Tuning colloidal quantum dot band edge positions through solution-phase surface chemistry modification

Band edge positions of semiconductors determine their functionality in many optoelectronic applications such as photovoltaics, photoelectrochemical cells and light emitting diodes. Here we show that band edge positions of lead sulfide (PbS) colloidal semiconductor nanocrystals, specifically quantum dots (QDs), can be tuned over 2.0 eV through surface chemistry modification. We achieved this remarkable control through the development of simple, robust and scalable solution-phase ligand exchange methods, which completely replace native ligands with functionalized cinnamate ligands, allowing for well-defined, highly tunable chemical systems. By combining experiments and ab initio simulations, we establish clear relationships between QD surface chemistry and the band edge positions of ligand/QD hybrid systems. We find that in addition to ligand dipole, inter-QD ligand shell inter-digitization contributes to the band edge shifts. We expect that our established relationships and principles can help guide future optimization of functional organic/inorganic hybrid nanostructures for diverse optoelectronic applications.

In order to use the computed band edge shifts for our QD models to predict the maximum possible band edge shift in the case of experimental conditions, that is, a larger QD with more ligands, we used an electrostatic model. 1 The electrostatic model is valid under the assumption that the QD is spherical, and its radius, r, is significantly larger than the ligand/QD interface where the surface dipole layer is present, Δx.
The product was purified by recrystallization from ethanol affording white needle like crystals (92% yield). The product was sufficiently pure after this step to use directly as a ligand for the oleate exchange process. 1  Computation methods for functionalized cinnamic acid ligand calculations. The functionalized cinnamic acid ligands were optimized in the trans conformation i.e., the acidic proton bound on either one of the carboxylic oxygen atoms. We computed the ligand dipole moment as projected on the molecular axis. The molecular axis was defined using atoms in position 1 and 4 of the benzene ring. It is known that dipole moments converge slowly as a function of the volume of the cell, we thus performed additional tests to verify the convergence of the results. We found it necessary to use cells as large as two times the greatest distance between two atoms within each model plus 5 Å.

Supplementary Note 3.
XPS Data Analysis. The valence band maximum with respect to Fermi energy (E ! − !"# ) (Fig. 3b) is not a simple extraction from the rise in photoelectron intensity (( ! − !"#$% ) is the intersection of the linear extraction of the rise in intensity and the baseline). Due to a low density of states at the valence band maximum, a correction to the extracted onset of photoelectron intensity is needed to determine the ( ! − !"# ) value for PbS QD films. This has been previously discussed by Miller et al. 2 Briefly, the correction depends on the band gap ( ! = optical band gap + exciton binding energy); the correction to the onset of photoelectron intensity is correction = 0.382 --0.226( ! ). For this study, the optical band gap and exciton binding energy of the native PbS QD ligand is 1.27 and 0.09 eV, respectively, which gives ! = 1.36 eV and a correction of 0.075 eV. Therefore, ( ! − !"# ) = ( ! − !"#$% ) -(0.075 eV) for the PbS QD films used in this study.
The XPS data highlights the influence of the ligand dipole. Fig. 3b and Supplementary Table 2 shows that the measured ! − !"# value is similar for all of our R--CA -ligand exchanges. This strongly suggests that the attachment of the ligand to the surface is the same for all ligands and that the ligand minimally perturbs the Fermi level within the PbS band gap. The significant change is observed in the XPS secondary electron cut--off region (Fig. 3a), which is tuned by the ligand dipole.
We are able to extract meaningful XPS data from QD films made from the as--synthesized OA --/PbS QDs (Fig. 3, black traces). In our lab, previous XPS measurements of OA --/PbS QD films where the QDs were synthesized using other methods (Hines and Scholes / (TMS) 2 Si / in--situ generated Pb(OA --) 2 ) showed high levels of photocharging, making all of the data collected subject to scrutiny and the band positions of OA --/PbS QDs difficult to determine. In fact, the majority of XPS literature data are for QD films fabricated using layer--by--layer ligand exchange techniques so that the resulting films are electronically conductive. We postulate that the narrow size distributions and pristine surface of the Owen thiourea PbS QD synthesis allows for improved charge transport, and subsequently, low levels of film photocharging (verified via power dependence of the secondary electron cutoff).  Table 3.

