Orbital Topology Controlling Charge Injection in Quantum-Dot

Letter pubs.acs.org/JPCL

Orbital Topology Controlling Charge Injection in Quantum-DotSensitized Solar Cells Thorsten Hansen,*,†,‡,∥ Karel Ž ídek,†,∥ Kaibo Zheng,†,∥ Mohamed Abdellah,†,¶ Pavel Chábera,† Petter Persson,§ and Tõnu Pullerits*,† †

Department of Chemical Physics and §Department of Theoretical Chemistry, Lund University, Box 124, SE 221 00 Lund, Sweden Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK 2100 Copenhagen Ø, Denmark ¶ Department of Chemistry, Qena Faculty of Science, South Valley University, Qena 83523, Egypt ‡

S Supporting Information *

ABSTRACT: Quantum-dot-sensitized solar cells are emerging as a promising development of dye-sensitized solar cells, where photostable semiconductor quantum dots replace molecular dyes. Upon photoexcitation of a quantum dot, an electron is transferred to a high-band-gap metal oxide. Swift electron transfer is crucial to ensure a high overall efficiency of the solar cell. Using femtosecond time-resolved spectroscopy, we find the rate of electron transfer to be surprisingly sensitive to the chemical structure of the linker molecules that attach the quantum dots to the metal oxide. A rectangular barrier model is unable to capture the observed variation. Applying bridge-mediated electron-transfer theory, we find that the electron-transfer rates depend on the topology of the frontier orbital of the molecular linker. This promises the capability of fine tuning the electrontransfer rates by rational design of the linker molecules. SECTION: Energy Conversion and Storage; Energy and Charge Transport

T

Previously, we have studied photoinduced electron injection into QD-sensitized nanowires using femtosecond time-resolved spectroscopy. Correlating the dynamics with time-resolved THz spectroscopy data, we could unequivocally identify the charge injection time scale.11 Further, we have demonstrated that multiple-electron injection can be utilized in these systems.12 Investigations of TiO2 sensitized by molecular dyes have shown that the chemical nature of linker groups can have significant influence on photoinduced electron injection rates in DSSCs.13 The rate of photoinduced electron transfer from QDs to metal oxide (MO) nanoparticles was studied recently for a range of combinations of materials and QD sizes by P. V. Kamat and co-workers.4 They were able to model the observed rates by a many-state Marcus equation and an elaborate electrostatic theory for the free energy. Recent work of our group is consistent with this description. In these studies, the QD to MO coupling was treated as constant, independent of energy. Recent work of Pernik et al.14 compared two cases, the direct attachment of QDs to MOs and QDs attached using a layer of linker molecules, and found only a small change in electron injection rates. This was not expected by the authors because the linker molecules increase the average QD to a MO distance

he quest to harvest an increasing fraction of the 120.000 TW of solar power that hits the surface of the Earth has spawned a range of novel solar cell designs in recent decades, including dye-sensitized solar cells (DSSCs) and bulk heterojunctions.1,2 In contrast to crystalline silicon photovoltaic devices, these consist of heterogeneous materials with morphology features on the nanometer scale. Their overall efficiency relies on a sequence of electronic events. The primary process of charge separation occurs via interfacial electron transfer and subsequent movement of the electrons and holes to the electrodes. DSSCs were invented by Mikael Grätzel and co-workers in the early 1990s, when they sensitized a nanostructured titanium dioxide surface with a ruthenium dye and immersed it in an electrolyte containing the iodine/triiodide redox couple.1 DSSCs comprise a growing research field and are commercially available for a variety of applications. Recently, a solid-state version was demonstrated, which solves the problem of having a liquid electrolyte and could expand the range of applications even further.3 Quantum-dot-sensitized solar cells are emerging as an alternative to DSSCs where nanoscopic semiconductor quantum dots (QDs) replace the chromophore molecules. QDs have certain advantages over molecular chromophores; they are photostable, and their absorption spectra are easily tuned by varying their size.4−9 QDs also allow for multiexciton generation, where multiple electrons can be harvested from one high-energy photon absorbed by a dot.10 © 2014 American Chemical Society

