Scanning Tunneling Spectroscopy of Free-Standing CdS

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Scanning Tunneling Spectroscopy of Free-Standing CdS Nanocrystals Fabricated by the Langmuir−Blodgett Method Kirill A. Svit† and Konstantin S. Zhuravlev*,†,‡ †

Rzhanov Institute of Semiconductor Physics Siberian Branch, Russian Academy of Sciences, 13, Lavrentieva avenue, Novosibirsk 630090, Russia ‡ Novosibirsk State University, 2, Pirogova Street, Novosibirsk 630090, Russia ABSTRACT: The energy spectrum and tunneling transport through ensembles of closely packed CdS nanocrystals (NCs) obtained by the Langmuir−Blodgett (LB) method have been investigated using the scanning tunneling spectroscopy (STS) technique at room temperature. NC ensembles were obtained by annealing the solid LB matrix in a vacuum or in an ammonia atmosphere. The STS data indicate the formation of point defects attributed to an excess of Cd atoms in NC capturing tunneling electrons and the effect of the ammonia atmosphere on the defect formation process. A high density of defects arising as a result of sintering NCs that lost a protective organic shell during the migration on the substrate surface is likely to cause a band gap narrowing in NCs located near the ensemble edge. The analysis of a dependence of the zeroconduction gap value on the NC size gives evidence of a strong effect of the Coulomb interaction between the carriers located in NCs and their polarization charges in the shells on the NC energy spectrum. A dielectric constant of the shell (εout = 10−16.5) and the energy barrier height for electrons (V0 = 0.6−0.8 eV) were determined. The shell comprises ammonia and organic molecules, the ammonia molecules making a major contribution to the shell dielectric constant and the organic molecules determining the barrier height.

I. INTRODUCTION Today, semiconductor nanocrystals (NCs) attract a great deal of attention because of the properties that are not manifested in a bulk material. NCs are interesting because of their characteristics that can be purposefully controlled by varying their size, shape, composition, and structure. This feature makes it possible to create devices based on new physical principles1 and to improve the performance of existing semiconductor devices.2 A2B6 semiconductor NCs are among the most actively studied NCs because of the potential of enhancing the performance of lasers, photodetectors, solar cells, etc.3−5 The NC size, shape, internal structure, and surface chemistry depend on the method and preparation conditions. Very popular colloidal NCs are typically covered by a surfactant that stabilizes its surface and prevents the irreversible aggregation of NCs, separating NCs from each other and from a substrate by a distance of ∼11 Å.6 In an alternative synthetic method, such as the Langmuir−Blodgett technique, the surfactant is not required for the separation of NCs, while short ammonia molecules with a length of approximately 3.5 Å can be used for NC surface passivation. Consequently, the interaction between NCs as well as between NCs and the substrate strengthens. Ensembles of closely packed NCs lying directly on the substrate can be obtained by removing the LB matrix.7 The most powerful tool for studying the NC electronic properties is scanning tunneling spectroscopy (STS).8−10 This method is an extension of the scanning probe microscopy © XXXX American Chemical Society

technique initially designed to investigate the surface morphology with an atomic spatial resolution. STS is based on measuring the dependence of tunneling current I on voltage V applied between a sharp metallic probe and a conductive substrate, i.e., differential conductance dI/dV. In this mode, the probe position is fixed, and the feedback loop is disabled. STS spectra provide information about the energy spectrum and the density of states of a substrate and/or NCs located on the substrate.11 The STS method allows the study of the NC charge state and single-electron phenomena in NCs.12,13 It was successfully used to measure single-particle energy levels, their degree of degeneration, electron−electron interactions, and the energy of traps in individual NCs,14−18 and also a collective phenomenon in the NC ensembles.19 Despite a large number of STS studies of NCs, those obtained by the LB technique have been scarcely investigated. To the best of our knowledge, only a few works have been devoted to the investigation of tunneling transport through NCs located in the Langmuir− Blodgett matrix,20,21 and a free-standing NC after the removal of the LB matrix has not yet been studied. At the same time, free-standing NCs obtained by the evaporation of the LB matrix may be more appropriate for STS studies, because a key Received: May 29, 2015 Revised: July 15, 2015

