Theoretical Characterization of Conduction-Band Electrons in

Oct 24, 2014 - Gerard M. Carroll , Alina M. Schimpf , Emily Y. Tsui , and Daniel R. Gamelin. Journal of the American Chemical Society 2015 137 (34), 1...
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Theoretical Characterization of Conduction-Band Electrons in Photodoped and Aluminum-Doped Zinc Oxide (AZO) Quantum Dots Joshua J. Goings, Alina M. Schimpf, Joseph W. May, Robert W. Johns, Daniel R. Gamelin,* and Xiaosong Li* Department of Chemistry, University of Washington, Seattle, Washington 98195, United States ABSTRACT: The electronic structures of n-type ZnO nanocrystals formed via photochemical reduction and by aliovalent doping with aluminum are investigated using timedependent density functional theory. Connections between the density functional theory results and a simple quantummechanical particle-in-a-spherical-potential model are highlighted. Molecular orbitals obtained from density functional theory reveal the often-invoked S-, P-, D-, ... type “super” orbitals used to characterize the absorption spectra of these materials.

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INTRODUCTION

Here we report the theoretical characterization of the lowenergy (ultraviolet/visible/near-infrared) electronic transitions of photodoped ZnO and Al3+:ZnO QDs using time-dependent hybrid density functional theory (TDDFT). We examine the electronic structures of the QDs using DFT, comparing the density of states for the two types of n-type QDs. We explore the connection between our computed DFT results and the simple quantum mechanical particle in a spherical potential model.19,38,39 This theoretical characterization allows for direct comparison of the electronic structures of these two systems, offering unique insight into their distinct chemical and physical properties.

Colloidal semiconductor quantum dots (QDs) containing excess delocalized charge carriers play important roles in the development of devices for solar energy conversion,1,2 IR plasmonics,3−8 information processing,9 and other technologies. Such n- or p-type semiconductor QDs have been prepared using remote doping,10−15 photodoping,3,13,16−22 aliovalent doping,5,21,23−28 or electrochemical oxidation and reduction.29−31 In most cases, aliovalent doping of colloidal semiconductor nanocrystals to yield band-like charge carriers has proven difficult because only a small fraction of dopant ions lead to charge carriers.21,28,32 Recently, high-quality colloidal Al3+-doped ZnO (Al3+:ZnO) nanocrystals have been reported in which Al3+ acts as an ionized shallow donor.26 In these Al3+:ZnO nanocrystals, electronic absorption spectroscopy reveals excess band-like electrons, similar to those in photodoped ZnO (e−:ZnO) nanocrystals.3,17−20,22,33−35 Explicit comparison of the electron paramagnetic resonance (EPR) and electron absorption spectra of Al3+:ZnO and e−:ZnO nanocrystals shows the two species are nearly indistinguishable.21 Despite these similarities, however, they show qualitatively different chemical reactivity; Al3+:ZnO is completely stable against oxidation by O2, whereas e−:ZnO rapidly oxidizes when exposed to air.13,16−18,36,37 Consequently, while it is possible to determine the number of conduction band (CB) electrons per nanocrystal in photodoped ZnO nanocrystals via anaerobic titration with mild oxidants,17,19,34 the stability of CB electrons in Al3+:ZnO nanocrystals prevents such characterization. Instead, the number of CB electrons in Al3+:ZnO nanocrystals has been estimated via EPR and absorption spectroscopies. NIR absorption increases, for example, as more electrons are added to the ZnO nanocrystals or as more Al 3+ is incorporated.21 © 2014 American Chemical Society

