Crystal Phase Transitions in the Shell of PbS/CdS Core/Shell Nanocrystals Influences Photoluminescence Intensity

We reveal the existence of two different crystalline phases, i.e., the metastable rock salt and the equilibrium zinc blende phase within the CdS-shell of PbS/CdS core/shell nanocrystals formed by cationic exchange. The chemical composition profile of the core/shell nanocrystals with different dimensions is determined by means of anomalous small-angle X-ray scattering with subnanometer resolution and is compared to X-ray diffraction analysis. We demonstrate that the photoluminescence emission of PbS nanocrystals can be drastically enhanced by the formation of a CdS shell. Especially, the ratio of the two crystalline phases in the shell significantly influences the photoluminescence enhancement. The highest emission was achieved for chemically pure CdS shells below 1 nm thickness with a dominant metastable rock salt phase fraction matching the crystal structure of the PbS core. The metastable phase fraction decreases with increasing shell thickness and increasing exchange times. The photoluminescence intensity depicts a constant decrease with decreasing metastable rock salt phase fraction but shows an abrupt drop for shells above 1.3 nm thickness. We relate this effect to two different transition mechanisms for changing from the metastable rock salt phase to the equilibrium zinc blende phase depending on the shell thickness.


Characterization Techniques Transmission Electron Microscopy
A JEOL 2011 FasTEM transmission electron microscope (TEM) operated at an acceleration voltage of 200 kV was used to obtain high resolution TEM images. The direct electron beam intensity used for imaging mode was detected by a CCD camera. The TEM images were created and analyzed by a supplementary Digital Micrograph software package. TEM image contrast differences can be created by many types of amplitude and phase contrasts. S1 In this work, the darkfield images in Figure S1d,e were created by using diffraction contrast. In Figure S1d only the electron diffraction spots characteristic for the rocksalt (RS) crystal structure were used and in Figure S1e only zincblende (ZB) peaks were used for image formation. Thus the bright regions in S1d mainly concentrated in the core corresponds to regions depicting the RS crystal phase, whereas in S1e the bright parts within the shell S2 region originate from ZB crystal phases.

Anomalous Small Angle X-ray Scattering
Small angle x-ray scattering (SAXS) is a method widely used in the analysis of nanoscale structures. S2 The technique provides a number of structural parameters such as size and shape of particles, as well as their correlations and hence their volume fraction in the case of a denser particle system. In extension to SAXS, anomalous SAXS (ASAXS) S3-S6 allows element specific contrast variation between different phases in the sample and hence the possibility to determine chemical compositions as a function of particle dimension. S7,S8 The contrast variation in ASAXS is due to the dependency of the atomic scattering factor f (E) on the x-ray energy E, in particular, in the vicinity of x-ray absorption edges. Hence, for ASAXS experiments synchrotron x-ray sources have to be used where the x-ray energy can be continuously varied. The ASAXS-spectra for the large and small sample series have been measured at the 7T-MPW-SAXS beamline at the BESSY II synchrotron (HZB Berlin, Germany), whereas the medium sized NCs have been recorded at the beamline ID01 at the European Synchrotron Radiation Facility ESRF (Grenoble, France).
For the case of the PbS/CdS core/shell nanocrystals the contribution of Pb as the strongest scatterer (with the atomic number Z = 82e − ) to the total scattering amplitude f (Z, E) can be varied by tuning the x-ray energy just below, e.g., the Pb-LIII-edge at E = 13.035 keV. The atomic scattering factor f (Z, E) can be written as: ,where f 0 + f ′ (E) is the real part and f ′′ (E) the imaginary part of the scattering amplitude.
