Charging Quenches Multiple Exciton Generation in Semiconductor

Christine M. Isborn · Oleg V. Prezhdo* ... https://doi.org/10.1021/jp902621a .... (24-27) Our previous high level ab initio electronic structure calcu...
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2009, 113, 12617–12621 Published on Web 05/27/2009

Charging Quenches Multiple Exciton Generation in Semiconductor Nanocrystals: First-Principles Calculations on Small PbSe Clusters Christine M. Isborn and Oleg V. Prezhdo* Department of Chemistry, UniVersity of Washington, Seattle, Washington 98195-1700 ReceiVed: March 23, 2009; ReVised Manuscript ReceiVed: May 7, 2009

We demonstrate using symmetry adapted cluster theory with configuration interaction (SAC-CI) that charging of small PbSe nanocrystals (NCs) greatly modifies their electronic states and optical excitations. Conduction and valence band transitions that are not available in neutral NCs dominate low energy electronic excitations and show weak optical activity. At higher energies these transitions mix with both single excitons (SEs) and multiple excitons (MEs) associated with transitions across the band-gap. As a result, both SEs and MEs are significantly blue-shifted, and ME generation is drastically hampered. The overall contribution of MEs to the electronic excitations of the charged NCs is small even at very high energies. The calculations support the recent view that the observed strong dependence of the ME yields on the experimental conditions is likely due to the effects of NC charging. The generation of multiply excited states, or multiexcitons (MEs), in semiconductor nanocrystals (NCs) has received considerable attention and generated substantial controversy recently.1-11 The idea12,13 that MEs can be used to greatly enhance the efficiency of photovoltaic devices14 has led to an intense search for MEs in semiconductor NCs and their discovery in PbSe NCs.15 In contrast to bulk semiconductors, in which MEs are produced with low quantum yields, there was hope for significantly enhanced ME generation (MEG) efficiencies due to the quantum confinement effects in NCs.3 Quantum confinement is a remarkable phenomenon which allows one to continuously control NC properties simply by changing the NC size and shape; this is a sharp contrast to molecular systems, whose properties vary discontinuously and require modifications in composition and structure. MEs were first detected in the spectroscopic studies of PbSe NCs15-17 and were later observed in other types of NCs, including CdSe,18 Si,19 and InAs.20,21 Work by Klimov and co-workers confirmed that the onset of MEs in PbSe NCs occurs at energies below three times the NC band gap, in contrast to bulk PbSe, indicating a confinementinduced enhancement of MEG in NC materials.3 The spatial confinement of electrons and holes in small semiconductor NCs is thought to be beneficial for MEG in multiple ways. One proposed MEG mechanism is through an inverse Auger process,12,22 which involves photoexcitation of a high energy single exciton (SE). The strong Coulomb attraction between electrons and holes facilitates Auger-type processes that change the number of electron-hole pairs. The quantum confinement also increases energy spacing between electronic states. Once the spacing exceeds the energies of phonon quanta, the electron-phonon relaxation drastically slows down. This so-called phonon bottleneck to the electron-phonon relaxation12,23 generates an opportunity for the Auger-type processes to produce MEs. It should be noted that if the spacing between the * Corresponding author. E-mail: [email protected].

