Optical Excitations in Cadmium Sulfide Nanoparticles - The Journal of

J. Phys. Chem. C 2007, 111, 10761-10770

10761

ARTICLES Optical Excitations in Cadmium Sulfide Nanoparticles Johannes Frenzel,* Jan-Ole Joswig,† and Gotthard Seifert‡ Physikalische Chemie, Technische UniVersita¨t Dresden, D-01062 Dresden, Germany ReceiVed: February 9, 2007; In Final Form: May 2, 2007

Density functional-based calculations employing linear response theory have been performed on cadmium sulfide nanoparticles with up to 2000 atoms. We have considered different stoichiometries, underlying crystal structures (zincblende, wurtzite, rocksalt), particle shapes (spherical, cuboctahedral, tetrahedral), and saturations (unsaturated, partly saturated, completely saturated). We find strong excitonic onset excitations. For the saturated particles, the quantum confinement effect in the lowest excitation is visible as the excitation energy decreases toward the bulk band gap with increasing particle size. Dangling bonds at unsaturated surface atoms introduce trapped surface states that lie below the lowest excitations of the completely saturated particles. Zincblendeand wurtzite-derived particles show very similar spectra, whereas the spectra of rocksalt-derived particles are rather featureless. Particle shapes that confine the orbital wavefunctions strongly (tetrahedron) give rise to less pronounced spectra with lower oscillator strengths. Finally, we find a very good agreement of our data to experimentally available spectra and excitation energies.

1. Introduction Semiconductor and metal nanoparticles have been in the focus of scientific research for several decades. Their most important feature is that their size determines their electronic and optical properties.1,2 Thereby, these particles reveal new physical properties being at an intermediate level between an atomic or molecular and a bulk environment. Their unique electronic nature privileges them for a large variety of potential applications (e.g., biological labels,3-5 displays,6 solar cells,7,8 and quantum dot lasers9,10). Cadmium sulfide (CdS) is a II-VI semiconductor. For several hundreds of years, cadmium sulfide has been used as a pigment. Today, it provides useful properties for optoelectronic devices, such as photosensitive and photovoltaic devices, or as photoresistors.11 In 1982, Henglein12 observed a blue shift in the absorption spectrum of a colloidal solution of CdS with respect to the bulk band gap. This effect was later explained by Brus,13 who discovered its quantum-mechanical nature. Since then, much progress has been achieved in the controlled synthesis of these particles with respect to a narrow size distribution.14 In 1993, Murray et al.15 presented a method that allowed the size selective synthesis of cadmium chalcogenide nanoparticles on a macroscopic scale. This was an important step toward detailed investigations of the particles, their properties, and possible applications. In the size regime below approximately 10 nm, the physical properties of a material are dominated by quantum-mechanical effects. Therefore, the properties differ totally from those of * Corresponding author. E-mail: [email protected]. Present address: Max-Planck-Institut fu¨r Chemische Physik fester Stoffe, No¨thnitzer Strasse 40, 01187 Dresden, Germany. † E-mail: [email protected]. ‡ E-mail: [email protected].

the macroscopic material. The spatial restriction of the particle affects and reduces the de Broglie wavelength of the electrons. This effect is referred to as quantum confinement or quantum size effect (QCE/QSE), which can simply be described by the nonatomistic quantum-mechanical problem of the “particle in a box”. This is the basis of the effective mass approximation for the description of the electronic structure of nanoparticles.13,16-19 A second effect, which is important for small nanoparticles, is the influence of the surface. With decreasing particle size, the surface-to-volume ratio increases and more atoms are surface atoms or located near to the surface. The optical processes in these particles (e.g., technologically interesting luminescence processes) especially are affected by the surface structure.20,21 Extensive experimental and theoretical investigations of semiconductor nanoparticles have given a clear evidence that the electronic states located at the surface are strongly involved in the optical process.22-29 Defects in the surface saturation (dangling bonds) can cause trapped states. In contrast, the best efficiency in the photoluminescence quantum yield, a so-called “bright point”, was reported for nanoparticles with an optimal, defect-free and thus charge-carrier trap-free surface structure.30-32 In a previous study,33,34 we have shown that the electronic structure and the optical properties of CdS clusters with up to 450 atoms are sensitive to the underlying atomic structure. The surface especially has a major impact on the orbitals closest to the Fermi level. Hence, the role of surface passivation also becomes of elementary relevance for the optical properties of the particles. In this article, we now set the focus on the influence of the surface states and their passivation with respect to the optical excitation spectra of CdS nanoparticles. We will also pay