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METHODOLOGY All calculations were performed using the development version of the Gaussian program.40 Quantum dot electronic structures were obtained using the PBE1PBE hybrid DFT functional.41,42 The Los Alamos double-ζ pseudocore potential (LANL2DZ) and associated basis set were used for all atoms,43−45 with Zn2+ (3p, 4s, 3d), O2− (1s, 2s, 2p), H (1s), and Al3+ (3s, 3p) electrons treated using explicit basis functions. Nearly spherical ZnO quantum dots were constructed to have C3v symmetry using the experimental lattice parameters: a = 3.249 Å, c = 5.204 Å, and u = 0.382 Å.46 The resulting Zn33O33 and Zn84O84 structures have diameters (dQD) of ∼1.2 and ∼1.8 nm, respectively. The aluminum dopant was introduced by replacing a lattice-bound Zn2+ near the quantum-dot center with Al3+. In accordance with previous theoretical methods,47 pseudohydrogen atoms were used to passivate dangling bonds on the surfaces of the quantum dots; these atoms have modified nuclear charges of 0.5 and 1.5 to terminate surface O2− and Received: September 5, 2014 Revised: October 20, 2014 Published: October 24, 2014 26584

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Figure 1. Total and projected density of states (DOS) for an e−:Zn33O33 QD (right) and Al3+:Zn32O33 QD (left) with an Al3+ dopant in the central lattice position. Positive and negative values represent the spin-up and spin-down DOS, respectively. Note the 20× magnification of the Al3+projected DOS.

Figure 2. Absorption spectra of Zn33O33 QDs (left) and Zn84O84 QDs (middle) containing a single Al3+ dopant (red solid line), a single added e−CB (blue dashed line), or neutral (undoped) (black dotted line). Schematic of superorbital transitions is shown at right. Broken symmetry weakly allows S → D transitions as well as splitting the S → P transitions. All spectra were computed at the TD-PBE1PBE/LANL2DZ level of theory. Vertical lines correspond to TDDFT excited-state energies and oscillator strengths. TDDFT peaks are dressed with Gaussian functions with a broadening parameter of 0.16 eV.

Zn2+, respectively. This pseudohydrogen capping scheme leads to a well-defined bandgap and stable QD geometry. Replacing a Zn2+ lattice site with an Al3+ dopant was performed such that the total charge of the quantum dot remained neutral. Adding an additional electron to the ZnO QD resulted in a e−:ZnO QD with a total charge of −1. Calculations were also performed in which this charge is compensated by a surface +1 charge to yield a e−:ZnO QD with a total charge of 0. For these calculations, the surface charge compensation was achieved by modifying the nuclear charges of the pseudohydrogen atoms as described above and in the Results section. Excited-state energies and oscillator strengths were calculated with the linear-response time-dependent density functional theory (TDDFT)48,49 at the PBE1PBE/LANL2DZ level of theory, consistent with previous literature reports. Absorption spectra were obtained by dressing excited-state peaks with Gaussian functions with a broadening constant of 0.16 eV. To capture the broad shape of the first several frontier orbitals, we used an isosurface value of 0.007 for all orbital plots.

with the oxo-states in the valence band. Because of the additional charge introduced by replacing a Zn2+ with an Al3+, the valence band edge drops by ∼2 eV. In Zn33O33, the VB is completely full, and any additional electrons are added to the CB. The same is true for e−:Zn33O33, in which the added e−CB occupies a state ∼5 eV above the valence band edge. In the Al3+:Zn32O33 QD, the Al3+ dopant is a donor that introduces an additional electron ∼4 eV above the valence band edge. Although the added e−CB in e−:Zn33O33 and Al3+:Zn32O33 is predominantly Zn2+ in character, the e−CB in Al3+:Zn32O33 also shows Al3+ character. Overall, the added electron due to the Al3+ dopant is nearly identical to the added electron found in the photodoped e−:Zn33O33 QD. This result is consistent with experiment, in which Al3+:ZnO and e−:ZnO NCs show similar electronic structures.21 Experimentally, a conduction-band electron in an e−:ZnO QD is also compensated by a cation (e.g., H+, Li+), but it is uncertain where the charge-compensating cations are located. We have therefore explored various charge-compensation schemes in our calculations. In the e−:Zn33O33 QDs, we find that surface hydrogen atoms are too deep of donors, and the extra electrons are spatially localized. This result is inconsistent with experimental observations, a discrepancy that we attribute to the use of much smaller ZnO QDs in the calculations than studied experimentally. Increasing the QD volume lowers the CB potential relative to the hydrogen atom donor level, thus enabling donor ionization. To circumvent this problem in the calculations, we have also examined modification of the