Received: January 19, 2014 Accepted: March 14, 2014 Published: March 14, 2014 1157

dx.doi.org/10.1021/jz5001193 | J. Phys. Chem. Lett. 2014, 5, 1157−1162

The Journal of Physical Chemistry Letters

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sensitive to the structure of the molecule, which offers a novel strategy to chemically tailor the electron-transfer rates in QDsensitized solar cells. A range of experiments were performed to characterize the QD-sensitized nanowires. Representative data are shown in Figure 2. The as-obtained colloidal QDs are capped by oleic

by several Å, and electron tunnelling rates decrease exponentially with distance. It can be understood within a rectangular tunnelling barrier model, where the energy of the lowest unoccupied molecular orbital (LUMO) relative to the scattering energy sets the height of the barrier. In fact, the tunnelling current through a self-assembled monolayer of molecules is often well-fitted by the Simmon’s model.15,16 Thus, to maximize the electron-transfer rate, one should choose a short molecule with a low-lying LUMO energy. Several studies of linker molecule in QD-sensitized solar cells have been reported in the literature.14,17−26 Most of these have reported on dynamics measured with nanosecond time resolution. In contrast, the electron injection takes place already during the first picoseconds after excitation, as we showed previously using a combination of kinetics measured by THz and transient absorption (TA) spectroscopy.11 A recent study also studied the electron transfer using THz spectroscopy.27 In this work, we present ultrafast time-resolved measurements of photoinduced charge transfer from CdSe QDs into ZnO nanorods using three small saturated carboxythiols as linker molecules, mercaptoacetic acid (MAA), 2-mercaptopropionic acid (2MPA), and 3-mercaptopropionic acid (3MPA). The TA measurements were performed with femtosecond time resolution to capture details of the charge injection process. The measured electron-transfer rates are surprisingly different given the similarity of the linker molecules; see Figure 1.

Figure 2. (A) Absorption (black line) and emission (filled area) spectra of CdSe QDs in solution and attached to ZnO NWs. (B) Zinc oxide nanowires. (C) FT-IR spectra before and after linker exchange.

acid. The pronounced peak at a wavelength of 551 nm in the absorption spectrum represents the 1S exciton absorption of QDs. The QD size (3.1 nm) determined from it is consistent with the HR-TEM images. The emission band of these QDs is narrow, indicating a relatively narrow distribution of QD sizes. In addition, no broad red-shifted emission was found, which is typical for defect states on the QD surface; apparently, quenching by and emission from unwanted surface defects is negligible; thus, the QDs are well passivated by the surfactant molecules. In order to attach QDs to ZnO, oleic acid needs first to be exchanged to bifunctional linkers (i.e., MAA, 2-MPA, 3MPA) with a thiol group anchoring to the QD surface. After linker exchange and the washing process, the surfactant of the QDs is entirely replaced with linkers of interest, which can be verified by FT infrared spectroscopy (see Figure 2C), where the characteristic C−H stretching for oleic acid almost disappears while a new stretching mode for the COO− group occurs. Sensitization of QDs onto ZnO is then carried out by directly immersing ZnO nanowires into a solution containing a QD linker. QDs will spontaneously anchor to the nanowire surface via carboxyl groups. Absorption spectra of QDs attached ZnO nanowires keep the same exciton peak of QDs in solution (see the dashed lines in Figure 2A). The offset after band edge absorption is due to the light scattering of the nanowires, also seen in our previous work.

Figure 1. The electron tunnels from the conduction band of the QD, off-resonantly with the LUMO orbital of the molecular linker, and into the conduction band of the ZnO nanowire. The effective donor− acceptor coupling TDA(ε) depends on the donor−molecule coupling VDS, the molecular Green’s function GSO(ε), and the molecule− acceptor coupling VOA.

Transfer through the two molecules with virtually identical lengths and LUMO energies, MAA and 2MPA, differs by more than a factor of 3; thus, the rectangular tunnelling barrier picture is insufficient. We analyze the electron transfer using bridge-mediated electron-transfer theory,28 where the coupling, T(ε) ≃ VG(ε)V, is expressed in terms of molecule− semiconductor couplings, V, and the molecular Green’s function G(ε). This way, we can rationalize the variation in electron-transfer rate and identify the shortcoming of the rectangular barrier model. We will show that not only is the energy of the frontier orbital important, but also, its coefficients on the terminal atoms where the electron enters and leaves the molecule play a key role. The LUMO coefficients are very 1158