f 0 (Z) depends only on the number of electrons in an atom, whereas f ′ (E) and f ′′ (E) depends on the used x-ray energy. Thus the total amplitude f (E) deviates from the atomic number Z by varying the energy around an elemental absorption edge. The dispersion S3 corrections f ′ (E) and f ′′ (E) are related to each other by the well known Kramers-Kronig relations and the values of the scattering factors were calculated by the procedure described by Cromer&Libermann. S9 Hence, in ASAXS the scattered intensity is a function of the scattering vector q and the x-ray energy E, with q = 4π sin θ/λ and λ the x-ray wavelength: This equation consists of three parts: the energy independent normal SAXS term F 2 0 (q), the scattering cross term containing the resonant and non-resonant part F 0 (q)F R (q) and the pure resonant term F 2 R (q), which is related to the Pb-electron density. By using equation 2, the over determined system of m equations for m >3 measured energies can easily be solved numerically. The solution of this set gives the values of the three variables F 0 (q), F 0 (q)F R (q) and F R (q). S7,S8 The form factor F CS for a spherical core/shell particle is derived by subtracting the analytical form factor of a homogenous inner sphere (the core) from the outer sphere.
sin qr out − (qr out ) cos qr out (qr out ) 3 +3(∆η core (E) − ∆η shell (E)) sin qr core − (qr core ) cos qr core (qr core ) 3 , where r core denotes the radius of the inner sphere and r out is connected to the shell thickness t shell by r out = r core + t shell . ∆η core (E) is the energy dependent scattering length contrast between the core and the solvent, and ∆η shell (E) between the shell and the solvent.

S4
where r e is the classical electron radius and ∆ρ core,shell the total electron density difference and ∆ν core,shell the Pb-electron density difference between the nanocrystal and the solvent.
Hence, equation 2 was solved for each set of 5 scattering curves with a single spherical core/shell model using r core , t shell , ∆ν core,shell , ∆ρ core,shell as well as the total size distribution σ as fit parameters. The size distribution width σ is assumed to be the same for the core and the shell.
As an example, in Figure Figure S2: (a) Experimental ASAXS curves (symbols) fitted with a unique spherical core/shell model (lines) for the medium sized core/shell PbS/CdS NC-sample after 18h reaction time. The scattering cross section I(q, E) plotted over the scattering vector q were recorded at 5 different x-ray energies below the Pb-L III -edge. The curves, except the black ones measured at an energy far from the edge, are each shifted vertically by a factor of 2 to lower values for clarity. (b) The same as in (b) for the small core/shell particles after 29h reaction time. Here, the factor for the shift is 4.

1-core/2-shells Profile for the Small NCs
The ASAXS procedure described above gives for the core/shell profile of the small NCs (see Figure 2d in the main text) an inconsistent result for the CdS shell: A significant amount of Pb is detected within the CdS shell, but the total electron density is strongly reduced with respect to the theoretical CdS bulk value (see Figure S3b). A nearly two times heavier element like Pb (Z = 82e − ) compared to Cd (Z = 48e − ) should result in contrary in an increased electron density. This problem can be solved, when we use for the fitting procedure a 1-core/2-shells model. The motivation for assuming a not homogenous Pb distribution within the shell is based on the proposed mechanism for shell formations due to cationic-exchange detailed described very recently for ZnSe/CdSe NCs. S10 The exchange starts with a fast Cd 2+ for Pb 2+ exchange on the outer most surface layer, followed by a slower thermally activated solid-state cation diffusion. For a shell thicker than 1 monolayer (ML) CdS the Cd-ions have to diffuse inwards, whereas the Pb-ions outwards. This can be realized by the formation of Frenkel-pairs: S10 The Pb 2+ cations are diffusing towards the surface on interstitial lattice positions whereas Cd 2+ is diffusing inwards over the Pb 2+ vacancies. The surface Pb is finally removed from the surface by Cd-oleatic compound. This process is driven by the larger Cd-S bond strength with respect to PbS. S11 If, however, the Cd-oleate concentration in the solution is too small a certain amount of Pb 2+ will remain on the NC surface. From the ASAXS fits using the 1-shell model we receive 4.5 ± 0.25 Pb/nm 3 within the CdS shell of the small (D = 4.7 nm) NCs after 29 h exchange time. This Pb amount would corresponds to a ∼ 75% surface coverage of one monolayer of Pb on top of the NCs. Thus in a 2-shell fit, a surface shell with different electron density should be detectable with a thickness in the range between two times the ionic radius of Pb with 0.133 nm S12 and the ML thickness of PbS along the [1 1 1] direction of around 0.34 nm.
