NANO LETTERS
Level Structure of InAs Quantum Dots in Two-Dimensional Assemblies
2006 Vol. 6, No. 10 2201-2205
Dov Steiner,† Assaf Aharoni,‡ Uri Banin,‡ and Oded Millo*,† Departments of Physics and Physical Chemistry and the Center for Nanoscience and Nanotechnology, the Hebrew UniVersity of Jerusalem, Jerusalem 91904, Israel Received June 20, 2006; Revised Manuscript Received September 5, 2006
ABSTRACT The electronic level structure of colloidal InAs quantum dots (QDs) in two-dimensional arrays, forming a QD-solid system, was probed using scanning tunneling spectroscopy. The band gap is found to reduce compared to that of the corresponding isolated QDs. Typically, the electron (conduction-band) ground state red shifts more than the hole (valence-band) ground state. This is assigned to the much smaller effective mass of the electrons, resulting in stronger electron delocalization and larger coupling between electron states of neighboring QDs compared to the holes. This is corroborated by comparing these results with those for InAs and CdSe nanorod assemblies, manifesting the effects of the electron effective mass and arrangement of nearest neighbors on the band gap reduction. In addition, in InAs QD arrays, the levels are broadened, and in some cases their discrete level structure was nearly washed out completely and the tunneling spectra exhibited a signature of two-dimensional density of states.
Semiconductor nanocrystal quantum dots (QDs) exhibit discrete electronic level structure and are therefore referred to as “artificial atoms”. The atomic-like level spectra (s- and p-like states) pertain in particular to the nearly spherically shaped colloidal QDs,1 as directly confirmed by scanning tunneling microscopy and spectroscopy (STM and STS) measurements of individual QDs,2-6 corroborating conclusions drawn from optical data.7-9 The good control over size, shape, and size distribution of such colloidal QDs enables one to assemble them into dense close-packed arrays, constituting “QD solids” or “supercrystals”. By varying the QD density in the assembly, one can follow the transition from a collection of noninteracting, practically isolated QDs, to the regime where bulk solid-state properties emerge as the interparticle distance decreases, due to electron delocalization and coupling between the electronic wavefunctions of neighboring QDs. Specifically, the QD band gap is expected to reduce toward the bulk value, long-range electronic energy transfer may take place, Anderson-like metal-insulator transition may be observed in transport measurements, and (in the limit of very dense and ordered arrays) the discrete QD levels should evolve into collective minibands. In very dense two-dimensional (2D) arrays the formation of minibands could be reflected as steps in the tunneling spectra, manifesting the constant density of states (DOS) associated with each sub-band. Additionally, the charging energies will reduce, due to the proximity between the QDs and to the change in the effective dielectric function. Some of these * To whom correspondence should be addressed. E-mail: milode@ vms.huji.ac.il. † Racah Institute of Physics. ‡ Department of Physical Chemistry. 10.1021/nl061410+ CCC: $33.50 Published on Web 09/19/2006
© 2006 American Chemical Society
phenomena were clearly reflected in both optical and transport measurements performed on 2D and 3D QD solids.10-14 However, for the system of InAs dots, such a study was not reported yet. This system is expected to exhibit strong collective phenomena on account of the very light effective mass of the electron leading to an exciton Bohr radius of about 30 nm, significantly larger than the 5.6 nm Bohr radius of the CdSe system. The aforementioned optical and transport measurements were macroscopic in nature, and thus the local microscopic variations of the electronic coupling between the QDs were not monitored. Such variations are expected to occur in realistic colloidal QD arrays. The size distribution of the QDs, although quite narrow in ensembles produced nowadays in many laboratories, hampers the formation of perfect translational-invariant QD arrays exhibiting long-range order. Furthermore, the inter-QD coupling should depend also on the local nature of the capping ligands and the specific facets involved in the interparticle junctions, factors that affect the distance between neighboring dots and the tunneling barrier heights. This may result in coexistence of localized and delocalized electronic states within a sample, in analogy with the case of disordered solids.11 Therefore, a local probe investigation of the electronic level structure of QD arrays is essential for the understanding of the process of electron delocalization in QD solids and the consequent appearance of bulklike properties. STS is particularly suitable for this purpose, since it can provide information on the local DOS with sub-nanometer resolution. This technique has been successfully applied in studies of individual semiconductor QDs2-5 and nanorods,15 and recently also of metal-semiconductor nanojunctions,16 manifesting the ability to map the local DOS