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Figure 1. STM topography of CdS NCs obtained for (a) nonpassivated and (b) passivated 10 ML samples. The set point was 25 pA and 2.6 V. Transmission electron microscopy images of (c) passivated and (d) nonpassivated NCs synthesized on a 40 nm thick carbon substrate. Some NCs are marked by black contours.

annealed in the ammonia atmosphere at a pressure of 100 Torr (passivated samples); the second group was annealed in a vacuum (nonpassivated samples). The sample preparation procedure was described in more detail previously.23 The obtained NCs were investigated by scanning tunneling microscopy (STM) and STS. The measurements were taken utilizing the ultra-high-vacuum Omicron AFM/STM system at room temperature. STM probe tungsten tips were obtained by electrolytic etching. During STM, the tunneling current was measured at the grounded STM tip while a bias was applied to the HOPG substrate. STM images were obtained in a constant current mode with the following set-point parameters defining the tip−sample distance: the tunneling current and voltage were in the range of 0.025−1.04 nA and 2.5−3.4 V, respectively. The STS data were acquired in current imaging tunneling spectroscopy mode. During the I−V curve measurement, the bias voltage was swept once from −3 to 3 V starting from the negative voltage. Conductance spectra (a dI/dV value as a function of the voltage) were calculated from the measured I−V curves. The spectroscopic data were acquired in current imaging tunneling spectroscopy mode (CITS) wherein topographic images were recorded in constant current mode simultaneously with the I−V curves. CITS images were taken at a 100 × 100 point grid, with the feedback loop being disabled during spectroscopic acquisition.

parameter here is the distance between NC and the substrate along with the spacing between the neighboring NCs. In this paper, the tunneling transport and energy spectra in the ensembles of free-standing CdS NCs obtained by the Langmuir−Blodgett technique have been investigated by the STS method for the first time. Preliminary studies of the energy spectra in the ensembles of free-standing CdS NCs were reported in the previous publication.22 The paper is arranged as follows: experimental details in section II, experimental data obtained by the STS method and the results of our modeling in sections III and IV, respectively, and conclusions in section V.

II. EXPERIMENTAL DETAILS The samples with CdS NCs were prepared using the Langmuir−Blodgett method on a conductive highly oriented pyrolytic graphite (HOPG) substrate with an atomically smooth surface. To this end, LB film layers of cadmium behenate were grown by the substrate transfer through the monolayers (MLs) formed on the liquid subphase surface comprising cadmium chloride. A cadmium chloride solution was used as a subphase. ML transfer was conducted by a Y-type system at a surface pressure of 30 mN/m and a temperature of 22 °C. The samples containing four MLs (4 ML), eight MLs (8 ML), and 10 MLs (10 ML) with thicknesses of 12, 24, and 30 nm, respectively, were prepared by this method. It should be noted that with a further increase in ML number NCs start to pile on each other, and this fact together with a quite large NC size dispersion complicates the analysis. The films were sulfidized with hydrogen sulfide gas for 1−1.5 h at a pressure of 50−100 Torr and a temperature of 22 °C. As the result of the interaction between cadmium behenate and hydrogen sulfide CdS, NCs distributed in the LB matrix were formed. The final step was removal of the matrix by annealing at a temperature of 200 °C. The samples were divided into two groups that were annealed differently. The first group was

III. EXPERIMENTAL RESULTS Panels a and b of Figure 1 show the topographic STM images of 10 ML samples annealed in a vacuum and in an ammonia atmosphere, respectively. The set-point conditions were chosen to keep the probe sufficiently far from the NC and prevent image smoothing and tip damage during the scanning process. The most reproducible and distinct images were obtained at the set-point current in a range from 25 to 250 pA when the voltage was between 2.6 and 3.4 V. The high quality of the B

