Trap-Induced Dispersive Transport and Dielectric Loss in PbS Nanoparticle Films

2.1 Materials

Lead(II)acetate-trihydrate [Pb(OAc)₂·3 H₂O, 99.99%], diphenylether (≥99%), oleic acid (OA, C₁₈H₃₆O₂, ≥90%), acetic acid (C₂H₄O₂≥99.7%), toluene, and dichlorbenzene were purchased from Aldrich. Tri-n-octylphosphine (TOP, C₂₄H₅₁P≥97%) and bis(trimethylsily)sulfide [TMSS, (CH₃)₃SiSSi(CH₃)₃, 99%] were purchased from STREM chemicals. Ethan-1,2 dithiol (EDT) was purchased from FLUKA. Acetonitrile was purchased from Chemsolute. PANI:PSS was received from Ormecon GmbH.

2.2 Nanoparticle synthesis

PbS NPs were synthesized in a continuous flow reactor developed by the Centre for Applied Nanotechnology GmbH. A mixture of one equivalent Pb(OAc)₂·3 H₂O, OA and TOP in diphenylether was heated to 80°C. Acetic acid was evaporated under vacuum to form an OA-lead complex. A 0.5 M solution of bis(trimethylsily)sulfide-TOP was added under nitrogen protection to obtain particles. PbS NPs were isolated from the reaction mixture by precipitation with a polar solvent and subsequent redispersion in octane. The NPs show the absorption edge at 1033 nm, with corresponding band-edge emission at 1166 nm. The mean size of the PbS NPs is approximately 3 nm. High resolution transmission electron microscopy image of the PbS NPs along with optical spectra are presented in Supporting Information.

2.3 Device fabrication

Indium tin oxide (ITO) on a glass substrate was used as a high work function bottom contact. A diode with an area of 16 mm² was defined by structuring ITO. PANI:PSS was diluted 1:1 with water and spin-coated onto the ITO at 4000 rpm for 1 min and subsequently annealed at 140°C for 1 min. The active layer of PbS NPs was spincoated using an in situ ligand exchange approach. First, a highly concentrated PbS NP solution was spincoated at 1500 rpm followed by a mixture of acetonitrile and EDT (0.1 M). Next, actetonitrile and octane were used to remove the ligand excess. This procedure was repeated up to four times to replace the original ligand and to manufacture a PbS layer of approx. 180 nm thickness. Aluminum was evaporated on the active layer through a shadow mask to form the low work function top contact.

2.4 Electrical measurements

The impedance measurements were performed using Nova Autolab PGSTAT302N potentiostat equipped with the FRA32M frequency analyzer module. The applied AC voltage was set to 20 mV and the DC voltage offset was chosen between −0.5 V and 0.5 V. The frequency was swept from 1 MHz and 10 Hz. To avoid disturbance from any background noise, the sample was placed into a Faraday cage for the duration of the measurement. Measurements under illumination were recorded using LOT LS 0306 Solar Simulator equipped with 1.5 AM filter and 100 mW/cm² irradiation power.

3.1 Impedance and dielectric properties of PbS NP films in the dark

Figure 3 shows the Nyquist plot of the impedance recorded for the samples. The data taken from PbS films capped with the EDT ligand are shown as black squares (with PANI:PSS interlayer) and green triangles (without PANI:PSS interlayer), respectively. The data taken from PbS films capped with MPA ligands are shown as red circles (with PANI:PSS interlayer) and blue triangles (without PANI:PSS interlayer), respectively. We observe that the samples demonstrate a high capacitive component, i.e. the semicircles do not close at lower frequencies. To understand the influence of the PANI:PSS interlayer and ligands in more detail, we fit the impedance data using the circuit model consisting of one R-CPE and one RC element (Figure 2). The constant phase element (CPE1) accounts for non-idealities in the system response, i.e. dispersive transport. The impedance of the CPE is given by

Fig. 2:

Equivalent circuit diagram used for fitting impedance data in this study.

where Q is the effective coefficient, and α is a unit-less parameter between 0 and 1. If α=1, Q reduces to an ideal capacitor Q=C and if α=0, the CPE reduces to an ideal resistor Q=1/R.

Fits are represented as solid lines in Figure 3 and the details of the fitting analysis can be found in the Supporting Information.

Fig. 3:

Nyquist plot for the devices used in this study including fits at 0 V bias. For convenience PANI is used instead of PANI:PSS in the legend.

We now consider the voltage-dependence of the circuit elements. The series resistance R_s was found to be voltage independent and very comparable between the samples, with values in the range of 125–155 Ohm cm⁻², whereas resistances R1 and R2 exhibit bias dependent change, which we attribute to field-induced variations in Schottky barrier height. Ligands at the NP surface act as interface dipoles leading to changes in doping density and therefore alter the Fermi level of PbS [26], [27]. Depending on the electronic character of the ligands, NPs can exhibit either p- or n-type, as well as ambipolar transport. The energetic position of the Fermi level in NP films treated with EDT is expected to be close to the middle of the band gap, whereas MPA treated samples were shown to be rather p-doped with the Fermi level closer to the valence band. The variation in the position of the Fermi level for differently treated samples leads to variation in Schottky barrier height at the PbS-Al interface [20], which is qualitatively larger in the case of MPA treated samples and therefore shows higher values in R1 and R2 (see Supporting Information).

