Direct Evaluation of the Quantum Confinement Effect in Single Isolated

Aug 14, 2015 - Department of Chemistry, University of Alberta, 11227 Saskatchewan Drive NW, Edmonton, Alberta T6G 2G2, Canada. § NRC-National ... Ban...
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Direct Evaluation of the Quantum Confinement Effect in Single Isolated Ge Nanocrystals Oded Millo,*,† Isacc Balberg,*,† Doron Azulay,† Tapas K. Purkait,‡ Anindya K. Swarnakar,‡ Eric Rivard,‡ and Jonathan G. C. Veinot*,‡,§ †

Racah Institute of Physics and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Jerusalem 91904, Israel ‡ Department of Chemistry, University of Alberta, 11227 Saskatchewan Drive NW, Edmonton, Alberta T6G 2G2, Canada § NRC-National Institute for Nanotechnology, 11421 Saskatchewan Drive NW, Edmonton, Alberta T6G 2M9, Canada S Supporting Information *

ABSTRACT: To address the yet open question regarding the nature of quantum confinement in Ge nanocrystals (Ge NCs) we employed scanning tunneling spectroscopy to monitor the electronic structure of individual isolated Ge NCs as a function of their size. The (single-particle) band gaps extracted from the tunneling spectra increase monotonically with decreasing nanocrystal size, irrespective of the capping ligands, manifesting the effect of quantum confinement. Band-gap widening of ∼1 eV with respect to the bulk value was observed for Ge-NCs 3 nm in diameter. The picture emerging from comparison with theoretical calculations and other experimental results is discussed.

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tigations19,20 aimed at evaluating NC size-induced changes of the Ge-NC band gap have not yet provided a quantitative determination and even not some agreement as to the influences of QC.7,21−23 The vast number of studies examining the optical properties of Ge NCs point to the fact that common experimental methods such as photoluminescence (PL)24 or absorption23 are not adequate for conclusively evaluating the effects of QC in nanomaterials based on group-IV elements.7 Deficiencies of these methods arise because of known uncertainties associated with interpreting optical data (e.g., the initial and final levels involved in the optical process and the extrapolation of the optical absorption tail), complexities, and influences of NC surface chemistry as well as material purity. Of particular note, the role of surface-bonded species and defects remains a longstanding controversy dating back to the early studies of the optical response of Si NCs25 and later investigations of Ge NCs.17,26 These species can contribute to the NC optical transitions and compete with band-gap-based properties influenced by QC. Challenges associated with the impact of surface states and defects are more pronounced for Ge NCs compared with their Si counterparts because of ill-defined surface chemistry and typically complex-defective interfaces between the Ge NCs and the surrounding oxides.17,27 The fact

he most notable physical property of semiconductor nanocrystals (NCs) is the quantum confinement (QC) effect, which manifests itself by the widening of the fundamental band gap of the material upon decreasing NC size.1 The wide-ranging interest in these quantum-confined systems relates to the special mesoscopic physics that governs their properties as well as the various associated possible electronic2,3 and optoelectronic4,5 applications. Of the many NC−semiconductor systems that have been investigated in the context of QC, group-IV elements are among the most widely studied.6,7 From a fundamental viewpoint, interest in this class of materials arises mainly because the indirect band gaps of Si and Ge preclude a straightforward understanding of the observed relatively strong photoluminescence arising from associated NCs.8 From a more practical point of view, NCs made up of these elements are compatible with the robust microelectronics industry upon which much of modern technology is based while also being biologically and environmentally benign. In this work, we follow the widening of the single-particle (rather than excitonic) band gap of individual Ge NCs as a function of their size. The motivation of the present study is 2fold: First, the QC effect in the Ge NCs is expected9,10 to be much more dramatic than what is observed for its congener Si because of the smaller single particle (i.e., electrons and holes) and excitonic effective masses and the larger dielectric constant of Ge. Second, until quite recently11−14 (see later) many optical,7,15,16 quasi-optical,17,18 and other experimental inves© XXXX American Chemical Society