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sizes under the identical set-point conditions and using the same STM tip. The I−V curves mentioned exhibit the lowconductivity region, which is a typical semiconductor feature and relates to the forbidden states in the energy spectrum of a semiconductor. The I−V curves are nonsymmetrical with respect to the zero bias and are shifted toward the negative voltages, indicating that the equilibrium Fermi energy of NCs is located in the upper region of the band gap. We did not observe any steplike dependence of the current on the bias voltage that can be attributed to Coulomb staircase phenomena. Nevertheless, some weak structure can be discerned in these spectra. Solid lines in panels c and d of Figure 2 present the tunneling spectra corresponding to the aforementioned I−V curves. The tunneling spectra exhibit a zero-conduction gap (ZCG) corresponding to a very low current in the I−V curves. The ZCG value changes by 0.3 V only upon variation of the setpoint current in a wide range from 1.04 nA to 25 pA. The ZCG in the tunneling spectra relates to the NC band gap. The band gap weakly depends on the NC surface condition, and its mean value is 3 V for passivated NCs and 3.3 V for nonpassivated NCs. The broadening of the band gap for nonpassivated NCs is due to the 0.3 V increase in the positive voltage value where the current drastically increases, whereas the negative voltage value of the sharp current rises does not change after NC passivation. Figure 3 shows the typical I−V curves and the tunneling spectra of an initial HOPG substrate and a HOPG substrate

STM images gives evidence of good conductivity between an NC layer and the substrate for both types of samples. It is seen from the figures that NCs assemble in clusters on the HOPG surface. The clusters are three-dimensional and consist of a large number of NCs. To estimate a mean NC height, we analyzed the apparent height profiles of NCs lying directly on the substrate and not overlapping with the neighboring NC. The mean NC apparent height is approximately 3 nm for both types of samples, the NC height variation being quite large (∼25% of the average value), which leads to the absence of the long-range order in the ensembles, with only a very few areas demonstrating the short-range order (a closely packed structure). According to the STM data, the mean lateral NC size is ∼6 nm, but it is an approximate value because NCs overlap and their contours are hardly resolved. To determine a more precise lateral NC size, we used transmission electron microscopy (TEM). Because the NC size can depend on the substrate material, samples with NCs were prepared for TEM studies on 40 nm thick carbon substrates that are similar to the HOPG substrates used for STM and STS measurements. It is seen from the TEM images shown in panels c and d of Figure 1 that the mean lateral size of both passivated and nonpassivated NCs is ∼3.5 nm. It should be noted that we failed to obtain qualitative STM images from samples with fewer than eight MLs because the STM tip apparently dragged the small clusters during the scanning process, which blurred the image. The STS data, tunneling I−V curves, and corresponding tunneling spectra of passivated and nonpassivated NCs obtained are shown in Figure 2. Solid curves in panels a and b of Figure 2 show the typical tunneling I−V curves for passivated and nonpassivated NCs located deep inside a cluster, respectively. The curves were measured when the tip was positioned over NCs with equal

Figure 3. (a) Tunneling I−V curves and (b) tunneling spectra of the initial HOPG substrate (dashed line) and the HOPG substrate with NCs (solid line). The set-point conditions are 100 pA and 2.5 V.

after the deposition and removal of the LB matrix. The tunneling spectra are presented on a log scale to demonstrate the absence of a low-conductivity region related to the forbidden electronic states in both substrates. It is also seen from the figure that the tunneling current and conductivity are higher for the initial HOPG substrate than those for the treated one; moreover, for both substrates, the tunneling current grows faster at a negative bias. Figure 4 shows the experimental ZCG value as a function of NC radius (■). The figure shows that the ZCG value increases nonlinearly with a decrease in the NC size, which is typical behavior for the quantum size effect. In addition, we found that the tunneling spectra of NCs located near the cluster edge usually differ from those of NCs located inside the cluster. Hereafter, we call these NCs “unusual”. The dashed curves in Figure 2 present illustrative examples of the I−V characteristics and tunneling spectra of unusual NCs. The tunneling spectra of these NCs demonstrate that the ZCG value is less than the band gap of bulk CdS or even the absence of the gap. The ZCG value of unusual NCs

