Thioacetic-Acid Capped PbS Quantum Dot Solids Exhibiting Thermally Activated Charge Hopping Transport

Abstract

Size-controlled lead sulfide (PbS) quantum dots were synthesized by the typical hot injection method using oleic acid (OA) as the stabilizing agent. Subsequently, the ligand exchange reaction between OA and thioacetic acid (TAA) was employed to obtain TAA-capped PbS quantum dots (PbS-TAA QDs). The condensation reaction of the TAA ligands on the surfaces of the QDs enhanced the conductivity of the PbS-TAA QDs thin films by about 2-4 orders of magnitude, as compared with that of the PbS-OA QDs thin films. The electron transport mechanism of the PbS-TAA QDs thin films was investigated by current-voltage (I-V) measurements at different temperatures in the range of 293 K-473 K. We found that the charge transport was due to sequential tunneling of charge carriers via the QDs, resulting in the thermally activated hopping process of Arrhenius behavior.

Introduction

Recently, among metal chalcogenide quantum dots (QDs), PbS QDs have received much attention due to their technologically promising optical and electronic properties.1-3 These properties vary not only due to the quantum confinement effect, which significantly depends on the size of the PbS QDs, but also by the tunneling effect between adjacent QDs, which depends strongly on the capping ligand on the QDs. These two effects play important roles in the application of PbS QDs.4-7 With these properties, QDs can be used in light emitting devices, such as lasers for telecommunication,5,8,9 in modulators for extended telecommunication10 and in infrared light emitting diodes.11-13 In addition, due to the strong quantum size effect, PbS QDs are widely used in devices such as solar cells,14-17 infrared detectors,6,18 and optical switches.19 Moreover, the multiple excitons generated in PbS QDs can be detected and applied to produce highly efficient photovoltaic devices.20,21

Quantum dot (QD) solids, which comprise an important class of artificial solids, are predicted to exhibit novel properties arising from the coherent quantum mechanical interactions of their constituent quantum dots.22 The characteristics of individual quantum dots as well as the many-body exchange interaction in quantum dot solids can be controlled to yield a new type of condensed matter. In many optoelectronic applications, the conductivity of the QD solids is affected by the interdistance between the QDs, that is dependent on the capping molecule.23,24 Especially, PbS QDs can be prepared in many ways with different capping ligands.25-31 Since a long and insulating ligand strongly limits the charge transport among the QDs, it was replaced with a short and more conductive one by the ligand exchange process, effectively enhancing electron and energy transfers and increasing the electronic coupling between QDs.24 Especially, a short ligand which can undergo a condensation reaction on the surfaces of QDs can provide high electron mobility. In our previous study, under thermal annealing at 200-300 °C, the thioacetate (TAA) groups on the surfaces of cadimium sulfide (CdS) QDs condensed with the remaining L2Cd-(S(CO)CH3)2 (L=3,5-lutidine) molecules or with the QDs themselves to form a QD solid, which showed very high field effect mobility (48 cm2 V−11 S−11) in the Al/CdS QD film/ZrO2 TFT structure.32 This phenomenon was the origin of our condensable QD solids concept, which was one more clearly demonstrated in our other previous study about condensable InP QD solids.33 Herein, the condensation process between the thioacetate groups on the surfaces of adjacent QDs formed an ‒S‒ linkage that provided a very dense solid. This very short interdistance of about 4.15 Å (In-S-In bond length) between the QDs by the ‒S‒ linkage is interpreted to improve greatly the electronic coupling and dipole-dipole interaction between QDs.22,33-36

In this study, we demonstrate once again the condensable QD solids concept for the PbS QD solid, as in our previous studies about the CdS and InP QD solids.32,33 The ligand exchange process between the long insulating oleic acid (OA) ligand and the short thioacetic acid (TAA) ligand is successfully performed by directly treating spin-coated PbS-OA thin films with TAA solutions, in order to synthesize thioacetic capped PbS QDs (PbS-TAA QDs) thin films to realize PbS QD solids. The optical and electrical properties of the condensable PbS QD solid thin films are examined to discuss the electron transport mechanism of the solids.

 

Experimental

Materials. All reagents were supplied by Aldrich Chemical Co. (St. Louis, MO, USA): lead (II) acetate trihydrate (Pb(Ac)2·3H2O), oleic acid (OA), octadecene (ODE, 90.0 %), bis(trimethylsilyl)sulfide ((TMS)2S), thioacetic acid (TAA, 96%), dimethylsufoxide (DMSO), toluene (anhydrous, 99.8%), and acetone.