Supplementary Note 5.
Functionalized CA --Capped PbS QD Models. We built charge neutral QD models with Pb excess 4,5 and by satisfying charge orbital balance: 6,7 the formal charge of the PbS QD core is balanced by the formal and opposite charge of the R--CA -ligands bound on the surface of the QD. We started by cutting out isolated cubes from bulk PbS. Cubes with odd number of layers were off--stoichiometric while cubes with even number of layers were stoichiometric. We generated three structural models with varying amount of ligands. For model A, with formula [Pb 43 S 38 ][R--CA --] 10 , we first generated a five layer cube and cut off atoms to define a QD with small (111) and (110) facets and a near spherical shape. The surface was then passivated with 10 R--CA -ligands that were bound both on (111)  The surface was then passivated with four R--CA -ligands while making sure that all the ligands align along one Cartesian direction. We made this choice for computational reasons: by having ligands point in only one direction, we only had to use larger cell size in one Cartesian direction. To ensure charge balance, four iodine atoms were used to passivate the remaining four (111) facets. In all three cases, we generated several different binding conformations, and we verified that the models discussed here are the most stable structures. Supplementary Fig. 3 shows the ball--and--stick structural model of the relaxed 4--H--CA -covered models. The large variety of these models sampling several possible shapes, facets, and binding moieties allowed us to draw robust conclusions in regards of the band edge position and optical absorption of the ligand/QD complexes.

Supplementary Note 6.
Computation methods for ligand/QD band edge shifting calculations. The band edge shift of the QDs was computed by measuring the HOMO and LUMO energy of the ligand/QD complexes on an absolute energy scale with respect to the vacuum level as a function of the aromatic functional group of the R--CA -ligands. The HOMO was always localized on the QD core, with the exception of 4--N(CH 3 ) 2 --CA --, where the ligand states were too high in energy relative to the energy of QD states, and thus the HOMO was localized on the ligands. This is likely a result of the underestimation of ionization potentials using density functional theory in the PBE approximation. In order to disentangle this effect from the ligand dipole induced shift of the QD states, we performed a projected density of states analysis and defined the QD HOMO/LUMO as the first state from the band edge that was localized on the QD core. The projected density of states DOS for atoms i belonging to region is defined as: where i are atomic orbitals and j are Kohn--Sham states with energy j . We defined two regions: one that is comprised of the PbS QD core (DOS !" ( )) and another one that contains the ligands (DOS !"#$%& ( )). See Supplementary Fig. 4a for a breakdown of these contributions for ligand/QD complex model C.
Using the above definition of the ligand/QD complex HOMO/LUMO states, the computed band edge shifts for the various R--CA --/QD models are shown in Supplementary Fig. 4b as a function of the projected dipole moment of the R--CAHs.

