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Determination of the Electronic Energy Levels of Colloidal Nanocrystals using Field-Effect Transistors and Ab-Initio Calculations

Satria Zulkarnaen Bisri , Elena Degoli , Nicola Spallanzani , Gopi Krishnan , Bart Jan Kooi , Corneliu Ghica , Maksym Yarema , Wolfgang Heiss , Olivia Pulci , Stefano Ossicini ,* and Maria Antonietta Loi*

Dr. S. Z. Bisri, [+] Prof. M. A. Loi Photophysics and Optoelectronics Group Zernike Institute for Advanced Materials University of Groningen, Nijenborgh 4 Groningen, 9747 AG , The Netherlands E-mail: m.a.loi@rug.nl Dr. E. Degoli, [+] Prof. S. Ossicini Dipartimento di Scienze e Metodi dell`Ingegneria Università degli Studi di Modena e Reggio Emilia Via Amendola 2 Padiglione Morselli, Reggio Emilia I-42100 , Italy E-mail: stefano.ossicini@unimore.it Dr. N. Spallanzani, Prof. O. Pulci ETSF and Dipartimento di Fisica Università degli Studi di Roma Tor Vergata Via della Ricerca Scientifi ca 1 Rome I-00133 , Italy Dr. G. Krishnan, Prof. B. J. Kooi Nanostructured Materials and Interfaces Group Zernike Institute for Advanced Materials University of Groningen, Nijenborgh 4 Groningen, 9747 AG , The Netherlands Dr. C. Ghica National Institute for Materials Physics PO Box MG-7 , Bucharest-Magurele 0770125 , Romania Dr. M. Yarema, Prof. W. Heiss Institute for Semiconductor and Solid State Physics University of Linz Allenbergerstrasse 69 , Linz 4040 , Austria

DOI: 10.1002/adma.201400660

materials for exploring new concepts for increasing the photo-voltaic effi ciency based on multiple exciton generation or car-rier multiplication. [ 2–5 ]

In the case of a narrow bandgap semiconductor such as PbS, the optical bandgap E opt gap , determined from the fi rst absorption peak maxima, can be enlarged continuously from the bulk value of about 0.4 up to 1.5 eV, depending on the diameter of the NCs, [ 6–10 ] thus offering very interesting perspec-tives for light detection [ 11–14 ] and light harvesting. [ 7,8,11,15–22 ] In particular in the last case, the separation of electron and hole after photoexcitation is a necessary process. This separation has been attempted with the injection of photoexcited electrons from PbS onto mesoporous SiO 2 and TiO 2 fi lms, [ 15–17,19,20 ] TiO 2 nanoparticles, [ 8,23 ] C 60, [ 18 ] and fullerene derivatives. [ 9,12 ] In all these cases, the NCs must form a type-II heterostructure with the other material. Thus, it is of fundamental importance to control the energy alignment of the NC’s electronic bandgap with respect to that of the other semiconductor composing the heterojunction. This knowledge will allow tailoring the com-ponents of optoelectronic and photovoltaic devices avoiding the trial and error approach. However, this is not a simple task since these energies depend not only on the material, but also on size, shape, and capping agents, which can all introduce shifts in their position.

To date, precise measurements of electronic energy levels in semiconductor materials, including colloidal NCs are extremely challenging. For colloidal semiconductors in par-ticular, the current state-of-the-art methods have many limi-tations, which are aggravated by the presence of ligands on their surface. Ultraviolet photoemission spectroscopy (UPS) for the measurement of the NC’s highest occupied orbital (HOMO), [ 10,18,24–26 ] and inverse photoemission spectroscopy (IPES) for the measurement of the NC’s lowest unoccupied orbital (LUMO), [ 25 ] are rather imprecise in this case. A sim-ilar situation appears for cyclic voltammetry, [ 8,27,28 ] and the related cumbersome derivation from tunneling conductance spectra. [ 29–31 ]