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convoluted with a Gaussian response function (see the Supporting Information for details and best-fit parameters). For the sake of clarity, we will call the fitting components fast, slow, and nanosecond. The observed behavior is analogous to the previously reported measurements,11,29 where the combination of TA and THz spectroscopy has proven that the fast component on the picosecond time scale arises from the direct electron transfer to ZnO. The slow component can have ambiguous origin, either injection via the charge-transfer state or electron injection from a different class of QDs (for instance, QDs with a fast hole trapping or charged QDs). Finally, the nanosecond component can be assigned to QDs without direct attachment to ZnO.29 The fast component of the TA decay reflects the process calculated by the theory presented in the following paragraphs, that is, direct injection from QDs to ZnO from the lowest excited level. Therefore, we determine the electron-transfer rates as an inverse value of the fastest component lifetime with ∼5% precision and the resulting values listed in Table 1. The obtained electron injection times (3.8−16 ps corresponds to rates of 64−260 ns−1) are in agreement with previous measurements with the TA technique.4

Electron injection from the QD to MO can be monitored experimentally by using ultrafast TA spectroscopy. Electrons in QDs are first excited into the conduction band by a pump pulse. The electron rapidly relaxes to the lowest excited state within the time resolution of our setup. The relaxed electrons fill the lowest excited states. This leads to reduction of absorption (bleach), as illustrated in Figure 3A. The absorption

Table 1. Experimental and Theoretical Electron-Transfer Ratesa

Figure 3. (A,B) TA spectra measured for various delays (lighter color and arrow indicate increasing delay). (C) Comparison between TA dynamics of CdSe QDs (stars) and CdSe QDs attached to ZnO via a MAA linker (open circles) fitted by a three-exponential function (solid line). (D) TA dynamics for QDs attached to ZnO via various linker molecules.

experiment −1

k/ns MAA 2MPA 3MPA

change is measured by another femtosecond pulse (probe), which is delayed with respect to the pump pulse. Thereby, we can efficiently monitor the time-dependent concentration of excited electrons in QDs. In the case of QDs in solution, the bleach persists for nanoseconds without discernible change (see Figure 3A). This is a consequence of the long electron−hole recombination time in QDs. However, when QDs have been attached to ZnO nanowires, the bleach begins to recover already during first picoseconds after excitation (see Figure 3B) due to the additional process of electron transfer from the QD to ZnO. We have verified that linker exchange and QD deposition do not lead to the fast TA decay. In all cases (without attachment to ZnO), we observe that less than 5% of the TA signal is decaying during the first picoseconds after excitation (see the Supporting Information for the data). As the TA signal in CdSe QDs is sensitive only to the electron population in QDs and it is not affected by hole dynamics, the results imply that we do not observe creation of any new electron traps. The shape of the bleach spectrum is not changing with the pump−probe delay (see Figure 3A,B); therefore, we can describe the whole dynamics of the system by TA kinetics at a signal maximum. The difference between the two samples becomes clearly visible (see Figure 3C). To verify that the arising fast bleach decay originates from electron injection, we deposited the same QDs onto a glass surface. In this case, no electron injection occurred, and the deposited QDs did not show any fast decay of their TA signal (see the Supporting Information). The electron injection depends highly on the linker molecule (see in Figure 3D). In order to extract the electron-transfer rate, we fitted the measured kinetics by a three-exponential function

2.6 × 102 83 64

theory MAA

k

/k

1 3.2 4.1

kMAA/k/ 1 3.79 4.44

(3.70) (4.64)

a

Two relative rates have been obtained from both experiment and theory. Theoretical rates in parentheses include shifts in LUMO energies.

If we apply the Simmons model, which treats the linker layer as a tunnelling barrier, the electron injection rate is proportional to an exponential length dependence ket ∝ exp(−βd), where the barrier height determines the parameter β. However, the linkers MAA and 2-MPA have virtually identical LUMO energies and differ only by a methyl group present (2-MPA) or not present (MAA) in the molecule. MAA and 2-MPA thus have identical barrier parameters and should exhibit identical electron-transfer rates. Yet, the difference in the electron injection rate is almost the same as that for the MAA and 3MPA linker, where an additional methylene group increases the thickness of the linker layer by ≃1 Å.30 Clearly, a more detailed theoretical description of linker molecules is needed to understand the mechanisms behind this effect. The rate of electron transfer as described by Fermi’s golden rule 2π k= |T (ε)|2 ρ(ε) (1) ℏ is quadratic in the electronic coupling, T(ε), between the QD and the nanowire. Here, ρ(ε) is the density of final states. To appreciate the importance of the molecular linker, we must think of the electron injection as a scattering process mediated by the molecule and expand the transition operator as T (ε) ≃ VG(ε)V