Received: July 19, 2015 Accepted: August 14, 2015

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Figure 1. (a) Scheme of the measurement configuration. The STM tip is positioned above a ligand-capped Ge NC placed on a flame-annealed Au(111) film, forming a double-barrier tunnel junction configuration. (b) 300 × 300 nm2 topographic image of a flame-annealed gold film after NC deposition, in an area free of NCs. The atomic steps of the Au film can be seen. (c) Bright-field TEM image of an ensemble of 5.3 nm (average) Ge NCs, with an STM image of a single NC from this batch shown at the lower-left corner. (d) STM image showing a group of Ge NCs deposited on a gold substrate. The NCs were taken from a sample with TEM-determined average NC size of 10 nm. Cross sections taken along the lines drawn in the image are presented in the lower left corner. Applying the procedure explained in the text, the NC presented by the blue curve is estimated to be 10 nm in size, whereas the other is of size 9 nm.

corresponding data as quantitatively general. Hence, an independent nonoptical measurement on single isolated NCs is necessary for bringing this subject to a close. In this work we aim at doing so and by that to establish a well-based experimental evaluation of the QC effect in Ge NCs. The previously described considerations raise an important question of how to reliably evaluate the QC induced widening of the band gap of the Ge NCs. To overcome the two major difficulties previously discussed, (i.e., measurements of ensembles and the indirect determination of the band gap by optical means), we took a synergetic approach that is based on the study of individual-isolated Ge NCs and a direct measurement of the fundamental band gap. So far, individual isolated Ge NCs (though within an SiO2 matrix) have been investigated using optical measurements,45 while direct measurements of the gap were carried out on ensembles using scanning tunneling microscopy and spectroscopy (STM and STS).46,47 Because these studies address the previously mentioned challenges independently, uncertainty regarding quantitative conclusions remains. To date, most of the studies considering QC in Ge NCs were carried out on particles embedded in (or in contact with) matrices, revealing, unfortunately, Ge-related defect states that masked the manifestation of QC.16,21 It is not surprising then that surface passivation of Ge NCs by ligands has drawn much attention;48 however, to date its impact on QC has not been addressed. For example, a previous attempt to utilize the ligandcapped Ge-NCs was based on the quasi-optical measurement of the surface photovoltage,18 but the extrapolation of the spectra

that most of the optical studies to date have focused on the properties of ensembles of matrix-embedded Ge NCs21,26,28 adjacent to an oxidized substrate24,29−31 or nonisolated Ge NCs in contact with other NCs27,32−34 made the differentiation between the impact of QC and the presence of the resulting defects or the possible narrowing of the band gap due to neighbors35,36 extremely difficult. Indeed, there is no agreement even on the measured spectra between the numerous optical studies. Commonly, size-independent PL within the energy range of 2.1 to 2.3 eV is observed,37−39 and even at ∼2.6 eV.40 This type of optical response has been later attributed to types of surface or matrix defects.24,26,40,41 There is another complication related to the optical response from NC ensembles: The size distribution of the luminescent NCs does not necessarily overlap with the entire size distribution in the ensemble. This is primarily because nonradiative transitions may have different size dependence than the radiative ones, as previously discussed for both Si8 and Ge42,43 NCs. To our knowledge, until quite recently, there was only one44 report that appeared to show size-dependent PL from Ge-NCs embedded in SiO2 associated with QC but was not repeated on the same type of system; however, the recent PL and absorption-spectroscopy studies11−14 of colloidal Ge NCs appear to support those data, in particular, exhibiting the QC effect, and yield quite convincing results that are even amenable14 for comparison with theory. However, the previously mentioned disadvantages of the PL measurements and the fact that those works were not carried out on single isolated NCs, do not enable us to consider the 3397

