Theoretical Characterization of Electronic Transitions in Co2+-and

Apr 27, 2009 - B.ii.c) band-to-band transitions, and (III. ..... Experimentally, these two bands are observed at ∼0.5 and ∼2.0 eV in Co2+-doped Zn...
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J. Phys. Chem. C 2009, 113, 8710–8717

Theoretical Characterization of Electronic Transitions in Co2+- and Mn2+-Doped ZnO Nanocrystals Ekaterina Badaeva, Christine M. Isborn, Yong Feng, Stefan T. Ochsenbein, Daniel R. Gamelin,* and Xiaosong Li* Department of Chemistry, UniVersity of Washington, Seattle, Washington 98195-1700 ReceiVed: January 14, 2009; ReVised Manuscript ReceiVed: March 16, 2009

Linear response time-dependent hybrid density functional theory has been applied for the first time to describe optical transitions characteristic of Co2+- and Mn2+-doped ZnO quantum dots (QDs) with sizes up to 300 atoms (∼1.8 nm diam) and to investigate QD size effects on the absorption spectra. Particular attention is given to charge-transfer (CT or “photoionization”) excited states. For both dopants, CT transitions are calculated to appear at sub-band-gap energies and extend into the ZnO excitonic region. CT transitions involving excitation of dopant d electrons to the ZnO conduction band occur lowest in energy, and additional CT transitions corresponding to promotion of ZnO valence band electrons to the dopant d orbitals are found at higher energies, consistent with experimental results. The CT energies are found to depend on the QD diameter. Analysis of excited-state electron and hole density distributions shows that, for both CT types, the electron and hole are localized to some extent around the impurity ion, which results in “heavier” photogenerated carriers than predicted from simple effective mass considerations. In addition to CT transitions, the Co2+-doped ZnO QDs also exhibit characteristic d-d excitations whose experimental energies are reproduced well and do not depend on the size of the QD. I. Introduction The influence of transition-metal (TM) dopants on the electronic structures of semiconductor nanocrystals has attracted great interest for solar energy conversion,1 nanospintronics/ spin-photonics,2 and phosphor applications.3-6 Among other consequences, doping often introduces new sub-band-gap dopant-centered d-d and so-called charge-transfer (CT or “photoionization”) excited states. Photoinduced charge separation by CT excitation in doped semiconductor nano- and microcrystals has been exploited for solar photocatalysis7-11 and photocurrent generation in regenerative photovoltaic cells.12,13 Spectroscopic identification of CT transitions allows determination of the positions of the TM impurity donor or acceptor ionization levels relative to the respective band edges of the host semiconductor,13 a property that is usually known only approximately from universal alignment rules.14-16 In doped semiconductor quantum dots (QDs), confinement effects have been observed to shift the band edges relative to energetically pinned TM levels, resulting in diameter-dependent CT energies.17 Many colloidal and self-assembled doped semiconductor nanocrystals have been explored for magneto-optical and magneto-electronic applications.2,18-20 Dopant-carrier magnetic exchange interactions in these so-called diluted magnetic semiconductors (DMSs)21 give rise to “giant” Zeeman splittings of the semiconductor band structure, the signs and magnitudes of which are intimately linked to the energies of dopantsemiconductor CT configurations. Specifically, the dominant contribution to the excitonic giant Zeeman splittings measured in magneto-optical experiments, parametrized within the meanfield approximation by the kinetic p-d exchange energy, N0β, can be expressed in terms of the energies of virtual CT * To whom correspondence [email protected].

should

be

addressed.

E-mail:

transitions.16,22,23 Furthermore, high TC ferromagnetism in oxide DMSs was also related to the energies of various CT configurations.13,24-27 Despite the importance of CT states in TM-doped semiconductors, very little is presently known about their energies, intensities, and wave functions. Experimentally, CT transitions are often broad and difficult to analyze quantitatively due to spectral overlap with other features. At the same time, because they involve both highly localized impurities as well as delocalized bands and because they depend sensitively on dopant-semiconductor offset potentials, CT transitions have proven to be more difficult to describe theoretically than either the localized d-d or the delocalized band-to-band transitions. Therefore, there is a strong motivation to develop sound theoretical methodologies for describing CT excited states in TM-doped semiconductor nanocrystals. Our previous theoretical work28 focused on modeling the interactions of TM d levels with the valence band of the ZnO lattice in TM2+-doped ZnO nanocrystals. Two important results from our previous study28 underlie the investigations described in this article: (1) hybrid DFT functionals provide a good description of the interactions between the TM d levels and the host semiconductor lattice, unlike the LSDA or gradientcorrected DFT functionals, and (2) smaller DMS QDs carry the essential electronic structure features of larger QDs. Here, we extend those studies to address excited-state properties. Developing correct theoretical descriptions of the excited states of doped semiconductor nanostructures will assist the design and understanding of new functional materials. In this study, we present a linear response time-dependent hybrid density functional theory (TDDFT) characterization of the low-energy (ultraviolet/visible/near-infrared) electronic transitions in Co2+and Mn2+-doped ZnO nanocrystals with sizes up to 300 atoms (∼1.8 nm diam). We show that the TDDFT is a valid approach for describing the full range of electronic transitions in TM2+-