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RESULTS AND DISCUSSION Figure 1 shows density of states (DOS) plots for the e−:Zn33O33 QD and the Al3+:Zn32O33 QD with an Al3+ dopant in the central lattice position obtained using one-electron orbitals from a ground-state DFT calculation. The conduction band (CB) consists of primarily Zn2+ 4s and 4p character, and the valence band (VB) consists of mainly O2− 2p character. The Al3+ dopant, which replaces a Zn2+ lattice position, hybridizes 26585

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look identical for a given radius R. On the basis of this model, QDs with CB electrons have been termed “artificial atoms”, as they display s-, p-, d-, ... type orbitals, referred to as S-, P-, D-, ... type “super” orbitals.39 Figures 3−5 show the frontier and neighboring molecular orbitals (MOs) for the Al3+:Zn83O84 and e−:Zn84O84 QDs

pseudohydrogen nuclear charges such that the compensating +1 charge is diffused across the entire QD surface. Importantly, the energies of the electronic transitions in this diffusely chargecompensated e−:ZnO QD are indistinguishable (within ∼40 meV) from those of the uncompensated e−:ZnO QD. Because we are investigating energy differences between states here, the computed results are the same for e−:ZnO QDs and diffusely charge compensated e−:ZnO QDs. Figure 2 shows electronic absorption spectra calculated for Zn33O33 (dQD = 1.2 nm) and Zn84O84 (dQD= 1.8 nm) QDs obtained from linear-response TDDFT calculations. Spectra are included for neutral, undoped ZnO, Al3+:ZnO, and e−:ZnO QDs. The spectra show characteristic VB to CB transitions starting at ∼5.1 eV for the strongly quantum-confined (dQD= 1.2 nm) QDs and 4.3 eV for the larger (dQD = 1.8 nm) QDs, where quantum confinement is more relaxed. In contrast with the ZnO QDs, in which only VB to CB transitions are observed, the n-type ZnO QDs display a sharp, low-energy peak around 1.1 eV (1.0 eV) for the e−:Zn33O33 (e−:Zn84O84) and 1.6 eV (1.4 eV) for the Al3+:Zn32O33 (Al3+:Zn83O84). The lowest energy large peak for each of the n-type ZnO QDs consists of three electronic transitions, two of which are degenerate for the e−:ZnO and none that are degenerate for the Al3+:ZnO. A weak shoulder is also observed around 0.5 to 0.7 eV above the first peaks in the Al3+:ZnO and e−:ZnO spectra. As the QDs increase in size, the lower energy peaks for the different n-type ZnO QDs begin to converge energetically. In the dQD= 1.2 nm QDs, they differ by ∼0.5 eV. In the larger, dQD= 1.8 nm QDs, they differ by 0.4 eV. The higher energy shoulders also decrease in intensity with increasing QD diameter, although less so for Al3+:ZnO. The calculated spectra can be understood by treating the e−CB as a quantum-mechanical particle in a spherical potential.50,51 The electron is confined to the QD with a constant potential inside the QD and a relatively large potential outside the QD. This quantum-mechanical model is analytically tractable. The one-electron wave function, solved in spherical coordinates, is a product of a spherical harmonic function Yml (θ, ϕ) and a spherical Bessel function of the first kind jn(r) Ψ(r , θ , ϕ) = A nS jS (βnS r /a)Y Sm(θ , ϕ)

Figure 3. Structure of e−:Zn84O84 and Al3+:Zn83O84 QDs. For Al3+:Zn83O84, the Al3+ dopant is indicated by the magenta sphere. HOMO−1 and HOMO orbitals are shown for each QD, showing the valence band edge of the QD (HOMO−1), as well as the conduction band edge, which is occupied in both QDs (HOMO). The analytically derived S-type spherical harmonic is plotted for comparison, as predicted using the particle in a spherical potential quantum model.