with high spatial resolution. Recently, while preparing this manuscript, Liljeroth et al. reported STS studies PbSe arrays, showing significant band gap reduction and level broadening compared to the isolated QDs.17 In this Letter we present STS measurements on 2D InAs assemblies that exhibit short-range order. The band gaps of QDs within the arrays are found to reduce, and the discrete levels usually broaden, with respect to the corresponding isolated QDs. We find spatial variations in the degree of these effects, where, in particular, they appear to be smaller for QDs positioned at the periphery of the assembly. Interestingly, the red shift of the electron (conduction band, CB) ground state is larger than that of the hole (valance band, VB) ground state, reflecting the much smaller effective mass of the electron compared to the hole in InAs. Comparison with both InAs and CdSe quantum rod arrays provides insight into the role of effective mass and Bohr radius on the appearance of collective phenomena in nanoparticle arrays. InAs QDs, 4.2 nm in diameter with size distribution of better than 10%, were prepared using a solution-phase pyrolitic reaction of organometallic precursors.9 The narrow size distribution is critical for the formation of arrays exhibiting at least short-range order. The arrays were formed by allowing a drop consisting of InAs QDs dissolved in a 75/25% toluene/methanol solution to slowly dry on a flat Au(111) film. Methanol, a nonsolvent in this case, tends to improve the order and density in the QD assembly. Some of the arrays were annealed in ultrahigh vacuum for 5 h at 120 °C in order to further improve their properties.10 The minimal interdot distance was limited by the presence of the organic ligands (trioctylphosphine, TOP, which are ∼1 nm long) that terminated the QDs’ surface (for the purpose of chemical and electrical passivation). Transmission electron microscopy (TEM) measurements performed on arrays deposited on a TEM grid (using the same procedure described above) showed that the inter-QD spacing is indeed around 1 nm. However, somewhat smaller distances were also observed, possibly due to bending of the ligands or the formation of an interpenetrating structure. We note that this result is consistent with ref 14, where the interdot spacing in closed packed CdSe QD arrays is reported to be ∼1.1 nm (measured using small-angle X-ray scattering). The samples were mounted in a homemade cryogenic STM that was cooled down to 4.2 K for data acquisition. In order to ensure thermal stability, He exchange gas was introduced into the preevacuated sample/STM head space. The tunneling spectra were acquired by positioning and stabilizing the STM tip over specific QDs at different locations within an assembly and, for comparison, also on isolated dots that could be found on the same sample. We would like to make a short comment regarding these spectroscopic measurements. As noted above, the QDs were deposited on gold substrates, with no linker molecules. Nevertheless, since the QDs were capped by ligands, a double barrier tunnel junction was formed, consisting of the tip-QD and QDsubstrate junctions. As a consequence of the voltage division between these two tunneling junctions, the measured band gap was larger than the real single-particle gap by about 10% 2202
Figure 1. (a) 230 × 230 nm2 STM topographic image of an assembly consisting of 4.2 nm diameter InAs QDs. A smaller scale image showing the degree of local order is shown in the inset. (b) STM image showing isolated QDs, 4.2 nm in diameter. (c) Three tunneling spectra acquired on QDs at different locations: the black curve on an isolated dot shown in (b), the blue curve on a QD located at the edge of the void marked by the black circle in (a) and the top red curve on a QD located within the assembly, inside the white circle in (a). The two upper curves exhibit a red shift of the CB edge with respect to the black spectrum, while the VB edge remains intact. The measured bandgaps (bottom to top) are 1.4, 1.35, and 1.15 eV.