10.1021/jp900392j CCC: $40.75  2009 American Chemical Society Published on Web 04/27/2009

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doped ZnO QDs, including CT transitions and their dependence on quantum confinement. This TDDFT approach, therefore, provides a valuable tool for interpretation of the electronic structures and physical properties of this important class of materials. This paper is organized as follows: Section II introduces methods used in this article, including the structure of the quantum dots and a brief review of the linear response TDDFT theory. Section III.A presents analysis of the density of states of the ground-state wave function and optical properties computed using transitions between ground-state molecular orbitals. Section III.B presents optical properties computed with the linear response TDDFT. These results are described in two subsections, optical properties in pure (III.B.i) and TM2+-doped (III.B.ii) ZnO QDs. The latter topic is divided into four subsections: (III.B.ii.a) ligand-field transitions, (III.B.ii.b) CT transitions, (III.B.ii.c) band-to-band transitions, and (III.B.ii.d) quantum confinement effects on CT transitions. The results presented here represent a case study involving a prototype doped semiconductor nanocrystal system and help to define general electronic structure properties relevant to studies of other members of this class of materials. II. Methods All calculations were performed with the development version of the Gaussian program suite.29 Doped nanocrystal electronic structures were obtained with the PBE1PBE hybrid DFT functional.30,31 The Los Alamos double-ζ pseudocore potential (LANL2DZ)32-35 and the associated basis set were used for all the atoms with the Zn (4s, 3d); Co (3s, 3p, 4s, 3d); Mn (3s, 3p, 4s, 3d); and O (1s, 2s, 2p) electrons treated as valence electrons. Several wurtzite ZnO nanocrystals with diameters ranging from ∼0.4 nm (Zn6O6) to ∼1.8 nm (Zn141O141), all possessing C3V symmetry, were constructed according to the scheme described in ref 28. The lattice parameters were obtained from experimental data: a ) 3.249 Å, c ) 5.204 Å, and u ) 0.382.36 The dangling bonds on the surfaces of the nanocrystals were passivated with pseudo-hydrogen atoms, which have a modified nuclear charge of 0.5 and 1.5 to terminate surface O2- and Zn2+ ions, respectively. The O-H (1.057 Å) and Zn-H (1.731 Å) bond lengths were taken from optimized H4O and ZnH4 tetrahedra. This pseudo-hydrogen capping scheme leads to a well-defined band gap and stable nanocrystal geometry (see ref 28 for detailed discussion). When a transition-metal dopant is introduced into the ZnO nanocrystal, it is positioned near the center of the crystallite (Figure 1). Replacing Zn2+ with a TM2+ dopant ion is a charge-neutral substitution and retains the overall neutral charge of the nanocrystal. Two different methods for computing optical properties of the TM-doped nanocrystals were compared: transitions between single molecular orbitals were calculated, and a linear response TDDFT approach was applied. Excitations in condensed matter are often approximated as the difference in orbital energies for the occupied and unoccupied (or virtual) orbitals from the ground-state DFT calculations (e.g., refs 26 and 37). This method gives reasonable results for systems with moderate correlation. However, one-electron approximations are not ideal for description of TM electronic structures, where electron exchange and correlation effects often make greater contributions to the TM-based excitation energies than one-electron orbital splittings. In semiconductor QDs, the electron-hole interaction and relaxation of the electronic structure in response to photoexcitation also play an important role in the description of the excited states. As shown recently,38 Coulombic interaction

Figure 1. Top panel: Structure of the Zn83TMO84H*114 nanocrystal. The TM2+ dopant ion is placed close to the center of the nanocrystal and is shown as a ball. Bottom panel: Density of states (DOS) for (a) undoped ZnO, (b) Mn2+-doped ZnO, and (c) Co2+-doped ZnO nanocrystals (diameter ) 1.5 nm). Shaded regions indicate the partial contributions of TM 3d levels (10-fold magnification). Spin up and spin down are plotted as positive and negative DOS, respectively.

and correlation effects have to be considered to correctly describe the excited-state electronic structure of QDs. From the theoretical point of view, a better description of excited states can be obtained by the Green’s function based approach or the linear response time-dependent density functional theory (TDDFT). TDDFT has been successfully used to address excitedstate electronic structures of numerous TM coordination complexes and has recently been applied to extended quantum systems, such as carbon nanotubes and QDs.39-41 Within the linear response TDDFT formalism, the excitedstate properties are computed using only the first-order (linear) response of the TDDFT equation to an applied perturbation (see ref 42 for a detailed review). This method is commonly performed in the frequency domain and generally uses the DFT ground state as a reference. The linear response equation in matrix form is

[

][ ] [

][ ]

1 0 X A B X )ω 0 -1 Y B* A* Y

Aia,jb ) (εa - εi)δijδab + (ia | jb)

(1)

Bia,jb ) (ia | bj)

(2)

where X and Y are the electron density responses determined by solving this linear equation, ε is the orbital energy, (ia || jb)