(2)

where V is the coupling between the molecule and semiconductor and the retarded Green’s function G(ε) describes 1159



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the electron movement through the linker molecule.28 The coupling can be expanded in terms of the molecular orbitals, and in the relevant energy regime, the LUMO will dominate the transport. The energetics of the electron transfer is sketched in Figure 1. The electrons tunnel from the lower conduction band of the QD through the molecule and into the nanowire. The matrix element that couples the QD via the LUMO to the ZnO nanowire approximately factorizes into three contributions (see the Supporting Information for details) TAD(ε) ≃ ⟨A|V |M⟩

tendencies to aggregate and thus should be assigned different effective lengths, which would explain the observed difference in electron-transfer rate. This, we believe, could be an argument for substantially longer molecules with large conformational variations,31 but our short molecules are too similar to exhibit discernible variations in effective length. Limitations of the tunnelling barrier model have been reported in the literature, especially in the case of electron tunnelling through self-assembled monolayers. Akkerman et al. report that the tunnelling currents through alkanedithiols are well-described by the Simmon’s model, yet the barrier height decreases inexplicably with length.16 Thuo et al. reported odd− even effects in charge transport across n-alkanethiols, a molecular structure effect that may indicate shortcomings of the barrier model.32 Several groups have reported quantum interference effects in clear violation of the barrier model.33,34 When probing charge transfer at the femtosecond time scale, it becomes evident that the presence and chemical structure of linker molecules are important for the magnitude of the electron-transfer rate. Previous studies comparing different linker molecules in QD−MO systems have been conducted at the nanosecond time scale, orders of magnitude slower than the actual electron-transfer process. We conclude that the topology of the frontier orbital determines the electron-transfer rate. The need to know the orbital amplitudes on the terminal atoms takes us beyond the tunnelling barrier model. Orbital coefficients are very sensitive to the structure of the linker molecules, which is valuable for the development of QD-sensitized solar cells because it promises the capability of fine tuning the electron-transfer rate by design of the linker molecules.

1 ⟨M|V |D⟩ ε − εM

≃ VAOVSD ×

∑ cOLUMO ∑ cSLUMO × O

S

1 ε − εLUMO (3)

A full-fledged quantum chemical calculation of the entire QD−molecule−ZnO system, akin to what is being done in molecular electronics, would be needed to calculate absolute electron-transfer rates. In this work, however, we note that all linker molecules share the functional linker groups, a thiol binding to the CdSe QD and a carboxylic acid group binding to the ZnO surface. The matrix elements that couple the QD to the sulfur atom, VSD, and the oxygen atoms to the nanowire, VAO, are, to a good approximation, the same for all linkers. In this work, we aim at comparing the ratios between the transfer rates, thereby avoiding the expensive explicit calculation of the coupling matrix elements. This limits the generality of our approach; yet, for a comparison between similar linkers, it enables a simple intuitive analysis. Focusing on the LUMO, the molecular Green’s function is proportional to the sums over molecuar orbital coefficients at sulfur and oxygen. The variation of electron-transfer rates originates (almost) exclusively from this factor. The ratios between rates obtained from the calculations of these factors are shown in Table 1. The retarded Green’s function of the molecule reduces to the fraction 1/(ε − εLUMO), where ε is the energy of the tunnelling electron. We observe that this factor depends on how far offresonance the electron tunnels. Little is known about the detailed energetics of the LUMO relative to the band gaps of the QD and the nanowire. See the Supporting Information for an account of our simplistic model. Including this contribution corrects the relative rates by less than 5%. The corrected rates are shown in parentheses in Table 1. The conjunction of TA measurements and theoretical analysis shows that the rectangular barrier tunnelling picture of photoinduced electron transfer in QD-sensitized solar cells is insufficient. Application of brigde-mediated electron-transfer theory reconciles these inconsistencies. It is not sufficient to know the energy of the frontier orbital (which determines the barrier height); one should also know its distribution in space, especially its amplitude at the terminal atoms where the electron enters and leaves the molecule. A tunnelling barrier picture easily explains the observed lower transfer rate for the longer molecule. Our theoretical analysis indicates that the change in spatial distribution of the frontier orbital is the dominant effect, as opposed to the shift in LUMO energy. Our conclusions about limitations of the rectangular barrier tunnelling model, especially the exponential length dependence, are based on the assignment of identical barrier parameters to the molecules MAA and 2MPA. Potentially, these molecules could have unlike preferred conformations or