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above the band gap edge to ensure significant tunneling probability through the DBTJ. For acquiring the dI/dV−V tunneling spectra, proportional to the local density of states (DOS), Vs was reduced (after positioning the tip above the NC) to ∼0.95 V to be more sensitive to the gap edge. For each NC, the set-current, Is, was then reduced to the lowest value that allowed acquisition of smooth tunneling spectra, Is ≅ 0.1 to 0.3 nA. It should be noted that STM images of single NCs (such as those presented in Figures 1c,d) do not lend themselves to accurate determination of NC dimensions because of the convolution with the STM tip and the different DOS of the NC compared with its surroundings. Therefore, we have taken the most abundant NC size determined from the transmission electron microscopy (TEM) measurements to be the size of the most abundant NCs observed in the STM images of samples prepared from the same synthetic batch. Importantly, relative NC size distributions extracted from the STM measurements for a given sample correlated well with that determined from the corresponding TEM data. This good correlation also allowed us to confidently determine the sizes of different NCs within a single STM image (Figure 1d). Figure 2 presents three tunneling spectra measured on individual-isolated dodecyl-capped Ge NCs of three different

for the derivation of a quantitative estimate of the band gap shift had (as is typical for that method) the disadvantage of inaccuracy. In addition, that work had the disadvantages of reliance on ensembles of NCs that are subjected to the previously mentioned environmental27,35,36 and averaging45 effects. In the present work we applied STM and STS to systematically study the size and capping-ligand dependencies of the energy gap of isolated colloidal Ge NCs. The main advantage of this approach over optical methods is that in STS the conduction-band (CB) and valence-band (VB) states are monitored independently, allowing for a direct evaluation of the single-particle (rather than excitonic) band gap.49 This technique also allows the monitoring of doping effects that are manifested by shifts of the band edges with respect to the Fermi level.50 An additional benefit of this methodology is that NCs are addressed individually, enabling a direct size-spectrum correlation, thus avoiding ambiguities stemming from ensemble averaging. Indeed, STM/STS has proven to be very effective in probing the electronic properties of single colloidal semiconductor NCs of various types, albeit the studies so far focused mainly on NCs comprising groups II−VI, IV−VI, and III−V semiconductors.35,49−53 Only recently we applied it for individual group-IV colloidal Si-NCs, revealing the QC effect.54 The valuable insight gained from this latter work motivated us to perform STS measurements on individual, well-isolated, colloidal Ge NCs with the aim to shed light on the allimportant question of the QC effect in this system and its possible dependence on the type of capping ligands. As previously noted, STS studies of Ge NCs have already been reported;46,47 however, these studies involved densely packed arrays of apparently touching NCs. Ge NCs studied here possessed dimensions in the range of ∼3.0 to 10.5 nm in size and were terminated by three types of organic ligands: dodecyl, 3-dimethylamino-1-propyne, and 2dodecanone. The synthesis of these nanoparticles is briefly described in the Experimental Methods and in refs 40 and 55. Samples for the STM measurements (illustrated in Figure 1a) were prepared by drop-casting toluene (dodecyl and 2decanone terminated NCs) or methanol (3-dimethylamino-1propyne-capped NCs) NC solutions onto atomically flat flameannealed Au substrates, for which the atomic steps could be revealed in the STM images even after solution deposition. (See Figure 1b.) All of the measurements were performed at room temperature using Pt−Ir tips. Tunneling current−voltage (I−V) characteristics were acquired after positioning the STM tip above individual NCs, realizing a double-barrier tunnel junction (DBTJ) configuration49 (as depicted by Figure 1a) and momentarily disabling the feedback loop. Care was taken to retract the tip as far as possible from the NC so that the applied tip−substrate bias would fall mainly on the tip−NC junction rather than on the NC−substrate junction, whose properties (capacitance and tunneling resistance) are determined by the layer of organic capping ligands that cannot be modified during the STM measurement. This procedure significantly reduces the effect of apparent broadening of the measured band gap due to the voltage division between the two tunnel junctions in the DBTJ. Nevertheless, the measured band gaps are still estimated to be larger than the real NC gaps by a factor η = 1 + C1/C2 ≈ 5−10%, where C1 and C2 are the capacitances of the tip−NC and NC−substrate, respectively.49,52,56 The topographic images were measured with bias set values in the range Vs ≈ 1.5 to 1.8 V, which is well

