Detecting trap states in planar PbS colloidal quantum dot solar cells

The recently developed planar architecture (ITO/ZnO/PbS-TBAI/PbS-EDT/Au) has greatly improved the power conversion efficiency of colloidal quantum dot photovoltaics (QDPVs). However, the performance is still far below the theoretical expectations and trap states in the PbS-TBAI film are believed to be the major origin, characterization and understanding of the traps are highly demanded to develop strategies for continued performance improvement. Here employing impedance spectroscopy we detect trap states in the planar PbS QDPVs. We determined a trap state of about 0.34 eV below the conduction band with a density of around 3.2 × 1016 cm−3 eV−1. Temperature dependent open-circuit voltage analysis, temperature dependent diode property analysis and temperature dependent build-in potential analysis consistently denotes an below-bandgap activation energy of about 1.17–1.20 eV.

PbS colloidal quantum dots (PbS QDs) are attractive materials for next generation photovoltaic devices due to their facile solution processing, low material cost, long term air stability and possibility of tailoring their optoelectronic properties by tuning size, composition and surface chemistry [1][2][3][4] . However, PbS QDs in solution are typically surrounded by long aliphatic ligands and once they form solid film, the long ligands act as barriers for charge transfer and transport between neighboring QDs [5][6][7] . The ligand-exchange procedure, which is used to remove such long ligands can create many surface traps such as vacancies and dangling bonds 8,9 , these traps assist carrier recombination, and hence seriously limit the device performance 10,11 . Great efforts have been put in developing surface passivation approaches to reduce the traps, and power conversion efficiency (PCE) of PbS quantum dot photovoltaics (QDPVs) has been significantly improved (over 10%) [12][13][14][15] . Nevertheless, the achieved PCE is still far below the expected and the surface traps remains a key limiting factor for PbS QDPVs [16][17][18] .
Trap states in the PbS QDPVs has been carefully investigated to understand how they limit the device performance. For examples, Ip Here we employ Impedance Spectroscopy (IS) to obtain the information of the trap states in our fabricated device with currently most advanced architecture of ITO/ZnO/PbS-TBAI/PbS-EDT/Au (shown in Fig. 1(a)) 12,13 . In such a device the diode property is from ZnO/PbS-TBAI heterojunction, and the PbS-EDT layer acts as an electron-blocking layer between the PbS-TBAI layer and the Au anode 24 . For the ZnO/PbS-TBAI heterojunction, after suitable illumination (mainly for the UV region), the ZnO doping density is much higher than the PbS-TBAI doping density, thereby can be regarded as a N + P abrupt junction, with the depletion region locates in the PbS-TBAI film 25,26 . In our study we use AM 1.5 illumination (10 min AM 1.5 illumination) to generate a N + P ZnO/PbS-TBAI heterojunction, and then performed various measurements including current-voltage and capacitance-voltage under various temperatures to gain information in the PbS-TBAI film. Without the pre-illumination various expected parameters cannot be extracted and various curves were actually seriously distorted (shown in Supporting Information, Figs S1-S4), similar with what Willis et al. described 25 . IS were tested under a variety of temperatures between 193 K and 293 K under short-circuit condition.  Figure 1(c) is the cross-sectional scanning electron microscopy (SEM) image of the device. The current density-voltage (J-V) curve under AM 1.5 illumination at room temperature is given in Fig. 1(d). The short-circuit current density (J SC ), open-circuit voltage (V OC ) and fill factor (FF) are 25.03 mAcm −2 , 0.559 V, and 58.67%, respectively (seen in Table 1). The PCE of 8.21% is comparable to the reported device 12,24 . The external quantum efficiency (EQE) spectrum of the device is displayed in Fig. 1(e). The light and dark J-V curves of the device under various temperatures (33~293 K with a step of 20 K) are shown in Fig. 2(a,b), respectively. From the dark J-V curves, two parameters characterizing the property of diodes, namely ideality factor (n) and saturation dark current density (J 0 ), can be extracted with Shockley diode equation (1) listed below 23,27 :