In Figure  S8 the error between experimental data and fit for all 5 scattering curves simultaneously (see Figure S3a). The resulting electron density profile is shown in Figure S3b also as black line.
For the 1-core/2-shells fit at this fixed energy we use the program DECON S13 developed for retrieving the density profiles of polydisperse colloidal particles. The blue line in Figure S3a shows the resulting fit with the lowest mean deviation for a physical feasible electron density profile depicted in Figure S3b. Indeed, we receive a surface shell with reduced e − -density of  Figure S3c). This resulting SAXS curve (cyan line in Figure   S3a) shows, however, a slightly larger mean deviation with respect to the experimental data as compared to the 2-shells fit with a pure Pb-surface(blue line). (The mean deviation is weighed with the width of the experimental error band and thus the deviations at smaller q-values are more significant than at larger q-values, where the error band is increased.) Furthermore, one can assume a third alternative Pb distribution within the small PbS/CdS NCs, where all the Pb found in the shell is concentrated around the remaining PbS core (see sketch in Figure S3d). We calculate the core volume that can contain the total Pb-amount of about 250 Pb atoms within the whole NC. For this a core diameter of nearly 3 nm with the theoretical Pb-concentration for PbS of 18.9 atoms/nm 3 is needed as depicted as red line in the density profile of Figure S3c. The resulting simulated scattering curve (red line in Figure S3a) shows no agreement with the experimental data.
Finally, from this we can conclude that the detected shell-Pb for the small NCs is not ho-S9 mogenously distributed within the CdS-shell, but also not concentrated around the remaining PbS core. The remaining shell-Pb is most probably distributed on top of the CdS surface shell forming the outer most surface layer as sketched in Figure S3d. This Pb-distribution is found to be in good agreement with the proposed mechanism for a shell growth driven by cationic exchange. S10

Rutherford Backscattering Spectrometry
The Rutherford Backscattering Spectrometry (RBS) method is based on elastic collisions between energetically light ions (H, He with a few hundred keV up to 2 MeV) and the atomic nuclei in a stationary sample. Thus the method is free from any matrix effects.
Scattering kinematics permits to identify the elements present in a thin layer from the yield of particles backscattered from the sample in a large angle. RBS measurements were performed, employing the Van de Graaff accelerator AN700 (30 -700 keV). S14 The low beam currents employed guarantee a non-destructive analysis of the samples. Scattered ions were detected by two semiconductor surface barrier detectors. The Monte Carlo program SIMNRA S15 was used to evaluate the sample compositions by fitting the peaks corresponding to the individual elements in the measured spectra as shown in Fig. S4. Note, that the substrate signal does not influence the analysis.