Figure 2. (a and b) Tunneling I−V curves and (c and d) corresponding tunneling spectra of (a and c) passivated NCs and (b and d) nonpassivated NCs, respectively. Solid purple lines correspond to NCs located deep inside a cluster, and dashed green lines relate to NCs located near the cluster edge. The right ordinate axes correspond to the dashed curves. The set-point conditions are 25 pA and 2.6 V (a and c) and 25 pA and 3 V (b and d). C

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unusual NCs does not show any dependence on the NC height unlike that of usual NCs. As expected, the ZCG value of unusual NCs grows with their movement deeper in the cluster, reaching the ZCG value for usual NCs (∼3 V) ∼30 nm from the cluster edge (see Figure 6b). For the latter dependence, we chose NCs with a similar height (3−3.5 nm) to neglect the effect of NC height on the ZCG value.

IV. DISCUSSION A. Energy Band Diagram of NCs on the HOPG Substrate. In fact, we do not know a priori an energy band diagram of a tip/nanocrystal/HOPG configuration. Usually, a similar configuration is described by a double-barrier tunnel junction presented in Figure 7a.24 NC is coupled to the STM tip and the surface of a HOPG substrate by tunnel junctions. Electrons can tunnel through these junctions with different rates. However, the challenge arises because there are no apparent reasons for the existence of a barrier between NCs and the substrate because NCs are not covered by any surfactants and the HOPG substrate was cleaned by removing the top layer just before the deposition of the LB film. The STS spectra of the HOPG substrate with NCs (Figure 3b) do not contain a zero-gap plateau related to the remaining LB film. This means that NCs must be strongly coupled with the substrate, and carriers can freely travel from NCs into the substrate. Indeed, a good ohmic contact facilitates the measurement of high-quality STM images and prevents the appearance of steplike features in the I−V characteristics of NCs related to the Coulomb blockade observed previously for CdS NCs embedded in the LB matrix. However, we note that the absence of the steplike features in the I−V curves and peaks in the tunneling spectra can also be explained by coupling of neighboring NCs collected in arrays that create a plurality of interconnected capacities. This leads to an increase in the total structure capacity and a reduction of the Coulomb charging energy.25 Moreover, the coupling of neighboring NCs causes the broadening of energy levels in NCs, which smoothes out the I−V characteristics. On the other hand, a blue shift of a photoluminescence peak related to interlevel transitions in NCs observed previously26 allows us to infer that there is a barrier between NCs and the substrate. We assume that an insulating film with a thickness of a few atomic layers exists under NCs. It was previously shown that during the thermal evaporation of the fatty acid matrix the acid molecules split into water, carbon dioxide, and organic radical; the latter in turn forms paraffin that splits into simpler alkanes.27 It is most likely that alkanes with a high molecular weight (paraffin waxes) do not evaporate completely during the annealing and form a barrier film underneath NCs. This remaining film provides an electronic decoupling that is sufficient to cause quantum confinement in individual NC. At the same time, the electrons can still tunnel through the ultrathin insulating films, facilitating STM imaging at a low tunneling current. The weak dependence of the ZCG value on the set-point current indicates that the barrier between NCs and the substrate is smaller than the vacuum gap; thus, the tip/ nanocrystal/HOPG configuration forms an electrical device with two asymmetrical tunnel barriers. At the asymmetrical double-barrier tunnel junction, the applied voltage drops entirely over the NC/tip junction; a change in the bias results mainly in a shift of the tip Fermi level with respect to the valence and conduction band levels of NCs that are fixed relative to the substrate Fermi level, so at the positive and

Figure 4. Experimental dependence of the ZCG value on NC size (■). Band gap size dependences for spherical NCs in a vacuum calculated using the finite spherical potential well model with barrier heights (V0) of 4.8 eV (blue dashed line), 0.8 eV (red dotted line), and 0.8 eV, taking into account both voltage distribution and polarization energy (solid purple line).