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is the antisymmetrized two-electron integral, which includes both Coulomb and exchange (and correlation in TDDFT) terms, and ω is a matrix of eigenvalues representing the transition energies of the system. Here, we use the common notation in which i, j represent occupied orbitals and a, b are virtual orbitals of the ground-state configuration. Linear response TDDFT includes relaxation of the electron configuration as a result of excitation and calculates excitation energies as poles in the density response function rather than as simple differences between DFT orbital energies.42 Because it is superior in accuracy to molecular orbital energy differences and computationally much cheaper than multiconfigurational wave function based methods, linear response adiabatic TDDFT is an attractive method for calculating the photophysical properties of molecules and semiconductor nanocrystals. To elucidate the nature of the excited states in doped ZnO nanocrystals, the electron and hole density distributions that result from photoexcitation are constructed. The electron (Fe(r)) and hole (Fh(r)) distributions are defined as the positive and negative electron density differences between the excited and ground states (eq 3)

Fe(r) ) [Fn(r) - F0(r)]+ Fh(r) ) [Fn(r) - F0(r)]-

(3)

where Fn(r) and F0(r) are electron density distributions of the fully optimized excited and ground-state wave functions, respectively. III. Results and Discussion A. Ground-State Electronic Structure. Figure 1 shows the density of states (DOS), a plot of the occupied and virtual orbital energies, calculated for doped Zn83CoO84H*114 and Zn83MnO84H*114 nanocrystals, along with that of an undoped Zn84O84H*114 nanocrystal (diameter of ∼1.5 nm). The highest energy occupied band of ZnO predominantly consists of O22p levels, whereas the lower energy band with its maximum about 9 eV deeper into the valence band (VB) is built mostly from Zn2+ 3d levels (the partial O2- 2p and Zn2+ 3d contributions to the total DOS are shown in Figure 1a as the dashed and dash-dot lines, respectively). Near the edge of the conduction band (CB), the major contribution comes from the unoccupied Zn2+ 4s levels with about 10% of O2- 2p admixture. For all nanocrystal sizes studied here, the introduction of a TM2+ dopant ion does not affect the position of the CB minima compared to that of the pure ZnO nanocrystals. For both Co2+and Mn2+-doped ZnO nanocrystals, most of the TM2+ d electrons appear at the edge of the VB. In the pseudotetrahedral cation crystal field environment of wurtzite ZnO, electrons with the same spin are split by symmetry into two lower energy e orbitals (dx2-y2 and dz2) and three higher energy t2 orbitals (dxy, dyz, dxz), whereas exchange interactions lead to the splitting between electrons with different spins. The ground state of Co2+ is a high-spin d7 (S ) 3/2) configuration. In the Co2+-doped ZnO nanocrystal, all Co2+ spin-up 3d levels are covalently delocalized into the VB of the semiconductor. In our previous study,28 we described the two wide spin-up Co2+ d bands as bonding (satellite peak at ∼4.5 eV below the top of the VB) and antibonding (at the top of the ZnO VB) semiconductor O2-(p) and Co2+(d) interactions. The spin-down Co2+ d electrons are ∼1 eV above the edge of the ZnO VB with much more localized character. These results agree well with experimental photoemission data.43-45

Figure 2. Calculated and experimental optical energy gaps for ZnO nanocrystals. Experiments 1 and 2 are from ref 53. ∆E is the energy difference between the highest occupied and lowest unoccupied molecular orbitals from the ground-state wave function calculations. Eg is the first excited state in linear response TDDFT calculations.

Mn2+ in ZnO has a high-spin d5 ground-state configuration (S ) 5/2) with a calculated splitting between e and t2 levels of about 0.8 eV. The Mn2+ d electrons are positioned at the edge of the VB, and the e levels are mixed with the VB of ZnO. Unlike the Co2+-doped ZnO, the DOS for the Mn2+-doped ZnO shows no deep satellite peak corresponding to the TM2+-O2bonding interactions. In general, the Mn2+ d levels are positioned at higher relative energies than the corresponding Co2+ d levels. Although the one-electron orbitals represented in the DOS diagrams clarify the properties of the ground states of the doped nanocrystals, they do not provide accurate descriptions of the excitation energies, excited-state wave functions, or chargetransfer processes in these materials. As described above, excitations related to TM2+ d electrons define many of the physical properties of doped semiconductors and, in our case, when calculated with a hybrid DFT functional, the energy differences between single Kohn-Sham orbitals differ substantially from the experimental optical transition energies. For example, the calculated single-electron transition between the spin-down occupied Co2+ e levels and unoccupied t2 levels in Co2+/ZnO is ∼6 eV at the PBE1PBE/LANL2DZ level of theory, whereas the first d-d excitation is observed experimentally at ∼0.45 eV and corresponds to precisely this excitation. This 4A2 f 4T2(F) transition is described in ligand-field theory as occurring at an energy of 10 Dq, where 10 Dq describes the energy spacing between the d orbitals of t2 and e symmetries. In the next section, we show that TDDFT corrects these orbital energies and provides reliable information about excitations and excited-state character in pure and TM-doped semiconductor nanocrystals. B. Excited States and Optical Properties. i. Undoped ZnO Nanocrystals. The experimental low-temperature band gap of bulk ZnO is about 3.4 eV.46,47 Theoretical studies of bulk ZnO yield a broad range of estimated band-gap energies, however, ranging from less than 1.3 eV by LDA and pure generalized gradient density functionals48-51 to 3.2-3.7 eV by self-interaction corrected LDA48,51 and hybrid functionals.49,52 In Figure 2, we compare the calculated HOMO-LUMO gaps (∆E) with TDDFT first excitation energies, denoted as Eg, to estimate the effect of quantum confinement on the band-gap of ZnO QDs and to elucidate the importance of the electron-hole interaction. Experimental data53 for ZnO clusters over the same range of sizes are also included. Because of quantum confinement effects,