While in the case of CdSe, [ 27,28 ] InAs, [ 29,30 ] and Si NCs, [ 24,31 ] both HOMO energy (through the ionization potential ( IP , HOMO = – IP )) and LUMO energy (through the electron affi nity ( EA , LUMO = – EA )), and thus the electronic (or quasi-particle) bandgap E qp gap = IP – EA = LUMO – HOMO, have been experi-mentally determined using the above mentioned methods. For PbS NCs, only either IP , [ 10 ] or EA , [ 8 ] has been measured. Subse-quently, the corresponding EA or IP have been calculated either

Inorganic nanoparticles, such as colloidal semiconductor nanocrystals (NCs), are of great interest for their physical properties and for use in device applications, because of their remarkably broad absorption spectra (extending in some cases till the mid-infrared), and their high stability. [ 1 ] In col-loidal NCs, the surface is passivated with a shell of organic molecules coordinated to the surface allowing an easy disper-sion of the material in common solvents and a very precise control of their dimensions during synthesis. Carrier confi ne-ment inside semiconducting NCs has a direct effect on the color of the emitted and absorbed light, with the smaller crys-tals having a wider energy bandgap than the larger ones. This large tunability of their optical properties makes colloidal NCs highly interesting for photovoltaic and optoelectronic device applications. Moreover, semiconducting NCs are promising

[+] These authors contribute equally toward this manuscript.

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ON by EA = IP – E qp gap , or by IP = EA + E qp gap , choosing different

approximations for the electronic bandgap. In this work, we investigate the absolute energy of the

LUMO and HOMO energy states, and consequently the elec-tronic bandgap values, for PbS NCs of different sizes, through a combined experimental and theoretical effort. The experi-mental method relies on the measurement of ambipolar fi eld-effect transistors by using an ionic-liquid-based ion-gel gate. [ 32–36 ] This represents the fi rst successful application of this method to an array of fully quantum-confi ned systems. This method does not only allow the determination of the bandgap but also the higher energy levels of the NC array, which are characterized by slope variation (going true plateau) in the transfer characteristics. Our experimental results are directly compared with results obtained with advanced ab-initio calcula-tions, performed with density functional theory (DFT) using a fully relativistic approach, which allow a direct determination of absolute energy levels. The agreement between measured and calculated energy values is excellent. Finally, this method is very general and easily applicable to all colloidal semiconductors and quantum-confi ned solids.

As stated above, the determination of the NCs’ electronic bandgap requires, with high precision, the knowledge of the absolute position of both the HOMO and LUMO of the NCs with respect to the vacuum, i.e., the IP and the EA , as function of the NCs’ size. The difference between IP and EA gives the E qp gap , the electronic or quasi-particle bandgap, which is sub-stantially different from the optical bandgap E opt gap , because the latter also includes the electron-hole interaction. Several approx-imated approaches to determine the electronic gap have been proposed in the literature of the past few years. Hyun et al. [ 8 ] performed cyclic voltammetry on PbS quantum dots of different diameters (from 2.9 to 6.6 nm) and determined the absolute position of the LUMO. The HOMO was then calcu-lated through subtraction from the LUMO, which is not the true E qp gap , but the optical bandgap E opt gap determined by the fi rst absorption maximum. Consequently, the HOMO position is overestimated.

Jasieniak et al. have determined the absolute position of the HOMO for PbS nanoparticles with diameters ranging from 2.81 to 8.45 nm by using photoelectron spectroscopy in air (PESA). [ 10 ] Then, the LUMO was calculated by adding to the HOMO the E qp gap , calculated as E opt gap + J dir eh + J pol eh , that is the sum of the experimentally determined optical bandgap ( E opt gap ), the direct Coulomb interaction between a confi ned electron-hole pair ( J dir eh ) and the polarization energy ( J pol eh ). These summations were provided by an analytical formula, based on effective mass approximation [ 37 ] and size-independent dielectric constants. A summary of all these results is depicted in Figure 1 a.