Synthesis of PbS-OA QDs. PbS-OA QDs were synthesized and purified using a previously known procedure13 with a modification. First, 153 mg (0.4 mmol) lead (II) acetate trihydrate (Pb(Ac)2·3H2O) was dissolved in a mixture of 0.25 mL oleic acid (OA) and 3.75 mL octadecene (ODE, 90.0%). The mixed solution was heated at 150 °C for 1 h under vacuum condition to form the lead oleate solution, and, subsequently, the temperature was decreased to 90 °C under argon environment. A mixture of 42 μL of bis (trimethylsilyl) sulfide ((TMS)2S) and 2 mL of ODE were injected into the lead oleate solution under vigorous stirring, and the reaction was continued for nanocrystal growth for 2 min. The synthesized OA-capped PbS quantum dots (PbS-OA QDs) were isolated by precipitation with acetone, then centrifuged and redispersed in hexane. The isolation process was repeated three times to remove the unreacted species.

The Size Control of PbS-OA QDs: The size of the PbS QDs was controlled by changing the injection temperature from 90 °C to 150 °C. The diameter of the resultant PbS-OA QDs was calculated from the optical band gap value (in eV) by using the empirical equation developed by Iwan Moreels et al.37

The Fabrication of PbS-OA QD Thin Films and PbS-TAA QD Thin Films: PbS-OA QD thin films were fabricated by simply spin-coating the 5 wt % PbS-OA QD hexane solution onto substrates, where the PbS-OA QDs were the smallest ones because they had been synthesized at the injection temperature of 90 °C. The ligand exchange process between the oleic acid (OA) on the QDs of the PbS-OA thin films with thioacetic acid (TAA) was achieved by layer-by-layer deposition consisting of the following two steps. (i) PbS-OA QD thin films were fabricated by spin - coating 25 mg/mL PbS-OA QD hexane solution onto substrates. (ii) PbS-TAA QD thin films were fabricated by dipping the PbS-OA QD thin films in 0.1% TAA solution in acetonitrile (by volume) for 60 s, followed by dipping in the acetonitrile solution for cleaning. The layer-by-layer deposition was repeated several times to obtain PbS-TAA QD thin films of 40-50 nm thicknesses, as depicted in Scheme 1. All the QD thin films were cured at 80 °C to remove the remaining solvent, and then were cured at 200 °C for 1 hour under the vacuum condition of about 10−2 torr.

Scheme 1.Fabrication of PbS-TAA quantum dot thin film by “layer by layer” method.

Materials Characterization. Ultraviolet-visible (UV-vis) absorption spectra were obtained using a SCINCO S-3150 spectrometer. Photoluminescence spectra were obtained using a He-Cd (Kimmon Electric Co., IK3501R-G, Japan) excitation source at 325 nm and a photodiode array detector (IRY1024, Princeton Instrument Co., U.S.A). Fourier-transform infrared spectroscopy (FT-IR) was performed using a PerkinElmer (Waltham, Massachusetts, U.S.A) spectrometer with a resolution of 8 cm−1. Thermogravimetric (TG) analysis was conducted on a METTLER TOLEDO SDTA851e under N2 flow from room temperature to 500 °C. X-ray diffraction (XRD) spectra of the PbS QDs thin films were obtained using an X’Pert Pro Multi Purpose X-Ray diffractometer (PANalytical, Almelo, Nerthelands) equipped with a Cu Kα source operated at 40 kV and 30 mA. The 2θ angle was scanned from 10 to 90 degrees at an increasing rate of 2° per min and step size of 0.05°. The thicknesses of PbS-OA QD and PbS-TAA QD thin films were measured by the Field Emission Scanning Electron Microscope JSM-700F + EDS (Oxford). Metal-insulator-metal (MIM) devices were constructed by thermal deposition of aluminum (Al) top electrodes on the PbS QD thin films using a shadow mask. The PbS QDs thin films were prepared on a p-type silicon wafer, whose resistivity was less than 0.005 Ω·cm and thickness was 525 ± 25 μm. This low-resistivity silicon wafer acted as the back electrode of the MIM devices. Current-voltage (I-V) curves were obtained in air atmosphere at different temperatures in the range of 293 K-473 K using a HP 4145B semiconductor parameter analyzer.