10.1021/jp071125u CCC: $37.00 © 2007 American Chemical Society Published on Web 07/04/2007

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Figure 1. Optimized structures of experimentally characterized surface-saturated CdS nanoparticles. The Cd, S, and H atoms are represented by gray, yellow, and white spheres, respectively. The corresponding optical excitation spectra are presented in Figure 2, the lowest excitation energies are listed in Table 1.

attention to the underlying crystal structure, the particle shape, and their influence. For this purpose, we have performed density functional-based calculations on the particle structures and afterward linear response calculations to obtain the absorption spectra. All nanoparticles were taken as differently shaped cutouts from the three CdS bulk structures zincblende, wurtzite, and rocksalt. We will present our computational methods in Section 2, and in Section 3 the results will be discussed in detail. Finally, we conclude in Section 4. 2. Computational Details We have used a density functional tight-binding (DFTB) method for the structural optimization of the investigated nanoparticles. This method has been described in detail elsewhere.35-37 It is based on the density functional theory of Hohenberg and Kohn38 in the formulation of Kohn and Sham.39 The total energy of the system of interest relative to the isolated atoms is written as

Etot )

1

jk + ∑ Ukl(|R Bk - R B l|) ∑i i - ∑ 2 k*l jk

(1)

where i is the Kohn-Sham eigenvalue of the ith orbital of the system and jk is the energy of the jth orbital of the isolated atom k. Ukl is a pair potential between the atoms k and l. The single-particle Kohn-Sham eigenfunctions ψi(R B ) are expanded in a set of localized atom-centered basis functions φm(R B ). These functions are determined by self-consistent density functional calculations on the isolated atoms employing a large set of Slater-type basis functions. The effective one-electron potential in the Kohn-Sham Hamiltonian is approximated as a superposition of the atomic potentials. Moreover, only one and two center integrals are calculated to set up the Hamilton matrix. We have taken a minimal valence basis including the 4d, 5s, and 5p orbitals of cadmium and the 3s, 3p, and 3d orbitals of sulfur. Electrons below these levels were treated within a frozen-core approximation. For the exchange correlation functional the local density approximation has been applied.40 All structures have been optimized. The convergence criteria were the remaining and root-mean-square of the residual force, both 10-3 Hartree/Bohr.

TABLE 1: Calculated Lowest Excitation Energies of Different CdS Nanoparticlesa compound

structure

ωI [eV]

ωexp [eV]

ref

[Cd(SR)4]2[Cd4(SR)10]2[Cd4S(SR)10]4[Cd4S(SR)12]6[Cd8S(SR)16]2[Cd10S4(SR)16]4[Cd13S4(SR)24]6[Cd17S4(SR)28]2[Cd20S13(SR)22]8[Cd28S13(SR)42]12[Cd32S14(SR)36] [Cd32S14(SR)40]4[Cd35S28(SR)28]14[Cd54S32(SR)48]4[Cd54S32(SR)52]8[Cd55S28(SR)64]10[Cd92S55(SR)92]18-

mix tetr wz cubo mix tetr cubo mix tetr cubo mix mix tetr mix mix cubo cubo

5.54 4.90 5.04 4.98 4.72 4.59 4.43 4.27 4.29 3.97 3.75 3.99 4.03 3.04 3.71 3.63 3.36

5.17,b 4.40c 4.98c

47 48, 47 21 49 50 51, 52, 47 49 53 54 49 55,56

4.77b 4.43b 4.88,b 4.25c 4.28b 3.53c 3.82,b 3.46c

d

3.82c 3.70b

54 d

3.35b

49 49

a

The different shapes and crystal structures are denoted as follows: wurtzite (wz), zincblende tetrahedron (tetr), zincblende cuboctahedron (cubo), and mixed zincblende/wurtzite (mix). bThese experimental particles are saturated with aliphatic thiolates. cThese experimental particles are saturated with thiophenolates. dSome structures are modeled by adding four additional ligands to each edge of the experimental structures [Cd32S14(SR)36] and [Cd54S32(SR)48]4-. In our calculations, the particles were saturated with hydrogen.