(a detailed discussion can be found in ref 6). This factor, however, is not expected to vary much between measurements performed on the same sample, since care was taken not to change the STM bias and current settings (which determine the parameters of the tip-QD junction). Moreover, since all the assemblies were prepared using the same drop casting-drying procedure and under similar conditions, the QD-Au junction parameters, and consequently also the voltage division factor, should not vary much also between samples. This allows us to compare between spectra acquired at different locations on the same or on different samples. The annealing process did not yield a measurable change in the voltage division factor (for the same STM setting), as confirmed by comparing results obtained for single QDs on both types of samples. Figure 1 presents typical correlated topography-spectroscopy results acquired on arrays that were not annealed. The topographic image in Figure 1a shows that long-range order has not been achieved and that the assembly is interrupted Nano Lett., Vol. 6, No. 10, 2006
by voids (e.g., inside the black circle). Nonetheless, the QDs were densely (and locally close-) packed, as depicted by the inset that presents a small-scale topographic image. In some parts of the sample the QD density was much smaller, and scattered isolated dots were found, as shown by Figure 1b. In Figure 1c we present three tunneling spectra measured at three different types of locations. The lower (black) curve was acquired on the isolated dot encircled in 1b, and the measured band gap was Eg ∼ 1.40 eV. The spectrum exhibits tunneling into the discrete InAs electronic states along with single electron charging. In particular, the doublet at positive bias (around 0.8 eV) corresponds to the doubly (spin) degenerate 1Se (s-like) CB ground state. The three peaks at higher bias are attributed to the 1Pe (p-like) excited state, where the first (around 1.2 eV) is associated with tunneling into the 1Pe state under the condition that the 1Se shell is not fully charged (a detailed discussion of such a scenario can be found in ref 6). The middle (blue) curve was measured on a QD positioned at the rim of the assembly, namely, at the array-void interface marked by the black circle in Figure 1a. It is evident that the 1Se level is slightly shifted to lower energy while the valance-band ground state remained nearly intact, resulting in a reduction of the band gap by ∼50 meV. In addition, it appears that the CB level structure, in particular the 1Pe state, has been smeared. A further reduction of Eg, to ∼1.15 eV, takes place for QDs placed within the array, as demonstrated by the upper (red) spectrum acquired on a QD positioned inside the white circle marked in Figure 1a. Here too, the CB minimum redshifted while the position of VB edge remained unchanged. In addition, both VB and CB level structure appear to have undergone further smearing. In particular, we note that the 1Se single electron charging doublet has vanished. This could be attributed to a local change in the double barrier junction parameters to values for which merely resonant tunneling takes place (see, e.g., refs 3, 4, and 6). More probably, however, this observation is due to electron delocalization within the QD array, which is known to suppress the single electron tunneling effects, such as the Coulomb blockade and staircase. Additionally, the QDs’ charging energies are expected to diminish as the dots are brought closer together due to the consequent increase in their capacitance. This effect further contributes to the suppression of single electron charging effects in the tunneling spectra measured on our arrays. The effect of quenching of single electron charging effects was previously observed in STS measurements of metallic QD arrays.18,19 However, in these metallic systems, in contrast to our case, the tunneling spectra do not reveal a combination of both charging and quantized level-structure effects. The smaller band gap reduction that was observed consistently for QDs at the periphery of the assemblies compared to those located well within them is attributed to two factors. First, the number of nearest neighbors is smaller for QDs at the edges, a factor that acts to reduce the coupling-induced splitting of the conduction- and valance-band ground states (and other levels, of course), resulting in a smaller red-shift of the band gap. In a simple tight-binding model for a linear chain, square array, and cubic lattice, the bandwidth increases Nano Lett., Vol. 6, No. 10, 2006
Figure 2. Tunneling spectra focusing on the energy gap region. The upper two curves were acquired on a QD positioned within an assembly, showing red shifts of both CB and VB ground states relative to spectra measured on isolated dots, such as the lower curve.