Here, a novel experimental method to probe the energy levels of colloidal nanocrystal assemblies is proposed. We make use of a new type of fi eld-effect transistor (FET) devices, namely the electric-double-layer (EDL) gated ambipolar transistors (see Figure 1 b). The demonstration of ambipolar transistors of colloidal nanocrystal assemblies allows the characterization of both their hole and electron transport. [ 34,36,38–41 ] Through the utilization of ionic-liquid-based gating and the related ion gel, a very high carrier density (on the order of 10 [ 14 ] cm –2 ) can be accumulated at the semiconductor surface. [ 32,42 ] The

accumulated carrier density by this ion gel gating can fi ll vir-tually all the available carrier traps, which are estimated to be on the order of 10 12 –10 13 cm –2 in the best colloidal nanocrystal assemblies. [ 38,41,43,44 ] Because of the effective trap fi lling achieved thanks to the gating, it is possible to span the Fermi energy position over a broader energy interval than the HOMO and LUMO gap. [ 35,45 ] Through the observation of the current

Adv. Mater. 2014, 26, 5639–5645

Figure 1. (a) The HOMO and LUMO energies of PbS nanocrystals as function of the particle diameter. Red circles: present work ab-initio cal-culated values for both HOMO and LUMO levels. Red solid lines: fi t to a power law of our calculated values (see text). Blue squares: experimental LUMO energies determined by cyclic voltammetry and the corresponding HOMO energies calculated simply subtracting the experimentally deter-mined optical bandgap by Hyun, et al. [ 8 ] The blue solid lines are fi ttings to a power law, calculated by us taking into account their inferred EA value of +4.55 eV for PbS bulk. [ 8 ] Black diamonds: experimental HOMO energies determined by PESA and corresponding LUMO energies calcu-lated, as explained in detail within the main text, by Jaseniak et al. [ 10 ] The black solid lines are a fi t to a power law. [ 10 ] (b) Schematic of the ion-gel gated PbS nanocrystal transistor. (c) Stick and ball image of the optimized geometry (after full relaxation) of the spherical Pb 68 S 68 nanocrystal.

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onset in the transistor during gating, the HOMO and LUMO are the dominant parameters that determine the current onset in the ion-gel gated transistors. Therefore, this method can be applied as a tool to probe not only the electronic gap, but in general the energy levels of colloidal nanocrystals and of any nanostructured semiconductor.

From a theoretical perspective, it is possible to calculate the electronic bandgap of highly complex systems in a very precise way with the use of ab-initio methods. We therefore apply these advanced computational methods to get information about the size dependence of the ionization potential and the electron affi nity for PbS NCs and thus of the quasi-particle bandgap. Since fi rst principles theory can access small nanocrystals (<2 nm diameter, some hundreds of atoms), whereas experi-ments deal with nanocrystals sized 2 nm or more (thousands of atoms), our ab-initio approaches constitute a unique and very powerful instrument to control and design the properties of these materials, with an accuracy that complements experi-mental observations.

Calculations have been performed within density functional theory (DFT) using the Quantum ESPRESSO Package, [ 46 ] and fully-relativistic norm conserving pseudopotentials. Full relax-ation with respect to the atomic positions was performed for each system. Bulk PbS has a rock-salt (NaCl) structure. We model spherical PbS stoichiometric non-passivated nanocrys-tals starting from the initial bulk rock-salt structure. NCs have been obtained by cutting a spherical segment from bulk lattice starting at the center of the elementary cubic cell. For stoichio-metric NCs, the absence of surface states in the bandgap due to the unsaturated dangling bonds has already been demon-strated in the case of PbSe. [ 47 ] We studied six different PbS NCs with diameters ranging from 0.4 nm (Pb 4 S 4 ) up to 2 nm for Pb 104 S 104 . The stick and ball structure, obtained after full geo-metrical relaxation, of the Pb 68 S 68 NC is shown in Figure 1 c. In all cases we have included relativistic spin-orbit effects, since they play a signifi cant quantitative role in this material (see Supporting Information S1).