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Figure 3. Schematic illustration of the optical transitions observed in TM2+-doped ZnO. Note that, experimentally, the LVBMCT and MLCBCT transition energies do not sum to Eg as they are depicted (and as would occur in a one-electron picture) because of large electron-electron repulsion effects at the TM2+ dopant.

the calculated band-gap energy decreases with increasing size of the cluster. The deviation between experimental and theoretical results is more pronounced for smaller clusters, but experimental uncertainties in cluster size are also greatest for these data. Noticeably, the TDDFT-calculated Eg and ∆E values differ by as much as ∼1 eV for these nanocrystals because the electron-hole interaction plays a larger role in smaller QDs, as anticipated. As the size of the nanocrystal increases, the TDDFT energy corrections to the orbital energy gap become smaller. The calculated HOMO-LUMO gap and the TDDFT excitation energy, therefore, converge for larger undoped ZnO nanocrystals. ii. TM2+-Doped ZnO Nanocrystals. Generally, the electronic transitions associated with a TM2+ impurity doped into a II-VI semiconductor can be classified into three groups: (a) TM2+centered d-d transitions; (b) CT (or photoionization) transitions, which may involve either electron promotion from TM2+ d orbitals to the semiconductor CB or electron promotion from the semiconductor VB to unoccupied TM2+ d orbitals (describing the semiconductor host as a ligand to the TM dopant, these CT transitions can be classified as metal-to-ligand (CB) CT (MLCBCT) and ligand (VB)-to-metal CT (LVBMCT) transitions, respectively); and (c) band-to-band transitions, involving electron promotion from the VB to the CB of the host semiconductor.13,54,55 These various electronic transitions are illustrated schematically in Figure 3 and have been calculated using the TDDFT approach. Figures 4 and 5 show the TDDFT spectra for Co2+- and Mn2+-doped ZnO nanocrystals of different sizes. Experimental56,57 UV-vis absorption spectra for Co2+and Mn2+-doped ZnO nanocrystals with diameters of ∼5 nm are also shown for comparison. Figures 6 and 7 illustrate calculated electron and hole density distributions associated with the various characteristic electronic excitations in both Co2+and Mn2+-doped ZnO nanocrystals. These results are analyzed according to transition type in the following sections. a. d-d Transitions. The two lowest energy peaks in the calculated spectra of Co2+-doped ZnO (Figure 4b) are observed at ∼0.9 and ∼1.85 eV. These peaks correspond to the 4A2 f 4 T2(F) and 4A2 f 4T1(P) Co2+ d-d transitions, respectively. Both bands consist of multiple states, with splittings predominantly due to spin-orbit coupling and the lower axial cation site symmetry of wurtzite ZnO. Experimentally, these two bands are observed at ∼0.5 and ∼2.0 eV in Co2+-doped ZnO QDs, films, and bulk crystals.57-60 These bands originate from excitation of spin-down de electrons to unoccupied dt2 orbitals.

Figure 4. (a) Experimental absorption spectra of diluted and concentrated colloidal suspensions of Co2+-doped ZnO nanocrystals with diameters of ∼5 nm. (b) TDDFT oscillator strengths calculated for Co2+-doped ZnO nanocrystals of different sizes: (red circles) Zn14CoO15H*30; (green squares) Zn32CoO33H*60; and (blue triangles) Zn83CoO84H*114. The solid curves in (b) represent simulated spectra, obtained using the calculated spectral lines plotted with Gaussian functions and a line broadening parameter of Γ ) 0.16 eV, roughly approximated from the experimental spectra. Inset: Calculated size dependence of the band-to-band transition energy (EXC) and of the two MLCBCT transition energies (MLCT1 and MLCT2).

Figure 6a,b shows that electron and hole density distributions associated with such excitations are highly localized around the Co2+ ion, with small contributions from neighboring O2- anions. To first-order, neither transition is electric dipole allowed because of parity selection rules for d-d transitions, but they gain oscillator strength through hybridization of the Co2+ d orbitals with the neighboring O2- p orbitals (covalency) allowed in the reduced-symmetry cation point group. The computed oscillator strength of f ) ∼0.0015 for the set of 4T1(P) transitions is consistent with the experimental oscillator strength of f ≈ 0.0052 for this transition.58 The excitation energies and oscillator strengths of the Co2+ d-d transitions remain relatively constant as the size of the nanocrystal increases, in good agreement with the experimental observations.57 This result supports the conclusion from the ground-state electronic structure calculations that the TM2+ d levels are energetically “pinned” with respect to the ZnO CB and VB edges. Experimentally, a third d-d transition, 4A2 f 4T1(F), is observed at ∼1 eV in Co2+-doped ZnO58 and corresponds formally to a two-electron excitation from the de orbitals to the unoccupied dt2 orbitals in the weak field limit. Configuration interaction between the 4T1(F) and 4 T1(P) terms gives this transition partial electric dipole allowedness. Such multielectron excited states are beyond the single reference linear response TDDFT method, and this transition is, therefore, not discussed here. For the Mn2+-doped ZnO nanocrystals (Figure 5), all the d-d excitations have negligible oscillator strengths because there are no spin-allowed Mn2+ d-d transitions. These transitions are not observed experimentally, but the lowest energy d-d excited state of