 

Results and Discussion

PbS QDs are applied in many fields mainly because of their tunable optical and electrical properties by variation of their diameter. In our study, the diameter of PbS-OA QDs was varied by changing the injection temperature. As the injection temperature was decreased, the size of PbS quantum dots was decreased, as evidenced by the blue shift of the UV-vis absorption peak to a smaller wavelength (Figure 1(a)). The optical band gap was calculated by Eq. (1), where h is Planck’s constant, c = 3 × 108 m/s, and λmax is the excitonic peak wavelength.

The diameter of the PbS-OA QDs (d in nm) was calculated by using the empirical Eq. (2) developed by Iwan Moreels et al.37 We found that the QD diameter was gradually increased as the injection temperature was increased, as shown in Figure 1(b).

The optical properties of the smallest PbS-OA QDs, which was synthesized at the injection temperature of 90 °C, were investigated by UV-vis absorption spectroscopy and photoluminescence (PL) spectroscopy, as shown in Figure 2. The UV-vis absorption and PL peaks are located at 765 and 818 nm, respectively, indicating their significant blue-shifts to the near-infrared region of 700-900 nm, as compared with those of bulk PbS phase, whose band gap energy is 0.41 eV; λmax = 3020 nm. These blue shifts are surely due to the strong quantum confinement effect.

PbS-OA QD thin films were fabricated by simply spincoating the 5 wt % PbS-OA QD hexane solution onto substrates, where the PbS-OA QDs were the smallest ones that had been synthesized at the injection temperature of 90 °C. The ligand exchange process between the oleic acid (OA) on the QDs in the PbS-OA thin films with thioacetic acid (TAA) was performed, as discussed in the experimental section. This layer-by-layer deposition process was repeated to give PbS-TAA QD thin films of 40-50 nm thicknesses, as depicted in Scheme 1.

Figure 1.(a) UV-vis spectra of the PbS-OA QDs (in hexane solution) for different injection temperatures and (b) Variations of the QDs diameter according to injection temperature.

Figure 2.UV-vis absorption and PL spectra of the PbS-OA QDs in hexane solution, which were used in ligand exchange.

From the FT-IR spectra (Figure 3(a)) of the PbS-OA and PbS-TAA QD thin films, the intensities of the aliphatic C-H stretching peaks around 2800-3000 cm−1 for the PbS-TAA thin film were significantly decreased, as compared with those for the PbS-OA thin film, confirming the replacement of the long chain OA ligand with the short chain TAA ligand. In addition, two new peaks were observed at about 980 cm−1 and 624 cm−1 in the FT-IR spectra of the PbS-TAA QD thin films, indicating the existence of the TAA molecules on the surfaces of the QDs. Based on the peak assignments in a previous study,38 we assert that the former 980 cm−1 peak is due to C-S stretching vibration in the thioacetate resonance structure, which is ƞ3-coordinated to the PbS QD surface, and the latter 624 cm−1 peak is attributed to C-S stretching vibration in the –S-C(=O) bond, where the sulfur atom is covalently bonded to the Pb element of the QD surface. Furthermore, in the FT-IR spectrum of the TAA capped PbS QD thin film, there are no peaks assigned to carbonyl group in the range of 1700 cm−1-1750 cm−1. Instead, the peaks around 1400 cm−1-1500 cm−1 are attributed to the thioacetate (-SC(O)CH3) resonance structure which is ƞ3- coordinated to the PbS QD surface. This kind of decrease in vibrational wavenumber of the carbonyl group is similarly observed even in the FT-IR results of the OA-capped PbS QD thin film where the peaks of carbonyl group in the range of 1700 cm−1-1750 cm−1 are not observed and, instead of it, those of carboxylate resonance structure ƞ3-coordinated to the PbS QD surface in the range of 1400 cm−1-1500 cm−1 are found. Moreover, the disappearance of S-H stretching at 2600-2550 cm−1 was due to the bonding of the sulfur atom with the lead atom on the QD surfaces,39 implying a reaction between TAA molecules and PbS QDs. Figure 3(b) shows a peak at 3005 cm−1 corresponding to Csp2-H stretching vibration on the OA ligand. After the ligand exchange process, the peak intensity was decreased. The Csp2-H infrared absorption cross section is assumed to be independent of surface coverage as confirmed by similar surfaces.40 Therefore, the surface coverage of the TAA ligands (or ligand exchange percentage) was determined from the relative decrease in the integrated IR absorbance of the Csp2-H peak given by Eq. (3):

where IACsp2before and IACsp2after are the integrated absorbances due to the Csp2-H peak at 3005 cm−1 before and after the ligand exchange, respectively. Finally, the surface coverage of TAA ligands (or the ligand exchange percentage) is determined to be 64%, implying that the surface coverage of OA ligands continues to be 36%.