In order to calculate the electronic bandgap of the PbS NCs we use the so-called ΔSCF method, i.e., we determined E qp gap = IP-EA = (E N–1 – E N ) – (E N – E N+1) , where E N+1 , E N–1 and E N are the DFT total energies of the system containing N+1 , N–1 and N electrons, thus taking into account the electron addition or removal to the NCs in order to calculate EA and IP respec-tively. This means that for each NC, we need three different total energy calculations for the determination of the electronic bandgap. Since the ΔSCF method is valid only for fi nite sys-tems, we had to go beyond the one-particle approach through the calculation of the self-energy corrections by means of the GW method in order to obtain the quasi-particles energies of the PbS bulk. [ 48 ] For completeness, this type of calculation has also been performed for the smallest nanocrystals in order to compare, in this case, the two methods. It should be noted that the laboriousness of the GW approach prevents its use for the larger NCs. Moreover, since the bulk E qp gap alone does not give information about the EA and IP of the three-dimensional PbS, in this case we have performed also calculations starting from a thin fi lm (slab) along the [100] direction (12 layers of PbS, plus 12 layers of vacuum) and have aligned the energy bands with a bulk-projected calculation. From the knowledge of the

bulk HOMO and LUMO, and from the knowledge of the slab vacuum energy level, we were able to calculate EA and IP in the bulk limit. All calculated results are presented in Table 1 and have been used for the data and fi t presented in Figure 1 a (for more details see Supporting Information).

First of all, we note from Table 1 that, for E qp gap , the agree-ment between the two types of calculations ( E qp gap determined through the difference between IP and EA or by GW cor-rection) shown in the case of the smallest Pb 4 S 4 NC is good and in line with recent outcomes for different semiconductor nanoclusters. [ 49,50 ] Second, if we look at our calculated values for the EA (+4.34 eV) and the IP (+4.87 eV) for PbS bulk, we see a strong agreement with the reported experimental values of +4.6 eV and +5.0 eV. [ 51 ] Moreover, the increasing quantum confi nement effect on the band-edge levels with decreasing nanocrystals diameter is evident. Using all the data in Table 1 , our size-dependent band-edge extremes LUMO (= – EA ) and HOMO (= –IP ) can be fi tted, without any parameter, to the func-tional forms LUMO ( d ) = – 4.34 + 1.46 d −0.77 and HOMO ( d ) = – 4.87 – 1.44 d −0.88 . It is thus possible to compare our results with previous experimental reports, as shown in Figure 1 a.

From the comparison two observations emerged. Firstly, a substantial agreement between the theoretical results (our fi t) and the experimental data (in the region between 3 nm and 10 nm) related to the experimentally determined HOMO values of Jasieniak et al., [ 10 ] and to the LUMO values of Hyun et al. [ 8 ] It must be taken into account that in our NCs the diameter has been directly calculated looking at the optimized geometry of the clusters, whereas in the reported experiments, [ 8,10 ] they have been deduced from the fi rst absorption maxima making use of different calibration procedures. Moreover, in the above-cited experiments the PbS NCs were passivated by ligands, which are not considered in our calculations. In the case of InAs, [ 30 ] and CdSe NCs , [ 10,52 ] it has been demonstrated that the ligands can shift the band-edge energies up to about 0.3 eV. Secondly, concerning the behavior of the different fi ts at smaller NCs diameters (below 2 nm), we note that our LUMO energy level increases slowly with respect to the LUMOs of Hyun et al., [ 8 ] and Jasieniak et al. [ 10 ] Some differences in this region are also present for the HOMO energy level behaviors.

To rationalize these differences and highlight the trend with respect to quantum confi nement, we report in Figure 2 a the mag-nitude of the HOMO energy level shifts ΔHOMO ( d ) with respect

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Table 1. Calculated HOMO ( IP ), LUMO ( EA ) band-edge energies and quasiparticle gaps ( E qp gap = IP – EA ) for PbS bulk and PbS nanocrystals. For Pb 4 S 4 NC the value showed in parenthesis for E qp gap is the outcome of the GW calculation.