10.1021/jp902621a CCC: $40.75

electronic states does not exceed the phonon quanta, which is the case at higher excitation energies, quantum confinement creates the opposite effect.24-28 Another proposed mechanism of MEG is through direct excitation.17,29 In this mechanism, the electron-hole interaction causes coupling of ME states with SE states, allowing direct optical excitation of MEs. Because the direct ME excitation is independent of the phonon bottleneck, it has significant advantages over the inverse Auger mechanism, which proceeds in parallel with the electron-phonon relaxation and, therefore, requires the phonon bottleneck. The direct mechanism is consistent with the experiments that show no bottleneck to the electron-phonon relaxation in PbSe NCs.24-27 Our previous high level ab initio electronic structure calculations showed that direct excitation of MEs is extremely efficient in very small clusters.29 This is particularly true for PbSe, due to its band structure symmetry. Conflicting reports of MEG efficiencies have appeared in the literature recently.1-11 A difference of more than 3-fold in apparent ME yields has been measured for NCs under static and stirred conditions.1,3 The probable explanation for the reported discrepancies is the photoionization of the NCs. Because uncompensated charges can be long-lived, the effect can be quite significant, leading to charging of a large fraction of NCs. This may occur particularly well in static samples of NCs. Accumulation of long-lived charges can increase apparent MEG efficiencies, since Auger recombination of charged SE and ME species can produce extraneous MEG-like signatures.3,8 In addition to providing misleading MEG-like signatures, NC charging can affect true MEG yields as well, since it is known to greatly affect other optical properties of semiconductor NCs. For instance, charging produces spectral shifts and bleaches the band-edge interband absorption resulting in luminescence blinking.30 While the differences in the MEG efficiencies discussed above are thought to be due to uncontrolled charging of the NCs, the charging can be controlled by either electrochemical or chemical means involving strong reductants or oxidants.3  2009 American Chemical Society

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Figure 1. Types of electronic transitions in the anion NC. The scheme shows conduction band (CB), single exciton (SE), mixed CB and SE, and multiexciton (ME) transitions. Similar types of transitions exist for the cation, with the CB transitions replaced by VB transitions.

Fundamental studies of the properties of charged NCs becomes the next essential step toward photovoltaic, electro-optical and other applications of semiconductor NCs. Theoretical modeling of the optically excited states of the NCs is an important component of the ongoing efforts, since it creates a rigorous understanding of the available data and provides guidelines for future experiments. In this letter we show for the first time using high-level ab initio electronic structure theory that the charging of NCs greatly affects their optical properties and the nature of electronically excited states. In particular, the efficient generation of MEs by direct photoexcitation in small neutral PbSe NCs is completely quenched in the relevant energy range by NC charging. The overall features of the electronic spectrum are notably blueshifted. Even though a number of low energy excited states appear in the charged NCs, these states are not optically active. The calculations allow us to characterize the excited states as SEs or MEs, or superpositions thereof that dephase into SEs and MEs by coupling to phonons,16,31-33 and to address the threshold energy and efficiency of MEG. Transitions of the extra electron (hole) in the conduction (valence) band of the anion (cation) mix with the SE and ME states. In contrast to the neutral species, in which MEs can be excited with a near 100% efficiency starting at energies less than three times the lowest excitation energy, only small traces of ME character are seen in the charged NCs and only at very high excitation energies. The reported data rationalize why MEs will appear only at elevated energies upon charging, and show that MEG detection is much more difficult in charged NCs. Electronic excitations of the neutral NC can be characterized as SEs and MEs. These two types of transitions can mix and may be present simultaneously within a single electronic excitation. Charged NCs contain an extra particle: an electron in the conduction band (CB) of the anion and a hole in the valence band (VB) of the cation. Therefore, in addition to SE and ME transitions there are also CB and VB transitions. Because of these additional types of excitations, transitions involving two electrons do not necessarily produce MEs in the charged NCs. ME states are defined as excitations with two or more electrons promoted across the band gap. The charged species runs into situations in which two electrons are excited, but only one of them moves across the band gap, while the other one is the extra charge that is traveling within the CB or VB. This type of excitation dominates at low energies and causes problems with MEG generation in charged NCs. Figure 1 classifies four possible types of transitions for the anion NC, in which an extra electron appears in the CB. Transitions involving