obtained from DFT. These frontier orbitals dominate the lowenergy excitations observed in Figure 2, which are described well as intraconduction band transitions. Note that these transitions in our one-electron-reduced QDs are different from the plasmonic absorption features that might be expected upon introduction of multiple electrons. These are, to our knowledge, the first published images of DFT-generated atom-like super orbitals in II−VI semiconductor QDs, supporting the treatment of CB electrons as S-, P-, D-, ... type electrons arising from the spherical potential model. Figure 3 shows the highestoccupied molecular orbital (HOMO) and HOMO−1 for these two QDs, which reveal the difference in character between the bottom edge of the CB and the top edge of the VB for each QD, respectively. The HOMO−1 orbitals are localized along the bonds of the QD and show oxo p-type character, as expected from the DOS in Figure 1. The HOMO, which describes the free CB electron, shows S-type super orbital character, analogous to the analytic s-type spherical harmonic that is plotted for comparison. Only the spin-up MOs are given, but the filling of the orbitals follows similar to the filling of hydrogen-like orbitals, where opposite spin electron pairs fill each spatial MO. Because of the nearly centrosymmetric character of the QDs and the resemblance of the super orbitals to the atomic orbitals, it is natural to expect that the doped QDs will show similar spectral properties as the hydrogen atoms they resemble. Figures 4 and 5 show the continued atom-like behavior of the first eight lowest unoccupied molecular orbitals (LUMOs) in both Al3+:ZnO and e−:ZnO QDs, which reveal their P- and D-type super orbital character. Given this atom-like model of the CB levels, we can begin to interpret the absorption spectra of the Al3+:ZnO and e−:ZnO QDs in Figure 2. Indeed, the spectral similarities become apparent once we compare their transition moment integrals. The electric-dipole transition moment integral for a transition from an initial state n to a final state l is given by the expression

(1)

where A nS is a normalization constant, jS is the S th spherical Bessel function of the first kind, and βnS is the nth zero of the S th spherical Bessel function. l is the angular momentum quantum number and m is the projection of the angular momentum onto the quantization axis. In this model, the electron has energy levels that depend only on the n and l quantum numbers, such that energy E is

En , l =

βn2, l ℏ2 2me*R2

(2)

where R is the radius of the sphere, m*e is the effective mass of the electron, and βnS is again the nth zero of the S th spherical Bessel function. Computation of these zeros has no general formula and must be done numerically. The wave functions for the particle-in-a-sphere are closely related to the solutions for the particle in a Coulombic potential (e.g., a hydrogen atom), with the only major difference being that the potential for the particle in a sphere goes as 1/R2, whereas the hydrogenic solutions go as 1/R. The angular dependence is identical between the two models, and so the shapes of the orbitals will

μ ln = ⟨Ψ|l μ|̂ Ψn⟩ 26586

(3)

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splittings and the S → D transition intensities both decrease with increasing nanocrystal size. Although the Al3+:ZnO QDs show the same trend with increasing size, the effects of low symmetry are more pronounced at larger diameters due to the Al3+ impurity; as a result, weakly allowed S → D transitions persist even in larger AZO QDs. Moving the Al3+ dopant further off center (Figure 6) lowers the effective symmetry

Figure 4. First three unoccupied orbitals of the conduction band are shown for both e−:Zn84O84 and Al3+:Zn83O84 QDs. Analytical P-type spherical harmonics are plotted for comparison. Figure 6. Al3+:Zn32O33 QDs, looking down the C3v axis, with Al3+ indicated by a pink sphere. On the left is the “centered” Al3+:ZnO QD, with the Al3+ dopant occupying a central lattice site. On the right is the “off-center” Al3+:ZnO QD, with the Al3+ dopant occupying an offcenter lattice site. Moving the Al3+ dopant away from the center of the QD splits the S → P electronic transitions into three components and decreases its intensity, as described in Figure 7

more and splits the three S → P components relative to the more centrally doped Al3+:ZnO QD (Figure 7). The addition of more Al3+ per nanocrystal increases the effective symmetry and has the opposite spectroscopic effect. Figure 5. Lowest unoccupied molecular orbitals (LUMOs 3−7) corresponding to D-type super orbitals are shown. Analytically derived D-type spherical harmonics are plotted for comparison.