spans the range from 0 to 2.4 V, with a typical value of ∼1.7 V. The tunneling current through unusual NCs starts to increase at a voltage lower than that for usual ones; moreover, the tunneling current grows in the same fashion at negative and positive voltages, so the I−V curves become quite symmetrical with respect to the zero bias. These features were observed for both nonpassivated and passivated NCs; nonetheless, the data for nonpassivated NCs located near the cluster edges are very noisy, which complicates their analysis, so below we consider this phenomenon mainly for passivated NCs. To find the location of unusual NCs, current-imagingtunneling spectroscopy (CITS) was used. CITS is a kind of the STS technique in which an I−V curve is recorded at each pixel of the STM image showing the spatial tunneling current distribution at the selected bias value. We chose a negative bias of −3.1 V at which the tunneling current through usual and unusual NCs differs most considerably; thus, the brighter area of a CITS image corresponds to the higher tunneling current flowing through unusual NCs. A typical CITS image of an NC cluster is shown in Figure 5. As seen from the figure, unusual NCs concentrate near the

Figure 5. (a) STM topography of the cluster edge obtained at 25 pA and 2.6 V and (b) CITS image of this edge obtained at a bias of 3.1 V.

cluster edge, and it ceases to meet such NCs in the heart of the cluster. The distance from the cluster edge at which unusual NCs can be met reaches several tens of nanometers; however, some clusters do not contain unusual NCs. To find any regularity, we investigated the size and location dependences of the ZCG value for unusual NCs. Figure 6 shows a typical dependence of the ZCG value on (a) the height of unusual NCs and (b) the distance from the edge inward the cluster. An STM image of the studied NCs is presented in Figure 6c. It is seen from Figure 6a that the ZCG value of D

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Figure 6. (a) ZCG as a function of NC height. (b) ZCG value of NCs as a function of distance from the cluster edge inside the cluster along the arrow shown in the STM image on the right. (c) STM image of the studied sample. Asterisks and crosses mark NCs whose ZCG values are presented in panels a and b, respectively.

Figure 7. (a) Typical double-barrier tunnel junction and corresponding energy diagrams of the investigated structure (b) in equilibrium (V = 0) and (c) at a positive bias.

negative bias a tunneling current flows via the levels of the conduction and valence bands, respectively. B. Charged State of NCs. The asymmetry of the I−V curves (Figure 3) indicates that the NC Fermi level is shifted toward the conduction band. This Fermi level position can be due to the presence of defects caused by an excess of cadmium. The fact supporting this is that the LB method does not provide complete sulfidation. These defects are cadmium interstitials (donor type) lying 1.68 eV above the conduction band, antisite defects (acceptor type) lying 1.5 and 2 eV above the valence band edge, and a sulfur vacancy28 (donor type) lying 0.1 eV below the conduction band edge. Their simultaneous presence fixes the Fermi level position in the upper part of the NC band gap. It is commonly recognized that the sulfur vacancy is a dominant defect in CdS because of the lowest formation energy among the intrinsic defects.29,30 During the evaporation of the LB matrix by annealing, the sulfur vacancies can be partly filled with excess cadmium atoms; i.e., the antisite defects are formed. The broadening of ZCG for nonpassivated NCs (annealed in a vacuum) can be due to electron capture by the antisite defects in NCs. Energy diagrams of the tip/nanocrystal/HOPG configuration presented in panels b and c of Figure 7 illustrate the processes occurring during the I−V curve measurement. At equilibrium (Figure 7b), the antisite acceptor lying in the upper part of the band gap is neutral. At the beginning of the measurement, a negative bias is applied to the substrate and the neutral acceptor does not prevent the tunneling of electrons from the substrate to the tip via NCs. At a positive bias (Figure 7c), when the Fermi level of the tip is aligned or above the acceptor level, an electron tunnels from the tip to the acceptor