EA [eV]

IP [eV]

E qp gap [eV]

Diameter ( d ) [nm]

PbS bulk 4.34 4.87 0.53 ∞

Pb 104 S 104 3.55 5.60 2.05 2.04

Pb 80 S 80 3.30 5.65 2.35 1.88

Pb 68 S 68 3.43 5.72 2.29 1.69

Pb 44 S 44 3.47 5.93 2.46 1.49

Pb 28 S 28 2.89 6.19 3.30 1.23

Pb 4 S 4 1.74 7.66 5.92 (5.5) 0.46

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to the bulk value as function of the corresponding shift of the LUMO, ΔLUMO ( d ), and of the PbS NCs diameter. The dashed line corresponds to the value of ΔHOMO ( d ) /ΔLUMO ( d ) = 1. For all the diameters our results are not far from this line. It is worthwhile to note that within an infi nite barrier confi nement model, ΔHOMO ( d ) /ΔLUMO ( d ) = m e

* /m h * , where m e * and m h *

are the effective mass of the electron and hole, respectively. Thus, ΔHOMO ( d )/ ΔLUMO ( d ) close to unity means that the two effec-tive masses are similar, in agreement with the expected ratio of the effective masses in bulk PbS (see Ref. [47] and references therein [ 53 ] ). This is not the case for the fi ts inferred from the experimental data of Hyun et al. [ 8 ] and Jasieniak et al. [ 10 ] In our view this is due to the fact that these experimentally studied NCs all lie in the same size region (i.e., between 3 nm and 7 nm), where the dependence on size for either the determined EA or IP levels is small (fl at level regions), thus it is easy to overestimate the weight of this region in the fi t, when extrapolating to other dimensions.

Finally, from our data in Table 1 and Figure 1 a it is possible to obtain the calculated quasiparticle bandgap for the PbS NCs

as a function of their size. These data are reported in Figure 2 b. Here, we note a very good agreement between our theoretical data and the experimental ones of Jasieniak et al., [ 10 ] whereas our values are above the experimental data of Hyun et al., [ 8 ] or Gocalinska et al. [ 9 ] This behavior is actually correct, since in the determination of the E qp gap only Jasieniak et al. [ 10 ] have consid-ered the many body corrections with respect to the E opt gap , while in the case for Hyun et al., [ 8 ] and Gocalinska et al., [ 9 ] the smaller optical gap has been used. This is also confi rmed by the com-parison of our values with those calculated by Kane et al., [ 54 ] who uses the empirical tight-binding method for optical bandgap cal-culations of PbS NCs of similar diameter. Also here, correctly, our quasiparticle values are above the optical ones.

It is also worth comparing our ab-initio results for E qp gap with those determined directly by our experimental technique, based on the measurement of ambipolar FETs with cross-linked col-loidal nanocrystals of different diameter gated by [EMIM][TFSI]-based ion gel ( Figure 3 a). The experimental bandgap of the PbS nanocrystals is then estimated from the threshold voltage ( V Th ) of both hole and electron accumulation. Conventionally, the V Th values are extracted from the intercept of the linear extrapolation of the drain current in the transistor I D −V G transfer characteris-tics with V intercept = V Th ± V DS (Figure 3 b). The V Th value extracted by this method is prone to be affected by the applied drain voltage, in addition to the transistor external resistance. On the other hand, the extraction of the V Th from the onset of the transcon-ductance ( g m = ∂I D /∂V G ) – GMLE method – provides a cleaner universal value that is self-consistent with all applied drain volt-ages. It is directly connected with the onset of the inversion layer build-up in the semiconductor channel, free from the infl uence of the device structure and geometry. [ 55 ] Thus, it is suitable for our purpose, i.e., probing only the properties of the nanocrystal assemblies. Using the V Th value extracted by this GMLE method from both p-channel and n-channel operations, the bandgap can be easily determined from E G = e·( V Th.hole + V Th.electron ). A detailed overview of the transistor measurements performed with [EMIM][TFSI] gate are reported in Figure S4, S5, and S6 of the Supporting Information.