For electrons moving in a centrosymmetric potential, for example, the hydrogen atom or the extra electron in a QD, the transition moment will be nonzero as long as the integral is symmetric; this is the well known parity (or Laporté) selection rule. The electron initially resides in an S-type super orbital (1Se) with gerade (g) symmetry, and the transition moment operator, μ̂, has ungerade (u) symmetry. Thus, S → P transitions evaluate as g × u × u = g and are electric-dipoleallowed. In contrast, D-type super orbitals have g symmetry and the S → D transition moment integrals evaluate as g × u × g = u, which is zero. Thus, the 1Se → 1De transition is electricdipole-forbidden in a centrosymmetric n-type nanocrystal. If the QDs were perfectly centrosymmetric, we would observe just one S → P transition, but these QDs are not perfectly centrosymmetric: the ZnO QDs have C3v symmetry, whereas the Al3+:ZnO QDs have no symmetry. For this reason, we see a low-symmetry splitting of the S → P band into two transitions for the e−:ZnO nanocrystal, where the higher energy feature consists of two degenerate transitions from S → (Px, Py) and the lower feature corresponds to S → Pz. The Al3+:ZnO QDs are even lower in symmetry, and we see all three S → P components at unique energies. The weak higher energy shoulders next to the S → P peaks correspond to weakly allowed 1Se → 1De transitions, which gain intensity via lowsymmetry S−P and P−D mixing (intensity borrowing), accompanied by a commensurate decrease in S → P intensity. As the QD sizes increase, the effects of the noncentrosymmetric environment become less pronounced. For example, the P

Figure 7. Computed absorption spectra of Al3+:Zn32O33 QDs. In the first case, the Al3+ dopant is located near the center of the QD. In the second, the Al3+ dopant is located closer to the surface (although it is not on the surface). The latter position breaks the inversion symmetry most and results in the greatest splitting of the three S → P components, which are degenerate in a perfectly centrosymmetric environment. All spectra were computed at the TD-PBE1PBE/ LANL2DZ level of theory. Vertical lines correspond to TDDFT excited-state energies and oscillator strengths. TDDFT peaks are dressed with Gaussian functions with a broadening parameter of 0.16 eV.

Experimentally, such low-symmetry effects have not been observed in n-type ZnO nanocrystals, but very similar splittings of 1Se → 1Pe components have been observed in small colloidal n-type CdSe QDs. As in our calculations, this splitting becomes unresolved in n-type CdSe QDs when the diameter is increased.12,20 Our computations strongly support the inter26587

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symmetry. This lower symmetry is evidenced by an off-center Al3+:ZnO S-type orbital (Figure 3) compared with the nearly centrosymmetric e−:ZnO S-type orbital. The low symmetry completely breaks the three-fold degeneracy of the S → P transition in the Al3+:ZnO QDs compared with the e−:ZnO, which has axial symmetry. Additionally, the reduced symmetry in Al3+:ZnO introduces intensity to S → D transitions relative to e−:ZnO, which would otherwise be forbidden in a centrosymmetric system. Finally, because Al3+ adds positively charged centers to the QD lattice, there exist higher energy transitions relative to e−:ZnO on account of the increased Coulombic attraction between the added electrons and the Al3+ centers. There is no such charge-compensating center inside the models of e−:ZnO QDs, which results in lower energy IR absorptions. Experimentally, charge-compensating ions for e−:ZnO, for example, H+ or Li+, may change the location of the IR absorption features. This will be the focus of future work. This conclusion has implications for many types of carrier-doped semiconductor nanostructures and suggests that the new IR absorption feature is influenced by not only the introduction of charge-carriers but also the charge-compensating ions that accompany them.