Sample preparation. Toluene and TCE solutions of PbS, PbS/CdS, and PbS/CdS/SiO2
NCs were spin-coated at 2000 rpm for 3 min. The concentration was adjusted in a range of 5-10 mg/ml in order to obtain (sub-)monolayers of NCs. The HF-treated polished silicon was used as a substrate. In Table S1 the RBS results from the large and the small sample series are summarized together with the total Pb concentration derived from the ASAXS density profiles. For the medium sized NC sample series no RBS-data are available. S10 counts Figure S4: (a) RBS spectrum of a one monolayer thick NC film consisting of large PbS/CdS NCs after1 h reaction time, presented along with the results of Monte Carlo simulations. Silicon is used as substrate. Photoluminescence spectroscopy data and peak shift analysis  Additionally, we analyze additional to the total integrated PL peak intensity, the peak wavelength λ max as a function NC diameter, shell thickness and crystalline phase fraction within the shell. The peak wavelength is related over E 0 = hc/λ max to the band gap energy S12 E 0 of the quantum dot, with h as the Planck constant and c the speed of light. PbS is a narrow gap semiconductor, with a bulk band gap of 0.41 eV, and a large exciton Bohr radius of around 18 nm. S16 The PbS band gap E 0 can be tuned by varying the particle diameter over a large spectral range in the near infrared. When the NC diameter is decreased λ max depicts a blue shift, thus E 0 value is shifted to higher energy values. This sizing curve of the band gap energy E 0 derived empirical from Moreels et al. S16 follows a modified 1/d law, with d the PbS NC diameter: Additionally to this size effect the PL energy can be shifted to longer wavelengths due to an transfer of excitonic energy to the molecular vibrational modes of organic ligands on the NC surface. S17 An even stronger effect due to the large excitonic Bohr PbS is expected for PbS NCs covered with a shell, where the excitonic wave function can extend into the shell region, depending on the band gap of the shell material relative to the core material (for a review see Ref. S18). A strong effect on the PL is expected for an energy level alignment between core and shell, where either the hole or the electron wave function is localized within the shell. For this staggered type-II band alignment S18 a signif icant red-shift of the emission peak wavelength is expected, when the core is covered by a shell. In the PbS/CdS core/shell systems, a small conduction-band offset and a large valence-band offset suggest that the electron wave functions extend into the CdS shell, while holes are efficiently confined in the PbS core. S19 For the case of our investigated large, medium and small sized core/shell NCs we expect, a blue-shift due to the shrinking core and an additional a red-shift with increasing shell thickness. Furthermore, if the RS − ZB phase fraction within the CdS shell as a significant influence on the band structure alignment, we should observe an additional shift of the emission peak energy.
For this analysis we have plotted the experimental PL peak energy derived from λ max of S13   all NC samples as a function of the NC core-diameter together with the sizing curve of the band gap energy E 0 of equation 5 in Figure S6. It can be clearly seen that all pure PbS NCs without CdS shell and the large NCs with the thin shell below 1 nm nicely follows this sizing curve, i.e. the PL peak energy is shifted to higher energies with decreasing PbS core. The PL energy of the medium and small core/shell NCs with thick shells above 1 nm depicts, however, a significant deviation from this curve (see Figure S6a). That means apart from the blue-shift of the PL peak due to the shrinking PbS core, λ max is additionally red-shifted, i.e. shifted to lower energy values. To study this shell induced effect in more detail, we normalized the PL peak energy values to the NC diameter using equation 5 as shown in Figure S6b. This core corrected PL energies for the pure PbS NCs and for the thin shell core/shell NCs are now rather constant over the NCs diameter as expected. The PL peak energies for the medium and small core/shell samples shows in contrast a strongly decreased energy value as a function of the shell thickness. The lowest PL energy is found for the largest shells of around 2 nm thickness. This is in agreement with the model proposed for the type-II staggered band gap alignment, where the electron wave function of the exciton extends into the shell. With increasing CdS shell and larger separation of the electron-hole pair, the effective band gap is decreased and results in a red-shift of the emission peak. S18 Furthermore, we can check, if the amount of the metastable RS crystal phase within the shell has any influence on the the band gap alignment and thus on the PL emission. In Figure S6c the double normalized PL energy values are shown, i.e., normalized to the NC diameter as well as to the shell thickness. These relative PL values are plotted over the RS − ZB phase fraction within the shell, where the amount of the RS phase varies within the shell from about 90% down to 5%, when the CdS shell reaches its equilibrium ZB crystal structure. In Figure S6c there is no influence of the crystal structure on the PL peak energy observable, and hence on the band alignment.
To conclude the analysis of the PL peak wavelength values, we can sum up three experimental findings. S15 i.) The emission peak wavelength values of the pure NCs and the core/shell NCs with thin shells follows very well the sizing curve found for the band gab energy E 0 of PbS NCs. The λ max value is shifted to shorter wavelengths with decreasing diameter. This is an independent optical confirmation of the determined PbS core diameters derived by our ASAXS method.
ii.) This size induced blue-shift is partly compensated for the medium and small sized core/shell NCs due to a shell induced red-shift. This red-shift increases with increasing shell thickness and can be related to an extension of the excitonic wave function into the CdS shell.
iii.) The crystalline phase within the shell, either RS or ZB, has no influence on the PL wavelength and hence no significant impact on the core/shell band alignment.