In order to compare these results with the theoretical out-comes, we need to check the relationship between the probed energy bandgap values and the NCs size. For this purpose, the diameters of the corresponding nanocrystals were measured using high angle annular dark-fi eld (HAADF) combined with scanning transmission electron microscopy (STEM), HAADF-STEM (insets of Figure 3 b). Finally, Figure 3 c shows the com-parison between the experimentally and theoretically deter-mined energy bandgaps versus PbS NCs diameters. There is a very good agreement between the trend of the theory and the experimental values, demonstrating the reliability of the FET method to determine bandgaps of semiconducting sys-tems. The constant (0.3 eV) high energy shift of the theoretical data points respect to the experimental one can be ascribed to the effect of the ligands and/or to the dielectric constant of the NCs assembly in the experiment. Thus, by combining theory with experiments, we are able to determine with high precision the absolute energy of LUMO and HOMO states for PbS NCs and its dependence on NC diameter, which is a fundamental step for the design of heterojunctions involving nanocrystals.

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Figure 2. (a) The magnitude ΔHOMO of the HOMO energy level shift as function of the magnitude ΔLUMO of the LUMO energy level shift with respect to the PbS NCs diameter. The dashed line refers to ΔLUMO/ΔHOMO = 1. The red solid lines represent our calculated results. The results determined by Hyun et al. [ 8 ] and Jaseniak et al. [ 10 ] are also rep-resented. (b) The quasiparticle energy bandgap E qp gap as function of the PbS NCs diameter. Red circles and red solid lines: our calculated results and the derived fi t. Results are compared with data reported by Jaseniak et al., [ 10 ] Hyun et al., [ 8 ] and Gocalinska et al. [ 9 ]

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From the transfer characteristics of ion-gel-gated fi eld-effect transistors, we are able not only to provide the values of the LUMO and HOMO energy levels, but also to access the higher energy levels of the quantum-confi ned systems by tuning the Fermi level in a broader energy range. The Fermi level tuning range for ionic-liquid-gated transistors is determined by the elec-trochemical window of the utilized ionic liquid. This is defi ned as the maximum limit for the applied gate voltage where the interac-tion between ions in the ionic liquid and the charge carrier in the semiconductor is still solely electrostatic, i.e., before any electro-chemical process (reactions) can take place on the semiconductor surface. [EMIM][TFSI] has a limited electrochemical window only allowing an approximately 3 V range (from −1.5 V to ∼1.5 V), but the electrochemical window can reach almost 6 V in [DEME][TFSI] by changing the anion of the ionic liquid (see Figure 4 a).

Figure 4 b shows the comparison of the V G -dependent capaci-tance at the interface of the PbS nanocrystal fi lm and [EMIM][TFSI] and [DEME][TFSI] ion gels. Therefore, when [DEME][TFSI] is used as gate dielectric, a higher gate voltage can be applied, leading to larger charge carrier accumulation at the

semiconductor interface. Charge carrier den-sity up to 3.5 × 10 14 /cm 2 (at V G = 3 V) can be accumulated on the nanocrystal layer. Therefore, [DEME][TFSI] ion gel can be used to further shift the Fermi energy level of our nanocrystals.

[DEME][TFSI] ion-gel-gated transistors were made with all the NC sizes under investigation. I D -V G transfer characteris-tics of n-channel operation were meas-ured up to V G = 3.0 V (Figure 4 c–f) (see also Figures S7, S8, and S9). Conven-tionally the I D –V G transfer characteristics of fi eld-effect transistors operating in the linear regime, including those with [EMIM][TFSI] gate, monotonously increase with a nearly constant slope, constant transcon-ductance, from which mobility value can be extracted. However, I D –V G transfer charac-teristics obtained from [DEME][TFSI]-gated nanocrystal transistors show several varia-tions of I D –V G slopes with different threshold values. In most cases, the slope at higher V G is larger than the one preceding it, as indicated by the dashed blue lines in Figure 4 c–f. In the case of the smaller NCs, the regions with dif-ferent slopes are separated by a voltage range, in which the current has smaller gradient indicating reduced charge mobility. These anomalies in conductivity can be attributed to the fi lling of the higher energy sub-bands (see inset in Figure 4 c–f) of the superlattice formed by the nanocrystal array used as active layer of our transistors. The energy differences between sub-bands are shown in Table 2 . Similar anomalies have been reported by Van-maekelbergh and Guyot-Sionnest measured with electrochemical devices using permeated aqueous ionic solution, [ 56,57 ] and interpreted as