Furthermore, we have used time-dependent density functional response theory (TD-DFRT-TB) for the calculations of the excitation spectra.41-43 To obtain the excitation energies, the coupling matrix, which gives the response of the potential with respect to a change in the electron density, has to be built. This is also referred to as linear response theory.44,45 In our scheme, we approximate the coupling matrix (so-called γ-approximation42), which allows an efficient calculation of the excitation energies and the required singlet oscillator strengths within a dipole approximation. The presented spectra are broadened by Gaussian functions of 0.03 eV width. All calculations have been carried out using the DFTB and TD-DFRT-TB implementations in the deMon 2003 code.46 3. Results A number of clusters have been synthesized with exact stoichiometries, and their energetically lowest optical transitions

Optical Excitations in Cadmium Sulfide Nanoparticles

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Figure 2. Calculated TD-DFRT-TB spectra of different surface-saturated CdS nanoparticles (black). Additionally, the corresponding spectra of the partly unsaturated structures [Cd32S14(SR)36] and [Cd54S32(SR)48]4- are shown (blue). The oscillator strengths of the latter are scaled. All curves are normalized with respect to the number of Cd atoms.

have been measured.21,47-56 We have optimized these structures with the DFTB method (cf. Figure 1) and calculated their absorption spectra with the TD-DFRT-TB scheme. The onset peaks in the spectra are the lowest-excitation energies (corresponding to the transition between highest occupied and lowest unoccupied molecular orbital, HOMO and LUMO), which are summarized in Table 1 and compared to the experimental data. With increasing particle size given by the number of Cd atoms, the calculated onset energies are decreasing. All calculated excitations lie in the range of 5.5-3.4 eV, which is well above the bulk limit (2.58 eV).57 Compared to the experimental values, they vary by (20%. These deviations may have several reasons. First, model structures are used, which are saturated with hydrogen atoms instead of thiophenolate or aliphatic thiolate ligands as in the experiment. Thus, the influence of ligand molecules on the optical properties is not fully covered. The deviations are especially large when the surfactant is a chromophore itself (e.g., phenolate, marked b in Table 1) that is incorporated in the optical process.58 For alkyl ligands, the deviations are not as large. Compared to this dominating effect, solvent effects seem to have no significant impact on the electronic and optical properties and can be neglected in the calculation.59 Considering these effects, the calculated values are well within the error bars of the experiments. The calculated singlet-absorption spectra of the particles are shown in Figure 2. Beside the energies of the onset excitation, the most eye-catching feature in almost all spectra is the highoscillator strength of these onset peaks, which suggests that these excitations have an excitonic character. A closer analysis of the wavefunctions shows that the hole wavefunction consists mainly of contributions from the HOMO - i (i ) 0, 1, 2), which are degenerate. Their energy differences are less than 1 meV and therefore they can be considered as degenerate. The electron wavefunction, in contrast, consists exclusively of contributions of the LUMO. A projection of the atomic- and orbital-resolved Mulliken populations shows that all the HOMO - i (i ) 0, 1, 2) and the LUMO are spatially delocalized over the entire nanoparticle. The overlap of the molecular orbitals (MOs) participating in the transition is therefore very large.