Letters one electron are either SE or CB. Transitions involving two electrons are either MEs or mixed SE + CB transitions. For clarity, Figure 1 shows only the anion scheme. Similar transitions occur in the cation, with the VB transitions replacing the CB transitions. The electronic structure of the excited states in the charged and neutral Pb4Se4 NCs is investigated here using the symmetry adapted cluster (SAC) theory with configuration interaction (CI),34 as implemented in the Gaussian 03 program suite.35 SAC-CI is a state-of-the-art quantum chemical methodology that includes many-body correlation effects in the SAC ground state and additional correlation/excitonic interactions in the CI excited state. SAC starts with the single-particle description and explicitly includes ground state electron correlation effects through a cluster expansion, dramatically improving the description of the ground state wave function.34 For the CI, high-order excitation operators are applied to the correlated SAC ground state, producing states of both SE and ME character. Because the SAC-CI wave function is a many-body wave function instead of a single-particle wave function, as is calculated with Hartree-Fock and density functional theory methods, the doubly excited ME states gain some oscillator strength by mixing twoelectron transitions with other kinds of transitions. The mixing provides the relaxation of the ground state wave function due to the electron-hole interaction. Thus the excitonic effects are included in the description of both the ground and excited states, and make the direct excitation of MEs possible in NCs. The SE and ME data are obtained in this work by summing the squares of the SAC-CI excited state expansion coefficients corresponding to the specified transition types shown in Figure 1. SAC-CI is different from single-configuration approaches, such as time-dependent Hartree-Fock (TDHF) or density functional theory (TDDFT),36,37 which have difficulties producing states with ME character.38,39 Because of the computational expense of the SAC-CI method, the calculations are performed on a small Pb4Se4 NC. The geometry of the Pb4Se4 NC was optimized using DFT with the B3LYP functional and the LANL2dz basis set and pseudopotential. LANL2dz includes relativistic effects within the parametrizing of the effective core potential for the core electrons, but no polarization or diffuse functions, which can be particularly important in describing the diffuse electron cloud of anionic systems. During the geometry optimization the Pb4Se4 NC was constrained to preserve the symmetry of the bulk structure of PbSe. The optimized geometry of neutral Pb4Se4 was subsequently used for the studies of the electronically excited states of the anionic and cationic Pb4Se4. In the SAC-CI calculations, also using the LANL2dz basis, all valence orbitals were included in the active space. For the neutral NC, we used excitation operators through quadruples, calculating 1000 excited states of each B symmetry, giving the highest excitation at 13.3 eV. For the charged NC, the excitations were computed from the lowest energy ionized doublet state as the reference, according to the SAC-CI general-R (through sextuples) implementation in Gaussian03. Again, 1000 states were calculated for each symmetry, up to an excitation energy of 16.4 eV for the anion and up to 13.5 eV for the cation. Excited state cation doublet wave functions are created with coupled ionization and excitation processes, i.e. do not occur stepwise. This means that an electron cannot be excited directly into the hole created from the ionization process within the SAC-CI model. To create valence band transitions for the cation, we have used the SAC method to correlate the closed-shell dication, and then the CI excitation to get electron promotion into the empty level.

Letters

Figure 2. Electronic spectra of the neutral and charged Pb4Se4 NCs calculated using SAC-CI. The calculations are performed with highorder CI excitation operators, and using the double-ζ basis set. The charged NCs exhibit many excitations at low energies compared to the neutral NC. These early excitations show weak optical activity and are due to CB and VB transitions that are not available in the neutral system. The spectral features of the charged NCs are blue-shifted relative to the neutral NC.