linearly with the number of nearest neighbors. Second, the interdot spacing is somewhat larger at the edges (the arrays are locally more dilute there), thus reducing the electrical coupling between neighboring QDs. The data presented in Figure 1 depict the more common, weak interdot coupling scenario, where the band gap reduced by less than 0.25 eV and the VB edge hardly shifted. In some regions, however, larger reductions in the gap, of up to ∼0.4 eV, were detected. In that case, as portrayed by Figure 2, the VB ground state also red-shifted considerably, yet less than the CB edge. These larger shifts manifest stronger local inter-QD coupling and electron delocalization. This is possibly due to lower local density of the capping ligands, enabling ligands of neighboring QDs to form an interpenetrating structure and/or to bend, and thus to reduce the QD spatial separation. In an attempt to enhance the latter effect, we have annealed some of the arrays at 120 °C for 5 h in ultrahigh vacuum conditions. This procedure, however, did not yield any apparent improvement in the order of our arrays. Moreover, the tunneling spectra measured on the annealed arrays (see Figure 3) did not reveal further significant reduction of the band gap values compared to those corresponding to the upper two curves in Figure 2, namely, Eg was ∼1.0 eV. However, such gap values were the typical ones found in the annealed arrays (and gaps as small as 0.9 eV were also measured occasionally), in contrast to the situation of the nonannealed assemblies discussed above. Moreover, in some cases, as shown in Figure 3, the CB DOS exhibited a steplike structure over which traces of the discrete QD level spectrum were superimposed. Such spectra are consistent with the onset of a collective 2D level structure. We find this result quite surprising, since the typical interdot separation in our samples appears to be rather large for minibands to develop. Possibly, these 2D-like DOS structures are associated with collective levels spanning a few strongly coupled QDs and can be viewed as precursors of the formation of minibands. We would like to note here that collective minibands can develop also in assemblies that do not exhibit long-range order (such as ours). The existence of long-range order will naturally result in well-defined energy-level dispersion in k-space (lacking in disordered assemblies) to which, however, 2203
Figure 3. Tunneling spectra measured on an annealed assembly, exhibiting gaps of about 0.95 eV. The curves manifest the emergence of a 2D-like DOS at positive bias (conduction band) over which traces of the discrete states are superimposed (in particular in the two lower curves).
tunneling spectroscopy performed with STM is not very sensitive. The band gap value is the most direct measure for the degree of quantum confinement in the QDs. We shall use this criterion to estimate the loss of quantum confinement in our arrays, due to interdot coupling. The measured gap of the isolated QD (see Figure 1) was ∼1.4 eV, while for bulk InAs Eg ) 0.42 eV. Considering now the ∼10% voltage division induced enlargement of the measured band gap, we find that the confinement energy of QDs within the annealed array reduced considerably, from ∼0.85 eV to (typically) 0.45-0.5 eV in the annealed arrays. By and large, the gap reduction is much smaller in the arrays that were not annealed, where typically the confinement energy was found to be ∼0.65 eV. The annealing process thus clearly promoted electron delocalization. The band gap reduction that we found seems to be surprisingly large, considering the relatively large inter-QD separation of at least 1 nm, determined by the length of the capping ligands. Our calculation for a system of a pair of coupled QDs, as well as calculations performed by other groups,20-22 yield a much smaller estimate for the gap red-shift, on the order of a few tens of millielectronvolts. It may well be that the capping ligands provide routes for charge-carrier hopping between neighboring dots, thus enhancing the degree of electron delocalization. It is also possible that the confinement potential is smaller for dots in dense arrays compared to the isolated QDs. Both effects, which could also aid the emergence of a 2D level structure, were not considered in the previous calculations. We would like now to compare our results with previous data, obtained using various “macroscopic” optical spectroscopy techniques. Artemyev et al. reported absorption and photoluminescence measurements on three-dimensional CdSe QD assemblies as a function of density.11 The absorption edge of the small dots studied red-shifted systematically with increased QD concentration and the spectra evolved from those exhibiting discrete absorption peaks to smooth nearly structureless curves. Specifically, upon changing the average interparticle distance from above 1 to 0.6 nm, the absorption 2204