Figure 3.(a) FT-IR spectra of PbS-OA and PbS-TAA QDs thin films, (b) FT-IR spectra of C=C bond peak of OA in PbS-OA and PbS-TAA QDs thin films.

As shown in Figure 4, the XRD patterns indicate the high crystallinity of the PbS-TAA QD thin films,showing various diffraction peaks at 2θ values of 26.02°, 30.09°, 43.07°, 50.98°, 53.36°, 62.88°, 69.02°, 70.88° and 79.80°. All these diffraction peaks can be assigned to the diffractions from the (111), (200), (220), (311), (222), (400), (331), (420), and (422) planes, respectively, of the face-center-cubic rock salt structured PbS.2,31,36 The average diameter of the QDs in the thin films (D) was calculated from the Debye-Scherrer formula,41

where k is the shape factor of about 0.9, λ is the x-ray wavelength (0.15405 nm), β is the full width at half maximum (FWHM) of the main diffraction peak from the (111) plane and θ is the diffraction angle. The average diameters of PbS-OA QD and PbS-TAA QDs in the thin films were 3.03 nm and 3.74 nm, respectively, indicating that a surface reaction must have taken place during the dipping step of the PbS-OAA QD thin films in the TAA solution in the ligand exchange process. The increase in the diameter of the QDs can be explained by the Osttwald ripening process: a large particle grows at the expense of smaller ones. This phenomenon was previously mentioned by Kumacheva’s group for thiolate capped-PbS QDs.42 The TAA ligand, having a higher electron donating ability than the OA ligand, is thought to etch away the Pb element in the PbS QD surface like the OA ligand,43 as shown in the upper part of Scheme 2, inducing the breakage of the Pb-S bond on the QDs surfaces producing smaller quantum dots. Subsequently, the small QDs in the Ostwald ripening process are exhausted to produce larger QDs, as shown in the lower part of Scheme 2.

In order to validate the etching mechanism of the surfaces of the PbS QDs by the TAA molecules, the following test ligand exchange reaction in PbS-OA QDs solution was performed. After the TAA molecules were added to the PbS-OA QDs in hexane, a black precipitate of PbS-TAA QDs was abruptly formed. The black QDs precipitate was purified by centrifugation. Then, we monitored the change of the black QDs precipitate in the DMSO solvent to confirm the etching mechanism. The precipitate was not soluble at all initially, but after three days, the solution became dark orange, with the precipitate still existing in the solution, implying that the precipitate was partially soluble in the DMSO solvent. This result suggests that some of the QDs in the DMSO solvent became smaller due to the etching reaction, which generated the lead thioacetate complex Pb(S(CO)CH3)x that is dissolved into the DMSO solvent. Pb(S(CO)CH3)x can dissolve in DMSO and turn the solution dark orange. To confirm the color of the lead thioacetate complex Pb(S(CO)CH3)x, we mixed lead acetate Pb(OCOCH3)2 with thioacetic acid in the DMSO solvent, stirred the solution for 30 min, and then, filtered it to obtain a dark - orange solution with low concentration of Pb(S(CO)CH3)x. The UV spectrum of the PbS-TAA QDs solution, which was stirred in the DMSO solvent for 3 days, was similar to that of the lead thioacetate complex Pb(S(CO)CH3)x (Supporting information Fig. S1).

Figure 4.X-ray diffraction (XRD) data of PbS-TAA QDs (red line) and PbS-OA QDs (blue line).

Scheme 2.Expected scheme for increasing the size of QDs during the ligand exchange process.