state. The negatively charged ionized acceptor repulses the following tunneling electron, preventing its tunneling. To compensate for the Coulomb forces and to facilitate the tunneling, a higher bias is needed, which leads to the I−V curve shift. A similar shift of the tunneling spectra of CdSe/ZnS core/ shell NCs was observed by Hummon et al. and attributed to the charging of the trap states located near the middle of the band gap. The absence of the charging effect in passivated NCs can be explained by the effect of the ammonia atmosphere on the defect formation process. Indeed, ammonia molecules that cover the NC surface can hold cadmium atoms and prevent their transition to sulfur vacancies. Because ∼30% of atoms in NCs with a 3 nm diameter belong to the surface, the consolidation effect of ammonia molecules can be essential. C. ZCG Size Dependence. To describe the dependence of ZCG on NC size presented in Figure 4, we used a finite spherical potential well model developed by Giovanni Pellegrini et al.,31 which is widely utilized to analyze the quantum size effect in NCs surrounded by barriers with different heights (V 0 ). 32 We used the finding of Facci and Fontana demonstrating that ellipsoid-shaped NCs initially formed in the LB film become spherical in shape after being annealed at temperatures above 100 °C.33 We started from NCs in a vacuum, confined by a barrier with a height of ∼4.8 eV, i.e., the CdS electron affinity (blue dashed line in Figure 4). Then, by varying the barrier height, we obtained a slope of the curve corresponding to the experimental dependence at V0 = 0.8 eV; however, the calculated curve (red dotted curve in Figure 4) lies below the experimental data. The obtained barrier value indicates that NCs are surrounded by some shell; therefore, to correct an absolute value of the NC E

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energy is positive; its value can be quite large. If εout > εin, the polarization energy is negative and its value is small. Therefore, the polarization energy reduces the ZCG value only in the percentage. Then, we took into account that the voltage applied between a STM tip and a substrate (Vfull) was distributed between a vacuum gap and NCs (VNC). To account for that, we introduced a coefficient (η) that determined a part of the voltage applied to the vacuum gap.

band gap (Eg), we should take into account the Coulomb interaction between the carriers located in NCs and their polarization charges in the shell (the polarization energy) following an approach developed by Jdira et al.34 Equation 1 shows the dependence of the polarization energy (Σ) on a dielectric constant mismatch between NCs and the surrounding homogeneous materials. The Σ value obviously depends on the NC radius (R): Σ (R ) = ×

⎞ εin − εout ⎛ εin + εout 0.376εout − + 0.933⎟ ⎜ εin(εin + εout) ⎝ εout εin + εout ⎠

e2 8πε0R

η = (Vfull − VNC)/Vfull

The η coefficient value was calculated by solving the Poisson equation using the TCAD software for NCs with diameters within the range of 2.6−4.0 nm and with the distance between NCs and the tip varying from 0.8 to 1.0 nm. The calculated value lies within the range of 0.79−0.85, which is very close to the values obtained from the solution of the Poisson equation for CdSe NCs investigated by Bakkers et al. The relation between the experimental STS data and the value of the NC band gap calculated in the framework of the model described above is given by the following equation:

(1)

where εin is a dielectric constant of the NC material and εout is an effective dielectric constant of the surrounding medium. Because there is no infinite homogeneous medium around NCs, we interpret εout as some effective dielectric constant of the whole environment of NCs. Nanda et al.31 showed that the dielectric constant εin of NC depended on its size: ⎛ 1 1 1 1⎞ = −⎜ − ⎟ ε(r ) ε∞ ⎝ ε∞ ε0 ⎠ ⎡ exp( −r /pe ) + exp(−r /ph ) ⎤ ⎥ ⎢1 − 2 ⎦ ⎣

ηΔVSTS = ESe − Sh + ΣSe +ΣSh

(5)

