.7 nm NCs is probably due to the other effect of the confinement of the positron wave function described by A. Calloni et al. 21 .