The picture changes if the nanoparticles are partly (or totally) unsaturated. A population analysis shows that the LUMO is then localized at the unsaturated Cd atom causing a surface state (cf. Figure 3). For some totally unsaturated particles, the spectra are also shown in Figure 2. They show absorption below the onset excitation energy of the saturated particles, which have almost negligible oscillator strengths. However, a strong excitonic absorption is obtained for both structures. In the spectra of the unsaturated CdS particles, these have slightly higher excitation energies but reduced oscillator strengths. In summary, already these small and well-defined particles exhibit an excitonic character of the onset excitation due to a maximal overlap of the wavefunctions of the participating MOs. Using the same approach, we have calculated the optical absorption spectra of much larger nanoparticles with up to 2000 atoms. The obtained singlet-excitation spectra of spherical, zincblende-derived particles (saturated and unsaturated) are presented in Figure 4. Here we can observe, that the onset excitation energies smoothly decrease with increasing particle size for the saturated particles, but randomly fluctuate for the unsaturated ones. Again, this is caused by excitations involving the surface states. We have shown this behavior for unsaturated zincblende- and wurtzite-derived clusters with up to 230 CdS pairs in an earlier study34 using the same theoretical method. There, we have addressed these low-lying excitations to collective excitations, as observed experimentally in metal clusters as surface plasmon excitations. From these new calculations, it is clear that these low-lying excitations in the spectra exhibit rather weak oscillator strengths and are localized at single surface cadmium atoms. Hence, an evidence for a plasmon- or an exciton-like character is not given. In Figure 5, we compare the MO eigenvalue spectra of the states close to the Fermi level as a function of particle size corresponding to Figure 4. Trend lines are drawn to show the energetic behavior of the frontier orbitals for the saturated particles. On the one hand, the diagram shows very clearly the QCE, because the gap decreases from 4.4 to 2.8 eV with increasing particle size. On the other hand, we can observe that the surface states in the unsaturated particles close the original


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Figure 3. Frontier orbitals of the cuboctahedrally shaped [Cd147S92(SH)123]13- particle. One single -SH group at a Cd atom is missing, which induces a localized surface state. The corresponding spectrum is shown in Figure 11d. The MOs are projected as atomic- and orbital-resolved Mulliken populations represented as spheres centered at the corresponding atoms (S yellow; Cd gray).

Figure 4. Calculated TD-DFRT-TB spectra of unsaturated (blue) and completely saturated (black), zincblende-derived, spherical CdS nanoparticles with radii of r ) 0.5-1.5 nm. The oscillator strengths in the spectra of the unsaturated clusters are scaled. All curves are normalized with respect to the number of Cd atoms.

gap so that the lowest excitations are even lower than the bulk band gap of 2.58 eV. The oscillator strengths of the low-lying

excitations are very weak but increase with the number of unsaturated Cd atoms (cf. Figure 4).



Figure 5. Eigenvalue spectra of the molecular orbitals closest to the Fermi level. The energy levels of the saturated nanoparticles are depicted in black, and those of the corresponding unsaturated particles are depicted in blue. The number of Cd atoms is given below each set of eigenvalues representing the particle size. The corresponding linear response spectra are depicted in Figure 4.

Figure 4 shows additionally a second excitonic absorption peak of similar oscillator strength occurring at higher energies. This is not observed in the spectra of the smaller structures but rather becomes characteristic for particle radii larger than 1 nm. Similar to the first excitonic excitation, this second has the following contributions: The hole wavefunction consist mainly of the up to fivefold-degenerated HOMO - i (i ) 3, 4, 5, 6, 7) and the electron wavefunction of the threefold-degenerated LUMO + j (j ) 1, 2, 3). The wavefunctions of these MOs have angular momenta l ) 1 (1p character) according to those obtained from spherical jellium model calculations. Thus, the excitation results from a 1p-1p transition, whereas the onset excitation results from a 1s-1s transition. For a cuboctahedral nanoparticle we show the frontier orbitals in Figure 6 where the 1s character (l ) 0) of HOMO - i (i ) 0, 1, 2) and LUMO and the 1p character (l ) 1) of the HOMO - i (i ) 3, 4, 5, 6, 7) and LUMO + j (j ) 1, 2, 3) can be clearly seen. In contrast to the onset excitations, these second peaks have also minor contributions from transitions that are collectively excited to the LUMO. These originate from occupied MOs that lie below the HOMO. The mixing has a relevant contribution to the absorption. With increasing excitation energy, the corresponding oscillator strength of these higher-lying transitions is also increasing. This effect can be addressed to the increasing density of the electronic states forming a band in the bulk limit. However, the mixing of several single transitions at higher energies does not allow any assignment of further angular momenta. The observed discretization of the excitonic absorption peaks in the calculated spectra is directly related to the QCE. For smaller particles (r e 1 nm) only the atomic angular momentum s of the MO wavefunction is observed, whereas larger structures show also p character. Similar observations are made for metal clusters calculated with the jellium model.60 The character of their MO wavefunctions can also be interpreted in the sense of molecular orbital theory.61,62 In contrast to metal clusters, “magic numbers” for certain stable cluster sizes are not observed