The SAC-CI spectra for the neutral and charged NCs are shown in Figure 2. The charged species have low energy excitations that are transitions of the extra particle, electron or hole, within either the CB or VB for the anion and cation, respectively. Such low energy excitations are not present in the neutral species. These low energy transitions have low oscillator strength and contribute little to the optical absorption spectrum. For the anion, electronic excitations involving transitions across the main band gap start at 4.2 eV. For the cation, they start at 5.3 eV. The band gap transitions start at an earlier energy of 2.9 eV in the neutral NC; thus, the band gap transitions are blue-shifted for the charged NCs by 1-2 eV. However, these lower energy single exciton (SE) transitions in the neutral NC have extremely small oscillator strengths, less than 10-3. The first transitions with significant oscillator strength occur at 4.0 eV in the neutral NC. As can be seen by examining the features of the three spectra shown in Figure 2, the absorption peaks are shifted to higher energies in the charged clusters, even though the CB and VB transitions generate low-energy excitations. Figures 3 and 4 show contributions of different types of transitions into the electronic excitations of the anion and cation NCs. The transition types are defined in Figure 1 above, and are repeated as inserts in Figures 3 and 4. The data are key to understanding the efficiency of MEG in charged NCs. Moderate ME contributions start at 14 eV in the anion NC, and no ME contributions are seen with the cation up to 13 eV. These results are very different from the corresponding calculations performed on the neutral PbSe NC in our earlier work.29 In the neutral NC, SE transitions dominated the excitations up to an energy of 8 eV, at which point a dramatic switch to transitions of predominantly ME character took place. Thus, not only does the onset of MEG occur at a much higher energy in charged NCs than in the neutral, but the ME character of the excited states is decidedly quenched. The stark differences between the ME results of the neutral and charged NCs can be rationalized by the presence of the extra charges in the CB and VB. From the data shown in Figures 3 and 4, it is clear that the CB and VB transitions not only dominate the electronic excitations at low energies, but also continue to play a large

J. Phys. Chem. C, Vol. 113, No. 29, 2009 12619 role at all energies, affecting both the energy and contribution of the SE and ME states. Purely VB transitions become mixed VB+SE and SE transitions at around 8 eV in the cation, Figure 4. A similar switch occurs in the anion, Figure 3, however, it is less pronounced. While the first SE of the neutral NC is at 2.9 eV, the SE band gap transitions occur at much higher energies in the charged NCs, at 4.2 and 5.3 eV for the anion and cation, respectively. The higher energies for the charged species are due to the SE mixing with the CB and VB transitions. Since the CB and VB transitions are energetically lower than the SE transitions, the latter are pushed up in energy by the mixing. SEs mix with the CB transitions over a much broader energy range than with the VB transitions, compare bottom left panels in Figures 3 and 4. Transitions with a small amount of ME character start at 14 eV in the anion. In comparison, the sharp onset of MEs occurred between 8 and 9 eV in the neutral NC.29 This onset energy corresponds to 2.5× the first SE energy. It is clear from the available data that the onset of MEs in the charged NCs takes place at energies in excess of 3× the first SE energy of the charged species. Since the ME transitions mix with both CB and SE transitions, they also are pushed to higher energies. The onset of ME excitations is quite sharp, and one may expect that the ME contribution will rapidly rise above the 30% seen in Figure 3 at increased energies. This expectation cannot be currently tested due to the rapid increase of the number of states and, therefore, computational expense with increasing energy. States at the highest energies of the cation show an increase in ME character (Figure 4), and one can expect to see MEs at higher energies, however, such calculations are very challenging at present. The current study focused on a very small PbSe NC in order to perform rigorous ab initio analysis of the high energy electronically excited states. Qualitatively, the conclusions of this work apply to larger NCs, however, quantitatively, we expect the charging effect to be less pronounced. Both the strength of the electron-hole interaction and the effect of an extra charge on the NC electronic structure should decrease with increasing system size. An extra or missing electron should have little effect on the properties of a large NC. While MEG efficiency will decrease in larger NCs due to decreased electron-hole Columb interaction,2 the detrimental effect of an extra charge on MEG should diminish in larger NCs as well. Instead of considering the effect of a single extra electron or hole on the electronic structure of NCs of increasing size, one can think of the effect of a constant density of excess charge. This is a valid viewpoint, since larger NCs can support multiple charges. In this case, one can expect a qualitatively different situation. Multiple charges of the same sign will repel and, therefore, will localize on the surface of the NC. This will create a charged surface layer, whose properties will be very different from those of the NC core. One can expect that the electronic structure of the core region of large NCs will be relatively independent of the charging. On the other hand, the surface will be affected significantly and is likely to undergo substantial structural and even chemical rearrangements, creating defects and trap sites that will greatly influence the fate of the electronic photoexcitation. The electron-phonon and Auger-like dynamics of large multiply charged NCs should be primarily governed by the surface layer. Similarly, environmental effects, such as capping of the NC surface or the surrounding dielectric, will also affect the surface charge distribution and the resulting ME behavior.