pretation of this structure as arising from low-symmetry splitting of the 1Pe degeneracy. In contrast with the n-type QDs, the neutral, undoped ZnO QDs lack these transitions due to their unoccupied conduction band. The only transitions observed are VB to CB transitions. It is interesting to note the trends in absorption intensity for the three systems. The neutral ZnO nanocrystals have the strongest first VB → CB transitions, followed by the photodoped e−:ZnO nanocrystals, and finally the Al3+:ZnO nanocrystals have the weakest transitions. These trends can be understood by considering changes in densities of states. Band-to-band intensities are proportional to the available DOS in the conduction band. In the photodoped n-type ZnO QDs, the added electron occupies an otherwise unoccupied orbital at the CB edge, reducing the available DOS for optical excitation at that edge. Thus, absorption decreases at the absorption edge. This trend is observed in the computed spectra in Figure 2. For the Al3+:ZnO QDs, there is a further reduction in the CB bandedge DOS as a result of replacing one Zn2+ with an Al3+, further decreasing the absorption. The effect is most pronounced in the smaller Zn33O33 QDs, whereas the interband transition intensities become more similar in the larger Zn84O84 QDs. The higher energy of the Al3+:ZnO S → P transitions, as opposed to the e−:ZnO QD, can be accounted for by the higher effective potential as a result of the Al3+ center. Replacing a Zn2+ center with an Al3+ center can be thought of as adding a positive point charge within the background potential of the QD. The difference between the Al3+:ZnO and the e−:ZnO systems, then, is the same as that considering the quantummechanical solution to the hydrogen-like atom. The energy levels for hydrogen-like atoms go as En ∝

Z2 n2

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AUTHOR INFORMATION

Corresponding Authors

*D.R.G.: E-mail: [email protected]. *X.L.: E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are thankful for financial support from the U.S. National Science Foundation (CHE-1265945 to X.L., DMR-1206221 to D.R.G, DMR-1408617 to X.L. and D.R.G., and Graduate Research Fellowship DGE-1256082 to A.M.S. and J.J.G.) and the Department of Energy (DE-SC0006863 to X.L.). Additional support to X.L. from the University of Washington Student Technology and Royalty Research Fund is gratefully acknowledged.

(4)

where Z is the charge of the potential and n is the principal quantum number. There is a direct Z dependence on the electronic energy levels as well as the electronic transition energies; the stronger the Coulombic potential, the higher the electronic transition energy. While the potential in the Al3+:ZnO and the e−:ZnO QDs is more complicated than the simple model suggests, it is sufficient to illustrate why introducing the additional charge of an Al3+ center raises the 1Se → 1Pe energy relative to the e−:ZnO QD.

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REFERENCES

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CONCLUSIONS We present a theoretical comparison of two different n-type ZnO QDs, both containing an added electron in the conduction band. The two QD types include: Al3+:ZnO, whose added electron originates via aliovalent doping with Al3+, which introduces an e−CB while maintaining a neutral charge on the QD, and e−:ZnO, in which an added electron is introduced via photodoping13,16−18 or chemical reduction,14 resulting in a QD with a single negative charge (compensated by H+ or another countercation). We find that, in general, both systems have similar electronic absorption spectra, with most features accounted for by the quantum-mechanical model of the particle in a spherical potential. That is to say, the added electron occupies an S-type super orbital and has three (neardegenerate) strong transitions to P-type super orbitals, analogous to s → p transitions in hydrogen atoms. While both QD systems have similar spherical symmetry, they are not perfectly centrosymmetric, with the Al3+:ZnO having the lowest 26588

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dx.doi.org/10.1021/jp5090229 | J. Phys. Chem. C 2014, 118, 26584−26590

The Journal of Physical Chemistry C

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dx.doi.org/10.1021/jp5090229 | J. Phys. Chem. C 2014, 118, 26584−26590