because the concept of magic numbers cannot be applied here as the shell filling occurs in each cluster separately up to the 3s sulfur states. The shell filling is therefore not varying with the cluster size. We have shown earlier,33 that stoichiometric CdS clusters derived from either zincblende or wurtzite structure exhibit almost identical electronic properties. At this place, we will investigate the impact of the structure on the optical properties for larger particles. Figure 7 shows the spectra of particles with different structures (spherical cut-outs from zincblende, wurtzite, and rocksalt lattices) but for comparable sizes. Qualitatively, the spectra of zincblende- and wurtzite-derived particles look rather similar. The differences are marginal. For the hexagonal wurtzite structures, the onset excitation is a double peak with a splitting smaller than 0.1 eV and a ratio of 2:1. It is caused by the lowered (hexagonal) symmetry compared to the cubic zincblende, which reduces the degeneracy of the HOMO. The splitting is also found for the second and other higher excitonic absorption peaks. However, the characteristics of the optical absorption changes completely when the underlying structure is the high-pressure rocksalt modification.63-65 Consistent with the experiment, the obtained spectra look typical for an indirect semiconductor. The oscillator strength of the low-lying excitations is reduced by some orders of magnitude. The single excitations are close in energy, so that effectively a continuous, featureless absorption spectrum arises. Thus, no excitonic excitations are observed, but the onset excitation energies of the completely saturated particles decrease with increasing particle size. The results so far have shown that in a spherical confinement the wavefunctions of the orbitals closest to the Fermi level feature the angular momenta of a spherical jellium. Because a different confinement may influence the optical properties of the nanoparticles, the influence of their shape will be investigated in the following. In Figure 8, the calculated excitation spectra of completely surface-saturated CdS nanoparticles with comparable sizes are shown, which are zincblende derived and


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Figure 6. Frontier orbitals in a cuboctahedral confinement. The electronic wavefunctions of the MOs closest to the Fermi level show a spatial angular momentum splitting, which is shown exemplarily for [Cd309S216(SH204)]18-. The MOs are projected as atomic- and orbital-resolved Mulliken populations represented as spheres centered at the corresponding atoms (S yellow; Cd gray).

Figure 7. Calculated TD-DFRT-TB spectra of completely saturated spherical CdS nanoparticles with zincblende (left column), wurtzite (middle column), and rocksalt crystal structure (right column). All curves are normalized with respect to the number of Cd atoms.

have spherical, tetrahedral, and cuboctahedral geometries. The spectra of spherical and cuboctahedral nanoparticles are almost identical, because their shapes are very similar. For these two types, the deviations are more pronounced for the smaller than for the larger clusters, because structural differences between a spherical and a cuboctahedral geometry are larger in a small particle. Also, the spectra of the tetrahedral particles show the same features. The excitation energies are almost identical for particles with the same number of Cd atoms. However, because the

confinement in a tetrahedron is much larger than in a sphere (and thus the overlap of the participating MOs is smaller), the peaks are only about half as high as those of the spherical and cuboctahedral particles and the fine structure is less pronounced. For particles with a similar number of Cd atoms and similar volume, the shape has no influence on the onset excitation energy. This holds also for the higher excitations in the spectra. In Figure 9 the lowest excitation energies are shown as a function of particle size and compared to available experimental



Figure 8. Calculated TD-DFRT-TB spectra of completely saturated, zincblende-derived, spherical (left column), cuboctahedral (middle column), and tetrahedral (right column) CdS nanoparticles with comparable sizes. All curves are normalized with respect to the number of Cd atoms.