due to the successive fi lling of the localize energy levels of the NCs.

In our case, the measurements are obtained on channels of 20 µm and a width of 10 mm. So the evidence of sub-band fi lling anomalies indicate the formation of delocalized energy states in colloidal nanocrystals super lattices. The dissimilarity between the curves of small and large NCs, with the absence of a plateau in the I D –V G transfer characteristics, can be explained by the lowest quality of the superlattice array with larger inho-mogeneity when bigger NCs are used. However, also the smaller spacing between the energy levels in larger crystals is a possible explanation of the lack of the plateau in the transfer characteristics. This is confi rmed by the theoretical outcomes, performed populating adequately the LUMO+1 level, that reveal in the case of small nanocrystals (Pb 4 S 4 and Pb 48 S 48 ) energy dif-ferences between the LUMO+1 and the LUMO levels of the order of 0.98 eV and 0.56 eV, respectively, and much smaller for larger NCs.

In conclusion, combining ab-initio results and new electric-double-layer-gated devices we have demonstrated that it is

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Figure 3. (a) Schematic of the crosslinked PbS nanocrystal assemblies and chemical struc-tures of 3-mercaptopropionic acid (3MPA) and of [EMIM][TFSI] (ionic liquid) and PS-PMMA-PS block copolymer, which constitute the ion gel. (b) I D −V G transfer characteristics of the [EMIM][TFSI]-gated FET of different nanocrystal diameters. The charge carrier accumu-lation thresholds refl ect the relative position of the LUMO and HOMO. The n-channel regime (0 V < V G < 1 V) was measured with V DS = 0.2 V, while the p-channel regime (−1 V < V G < 0 V) was measured with V DS = −0.2 V. The dashed lines showed the linear extrapolations of the drain current of I D −V G transfer characteristics that conventionally are an approximation of the threshold voltage values. (Insets) HAADF-STEM images of the cor-responding nanocrystals assemblies after ligand exchange. The size of the STEM images is (50 nm × 50 nm). (c) Comparison of the values extrapolated from the calculations (red circles) of the size dependent bandgap and the measured bandgaps probed using the ion-gel-gated FET technique (blue circles) via the transconductance ( g m = ∂I D /∂V G ) onset threshold. The nanocrystals diameters are measured using HAADF-STEM.

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possible to study the electronic properties of colloidal nanocrys-tals quantitatively. The absolute energy position of the LUMO and HOMO states, and thus also the bandgaps of PbS NCs, have been determined with precision as function of the nano-particle size. Since the determination of the energy levels allows predicting suitable band alignment favoring charge transfer in composites and heterojunctions, our results are of paramount importance in the long way toward effi cient nanocrystal-based devices. Uniquely, also the higher energy levels are determined from the anomalous slope and the plateau of the fi eld-effect transistor transfer characteristics, which represents the fi rst experimental demonstration of electronic state delocalization (mini-bands formation) in NC superlattices.