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Letters

Figure 3. Contributions of the different transition types defined in Figure 3 to the excited electronic states of the Pb4Se4 anion NC, as a function of excitation energy. The fractional contribution of a specific transition type is computed by summing the squares of the corresponding SAC-CI expansion coefficients. The lowest energy excitations are dominated by the CB transitions. Both SEs and particularly MEs are pushed to higher energies in the Pb4Se4 anion compared to the Pb4Se4 neutral NC29 due to mixing with CB transitions. ME contributions start to appear at 14 eV, which is 3.5× the energy of the first SE state at 4 eV. This is in contrast to the sharp onset of MEs observed for the neutral NC at 8 eV, which is approximately 2.5× the energy of the first SE state in the neutral system.29

Figure 4. Contributions of various types of transitions to the excited electronic states of the Pb4Se4 cation, compare with Figure 3. VB transitions mix with both SE and ME transitions, pushing them to higher energies. Transitions with ME character are seen only in the highest energy states within the present energy window.

The quenching of MEG due to NC charging has been established in this work for MEG by direct photoexcitation that is particularly efficient in PbSe NCs.17,29 The reported findings suggest that MEG by the inverse Auger mechanism,12,22 which

is important in other materials including CdSe,29 should become less efficient as well. In particular, Auger-type transitions from SEs to MEs rely on the much higher density of ME states relative to SEs above the MEG threshold. The density of the

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new types of states created by the presence of a charged particle in the VB or CB dominates ME state density at low and intermediate energies. Therefore, the threshold for the inverse Auger process will be shifted in charged NCs to higher energies and away from the energy range that is relevant for photovoltaic applications. In conclusion, we show by rigorous electronic structure calculations that the presence of either positive or negative charge greatly affects the nature of electronic excitations of small semiconductor NCs. The extra particles in the CB and VB create the possibility of intraband transitions, which are not possible in neutral systems. This statement applies to NCs of all sizes, and therefore, the results obtained for the small NCs apply qualitatively to larger NCs as well. In particular, the intraband transitions entirely dominate low energy excitations of charged NCs. However, these excitations are not optically active. Optically active excitations involve electron transitions across the band gap. These states are pushed to higher energies in the charged NCs relative to the neutral species, due to coupling with the intraband transitions. The statistically large number of the intraband transitions relative to the transitions of the other types, as well as mixing of these low energy transitions with the band gap transitions, push MEs to very high energies. The ME thresholds in the charged NCs are higher than 3× the lowest energy band gap excitations. This should be compared with the 2.5× band gap thresholds of the neutral NCs.29 In turn, the band gap excitations are also higher in energy in the charged than in the neutral NC. The calculations indicate that NC charging greatly obstructs MEG. A similar reduction in the MEG efficiency was seen experimentally upon photodoping, i.e., photoinjection of an exciton prior to MEG.40 Assuming that the charging mechanisms strongly depend on the surface chemistry and photochemistry of NCs, the reported results rationalize why MEG yields show strong dependence on the experimental conditions.3 Acknowledgment. The research was supported by NSF Grant CHE-0701517, DOE Grant DE-FG02-05ER15755, NSF-CRIF Grant CHE-0342956, and University of Washington Royalty Research Fund. References and Notes (1) (2) (3) (4) (5) (6) (7) (8) (9)

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