Figure 9. Size dependence of the lowest excitations of [CdmSn(SR)i]q nanoparticles. Upper panels: Calculated and experimental values of small nanoparticles (cf. Table 1). Middle panels: Calculated values of spherically (sph), cuboctahedrally (cubo), and tetrahedrally (tetr) shaped nanoparticles, as well as zincblende- (zb), wurtzite- (wz) and rocksalt- (rs) derived structures. Lower panels: Comparison of calculated and experimental values of nanoparticles with different saturations (SPh and S(CH)x).66,67

data.66,67 In general, these experimental curves are well reproduced by our computed values. When extrapolating the particle size toward the bulk limit, the experimentally observed asymptotic decay toward the bulk band gap is also present. The

calculated values underestimate the experimental ones by approximately 10%. However, the agreement holds only for the experimental values obtained from alkylthiol-saturated nanoparticles. There


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Figure 10. Influence of the compensating charge q on the optical properties. Calculated TD-DFRT-TB spectra of three different, completely saturated [CdmSn(SH)i]q nanoparticles with cuboctahedral shape and different charges: q ) 2(m - n) - i (black) and q * 2(m - n) - i (blue). All curves are normalized with respect to the number of Cd atoms.

Figure 11. Influence of a single surface defect (dangling bond) on the optical excitation spectra. Calculated TD-DFRT-TB spectra of saturated CdS nanoparticles with cuboctahedral shape. The spectra of the modified [Cd147S92(SH124)]14- particle are shown having one dangling bond at a single- (a), double- (b), triple-bonded S atom (c). Panel (d) shows the spectrum of the particle with a dangling bond at a triple-bonded Cd atom. All curves are normalized with respect to the number of Cd atoms.

is a large, but constant shift compared to the gap energies of particles saturated with thiophenolate. It can be addressed to the direct incorporation of the ligands into the optical processes. Because the phenyl ring is a chromophore itself, its π-system participates in the optical transitions68,58 and lowers the onset absorption peak. So far, we have not addressed the influence of different charges on the particles. The investigation of the structural properties has shown that the charge as well as the presence of dangling bonds is relevant for the local stabilization of the particle surface. Therefore, we will now focus on the influence of the charge on the optical absorption spectra. Two sets of spectra of completely saturated [CdmSn(SH)i]q nanoparticles are presented in Figure 10, one with a charge of q ) 2(m - n) - i, the other with q * 2(m - n) - i. The latter are not charge compensated, which experimentally corresponds to missing counterions. Only for the structures with the appropriate charge q ) 2(m - n) - i characteristic spectra, including the earlier observed features, are obtained. The uncompensated particles show numerous excitations at very low energies with large oscillator strengths. For excitation energies, which are higher than the onset excitation of the charged particles, the spectra similarly continue. The charge compensation ensures that the nanoparticles have an electronic structure comparable to the completely occupied S 3p bands in the bulk. This is important to obtain the correct absorption spectra. The influence of a single surface defect on the optical absorption is also important. Therefore, single surfactants have been removed from certain positions at the surface of [Cd147S92(SH124)]14-: from a single-bonded S atom (a), from a double-bonded S atom (b), from a triple-bonded S atom (c), and from a triple-bonded Cd atom (d). Removing the ligands causes one or more dangling bonds at these atoms. The calculated absorption spectra of these particles are shown in Figure 11. For spectra of the structures with dangling bonds at an S atom (Figure 11a-c), the result is completely in agreement with those

of the completely saturated nanoparticles. In contrast, for the nanoparticle with a dangling bond at a Cd atom (Figure 11d) the influence on the optical properties is much larger. Despite the correction of the particles’ charge, a sub-band gap state is created, which in the absorption spectra causes an excitation below the onset peak with a weak oscillator strength. According to the participation analysis of the frontier orbitals, this subband gap state is located exactly at the introduced saturation defect as shown in Figure 3. The next higher states show again the characteristic spatial delocalization, as well as the angularmomentum dependence of the electronic wavefunction. However, the LUMO + 1, which corresponds to the electron wavefunction in the first excitonic excitation, has also large contributions of the surface defect. By a single saturation defect, the oscillator strengths of all excitonic absorptions are reduced by approximately 20%. Similar results have been found for the small, tetrahedrally shaped nanoparticles (cf. Figure 1), so that we find that only dangling bonds at Cd atoms influence the optical absorption properties. A similar behavior has been observed by Fu and Zunger69 for InP particles. Alternatively, the experimental results of Lifshitz et al.22,23 on the excitation relaxation processes for CdSe particles suggest the presence of a sub-band gap state with a clear dependence on the particle structure. The authors argue that the recombination takes place at a low-symmetry site, such as one near the surface, and furthermore that the hole is delocalized, whereas the electron is localized at the surface. Accordingly, Bawendi et al.24 observed that the band-edge luminescence is trapped and localized on the surface. These experimental observations are in agreement with the results of the present work. 4. Conclusions In this study, we have investigated the optical absorption spectra of cadmium sulfide clusters and nanoparticles. We have especially paid attention to the effects of saturation, dangling bonds, particle shape, and underlying crystal structure. The