Supplementary Note 7.
Polarizability effects on ligand/QD band edge shifting. Although the predicted range of band edge shift was in good agreement with the experimental results, there were a few cases where the agreement was not perfect. Thus, as summarized in the main manuscript, we have also considered additional effects that may be responsible for the residual differences.
We used computational methods to study ligand interactions on the surface of QDs (see below for intra--QD ligand shell effects and the main text for inter--QD ligand shell effects). Although surface coverage effects are taken into account by our electrostatic model, early experiments on monolayers of self-assembled molecules on bulk CdSe films 8 suggested that in the case of close packed ligand coverage, the effective dipole felt by the surface might be reduced due to depolarization effects. Since depolarization effects are proportional to the polarizability the ligand, and fluorinated bonds are known to be less polarizable than other considered functional groups (see below for a longer discussion on the polarizabilities of the ligands), we anticipated that the residual differences between theory and experiments might be attributed to functional group dependent depolarization effects.
In our simulations on isolated QDs, we did not use full surface coverage to reduce the computational burden of the calculations, however, we studied full surface coverage in the case of slabs. We thus analyzed depolarization effects on flat surfaces, where the shift in the band edge energy is given by: Here, incorporates dielectric screening effects at the monolayer/slab interface and is the surface area. Since the dielectric constant is not well defined for a monolayer of ligands, following earlier works, 9,10 we have developed a classical electrostatic approach to take into account dielectric screening, sometimes also called local field effects. In this picture, the dipole moment of a ligand is renormalized due to the electric field of neighboring dipoles. The effective surface dipole is reduced and the band edge shift becomes: where is the polarizability of the ligands, is the lattice constant of the monolayer and is a unitless constant that is dependent on the geometry of the 2D lattice of the monolayer. It is 9.03 for a square and 11.04 for a hexagonal lattice, 11 the latter is relevant for bulk PbS(111) surfaces. Additional effects, (4) such as screening from the substrate and the presence of image dipoles, should also be taken into account. Indeed, according to Ref. 9 , the presence of a substrate with dielectric constant ! further contributes to the depolarization of the ligand dipoles: Since the dielectric constant of PbS is high (for example, the low frequency dielectric constant is 169), 12 image dipole effects are changing the proportionality constant of the polarizability by a factor of two to a very good approximation.
In order to test the above electrostatic model, we computed the polarizabilities of the ligands using a finite field approach. A small external sawtooth potential was applied in each Cartesian direction and we measured the change in the dipole moment along Cartesian direction . The polarizability tensor !" is then obtained by a central difference formula: We used an electric field with magnitude of 0.001 Hartree atomic units. We only allowed the charge density to respond to the external potential (the atoms were not allowed to relax), therefore the computed values are high frequency polarizabilities and are expected to underestimate the full, static polarizabilities. We also computed the polarizabilities projected on the molecular axis : We also verified on a single ligand that the finite field calculations are in the linear regime by computing the dielectric constant of the ligand in a cubic box with lattice constant of 40 Å using density functional perturbation theory techniques and then using the Clausius--Mossotti formula to extract the polarizability. The isotropic polarizabilities computed with the two different techniques agreed within 2% for 4--H--CAH. All finite field polarizability calculations were run in a cell size of at least 25 Å and we verified the convergence of the results by increasing the box size of the 4--H--CAH by 5 Å and finding that the results only changed by 0.1%. Supplementary Fig. 6a shows the polarizability and projected polarizabilities of the ligands as a function of the functional group on the ligands. We find that the polarizability is proportional to the HOMO--LUMO gap of the molecules. More importantly, we see that the polarizability of the 4--CN--CAH ligand is only marginally larger than those of 3,5--F--CAH and 4--CF 3 --CAH and thus it is not likely that depolarization are alone responsible for the observed differences. This conclusion is also supported by Supplementary Fig. 6b, which represents the renormalized projected dipoles ( ′) using the projected polarizabilities: ′ = (1 + ! ! ! 2): the absolute magnitude of the renormalized dipoles change substantially, but the trend did not change. Here, we used = 11.04 and = 4.25 Å, which are the lattice sum and the lattice constant of the surface unit cell of the PbS(111) surface, respectively.
Although the above analysis suggests that depolarization effects are very likely not responsible for the observed differences in the band edge energies, we constructed slabs of bulk PbS (111) with two different surface coverages to further analyze band edge shifts using more realistic models. Slab (A) was obtained by making a Pb terminated 3x1 (111) slab of PbS with inversion symmetry and then removing one out of three Pb atoms on both facets while maintaining the inversion symmetry. The formula of the slab was Pb 13 S 12 . Both facets were passivated with deprotonated cinnamic acids bound in the groves of the top Pb layers. We chose this binding conformation because recent calculations on simple acids suggest that this is the most energetically favorable binding conformation under similar surface coverage conditions. 13 The surface coverage was 44 Å 2 /ligand. Slab (B) had a 1x1 surface unit cell of the (111) slab of bulk PbS again with inversion symmetry. The formula was Pb 5 S 4 . We then passivated both facets with deprotonated cinnamic acids. We tried several different ligand arrangements and found that the chelating binding is the most energetically favorable. We used a k--point sampling of at least 4x4x1 of the surface primitive unit cell, which is sufficient to obtain converged trends.
We then computed the valence band maximum (VBM) by measuring the VBM of the slabs relative to the average electrostatic potential in the middle of the vacuum region along the direction z. By construction, the dipole moment of the entire slab was zero and thus the electrostatic potential was flat in the vacuum region. We note that these slabs are not thick enough and thus confinement effects can be observed for the absolute position of the VBM and for the band gap. However, the relative trends between the different ligands should be largely unaffected. Supplementary Fig. 7(a--d) shows the structural models of both slabs and Supplementary Fig. 7e represents the VBM w.r.t vacuum as a function of the functional group on the ligands. Since we were interested only in ligands that were either fluorinated or were outliers in the experiment, we did not consider the ligands with larger functional groups. Interestingly, the data shows that depolarization effects may indeed take place, since the ratio of the ranges of band edge shift for the two different models is about 1.8. Should depolarization effects not take place, this value would equal 3.0, since the surface coverage differs exactly by three. However, the trend still follows the trend predicted by the dipoles, in agreement with the analysis above about the surface polarization effects. We thus conclude that surface polarization is unlikely to be the only property responsible for the observed differences.