The effects of the capping ligand and annealing temperature on the UV-vis absorption spectra of the PbS QD thin films are summarized in Figure 5(a). The excitonic peaks of the PbS-TAA QDs thin films were more red-shifted compared with those of the PbS-OA QDs thin films, well consistent with the size increase of PbS-OA QDs (3.03 nm) to the size of PbS-TAA QDs (3.74 nm) in the XRD result. The excitonic peaks of the PbS-OA QDs thin films were maintained with increasing annealing temperature, whereas those of the PbS-TAA QDs thin films were red-shifted from 886 nm to 906 nm with increasing curing temperature from 80 °C to 200 °C. We suggest that this red shift was originated from the condensation reaction between the thioacetate groups on the adjacent QDs at the high annealing temperatures (reaction R1). This condensation reaction decreases the distance between adjacent QDs, which was the case with condensable InP QDs.33 We can find an another research result to ensure the possibility of the condensation reaction of two thioacetate groups coordinated to Pb metal ions in a previous study,44 where Pb(SCOCH3)2·18-crown-6 undergoes thermal decomposition to give rise to crystalline PbS phase. The formation of PbS phase cannot explained chemically without assuming the condensation reaction of two thioacetate groups coordinated to the Pb metal ions.

Nozik’s group reported a red shift for InP QDs upon UV absorption due to the decrease in the interdistance between the QDs on the thin film. The InP QDs films with the interdistances of 0.9 nm and 1.8 nm showed red shifts of 140 meV and 18 meV, respectively.23 In our previous study of InP-TAA QDs thin films, we also observed a red-shift from 550 nm to 570 nm as the curing temperature is increased.33 This shift was due to the condensation reaction that decreases the interdistance between the adjacent QDs. Thus, a change on the interdistance between the QDs is the key to the red shift upon UV absorption. Two physical phenomena owing to the decrease in the interdistance can explain the red shift: (i) electronic coupling and (ii) dipole-dipole interaction. Electronic coupling is generated when the interdistance between the QDs is decreased to an extent that the electronic wave functions of individual QDs in close proximity can hybridize together to form delocalized states or minibands.23,33,36 This electronic coupling is dependent on the size of QDs23,45-47 and is increased exponentially with the decrease in the interdistance between the QDs. The increase in the electronic coupling reduces the energy of excitonic transition, resulting in the red shift on the UV absorption spectroscopy. In addition, dipole-dipole interaction between the QDs due to the decrease in the interdistance between the QDs is also related to the red-shifts mentioned above.35 In this model, the transition dipole moment of light absorbing QDs may induce dipole moments in the neighboring QDs in their ground state. The dipole-dipole interaction adds an additional Coulomb term to the dipole transition, thus reducing the energy of excitonic transition.

Figure 5.(a) UV-vis absorption spectra of PbS-OA and PbS-TAA QDs thin films cured at 80 °C and 200 °C, respectively, and (b) PL spectra of PbS-OA and PbS-TAA QDs thin films cured at 200 °C.

At the same measurement conditions, the PbS-OA QDs thin films showed high photoluminescence (PL) efficiencies, while the PbS-TAA QDs films showed complete PL quenching (Figure 5(b)), which can be explained by the increased number of surface dangling bonds after the ligand exchange process. Additionally, a strong electronic coupling between the neighboring quantum dots can cause hybridization of band edge orbitals and the transfer of exciton energy from a large bandgap quantum dot to small bandgap quantum dot, which can decrease in the PL intensity; therefore, a strong electronic coupling is responsible for the PL quenching phenomenon.48 In addition, the strong dipole-dipole interaction in a PbS-TAA QDs film enhances the FRET (Förster resonance energy transfer) process inside the PbS-TAA QDs, which leads to PL quenching.33

A metal-insulator-metal (MIM) structure was fabricated to investigate the electrical properties of the PbS-OA QDs and the PbS-TAA QDs thin films, whose thicknesses were the same in the SEM images (Figure 6). After the ligand exchange from the OA (C17H33COOH) to TAA (CH3COSH) on the surface of a PbS quantum dot, the number of carbon atoms on the alkyl chain was decreased by about 17 times, according to the equation G-G0exp(-βn), where G0 is the pre-factor, β is the decay constant (β~1.2) and n is the number of carbon atoms on the alkyl chain.49 At the initial state of baking at 80 °C, the conductivity of the PbS QDs thin films is expected to increase by about 8.3 orders of magnitude after the ligand exchange process:

where G1 and G2 are the conductances of the PbS-OA QDs and PbS-TAA QDs thin films.

Figure 6.FE-SEM of PbS-OA and PbS-TAA films cured at 200 ℃.