Optical Excitations in Cadmium Sulfide Nanoparticles spectra have been obtained using linear response theory within the TD-DFRT-TB scheme. For a set of small but experimentally very well characterized clusters, we find a very good agreement of the lowest excitation energies. The quantum confinement effect is nicely observable from the results, because the lowest excitation energies decrease with increasing particle size approaching the bulk band gap for very large structures. Deviations may result from the use of model structures and the surface saturation with hydrogen atoms instead of larger ligands. The most eye-catching feature in almost all spectra is the high-oscillator strength of the onset peaks. The corresponding excitations involve the occupied and unoccupied orbitals near the Fermi level. A wavefunction analysis of these has shown that they are spatially delocalized over the whole nanoparticle. Moreover, they show the shape of the atomic angular momenta (s for the small clusters, s and p for larger ones). The dangling bonds in the unsaturated nanoparticles cause trapped states located at the unsaturated Cd atoms. These trapped states are located at the surface and result in sub-band gap states with only small oscillator strengths, which are in many cases even lower than the bulk band gap. Larger nanoparticles (r g 1 nm) with up to 2000 atoms show very similar behavior as the small ones. Completely saturated structures show comparable spectra with a pair of two strong onset peaks. One is the result of an s-s excitonic transition, the other of a p-p excitonic transition. The second peak shows also minor contributions from collective excitations, whereas the onset peak results from a purely excitonic excitation. The underlying crystal structure (zincblende, wurtzite, rocksalt) has influence on the shape of the spectra. They are qualitatively quite similar for zincblende- and wurtzite-derived structures (small differences occur mainly due to a symmetry lowering), whereas the rocksalt-derived particles show very different, continuous, and featureless spectra. Here, we do not observe excitonic excitations. Besides spherical-shaped particles, we have also investigated zincblende-derived spherical, tetrahedral, and cuboctahedral CdS particles. The spectra of larger spherical and cuboctahedral particles are almost identical, and especially for larger particles with similar sizes and volume the shape has no influence on the position of the onset excitation peaks. Because the tetrahedrally shaped nanoparticles confine the wavefunctions of the participating orbitals more strongly, the spectra of these particles show less pronounced excitations with smaller oscillator strengths. Acknowledgment. This work was supported by SPP 1072 of the Deutsche Forschungsgemeinschaft (Project No. Sp 439/ 9-1). References and Notes (1) Yoffe, A. D. AdV. Phys. 2001, 50, 1. (2) Schmid, G., Ed. Nanoparticles. From Theory to Application; WileyVCH: Weinheim, 2004. (3) Chan, W. C. W.; Nie, S. Science 1998, 281, 2016. (4) Bruchez, M., Jr.; Moronne, M.; Gin, P.; Weiss, S.; Alivisatos, A. P. Science 1998, 281, 2013. (5) Jaiswal, J. K.; Goldman, E. R.; Mattoussi, H.; Simon, S. M. Nat. Methods 2004, 1, 73. (6) Colvin, V. L.; Schlamp, M. C.; Alivisatos, A. P. Nature 1994, 370, 354. (7) Huynh, W. U.; Dittmer, J. J.; Alivisatos, A. P. Science 2002, 295, 2425. (8) Gur, I.; Fromer, N. A.; Geier, M. L.; Alivisatos, A. P. Science 2005, 310, 462. (9) Klimov, V. I.; Mikhailovsky, A. A.; Xu, S.; Malko, A.; Hollingsworth, J. A.; Leatherdale, C. A.; Eisler, H.-J.; Bawendi, M. G. Science 2000, 290, 314.

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Optical Excitations in Cadmium Sulfide Nanoparticles - The Journal of

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