Experimental Section Ab initio calculations : Calculations have been

performed within Density Functional Theory (DFT) using the Quantum ESPRESSO Package, [ 46 ] and fully-relativistic norm conserving pseudopotential with the Perdew-Zunger exchange-correlation functional, [ 58 ] and an energy cutoff of 100 Ry. Full relaxation with respect to the atomic positions was performed both for PbS bulk and for all PbS NCs systems. Relativistic spin-orbit effects have been included. Regarding the quasi particle GW calculations in PbS bulk, we used 60 Chadi-Cohen k -points in the irreducible part of the Brillouin Zone, 300 bands and 1037 plane waves in the screen and in the correlation part of the self-energy ( Σ c ) and 4477 plane waves in the exchange part ( Σ x ). The calculated bulk lattice constant and the resulting electronic band structure are in good agreement with previous calculations, [ 53,59 ] and show the importance to take into account relativistic spin-orbit effects. Concerning the smallest NC, Pb 4 S 4 , we used an fcc cell with 40 au distance between the images of the clusters, cutting the Coulomb interaction at 20 au. The GW corrections to the DFT Kohn-Sham eigenvalues were calculated using 3000 bands and 60000 plane wave in the correlation part Σ c and 80000 plane waves in the exchange part Σ x (see Supporting Information).

Device measurements : The details of the fabrication of PbS nanocrystal ambipolar transistors have been reported elsewhere. [ 38,44 ] Transistor measurements were performed using a probe station in a nitrogen-fi lled glovebox at room temperature in the dark. An Agilent E5270B was used to acquire the transistor parameters. The gate voltage was scanned at 10 mV/s, so that the device is operated at the maximum capacitance of the ion gel in the electrostatic regime without electrochemical reactions. The electrochemical properties of the ion gel were measured using an electrochemical impedance analyzer (Bio Logic, SP-200). Capacitance measurements were done on PbS transistor device structures.

STEM measurements : Scanning transmission electron microscopy (STEM) combined with high angle annular dark-fi eld (HAADF) imaging was used to analyze the PbS nanocrystals. A JEOL JEM-ARM 200F, 200kV FEG-STEM/TEM equipped with a CEOS spherical aberration (Cs) corrector on the illumination system (i.e., probe corrector) was used, which has a HAADF-STEM resolution of 0.08 nm. Samples for electron microscopy analysis were prepared using solutions of oleic acid-capped PbS nanocrystals. A drop of the solution was deposited on carbon coated copper grid and dried. The procedure was repeated by adding a drop of benzenedithiol and methanol to remove the oleic acid and the excessive carbon from the sample.

Supporting Information Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements The work in Groningen is supported by European Research Council (ERC) Starting Grant (No. 306983) “Hybrid Solution Processable Materials for Opto-Electronic Devices” (ERC- HySPOD ). The calculations have been performed within the ETSF collaborative project no. 173. We

Adv. Mater. 2014, 26, 5639–5645

Figure 4. (a) Molecular structure of [DEME][TFSI] ionic liquid, which has wider electrochemical window than the [EMIM][TFSI] (b) Comparison of V G -dependent sheet carrier density on PbS nanocrystal fi lms accumulated by [EMIM][TFSI] and [DEME][TFSI]. I D –V G transfer characteris-tics of the nanocrystal FETs with diameter: (c) d = 3.38 nm; (d) d = 3.72 nm; (e) d = 5.02 nm, and (f) d = 9.49 nm. The variations of I D –V G slope indicate the band fi lling process of different energy sub-bands of the nanocrystal superlattices.

Table 2. Energy of the electron energy-sub-bands of different nanocrystal diameters probed using ion-gel gated transistors.

Nanocrystal Diameter

3.38 nm 3.72 nm 5.02 nm 9.49 nm

E C+1 –E C 0.59 eV 0.22 eV 0.73 eV 0.34 eV

E C+2 –E C+1 0.39 eV 0.55 eV 0.54 eV 0.23 eV

5645

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wileyonlinelibrary.com© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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Adv. Mater. 2014, 26, 5639–5645

thank the Super-Computing Interuniversity Consortium CINECA, Italy for granting CPU time. W.H. and M. Y. acknowledge fi nancial support from the Austrian science fund FWF via the SFB Project IR_ON F25. S. Z. B. and E. D. contributed equally toward this research.

Received: February 11, 2014 Revised: May 22, 2014

Published online: June 12, 2014

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