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Figure 5. (a) Experimental absorption spectra for diluted and concentrated colloidal suspensions of Mn2+-doped ZnO nanocrystals with diameters of ∼5 nm. (b) TDDFT oscillator strengths calculated for Mn2+-doped ZnO nanocrystals of different sizes: (red circles) Zn14MnO15H*30; (green squares) Zn32MnO33H*60; (blue triangles) Zn83MnO84H*114. The solid curves in (b) represent simulated spectra, obtained using the calculated spectral lines plotted with Gaussian functions and a line broadening parameter of Γ ) 0.16 eV, roughly approximated from the experimental spectra. Inset: Calculated size dependence of the band-to-band transition energy (EXC) and of the two MLCBCT transitions (MLCT1 and MLCT2).

Mn2+-doped ZnO has been estimated from empirical ligandfield parameters to occur at ∼3.1 eV.56 b. Charge-Transfer Transitions. The DOS plots for the Co2+and Mn2+-doped ZnO nanocrystals (Figure 1b,c) imply two types of CT excitations: promotion of TM d electrons to the ZnO CB (MLCBCT) and promotion of ZnO VB electrons to vacant TM d orbitals (LVBMCT). Recent photoelectrochemical experiments12 have identified a low-energy CT band in Co2+doped ZnO that occurs in close proximity to the Co2+ 4T1(P) d-d band and that has been assigned as a MLCBCT transition on the basis of optical electronegativity calculations. This MLCBCT band is not clearly observed by electronic absorption spectroscopy (e.g., Figure 4a) because of its very broad band shape and small oscillator strength, but it is clearly observed with an onset energy of ∼1.75 eV in the photocurrent action spectra.12 In the calculated spectra for Co2+:ZnO (Figure 4b), a clear set of CT features is observed as a separate peak for the smallest nanocrystals, becoming an unresolved shoulder of the excitonic absorption band as the nanocrystal diameter increases (size effects on the CT transitions are discussed in section III.B.ii.d). Closer inspection shows that these CT features are best described as two sub-bands, both with MLCBCT character. The lower-energy MLCBCT sub-band (MLCT1) corresponds to excitation of Co2+ (spin-down) de electrons to the ZnO CB. The higher-energy MLCBCT sub-band (MLCT2) occurs 0.6-0.8 eV higher in energy and involves excitation of Co2+ (spin-up) dt2 electrons close to the edge of the VB into the ZnO CB. The energy difference between these two MLCBCT bands thus derives, in part, from the exchange-splitting energy between the Co2+ 3d spin-down and spin-up levels in the Co2+-doped ZnO.

Figure 6. Density distributions for photogenerated holes and electrons in various excited states of a Zn32CoO33H*60 nanocrystal, obtained using eq 3.

Figure 7. Density distributions for photogenerated holes and electrons in various excited states of a Zn32MnO33H*60 nanocrystal, obtained using eq 3.

Representative photoexcited hole and electron density distributions for the two MLCBCT excited states are shown in Figure 6c,d. The photoexcited electrons in the MLCBCT excited

Co2+- and Mn2+-Doped ZnO Nanocrystals states show substantial ZnO CB character (see Figure 6e) but remain partially localized around the Co2+ dopant. Such behavior is a result of the Coulombic interaction of this electron with the more localized photogenerated hole and translates into a smaller effective Bohr radius of this photogenerated CB electron than would be expected for a free CB electron. This contracted radius can be related to the relatively small photoconductivity and photochemical quantum efficiencies obtained from this low-energy CT excitation compared to those of band-to-band excitation.12 The photogenerated holes in the MLCBCT states are more localized than the photoexcited electrons (Figure 6e) but are also less localized than the holes of the Co2+ d-d transitions (Figure 6a,b). The limited mixing of the Co2+ de levels with the ZnO VB gives rise to small oscillator strengths for the lower MLCBCT transitions (on the order of f ) 0.0005). The sum of the individual calculated oscillator strengths can be compared to the experimental fMLCT, which is estimated as ∼0.001.12 The higher-energy MLCBCT sub-band exhibits much larger oscillator strengths (f ∼ 0.05) than those of the lower MLCBCT sub-band due to the stronger hybridization of the dt2 levels with the VB, which imparts a larger partial excitonic character to this MLCBCT transition. The very different intensities calculated for the two MLCBCT transitions support the general conclusion that dopant-semiconductor CT absorption intensity is borrowed from nearby band-to-band excitations via configuration interaction.12 As in Co2+:ZnO, the calculations also show sub-band-gap Mn2+:ZnO MLCBCT transitions that are split into two sub-bands (MLCT1 and MLCT2) separated by ∼0.8-1.0 eV according to the symmetry of the Mn2+ d donor orbitals: The lower subband originates from promotion of Mn2+-localized spin-up dt2 electrons to the ZnO CB. The second sub-band involves promotion of Mn2+ de electrons to the ZnO CB. Figure 7a,b shows electron and hole density distributions associated with these transitions. MLCBCT-state electron and hole density distributions are both very similar to those in the Co2+:ZnO QDs. The hole density distributions for the first and second MLCBCT bands consist of Mn2+ dt2 and de orbitals, respectively, mixed with O2- 2p orbitals. As a result of mixing with the ZnO VB, these transitions exhibit nonzero oscillator strengths. Similar to Co2+-doped ZnO, the dt2 levels have more extensive overlap with the ZnO CB and the oscillator strengths of the dt2 MLCBCT transitions are, therefore, an order of magnitude larger than those of the Mn2+ de MLCBCT band (f ∼ 0.01 vs 0.0008). The Mn2+: ZnO and Co2+:ZnO nanocrystals, thus, differ in the intensity ordering of their two MLCBCT sub-bands. A second type of CT transition, associated with electron excitations from the ZnO VB to empty TM d levels (LVBMCT), is also observed in experiment and TDDFT calculations. The first calculated LVBMCT transition is always higher in energy than the MLCBCT bands, which is consistent with experimental observations. It is calculated at ∼6.0 eV for the Zn33CoO33H*60 nanocrystal, ∼6.5 eV for the smaller Zn14CoO15H*36 nanocrystal, and ∼8.2 eV for the Zn14MnO15H*36 nanocrystal, with individual oscillator strengths ranging from f ) 0.005 to 0.01 for Co2+:ZnO and from f ) 0.0015 to 0.02 for Mn2+:ZnO. The sum of individual calculated oscillator strengths is comparable to the experimental oscillator strength for Co2+:ZnO, which is estimated to be ∼0.028 from the experimental ratio of fMLCT/fLMCT ∼ 0.038.12 This LVBMCT transition occurs within the ZnO gap for Co2+:ZnO but not for Mn2+:ZnO, and its significantly higher energy in Mn2+:ZnO is consistent with expectations