Figure 2. Tunneling spectra measured on dodecyl-functionalized Ge NCs of various sizes, as indicated. The quantum-confinement effect is clearly seen via the enlargement of the gap between valence-band (VB) and conduction-band (CB) states with decreasing NC size. The blue curve (5.3 nm NC) was measured on the QD shown in Figure 1c. The inset presents an I−V characteristics acquired aside of the NCs, showing no gap.

diameters ∼3.0, 5.3, and 10.0 nm. All spectra exhibit a gap in the DOS around zero bias, which was absent in spectra taken directly on the Au(111) substrate aside of the NCs (inset of Figure 2). The tunneling spectra clearly manifest the effect of QC on the band gap; it increases with diminishing NC size. The spectra acquired for 3-dimethylamino-1-propyne- (Figure 3) and 2-dodecanone- (Figure 4) functionalized Ge NCs follow the same trend. The former were measured on 5.5 nm NCs, and the extracted band gaps are slightly smaller than those found for the dodecyl-capped 5.3 nm NCs, while the latter were measured on 7.5 and 8.0 nm NCs and exhibit even smaller gaps. (See Figure 5.) The fact that the band gaps of Ge NCs functionalized with 3-dimethylamino-1-propyne and 2-dodeca3398

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Figure 5. Band gaps of Ge NCs as a function of NC size. The vertical error bars represent both the distribution of measured gap values and the uncertainty in determining the gap due to broadening of the measured ground-state level. The horizontal error bars reflect the uncertainty in NC size determination due to tip convolution and DOS effects discussed in the text. Black, blue, and green symbols correspond, respectively, to dodecyl-, 3-dimethylamino-1-propyne-, and 2-dodecanone-functionalized Ge-NCs. The red line was calculated using equation 1 in ref 57. The blue dashed line represents the band gap of bulk Ge.

Figure 3. Two tunneling spectra measured on two different 3dimethylamino-1-propyne-capped Ge NCs, 5.5 nm in diameter, shown in the insets.

of similar sizes, various types of behaviors: the chemical potential was positioned nearly at the midgap or slightly shifted toward either of the band-edges. (See Figures 2 and 4 and Figures S2−S4.) The QC effect in Ge NCs is clearly manifested in Figure 5, where we summarize the energy gaps that we obtained as a function of NC size. The gap values were determined directly from the dI/dV−V spectra by considering the energetic separation between two points, one on the positive bias side and the other on the negative bias side of each spectrum, corresponding to CB and VB states, respectively. Each point is taken as the mid value between the first peak (or shoulder) and the onset of detectable DOS on the corresponding side. Using this method, the band gaps extracted from the curves presented in Figure 1 are 1.65 (black curve), 1.37 (blue), and 1.05 eV (red). The error bars in Figure 5 reflect both the uncertainty stemming from this procedure of energy-gap determination (which attempts to account for possible level-broadening effects) and the (rather small, ±50 meV) variations in gap values among different NCs of the same measured diameter (typically 3 to 5 for each data point in Figure 5). The red curve in Figure 5 was calculated using the size-dependent VB- and CB-edge shifts derived by Niquet et al. from an sp3 tightbinding model, eq 1 in ref 57, taking the band gap of bulk Ge to be 0.66 eV. Our experimentally determined band gaps (Figure 5, data points) show a similar size dependence to that predicted by the tight-binding model for NC of size larger than 5 nm; however, a weaker size dependence in the diameter range between 3 and 4.5 nm is noted. This latter effect may result from the larger leakage of electron and hole wave functions in the smaller NCs due to reduced effective potential barrier heights they experience; this would be expected to relax the impact of QC. In addition, we note that all (except for the smallest NC) experimental gaps are larger than the theoretical prediction. This may be partly due to the aforementioned effect of voltage division, which is estimated to yield a 5−10% enlargement of the measured gap with respect to the real gap.49,56 The corresponding apparent band gap enlargement