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EXPERIMENTAL METHODS The QDs were fabricated following a method described in the literature.35 CdSe QDs capped by oleic acid were formed by hot injection of the trioctylphosphine−Se precursor into the oleic acid−Cd precursor. The desired size of QDs (3.1 nm) was obtained by sudden cooling of the mixture from the reaction temperature (240 °C) to room temperature in an ice bath. Asprepared QDs were purified twice before sensitization. For the sensitization, the surface capping of the QDs was exchanged from oleic acid to a bifunctional linker molecule. Subsequently the ZnO nanowire films, prepared by using the hydrothermal method,36 were immersed in the QD solution for 2 h in the dark. The samples were fully characterized by a high-resolution transmission electron microscope (JEOL 3000F), by a scanning electron microscope (LEO 1650), by a absorption spectrometer (Agilent), and by means of Fourier transform infrared spectroscopy (Nicolet). TA dynamics were measured by using a standard pump−probe setup.11 Laser pulses at 800 nm (80 fs pulse duration, 1 kHz repetition rate) were generated by a Ti:sapphire laser system and converted by an optical parametric amplifier to excitation (470 nm) and probe wavelengths (520−540 nm). To construct the TA signal, every second excitation pulse was blocked. TA spectra were recorded by using a supercontinuum generated in a thin sapphire plate as the probe beam, which was detected by a diode array coupled to a spectrograph. The excitation intensity was kept at ∼1014 photons/cm2/pulse. This corresponds to a mean number of excited electron−hole pairs less than 0.2. Under these conditions, nonlinear effects, such as Auger recombination, are of negligible magnitude. During the measurements, the samples were placed in a nitrogen 1160



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atmosphere to avoid oxygen-related photodegradation.37 We have also verified that the repetition rate of the excitation (500 Hz) is low enough to avoid cumulating charge in the excited QDs37,38 (see the Supporting Information for more details). The electronic structure was obtained by Kohn−Sham density functional calculations using B3LYP as the exchange− correlation functional and 6-311+G(d,p) as the basis set. All calculations were performed using the Gaussian 09 program. For the analysis of the LUMO orbital, the basis set was symmetrically orthonormalized.