In addition, after the ligand exchange process and after forming the completely condensed state of curing at 200 °C, we can expect that the conductivity of the PbS-TAA thin films will be significantly enhanced by at least 8.3 orders of magnitude. In reality, at 200 °C curing, the current densities across the PbS-TAA QDs thin films were higher than those of the PbS-OA QDs thin films by just about 2-4 orders of magnitude, as shown in Figure 7. These differences in the current density are much smaller than what was expected from the above theoretical estimation. This is may be due to the low ligand exchange percentage and the increase in the QD diameter, which were mentioned in the above results and discussions, and due to the increase in defect concentration.

Figure 7.Current density-electric field curves of PbS-OA (blue line) and PbS-TAA (red line) films cured at 200 °C. Inset picture shows the MIM structure.

For a more in-depth understanding of the charge transport mechanism in the PbS-TAA QDs thin films, as shown in Figure 8(a), we measured the I-V curves (current density-electric field curves) at different temperatures 293 K, 323 K, 373 K, 423 K, and 473 K for the PbS-TAA QDs film cured at 200 °C. All of curves were symmetric, sigmoid-shaped.

We mention that the effect of the irregularities in the QDs positions and in the strengths of the tunneling coupling on the physical properties of QD arrays is different between metallic and insulating samples. If the coupling between the dots is sufficiently strong and the system is well conducting, the irregularities are not very important.50 In contrast, irregularities become crucial in the limit of low coupling, where the system is an insulator.51 The key parameter that determines most of the physical properties of a QD array is the dimensional tunneling conductance g between neighboring dots.52 Samples with g > 1 exhibit metallic transport properties, while those with g < 1 show insulating behavior. All our samples belong to the insulating side of the metal-insulator transition. Therefore, the charge on each dot becomes quantized as in the standard Coulomb blockade behavior. In this case, an electron has to overcome an electrostatic barrier of the order EC in order to hop onto a neighboring dot, with EC being the Coulomb energy of a single dot. The problem of electron transport in QD arrays is twofold: (i) to understand the behavior of the density of states near the Fermi level and the role of the Coulomb correlations in forming this density of states, and (ii) to study the mechanism of electron tunneling through a dense array of QDs.

Figure 8.(a) I-V curves of PbS-TAA thin films cured at 200 °C for different temperatures. Inset picture shows the linear fit that allows the determination of the differential conductance G = dI/dV at the zero bias limit. (b) Inverse relationship between lnG and absolute T.

Charge disorder arises from variations in the local chemical potentials due to polarization by trapped parasitic charges in the substrate or in the ligand shells surrounding the dots. In practice, charge disorder is unavoidable for QD arrays; as a result, tunneling occurs along paths that optimize the overall energy cost. This results in two distinct regimes.53 At applied bias voltages and temperatures large enough to overcome local Coulomb energy costs, transport occurs by sequential tunneling between neighboring dots. At small bias and low temperatures, sequential tunneling is suppressed by the Coulomb blockade. In this regime, conduction involves higher order tunneling processes, the so-called cotunneling events, which can transport a charge over distances of several dots without incurring the full Coulomb energy costs. The crossover temperature between sequential tunneling and electron cotunneling is defined as Tcross = Ec2/T0, where T0 = e2/κξ is the characteristic temperature with κ and ξ being the effective dielectric constant and localization length, respectively. In our experiment, T > Tcross and therefore, electron transport was due to sequential tunneling, which led to the Arrhenius behavior for zero bias conductance.

Important information on charge transport mechanism can be deduced from the relationship between conductance (G) and temperature, where the G is simply calculated from the current density. The dependence of ln(G) on 1/T for the PbS-TAA QDs thin film annealed at 200 °C is shown in Figure 8(b). The values of lnG(T) show a linear relation from 323 K to 473 K, otherwise known as an Arrhenius-like T dependence.54 This relation confirms the sequential tunneling mechanism mentioned in the above discussion. The transport in this regime T > 323 K was a thermally activated transport of sequential tunneling shown in Figure 9. Therefore, Eq. (6) is as follows: 55