Figure 4. Tunneling spectra measured on two neighboring 2dedaconane-functionalized Ge NCs, 7.5 and 8 nm in diameter. The inset shows a topographic cross-section taken along the line connecting the two NCs where the arrows point to the corresponding spectra. Evidently, the band gap of the 7.5 nm NC is larger than that of the 8 nm one.

none fit the behavior of the dodecyl-functionalized ones (see Figure 5), and the very similar band gaps of the above 5.5 and 5.3 nm NCs functionalized by different ligands suggests that these type of ligands do not significantly affect the Ge NC band gap. This is consistent with our previous finding54 for Si NCs (it is not very likely that all three types of ligands used here have the same effect on the band gap); however, the ligands can affect the relative position of the Fermi level (chemical potential) within the gap.54 We note in passing that the spectra presented in Figure 3 suggest that surface functionalization with 3-dimethylamino-1-propyne has an effect akin to ntype doping, as the chemical potential (zero-bias) is evidently shifted toward the CB edge. This behavior was observed for all such Ge-NCs (additional spectra are presented in Figure S1 in the Supporting Information), while data for other capping ligands were not as systematic in that respect, showing, for NCs 3399

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The Journal of Physical Chemistry Letters factor (η = 1 + C1/C2) is expected to vary with NC size but, unfortunately, in a way that is not easily predicted. In addition to the size-dependent geometrical factor that should directly affect both C1 and C2, there may also be an indirect effect, as follows. The “leak out” of electron and hole wave functions from the NC is expected to increase with decreased NC size. This would affect the tunneling rates in both junctions and thus the tip−NC distance needed to achieve the specific set current (obviously affecting C1). Our results for the band gaps can be considered to be in good agreement with those of Nakamura et al.,46 as they also showed good agreement with the calculations57 of Niquet et al.; however, the spread in their results is quite larger than ours (by more than twice in some cases). This is probably due to two main reasons. First, the much better control over the tunnel junction parameters in our experimental procedure results in smaller spread of voltage division factor and the corresponding apparent band gap enlargement. We note that this effect has not been considered in previous publications46,47 reporting STS studies of Ge NCs. Second, as previously noted, proximity effects due to neighboring NCs that tend to reduce the gaps are eliminated in our experiment. We also wish to point out that because of the electron−hole Coulomb interaction, the reported excitonic band gaps that were determined from absorption and PL measurements are much smaller than those determined by STS. For example, Lee et al. found11 gaps around 1.08 to 1.09 eV for 4 nm NCs, much smaller than our STS-extracted gap value of ∼1.5 eV (see Figure 5), and similar difference holds also with respect to optical data presented in refs 12 and 13. Comparing the PL and STS data may provide then the first experimental estimate for this interaction and for the effective masses involved in these two manifestations of the QC effect in Ge NCs. With that respect it is interesting to note that while the tight-binding model fits well our STS data over the whole range of NC sizes (3 to 10.5 nm), Robel et al. show14 that it accounts well for their optical data measured11 on small (5 nm), measured by other groups,12,13 is well described by the effective mass approximation.14 The basic agreement between our results and those of Nakamura et al.46 provides a firm experimental basis for the discussion of QC in Ge NCs. Nesher et al. concluded58 on theoretical basis that the empirical-pseudopotential59 and tightbinding57 results are the most likely to be amenable. Our STS results in Figure 5 lend support to this view. In fact, the good agreement with the tight-binding theory (as well as with the empirical-pseudopotential model and calculations based on time-dependent local density approximation58 extrapolated to the NC size regime we studied) confirms the predicted indirect nature of the band gap in Ge NCs persists.57 Consequently, the observation of PL in these systems will depend on the efficiency of the nonradiative transitions.8 While it is well established that the strong confinement view has overestimated the QC effect in Ge NCs, the question of whether the band gap in Ge NCs Eg(Ge) will eventually become larger than the band gap of Si NCs Eg(Si) with decreasing NC size remains unanswered. It was suggested, based on theoretical grounds, that such a crossover will not take place;58 however, comparison of our Si-NC STS results54 and the present results involving Ge NCs suggest that this is possible because the confinement energy Eg−Eg0 (where Eg0 is the value of the bulk band gap) is larger for the Ge NCs. This is well-illustrated for 3 nm NCs, where this energy is 1 (±0.1) eV