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(9) Robel, I.; Kuno, M.; Kamat, P. V. Size-Dependent Electron Injection from Excited CdSe Quantum Dots into TiO2 Nanoparticles. J. Am. Chem. Soc. 2007, 129, 4136−4137. (10) Semonin, O. E.; Luther, J. M.; Choi, S.; Chen, H.-Y.; Gao, J.; Nozik, A. J.; Beard, M. C. Peak External Photocurrent Quantum Efficiency Exceeding 100% via MEG in a Quantum Dot Solar Cell. Science 2011, 334, 1530−1533. (11) Ž ídek, K.; Zheng, K.; Ponseca, C. S.; Messing, M. E.; Wallenberg, L. R.; Chábera, P.; Abdellah, M.; Sundström, V.; Pullerits, T. Electron Transfer in Quantum-Dot-Sensitized ZnO Nanowires: Ultrafast Time-Resolved Absorption and Terahertz Study. J. Am. Chem. Soc. 2012, 134, 12110−12117. (12) Ž ídek, K.; Zheng, K.; Abdellah, M.; Lenngren, N.; Chábera, P.; Pullerits, T. Ultrafast Dynamics of Multiple Exciton Harvesting in the CdSe−ZnO System: Electron Injection versus Auger Recombination. Nano Lett. 2012, 12, 6393−6399. (13) Persson, P.; Lundqvist, M. J.; Ernstorfer, R.; Goddard, W. A.; Willig, F. Quantum Chemical Calculations of the Influence of AnchorCum-Spacer Groups on Femtosecond Electron Transfer Times in Dye-Sensitized Semiconductor Nanocrystals. J. Chem. Theory Comput. 2006, 2, 441−451. (14) Pernik, D. R.; Tvrdy, K.; Radich, J.; Kamat, P. V. Tracking the Adsorption and Electron Injection Rates of CdSe Quantum Dots on TiO2: Linked versus Direct Attachment. J. Phys. Chem. C 2011, 115, 13511−13519. (15) Simmons, J. G. Generalized Formula for the Electric Tunnel Effect between Similar Electrodes Separated by a Thin Insulating Film. J. Appl. Phys. 1963, 34, 1793−1803. (16) Akkerman, H. B.; Naber, R. C. G.; Jongbloed, B.; van Hal, P. A.; Blom, P. W. M.; de Leeuw, D. M.; de Boer, B. Electron Tunneling through Alkanedithiol Self-Assembled Monolayers in Large-Area Molecular Junctions. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 11161− 11166. (17) Watson, D. F. Linker-Assisted Assembly and Interfacial Electron-Transfer Reactivity of Quantum Dot−Substrate Architectures. J. Phys. Chem. Lett. 2010, 1, 2299−2309. (18) Kamat, P. V. Manipulation of Charge Transfer Across Semiconductor Interface. A Criterion That Cannot Be Ignored in Photocatalyst Design. J. Phys. Chem. Lett. 2012, 3, 663−672. (19) Dibbell, R. S.; Youker, D. G.; Watson, D. F. Excited-State Electron Transfer from CdS Quantum Dots to TiO2 Nanoparticles via Molecular Linkers with Phenylene Bridges. J. Phys. Chem. C 2009, 113, 18643−18651. (20) Dibbell, R. S.; Watson, D. F. Distance-Dependent Electron Transfer in Tethered Assemblies of CdS Quantum Dots and TiO2 Nanoparticles. J. Phys. Chem. C 2009, 113, 3139−3149. (21) Kharkwal, A.; Sharma, S. N.; Chand, S.; Singh, A. K. Effect of Linker on the Photosensitization of ZnO Layers with CdSe Quantum Dots. Colloid Polym. Sci. 2011, 290, 49−61. (22) Krüger, S.; Hickey, S. Study of the Attachment of Linker Molecules and Their Effects on the Charge Carrier Transfer at Lead Sulfide Nanoparticle Sensitized ZnO Substrates. J. Phys. Chem. C 2011, 115, 13047−13055. (23) Lawless, D.; Kapoor, S.; Meisel, D. Bifunctional Capping of CdS Nanoparticles and Bridging to TiO2. J. Phys. Chem. 1995, 99, 10329− 10335. (24) Sun, X. W.; Chen, J.; Song, J. L.; Zhao, D. W.; Deng, W. Q.; Lei, W. Ligand Capping Effect for Dye Solar Cells with a CdSe Quantum Dot Sensitized ZnO Nanorod Photoanode. Opt. Express 2010, 18, 1296−1301. (25) Zeng, T.-W.; Liu, I.-S.; Huang, K.-T.; Liao, H.-C.; Chien, C.-T.; Wong, D. K.-P.; Chen, C.-W.; Wu, J.-J.; Chen, Y.-F.; Su, W.-F. Effects of Bifunctional Linker on the Optical Properties of ZnO NanocolumnLinker-CdSe Quantum Dots Heterostructure. J. Colloid Interface Sci. 2011, 358, 323−328. (26) Nevins, J. S.; Coughlin, K. M.; Watson, D. F. Attachment of CdSe Nanoparticles to TiO2 via Aqueous Linker-Assisted Assembly: Influence of Molecular Linkers on Electronic Properties and Interfacial Electron Transfer. ACS Appl. Mater. Interfaces 2011, 3, 4242−4253.

ASSOCIATED CONTENT

S Supporting Information *

Further details on sample characterization, transient absorption measurements, and electron-transfer theory are available. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (T.H.). *E-mail: [email protected] (T.P.). Author Contributions

T. Hansen, K. Ž ı ́dek, and K. Zheng contributed equally to this work. ∥

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge financial support from the Swedish Research Council (VR), the Knut and Alice Wallenberg Foundation, the Swedish Energy Agency, and the Lundbeck Foundation. We are grateful for the collaboration within the nmC@LU.

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REFERENCES

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Orbital Topology Controlling Charge Injection in Quantum-Dot

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