where ΔVSTS is the zero conduction gap, ESe−Sh is the effective band gap calculated using the finite spherical potential well model, ΣSe is the electron polarization energy, and ΣSh is the hole polarization energy. Equation 5 allows us to describe the experimental data at η ≥ 0.87, which slightly exceeds the calculated values. We assume that TCAD overestimates the voltage drop on NCs because it does not take into account the tunneling through them. When η = 0.87, which is close to the TCAD data, the calculated curve fits well the experimental data at εout values ranging from 10 to 16.5 and V0 values ranging from 0.6 to 0.8 eV (solid purple curve in Figure 4). Inaccuracy in the determination of these parameters is caused by the scatter of the experimental data. We assume that the high dielectric constant of the NC environment is due to the coating of the NC surface with ammonia molecules during the annealing process in the ammonia atmosphere. An ammonia monolayer is likely to cover the NC surface as the short-range van der Waals force binds ammonia molecules with NCs. On the other hand, the ammonia coating hardly explains the V0 value obtained because the equally expressed quantum confinement effect was also observed in nonpassivated NCs. To obtain the V0 value of ∼0.8 eV, the shell band gap has to be approximately 4 eV, if we accept that the confinement potentials are the same for electrons and holes. Such a shell can be formed by residues of the LB matrix. Thus, NCs are wrapped by a shell comprising ammonia and organic molecules both attached directly to the NC surface. Ammonia molecules make the main contribution to the shell permittivity and determine the value of the polarization energy, while organic molecules determine the NC confinement potential. Organic molecules are most likely to preserve underneath NCs, separating them from the substrate, because NCs hamper the evaporation of the organic molecules. The preservation of organic molecules covered by a thin solid film at a vaporization temperature was demonstrated previously. Thus, it appears that the upper part of NCs is covered by ammonia molecules whereas the bottom part is covered by the matrix residues. The confinement potential of this configuration has been poorly investigated; nonetheless, we suppose that the position of the energy levels in NCs is mainly

(2)

where r is the NC radius, ε∞ = 5.23 and ε0 = 9 are static and optical dielectric constants of CdS, respectively, and pe and ph are defined as ⎞1/2 ⎛ ℏ ⎟ pe = ⎜ ⎝ 2me*ωLO ⎠

(4)

(3)

⎞1/2 ⎛ ℏ ⎟ ph = ⎜ ⎝ 2mh*ωLO ⎠

where m*e and m*h are the electron and hole effective masses of CdS of 0.18m0 and 0.8m0, respectively, and ωLO = 300 cm−1 is the LO phonon frequency in CdS. According to eq 2, the ε value lies in the range of 5.851−6.16 for NCs with a radius within the range of 1.3−2 nm. Figure 8 depicts the dependence of the polarization energy on the εout value for NCs with a diameter of 3 nm. The εout value varies from 0 to 20 because the maximal εout value of 16.5 in the investigated system belongs to ammonia. It can be seen from the figure that the polarization energy strongly depends on the εout value if εout < εin. Within this range, the polarization

Figure 8. Polarization energy as a function of the dielectric constant of the NC environment calculated for 3 nm diameter NCs. The vertical red dashed line indicates the dielectric constant of NCs. F

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several times longer than a covalent one, which weakens the penetration of the substrate wave function inside NCs. We assume that the DIGS model can consistently explain the experimental data obtained. The mechanism inducing virtual gap states is similar to that of MIGS and predicts an almost symmetrical U-shaped density of the intragap states, as observed in our STS data. However, the origin of the states is different. In the DIGS model, it is intrinsic, whereas in the MIGS model, it is extrinsic. The DIGS density depends on the degree of disorder in NCs, and it is not obliged to correlate with NC size. Thus, the DIGS model does not contradict the data in Figure 6a, unlike the MIGS model. The location of unusual NCs near the cluster edge can be explained by the sintering of NCs that join to the cluster last. The sintering process alters the NC crystallinity at the sintering necks, creating defects and rendering the necks amorphous. Unusual NCs can lose their organic shell during the migration on the substrate surface, which slows or prevents the NC sintering process by reducing the surface diffusion coefficient.50,51 NCs without the organic shell have a high surface free energy and therefore a large sintering driving force, which explains the accumulation of unusual NCs at the periphery of the clusters.