onset monotonously shifted toward lower energies by up to ∼300 meV. This behavior was attributed by the authors to electron delocalization and the consequent evolution of collective QD-solid states. The red shift measured in that work is comparable to our observation, although one should keep in mind that the QDs studied by Artemyev et al. were much smaller than ours; thus larger wavefunction leakage is expected. This factor is compensated, however, by the smaller electron effective mass in InAs (0.023m0) relative to CdSe (0.14m0), possibly giving rise to the comparable results. Liljeroth et al. reported even larger (relative) reduction of quantum confinement in annealed PbSe arrays.17 This is consistent with the fact that in this system both electrons and holes have small effective masses (both smaller than 0.08m0),23 and not only the electron as in InAs. Finally, we should mention that, in contrast to our data and the works described above, Kim et al. found no evidence for interdot wavefunction coupling or for a systematic reduction of the band gap in CdSe QD assemblies under elevated pressure.24 The reason for this discrepancy is not yet clear to us. Possibly, the pressure-induced modification of the single QD spectra masked the collective array effect. Following the discussion above, it appears that the main factors that govern the band gap reduction in arrays are the effective mass of the charge carriers and the local arrangement of the QDs, in particular the number of and distance between nearest neighbors. To further test this conclusion we have investigated, using STS, InAs and CdSe nanorods assemblies prepared using a similar deposition procedure as described above for the QDs (the preparation of these nanorods is described in refs 25 and 15, respectively). Due to their elongated shape, the effectiVe number of nearest neighbors in 2D nanorod arrays (when good local alignment of the rods exists) is smaller compared to the case of close packed QD arrays. This number is typically two in the case of quasi-1D nanorods (where the excitonic Bohr radius, aB, is smaller than the nanorods length)26 and may be four in the opposite 0D case (including now the apexes), compared to six in close-packed QD arrays. On the other hand, the interparticle electronic coupling may be stronger along the side of the nanorods due to the larger contact area. We present here data for InAs nanorods, ∼4 nm in diameter and ∼15 nm long (where aB ∼ 34 nm), and CdSe rods, ∼4 nm in diameter and ∼40 nm long (aB ∼ 5.7 nm), constituting 0D and quasi-1D systems, respectively.26 The blue (lower) spectrum in Figure 4a was measured on an isolated CdSe nanorod, exhibiting a band gap of 2.4 eV. The red (top) curve is typical of those measured on CdSe nanorods in regions where the nanorods are locally well aligned and “close packed” (depicted by the STM image shown in the inset). The assemblies in rods tend to show side to side arrangements, due to stronger van der Waals attraction. These regions show a small red-shift of the band gap, of about 50 meV. Figure 4b presents similar measurements for InAs nanorods, and the observed corresponding band gap reduction within the array is much larger, ∼300 meV, from 1.2 to 0.9 eV. Note also that, as discussed above for the InAs QDs, here too the reduction takes place mainly Nano Lett., Vol. 6, No. 10, 2006
effects were more significant in InAs QD arrays that were vacuum-annealed, a process that could yield reduced inter-QD separation due to rearrangement of the capping ligands. In these assemblies we have also found evidence for the emergence of a 2D-like level structure, possibly heralding the formation of 2D minibands in the arrays. Our spatially resolved STS measurements revealed fluctuations in the degree of coupling from one QD to another in the assembly. Such fluctuations are expected to reduce, but obviously not to completely vanish, in apparently ordered arrays due to the inherent variations in the inter-QD junction parameters. Acknowledgment. We thank D. Azulay and H. Levy for their help in the calculation of the energy-gap shift. This research was supported in part by the Israel Science Foundation Center of Excellence program, the Israel-German DIP program, and the European Union SA-NANO program. References
Figure 4. (a) Tunneling spectra acquired on two CdSe nanorods, ∼4 nm in diameter and 40 nm long, one isolated (blue curve) and one within an array (red curve). The inset shows a STM topographic image of part of the array where the red curve was acquired. (b) The same, but for InAs nanorods ∼4 nm in diameter and 15 nm long. The band gap reduction within the array compared to the isolated nanorods is much larger for InAs.
via the red-shift of the conduction-band ground state. The larger band gap reduction observed for the InAs system is obviously due to the significantly lower electron effective mass compared to CdSe. Interestingly, the band gap reductions observed for the InAs QDs within the QD arrays were typically somewhat larger than those observed in the nanorod arrays. This may be due to the effect of number of nearest neighbors, as discussed above. In summary, there are three main factors governing the band gap reduction and collective electronic states in nanoparticle arrays: The effective mass of the charge carriers, the distance between nearest neighbors, and the corresponding coordination number. We have observed a pronounced reduction of the band gap of InAs QDs within dense assemblies, indicating electron delocalization, namely, coupling between the electronic wavefunctions of neighboring QDs. This effect was larger for QDs within the array compared to those at the edges, where the number of nearest neighbors is smaller. The red shift in the CB of the InAs QD arrays was significantly larger than that of the VB, consistent with the very light effective mass of the electron. InAs nanorod arrays also show a decreased gap, mainly due to a red shift of the CB, corroborating the above result, while CdSe nanorod arrays exhibited much lower reduction in Eg in light of the more localized nature of the carriers. These collective Nano Lett., Vol. 6, No. 10, 2006
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