The most intriguing behavior is observed in the CPE element values. α values are shown in Figure 6, they were found to be between 0.95 and 0.99 for devices prepared with MPA ligand and 0.85–0.97 for devices prepared with EDT (Figure 4a). The effective CPE coefficient Q increases for EDT devices by one order of magnitude for negative bias, indicative of charge build up, whereas the values for MPA devices show little dependence on bias voltage (Figure 4b). A decrease in α and increase in Q for EDT treated samples strongly indicate the presence of trap states, which manifest themselves as a distribution in carrier mobilities due to multiple trapping and release processes (α) and space charge (Q) [28], [29]. Experimentally, it was shown that EDT ligands introduce a higher density of trap states in the band gap of the PbS NPs compared to MPA [17]. Theoretical studies support these findings [30] demonstrating the emergence of gap states in PbS density of states structure for increased concentrations of EDT and for various binding configurations, i.e. mono- or bidentate. In the dark, the impedance spectra demonstrate that dispersive transport in EDT devices is prevalent, indicating that the electrical transport is bulk-limited. In contrast, the use of MPA ligands leads to better surface passivation, and therefore decreases trap state density. In these devices, the electrical transport seems to be rather limited by the Schottky interface, as inferred from voltage-dependent variations in the circuit element R2.

Fig. 4:

(a) α values and (b) Q values plotted against bias voltage for PbS-EDT devices with PANI:PSS interlayer (black squares) and without (green triangles), as well as for PbS-MPA with (red dots) and without PANI:PSS interlayer (blue triangles). α and Q were obtained from fits using the circuit model displayed in Figure 2.

The voltage-dependent dielectric loss spectra of NP films prepared with EDT and MPA ligands are shown in Figure 5a and b, respectively. We observe two peaks in the loss spectra of NPs films prepared with EDT (Figure 5a). The low frequency peak clearly demonstrates bias dependence, while the high frequency peak is bias independent. For MPA treated NP films, the low frequency peak is absent.

Fig. 5:

Representation of loss versus frequency for (a) PbS-EDT and (b) PbS-MPA diodes without the PANI:PSS interlayer for bias voltages in the range between +0.5 V and −0.5 V.

From the equivalent circuit analysis, we attribute the peak in the lower frequency range to the shallow traps in PbS induced by EDT, that yield the dispersive transport and is reflected in CPE parameters α and Q. We assign the frequency independent peak at high frequency to the deep traps in PbS quantum dots [30], [31], which were observed next to the shallow traps [17], [31].

To visualize shallow and deep trap states, we applied the model from Walter et al. [32]. In this model, variations in semiconductor capacitance with frequency are proportional to the energetic distribution of trap states N_T according to

From the plot of the derivative of dC/dω versus frequency (Figure 6) we observe features which can be attributed to the presence of shallow trap state densities (low frequencies) for EDT treated NP films, and the presence of deep trap state densities (high frequencies) which peak at around the same frequency for all devices. This might point to the traps originated from the stoichiometry of the PbS nanocrystals (ratio of Pb:S) [30].

Fig. 6:

Plot of the frequency dependent derivative of the capacitance for PbS-EDT diodes with (black squares) and without PANI:PSS interlayer (green triangles) as well as PbS-MPA diodes with (red circles) and without PANI:PSS interlayer (blue triangles) at 0 V bias. −ωdC/dω is proportional to the density of trap states and represent a trap states profile once plotted against frequency.

3.2 Impedance and dielectric properties of PbS NP films under illumination

Interestingly, under illumination the values of the circuit elements are very comparable for all devices (see Supporting Information). The CPE element reduces to a nearly ideal capacitor with frequency independent values, with α in the range of 0.96–0.98. We only notice variations in R1 with voltages in forward bias conditions and it was earlier attributed to the change in Schottky barrier. All of the other circuit element values are bias voltage independent. Generally, we observe an overall increase in capacitances and decrease in resistances for all devices. This is consistent with an increase in photo-generated charge density in the active layer, which facilitates trap filling [33].

Under illumination, the peak in the dielectric loss spectrum associated with shallow traps is no longer observed and deep trap peak is shifted to lower frequencies (Figure 7a). This behavior can be understood by considering the dC/dω versus frequency spectrum (Figure 7b). Variations in device capacitance are correlated to the trapping and release of carriers in states, assumed to be symmetrically centered around E_F [32]. Under illumination, photoinduced charge and trap filling results in shifting of E_F in the band gap. The analysis is not sensitive to the energetic direction of shifts in E_F, only differences in energy. Figure 7a and b together indicate that under illumination, the energy difference between E_F and the density of deep trap states diminishes.

Fig. 7:

(a) Loss spectra of PbS-EDT diode in dark (filled squares) and under illumination (open squares) at 0 V bias and (b) −ωdC/dω plotted against frequency for PbS-EDT and PbS-MPA diodes in dark (filled symbols) and under illumination (open symbols) displaying the trap states profiles of the devices in dark and under illumination. The dark trap states profile is the same as displayed in Figure 6.

Our impedance results demonstrate that PbS NP films prepared with the two different ligands demonstrate different trap profiles in the dark, but the same trap profiles under illumination. The results from the dark measurements are consistent with the findings from the study by Jeong et al. [17], in which it is reported that MPA is more effective for passivating surface states than EDT. Under illumination, however, we observe that the influence of the ligand on electrical transport vanishes, and electrical transport is limited by deep trap states related to PbS stoichiometry. The change in the electrical and dielectric properties of the PbS NP films upon illumination may be attributed to photoinduced trap filling of shallow surface states. However, it has also been argued that the increase in carrier density upon illumination cannot explain the relatively high values of photoconductivity observed in PbS NP films [19]. At high carrier densities increased carrier delocalization has been reported [34]. These results indicate that more detailed studies of carrier transport under different illumination conditions are necessary to fully understand electrical loss mechanisms in PbS NP films for opto-electronic applications.

In summary, we find that trap-induced dispersive transport plays a greater role in the dark and at lower devices biases, i.e. for LED applications. Under illumination, however, stoichiometric defects which induce deeper traps in the PbS nanoparticles may be more relevant for device performance.