determined by a barrier with a lower height (organic molecules), as in the case of the finite asymmetrical potential well.35 Note that for η ≥ 0.92 the product ηVSTS is larger than the NC band gap calculated using the finite spherical potential well model. To correct this difference, the polarization energy should be positive, which in turn requires εout < εin. Such a small value of the dielectric constant is typical of the matrix residues (higher alkanes) that are characterized by a dielectric constant of approximately 2.36 However, according to the TCAD calculations, the high η value is very unlikely for the considered configuration of the double-barrier tunnel junction. D. ZCG Narrowing. The ZCG narrowing of unusual NCs located near the cluster edge can be due to the appearance of a U-shaped density of states caused by the following: (1) heavy doping of NCs, (2) direct contact of NCs with the substrate, and (3) NC sintering.37 In the first case, a continuous energy spectrum near the band edges of NCs arises because of the impurity bands formed by the overlapped impurity states of both shallow donors and acceptors.38,39 In the second case, the virtual levels inside the band gap of NCs are induced by a metal-like wave function of the substrate penetrating deep inside NCs; these are the so-called metal-induced gap states (MIGS).40,41 In the third case, a sintering process might have altered the crystal structure of NCs at the sintering necks. Highly disordered boundaries can result in disorder-induced gap states (DIGS) inside the NC band gap.42,43 Let us consider these reasons for the ZCG narrowing. Symmetrical STS curves relative to the zero bias for unusual NCs (see Figure 2c,d) indicate that the Fermi energy is nearly centered in the band gap. Heavy doping must cause a shift in the Fermi level that can be clearly identified in STS of NCs by measuring the positions of the band edges relative to the zero bias.44 Strong compensation can keep the Fermi level near the center of the band gap; however, the shapes of the conduction and valence band tails must differ because of the heavier effective mass and the denser level structure of the valence band as compared to the light effective mass of the highly delocalized electron.45 Moreover, heavy doping hardly explains the spatial distribution of unusual NCs and the independence of the ZCG value of NC size (Figure 6). Indeed, if the background impurity is uniformly distributed in the initial LB film, the amount of the impurity entering into NCs is proportional to the NC size. The number of defects that can donate charge carriers was predicted to decrease with a decrease in the NC size because of an increase in the defect formation energy.46 Both numbers, however, are independent of the NC position on the substrate. The MIGS density decays exponentially in the gap with the distance from the substrate−NC contact. The decay length depends on the eigenstate energy within the gap and has a minimum at the virtual state branch point, originating from the semiconductor complex band structure, and grows at both valence and conduction band edges;47 therefore, the ZCG value must increase with an increase in NC height. Meanwhile, the ZCG value does not depend on the NC height (see Figure 6a). At the same time, a lateral dependence of the ZCG value was observed (Figure 6b). A similar phenomenon related to the lateral MIGS spreading was observed previously,48,49 with a MIGS decay length of ≤10 nm. The decay length estimated by fitting the data in Figure 6b by an exponential function gives a decay length of 74 nm, which is much larger than that predicted by the MIGS theory. Moreover, in our case, NCs are bonded to the substrate by the van der Waals forces with the bond length

V. CONCLUSIONS We studied the energy spectra and the tunneling transport through the ensembles of CdS NCs (nonpassivated and passivated by ammonia molecules) obtained by the Langmuir−Blodgett method. We showed that point defects attributed to an excess of Cd atoms affected the tunneling transport through separate NCs. This effect is more complicated in nonpassivated NCs because the ammonia atmosphere influences the defect formation process, decreasing the density of antisite defects in NCs. We demonstrated that the energy spectrum of NC is strongly influenced by the Coulomb interaction between the carriers localized in NCs and their polarization charges in a shell (the polarization energy). The shell dielectric constant εout = 10− 16.5, and the heights of the energy barrier created by the shell (V0 = 0.6−0.8 eV) were determined by comparing the experimentally measured values of the zero-conduction gap associated with the forbidden states in NCs and values of the NC band gap calculated within the spherical potential well model, taking into account the polarization energy and the voltage distribution in a tip/nanocrystal/substrate configuration. The shell comprises ammonia and organic molecules, wherein the ammonia molecules make a major contribution to the shell dielectric constant while the organic molecules determine the height of the confinement potential. We showed that the U-shaped intraband density of states of NCs located near the cluster edge was most likely to be related to defects arising as a result of the sintering of NCs that lost their organic shell during the migration on the substrate surface. Further studies could help quantify the effect of the shell on the defect density.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +7 (383) 330-69-45. Notes

The authors declare no competing financial interest. G

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ACKNOWLEDGMENTS We thank L. L. Sveshnikova for providing NCs studied in this work and S. A. Teys for conducting the STM measurements. We acknowledge financial support from the Russian Foundation for Basic Research via Grant 13-03-12118.

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