J. Phys. Chem. C, Vol. 113, No. 20, 2009 8715 from empirical optical electronegativities (∼6 eV in bulk Mn2+:ZnO, compared to ∼3.1 eV in bulk Co2+:ZnO).13,24,56 Although a quantitative comparison of absolute oscillator strengths between experiment and theory is difficult because the experimental absorption features are broad and overlapping, the results discussed above clearly illustrate that the trends in calculated oscillator strengths agree well with the trends in the experimental values. Furthermore, the calculated oscillator strengths provide insight into dopant-host hybridization and its role in governing the intensities of CT absorption bands in doped semiconductors. c. Band-to-Band Transitions. The last kind of transition found in these ZnO nanocrystals is the VB f CB electronic promotion to form excitonic states. Figures 6e and 7c show electron and hole density distributions of the lowest energy excitons in the Co2+- and Mn2+-doped ZnO QDs, respectively. The electron and hole density distributions in this excitonic excited state are clearly more delocalized than in the other excited states of the same nanocrystals (Figures 6 and 7). The electron density is somewhat more confined within the internal volume of the nanocrystal, whereas the hole density is shifted slightly toward the surface. As the nanocrystal size increases, the band gap decreases and the VB f CB transition shifts to lower energy due to the quantum confinement effect. In these calculations, this band shifts from ∼7 eV for the 0.5 nm diameter nanocrystal to ∼4.5 eV for the 1.5 nm diameter nanocrystal, as indicated in Figures 4 and 5. The energies of these band-to-band transitions are largely independent of the dopant at low doping levels. As a result, the energies and characteristics of the lowest excitonic states in ZnO nanocrystals doped with one Mn2+ or Co2+ impurity ion are very similar to those of the undoped ZnO nanocrystals. d. Quantum Confinement Effects and CT Transitions. The insets in Figures 4 and 5 illustrate the size dependence of the lowest MLCBCT excited states and the first ZnO excitonic transition. These CT transitions both shift to higher energy with decreasing nanocrystal diameter, as observed experimentally for Co2+:ZnSe QDs.17 Notably, the shifts of the CT transitions caused by quantum confinement are not as steep as those for the VB f CB transitions. Such behavior is expected when a CT transition originates from a “pinned” TM d level because, in this case, the size dependence of the CT excitation energy comes from just one of the two semiconductor bands. It is interesting to compare these TDDFT results for different nanocrystal sizes with those anticipated from the effective mass approximation commonly applied in the analysis of QD spectra. For spherical QDs with radius r, the correction to the energy of the excitonic transition, ∆EEXC ) EEXC(r) - Eg (r ) ∞), depends on the quantum confinement terms and the Coulomb interaction between the electron and hole, as described by the well-known eq 461,62

∆EEXC ≈

[

]

p2π2 1 1 1.8e2 + 2 m* m*h εr 2r e

(4)

where m*e and m*h are the effective masses (in units of electron mass) of the electron and hole in pure ZnO QDs, respectively, e is the electron charge, p is Planck’s constant, and ε is the dielectric constant. As described previously, a similar relationship holds for CT excited states17 and for certain trap states,63 for example, eq 5 for an MLCBCT state where the hole is localized on the dopant cation and, thus, is very heavy. In this

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Figure 8. Calculated MLCBCT and excitonic transition energies for (a) Mn2+:ZnO and (b) Co2+:ZnO nanocrystals, plotted against the first excitonic transition energy and extrapolated to the bulk Eg limit of 3.4 eV. The slopes, ∆EMLCBCT/∆EEXC, for the two MLCBCT transitions in each material are listed in Table 1. Extrapolation of the CT energies gives values of ∼2.7 eV for the lowest MLCBCT band in bulk Mn2+:ZnO and ∼3.3 eV for bulk Co2+:ZnO compared to the experimental values of ∼2.5 and ∼2.1 eV, respectively.