Analysis of the experimental derived x-ray diffraction data
In the Figures S8(a), S9(a), S10(a) all experimental derived x-ray diffraction (XRD) patterns of all investigated sample series together with their fits (Gaussian peaks with background) are shown. To analyze the measured XRD data quantitatively we calculated the diffraction patterns for the pure PbS NCs and the PbS/CdS core/shell NCs by means of the Debeyeformula, S20,S21  Figure S7). At the core/shell border and the outer NC-surface the unit cells were cut atomically sharp. (For the case of the small core/shell NCs the incomplete surface Pb-monolayer was neglected in the calculation due to its small contribution to the total scattering signal.) For this purpose we have written an own simulation software P CG−SW AXS were the geometrical 1-core/1-shell parameters, the chemical composition as well the crystal structure can be varied freely. S22 The values of the integral peak intensities and the shift of the peak positions derived from the simulated patterns, give the maximum impact of the shell being either fully in the RS Figure S7: Scheme to illustrate the crystal structures used in the calculations for the diffraction patterns: The pure PbS NCs as well as the PbS-cores are always kept in the bulk RS crystal structure of PbS. The CdS-shells are either fully in the RS structure of the core or fully in the equilibrium ZB crystal structure of CdS.
or ZB crystal structure (see Figures S8( S10(b)). Comparing these values with the all experimental obtained values for the large, medium and small NCs allowed to determine quantitatively the RS − ZB crystal phase fraction within the CdS-shell.
For the large core/shell sample series the contribution of the thin shell to the total diffraction signal is only around 30% and hence the observed change in the peak ratio as well in the peak shift (see Figure S8) is lower, as compared to the thick shells of the medium and small sized NCs (see Figures S9 and S10). For these core/shell samples the contribution of the core is below 6% and thus the experimentally observed peak changes could be even directly related to the amount of RS-ZB phase fraction within the CdS shell (see Figures   S9 and S10). S18 0 0  together with their fits (lines). The same fitting routine is used for the experimental and simulated data. The pattern for the pure PbS NCs is shown in black, whereas in cyan for a core/shell NC with a CdS-shell of 0.7 nm thickness and fully in the RS crystal structure; in red the same shell fully in the ZB structure. In blue the simulation for a 1:1 RS/ZB ratio within the shell is shown assuming an homogeneous distribution of the phases. S19 0 0  shown (open circles) together with their fits (lines). The pattern for the pure PbS NCs is shown in black, whereas in cyan for a core/shell NC with a CdS-shell of 1.4 nm thickness and fully in the RS crystal structure and in red the same shell fully in the ZB structure. In blue the simulation for a 1:1 RS/ZB ratio within the shell is shown assuming an homogeneous distribution of the phases. The pattern for the pure PbS NCs is shown in black, whereas in cyan for a core/shell NC with a CdS-shell of 1.9 nm thickness and fully in the RS crystal structure and in red the same shell fully in the ZB structure. In blue the simulation for a 1:1 RS/ZB ratio within the shell is shown assuming an homogeneous distribution of the phases.  Figure S11: The RS-ZB phase fraction as a function of the strain state within the CdS-shell is plotted for all three sample series. The values for the large, medium and small core/shell NCs with different shell thicknesses (black,cyan and green squares) are derived from the (220) peak positions. The straight lines are linear fits to the data. The maximum tensile strain of 0.02 for the CdS-shell (ZB, a CdS = 5.818Å) can be reached when the shell fully keeps the lattice constant of the PbS core (RS, a P bS = 5.936Å) marked with the red dashed line. The blue dashed line marks the value for the shell depicting the bulk lattice constant of ZB CdS. The negative compressive strain values for the 2 nm thick CdS-shells of the small sample series is related to an additional hydrostatic surface stress due to the small particle size.