for Ge, while it is 0.8 (±0.1) eV for Si. Hence, while quite smaller than initially claimed,58,60 the advantages previously mentioned concerning the QC in Ge NCs compared their Si counterparts seem to be justified. This is mainly in the potentially larger band gap interval for the same NC size range that can be achieved in comparison with Si NCs. In summary, our STS data acquired from isolated individual Ge NCs clearly manifest the effects of quantum confinement. The band gap increases monotonically from 0.97 to 1.67 eV with diminishing NC size in the measured range of 10.5 to 3.0 nm, achieving ∼1 eV widening with respect to the bulk gap value for the smallest NCs studied. The three capping ligands investigated in the present study, dodecyl, 3-dimethylamino-1propyne, and 2-dodecanone, appear to have no measurable effect on the band gap, indicating they act merely as surfacepassivating agents and do not affect the NC interior electrical properties. This further suggests that the present results provide an amenable quantitative evaluation of the quantum confinement in individual isolated Ge NCs.

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EXPERIMENTAL METHODS Ge NCs, 3 to 10.5 nm in diameter and having dodecyl surface termination, were synthesized using procedures developed in our laboratory in which Ph3PCMe2·GeH2·BH3 was decomposed thermally in the presence of 1-dodecene by applying microwave irradiation or hot-injection methods.40 We also studied ∼5.5 nm (average diameter) Ge-NCs with peripheral NMe2 surface groups that were prepared by microwave irradiation of Ph3PCMe2·GeH2·BH3 in the presence of 3dimethylamino-1-propyne as a capping agent.40,55 In addition, 8 nm (average size) 2-dodecanone-capped Ge-NCs were also investigated. These dodecanone-capped particles were prepared by microwave heating for 1 h at 190 °C a mixture of Ph3PCMe2·GeH2·BH3 precursor (30 mg, 0.076 mmol) and 5 mL of 2-dodecanone sealed in a microwave vial using a previously used workup procedure.37 Following the reaction, a mixture of toluene/methanol (1:4; 40 mL) was added, and the resulting red solid was recovered by centrifugation at 14 000 rpm. The supernatant was decanted and discarded. The pellet was redispersed in 40 mL of toluene/methanol (1:4) mixture with sonication. The cloudy mixture was centrifuged at 14 000 rpm to yield a red solid, and the procedure was repeated two more times to afford the Ge-NCs as a red solid. The purified solid functionalized Ge NCs were dispersed in appropriate solvents (hydrophilic 3-dimethylamino-1-propyne functionalized NCs in 100% ethanol and hydrophobic dodecyl- and dodecanone-functionalized NCs in toluene), and PL emission spectra of functionalized Ge NCs were taken using Carry Eclipse spectrophotometer at various excitation wavelengths (300 to 600 nm). Interestingly, the hydrophilic 3-dimethylamino-1-propyne-capped Ge-NCs showed a blue PL in 100% ethanol that cannot be associated with band gap emission, whereas the hydrophobic dodecyl- and dodecanone-functionalized NCs did not show any detectable PL.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.5b01541. Additional STS data, as referenced in the text. (PDF) 3400

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS O.M and I.B. acknowledge support from the Israel Science Foundation, the Harry de Jur Chair in Applied Science (O.M.) and the Enrique Berman Chair in Solar Energy Research (I.B.). The Veinot group acknowledges continued generous funding from the Natural Sciences and Engineering Research Council of Canada (NSERC), Canada Foundation for Innovation (CFI), and Alberta Science and Research Investment Program (ASRIP). E.R. and A.K.S. thank NSERC, CFI, and AlbertaInnovates Technology-Futures for support.

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