TABLE 1: Computed Values of ∆EMLCBCT/∆EEXC Obtained from the Slopes of the Linear Fits in Figure 8a,b for the Two MLCBCT Transitions in Mn2+:ZnO and Co2+:ZnO Nanocrystals Mn2+:ZnO Co2+:ZnO

∆EMLCBCT (1)/∆EEXC

∆EMLCBCT (2)/∆EEXC

0.49 0.59

0.52 0.72

scenario, the term (1)/(m*) h in eq 4 tends toward zero and can, thus, be neglected.

∆EMLCBCT ≈

[ ]

p2π2 1 1.8e2 εr 2r2 m*e

(5)

For the nanocrystal sizes considered here, the Coulomb term is estimated to be less than 20% of the total energy in eq 5. In the limit of small Coulomb terms, the ratio of eq 5 to eq 4 is simply the ratio of inverse effective masses given in eq 6.

∆EMLCBCT ∆EEXC

≈

m*e -1 m*e -1 + m*h -1

(6)

As calculated previously,64,65 m*e and m*h in bulk ZnO are approximately 0.28 and 0.59, respectively. If the electron in an MLCBCT excited state of a doped ZnO QD behaved like a free electron in the ZnO CB, the ratio in eq 6 would approach 0.68. As alluded to above, however, the effective masses of photogenerated bandlike carriers in CT states may be significantly different from those in excitonic states because of the electron-hole interaction involving the localized carrier. Application of eq 6 allows this scenario to be evaluated. Figure 8 replots the size-dependent transition energy data from the insets of Figures 4 and 5 as the energies of the MLCBCT transitions versus those of the first excitonic transition. For comparison, the excitonic energy is also plotted versus itself and fit to a straight line extrapolated to the Eg of bulk ZnO, 3.4 eV. The extrapolated bulk MLCBCT energies of the Mn2+:ZnO QDs are in excellent agreement with experimental values.13,24,56 The extrapolated bulk MLCBCT energies of the Co2+:ZnO QDs are overestimated by almost 1 eV compared with experimental data, which may be caused by overestimated hybridization of the Co2+ d levels with the VB of ZnO. The values of ∆EMLCBCT/ ∆EEXC, obtained from the slopes of the linear fits in Figure 8, are summarized in Table 1. The ∆EMLCBCT/∆EEXC values for Mn2+:ZnO QDs are significantly smaller than those for the free CB electron in ZnO QDs. This suggests that the photoexcited electrons in the MLCBCT

excited states of Mn2+:ZnO are “heavier” than those in the undoped ZnO excitonic states. This extra effective mass comes from the localized electron-hole interaction as already suggested by the electron and hole density distributions for MLCBCT transitions (Figure 7a,b). On the other hand, the ∆EMLCBCT/∆EEXC values for Co2+:ZnO QDs are closer to the free CB electron’s value. This picture is consistent with what was observed for Co2+-doped ZnSe QDs,17 where the MLCBCT transitions were accurately described as promotion of a localized Co2+ electron into a delocalized CB orbital (i.e., Co2+ f Co3+ + e-CB). Overall, the value of ∆EMLCBCT/∆EEXC from these TDDFT calculations agrees reasonably well with our general expectations from the effective mass approximation. IV. Conclusion Although standard orbital energy differences are able to provide a qualitative view of electronic excited states, they are incapable of describing d-d or CT electronic transitions in transition-metal-doped semiconductor nanocrystals. The lowenergy (ultraviolet/visible/near-infrared) electronic transitions of Co2+- and Mn2+-doped ZnO nanocrystals with sizes up to 300 atoms (∼1.8 nm diam) have now been investigated using linear response TDDFT. The TDDFT approach calculates d-d transitions in Co2+:ZnO nanocrystals at energies that agree well with experimental observations, and it also allows calculation of CT excited-state energies, oscillator strengths, wave functions, and dependence on nanocrystal diameter. The MLCBCT bands in both Co2+- and Mn2+-doped ZnO QDs have been shown to consist of two sub-bands, originating from promotion of TM electrons from the d orbitals of either e or t2 symmetry. These MLCBCT transitions gain intensity from covalency of the TM2+ d orbitals with the VB, which imparts partial band-to-band character to the transition. This covalency is greater for the d orbitals of t2 symmetry, and hence, CT transitions involving the t2 set of d orbitals carry greater oscillator strength than those involving the e set of d orbitals. All MLCBCT transitions, thus, exhibit nonzero oscillator strengths despite formally involving transitions between highly localized donor and highly delocalized acceptor orbitals. The calculated energies of the MLCBCT transitions in Mn2+:ZnO agree very well with experimental data, and those in Co2+:ZnO QDs are ∼1 eV higher in energy than experimental data. Compared to electrons in the excitonic VB f CB transitions, electrons in the MLCBCT transitions of Mn2+:ZnO have greater effective masses due to the electron-hole interaction involving the localized hole, whereas the effective masses of the promoted