where Ea is the activation energy for charge transport, kB is the Boltzmann constant, βd is the electron tunneling coefficient and δ is the QD edge-to-edge distance, in other words, interdistane. From the slope of the Arrhenius plot, we obtained the activation energy (Ea = 170 meV). In a previous report on gold nanoparticles connected by oligothiophene molecules,55 the activation energy was about 21-45 meV, which is smaller than our result (170 meV). Another, our result is similar with the previous study by Sargent’s group, who reported an activation energy about 160 meV for n-butylamine capped PbS-QDs.56 This similarity in the activation energy is very unusual if one considers that the condensation reaction of TAA ligands between the adjacent QDs gives Pb–S–Pb linkages of very short interdistance of 4.34 Å while the n-butylamines ligands of chain length of 5.12 Å provide an interdistance of approximately 10.24 Å.57 This is because a shorter interdistance give rise to a lower activation energy. The activation energy of 170 meV for our TAA-capped PbS QD solids, which is higher than expected, is attributed to the low ligand exchange percentage of 64%, which was previously mentioned in the FT-IR results. The remaining OA ligands are not likely to allow the physical situation in which the QDs interdistance is decreased to the extent of Pb-S-Pb linkage length between the QDs.

Figure 9.Activated hopping transport of sequential tunneling of PbS-TAA QDs thin films.

One assumes that, as for the interdistance of the PbS-TAA QDs, 64% of the sphere surface of a QD is separated by Pb-S-Pb linker length of 4.34 Å while the other 36% sphere surface of the QD is separated by 2 times the OA chain length of 39.2 Å as shown in Scheme 3.57 Herein, we can assert that first-order electron hopping rate constant, kET (s−1), can be calculated from nanoparticle film conductivities by assuming a cubic-lattice model, which was previously used to examine the electron transport for redox polymers arenethiolate-protected nanoparticles,58

where, R is the gas constant; F the Faraday constant; σ the conductivity per unit area (σ = G·thickness/area; Ω−1cm−1) at temperature T (K); δ the averaged core edge-to-edge distance (cm), as expressed by:

where α = 0.64 (ligand exchange ratio), lPb-S and lOA are the lengths of the Pb-S bond and the oleic acid chain; and Cexpt the solid state concentration (mol/cm3) of a PbS quantum dot, as expressed by:

where NA is Avogadro’s number and 0.52 is the filling factor for the PbS cubically close packed film, and the 103 factor converts the dimensions to molar concentrations, and r core is the radius of the PbS-TAA quantum dot. The results of the first-order electron hopping rate constant, kET (s−1), are summarized in Table 1. The kET = 3.41 × 106 s−1 for the PbS-TAA QD thin film cured at 200 ×C is estimated to be much smaller than that (2.6 × 108 - 1.1 × 1011 s−1) of the arenethiolate capped-Au nanoparticle thin films.58 This result supports the idea that the remaining long insulating OA, even after the ligand exchange process, limits the electron transfer in PbS-TAA QD solids.

Scheme 3.One assumes that, for the interdistance of the PbS-TAA QDs, 64% of the surface of a QD is separated by the Pb-S-Pb linker bond length of 4.34 Å while the other 36% of the surface is separated by 2 times the OA length of 39.2 Å.

In our PbS-TAA QDs thin film, its electrical properties and activation energy in the activated transport mechanism of sequential tunneling are expected to be significantly affected by the ligand exchange percentage and the relevant interfacial chemical state between PbS-TAA QDs which are surely to be tuned by changing ligand exchange reaction time in the layer-by-layer film formation. This issue will be further investigated with more controlled experiments in a separate study.

Table 1.Activation energy, conductivity data and self-exchange rate constants for PbS-TAA quantum dot thin films

 

Conclusion

Thioacetic acid capped-lead sulfide quantum dot (PbS-TAA QD) thin films were synthesized by the ligand exchange process of oleic acid capped- lead sulfide quantum dot (PbS-OA QD) thin films with thioacetic acid (TAA) using the layer‒by‒layer method, where ligand exchange percentage was 64%. By applying the ligand exchange process, the size of the quantum dots in the thin films was increased from 3.03 nm to 3.74 nm due to the Ostwald ripening process. The electrical conductivity of the PbS-TAA QD thin films was enhanced by about 2-4 orders of magnitude, as compared with that of the PbS-OA QD thin films. Thermally activated hopping transport of sequential tunneling was determined to be the dominant carrier transport mechanism in the PbS-TAA QD thin films. The activation energy of PbS-TAA QD thin films was estimated to be about 170 meV from the temperature-dependent electrical conductivity, which was not much higher than the activation energy of the n-butylamine capped PbS QDs thin film, because of the low ligand exchange percentage of 64% of the PbS-TAA QD thin films.