Co2+- and Mn2+-Doped ZnO Nanocrystals electrons in the MLCBCT transitions of Co2+:ZnO are close to those of the ZnO VB f CB excitations. These considerations are closely related to carrier escape probabilities in photocatalysis and photocurrent measurements on TM2+:ZnO nanostructures.12,13 In the broader context, this study represents the first TDDFT investigation of excited states of doped semiconductor nanocrystals, and it provides a new benchmark for the calibration of future DFT investigations of the electronic structures of this interesting and technologically important class of materials. Acknowledgment. This work is supported by the National Science Foundation (CHE 0628252-CRC and 0342956), ACS Petroleum Research Fund (46487-G6 and AC10 46040), and Gaussian Inc. E.B. is supported by the University of Washington UIF fellowship. Additional support to D.R.G. from the Dreyfus Foundation and the Sloan Foundation is gratefully acknowledged. References and Notes (1) Osterloh, F. E. Chem. Mater. 2008, 20, 35. (2) Beaulac, R.; Archer, P. I.; Ochsenbein, S. T.; Gamelin, D. R. AdV. Funct. Mater. 2008, 18, 3873. (3) Bol, A. A.; Meijerink, A. Phys. ReV. B 1998, 58, R15997. (4) Pradhan, N.; Goorskey, D.; Thessing, J.; Peng, X. J. Am. Chem. Soc. 2005, 127, 17586. (5) Beaulac, R.; Archer, P. I.; Gamelin, D. R. J. Solid State Chem. 2008, 181, 1582. (6) Norris, D. J.; Efros, A. L.; Erwin, S. C. Science 2008, 319, 1776. (7) Serpone, N.; Lawless, D.; Disdier, J.; Herrmann, J.-M. Langmuir 1994, 10, 643. (8) Kudo, A.; Sekizawa, M. Chem. Commun. 2000, 1371. (9) Iwasaki, M.; Hara, M.; Kawada, H.; Tada, H.; Ito, S. J. Colloid Interface Sci. 2000, 224, 202. (10) Zou, Z.; Ye, J.; Sayama, K.; Arakawa, H. Nature 2001, 414, 625. (11) Kato, H.; Kudo, A. J. Phys. Chem. B 2002, 106, 5029. (12) Liu, W. K.; Salley, G. M.; Gamelin, D. R. J. Phys. Chem. B 2005, 109, 14486. (13) Kittilstved, K. R.; Liu, W. K.; Gamelin, D. R. Nat. Mater. 2006, 5, 291. (14) Caldas, M. J.; Fazzio, A.; Zunger, A. Appl. Phys. Lett. 1984, 45, 671. (15) Langer, J. M.; Delerue, C.; Lannoo, M.; Heinrich, H. Phys. ReV. B 1988, 38, 7723. (16) Blinowski, J.; Kacman, P.; Dietl, T. Mater. Res. Soc. Symp. Proc. 2002, 690, 109. (17) Norberg, N. S.; Dalpian, G. M.; Chelikowsky, J. R.; Gamelin, D. R. Nano Lett. 2006, 6, 2887. (18) Oka, Y.; Kayanuma, K.; Shirotori, S.; Murayama, A.; Souma, I.; Chen, Z. J. Lumin. 2002, 100, 175. (19) Bacher, G. Top. Appl. Phys. 2003, 90, 147. (20) Hoffman, D. M.; Meyer, B. K.; Ekimov, A. I.; Merkulov, I. A.; Efros, A. L.; Rosen, M.; Counio, G.; Gacoin, T.; Boilot, J.-P. Solid State Commun. 2000, 114, 547. (21) Furdyna, J. K., Kossut, J., Eds. Diluted Magnetic Semiconductors; Academic: New York, 1988; Vol. 25. (22) Mizokawa, T.; Fujimori, A. Phys. ReV. B 1997, 56, 6669. (23) Kacman, P. Semicond. Sci. Technol. 2001, 16, R25. (24) Kittilstved, K. R.; Gamelin, D. R. J. Appl. Phys. 2006, 99, 08M112. (25) Pemmaraju, C. D.; Hanafin, R.; Archer, T.; Braun, H. B.; Sanvito, S. Phys. ReV. B 2008, 78, 054428. (26) Walsh, A.; De Silva, J. L. F.; Wei, S.-H. Phys. ReV. Lett. 2008, 100, 256401. (27) Lany, S.; Raebiger, H.; Zunger, A. Phys. ReV. B 2008, 77, 241201(R). (28) Badaeva, E.; Feng, Y.; Gamelin, D. R.; Li, X. New J. Phys. 2008, 10, 055013. (29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery , J. A., Jr.; Vreven, T.; Scalmani, G.; Mennucci, B.; Barone, V.; Petersson, G. A.; Caricato, M.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Li, X.; Hratchian, H. P.; Peralta, J. E.; Izmaylov, A. F.; Kudin, K. N.; Heyd, J. J.; Brothers, E.; Staroverov, V. N.; Zheng, G.; Kobayashi, R.; Normand, J.; Sonnenberg, J. L.; Ogliaro, F.; Bearpark, M.; Parandekar, P. V.; Ferguson, G. A.; Mayhall,

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