Results and Discussion
where R p is the parallel resistance, R a is the series resistance, q is the elementary charge, V is the output voltage, k is the Boltzmann constant, T is the temperature. In order to facilitate comparison, all the parameters for the devices extracted from J-V measurements under different temperatures are listed in Table 1 and plotted in Fig. 2(c,d). Figure 2(c), it is seen that V OC increases with decreasing temperature till 153 K, and then begins to saturate and later drops a little. The trend has also been observed by other groups, and can be attributed to low carrier mobility in QD layers under low temperatures 28,29 . In Fig. 2(c,d), it is shown that J SC , FF and R p decrease with decreasing T and R a increases with decreasing T. These all can be attributed to the limited carrier mobility under low temperatures, which hampers carrier extraction and enhances recombination. The PCE increases from 8.21% to a high value 9.41% when temperature decreases from room temperature to 233 K, and then begins to drop. It is worth noting here that n and J 0 show interesting trend with T. Generally, the values of n for the device increase exponentially when T is lower than 193 K. J 0 , meanwhile, decreases with decreasing T from 293 K to 193 K, and then starts to increase. From the reverse bias region of the dark current curves in Fig. 2(b), it can be seen that the reverse dark current decreases with decreasing T in the whole temperature range of 33~293 K, which should be the reasonable trend. The very large n and the enhanced J 0 in the temperature range of 33 to 193 K could be caused by the R a . Because at low temperature, R a becomes larger and larger, which is comparable to R p , and hence the Shockley diode equation cannot be simplified into the form of equation (1) and more voltage drops on R a . The high-quality Figures for Fig. 2(c,d) are also given in Supporting Information (Fig. S5). Therefore, the parameter extraction is meaningless when T < 193 K. So we focus our attention on carrier recombination mechanisms and discussed in the range of 193 K to 293 K. Figure 3(a) displays the measured V OC versus T, by extrapolating the V OC to 0 K, we obtain the maximum possible quasi-Fermi level separation achievable where screening effect of thermally generated electrons/holes is fully avoided: qV OC = 1.17 eV (qV OC is equal to the electron and hole quasi-Fermi level separation 26,30 ). As we know V OC can be written as 24 : and for a single thermally activated carrier generation-recombination mechanism, J 0 can be expressed as equation (3): where J 00 is the prefactor, E a is the activation energy. By substituting equation (3) into (2), V OC can be immediately expressed as straightforward form: OC a 0 0 SC From which E a can be directly determined as qV OC at T = 0. Meanwhile equation (3) can be simply reorganized into equation (5): 0 a 00 and hence from the dark J-V curves at different temperatures, E a can be extracted, which is 1.18 eV here (shown in Fig. 3(b)), in good agreement with the value (1.17 eV) extracted from the V OC -T plot. This consistence confirms that the ZnO/PbS-TBAI junction dominates the V OC . It is well-known that an activation energy equal to the absorber bandgap implies the dominance of bulk generation recombination in the absorber. An activation energy smaller than the bandgap often implies the significance of trap-assisted recombination 31 . Here E a (1.18 eV) is smaller than the optical bandgap of 1.34 eV (determined from the first exciton absorption peak of 927 nm), this suggests that V OC is affected by recombination either from ZnO/PbS-TBAI interfacial states or trap state in PbS-TBAI QDs layer. Figure 3(c) shows the Capacitance-Voltage (C −2 -V) plots of the device in the temperature range of 193 K to 293 K (The capacitance cannot respond promptly with the AC signals when T < 193 K, which could also be induced by the limited carrier mobility at low temperatures). From the C −2 -V plot, the built-in potential can be extracted based on the Mott-Schottky equation 25 : where V bi is the built-in potential, V is the applied voltage, A is the device area, N A is the doping concentration, ε is the relative permittivity, and ε 0 is the permittivity of vacuum. It can be seen that V bi increases linearly with decreasing temperature (Fig. 3(d)). The built-in potential at 0 K can be obtained from the extrapolated intersections of the fitting line with the y axis. As can be seen, the built-in potential at 0 K is 1.20 V which is in quite good agreement with extracted V OC at 0 K from the V OC -T plot and E a /q obtained from equation (5). Impedance Spectroscopy (IS) was used to analyze the dynamics of charge transfer and recombination in the device. Figure 4(a) shows the cole-cole plot (Z′ -Z: impedance imaginary part-impedance real part) with temperature varying from 193 K to 293 K with a step of 20 K. All the curves intersect with lateral axis at about 60 Ω at high frequencies region, which represents for series resistance of the devices 32 . While at low frequencies region, these plots intersect with lateral axis at different points which is related to the recombination resistance. The larger the recombination resistance, the less carrier recombination inside the device 32 . It is seen that the recombination resistance (the diameter of the Z′ -Z semi-circle) decreases rapidly from 1.8 kΩ to 0.8 kΩ as the device temperature decreases from 293 K to 193 K. As told above, the trend has also been observed by other groups, and can be attributed to low carrier mobility in QD layers under low temperatures 28,29 . We believe this is induced by the reduced mobility with decreasing temperature, which would slow down carrier transport and enhance carrier recombination inside the device.
The defect distribution at an energy E ω (below the conduction band and equal to E t ) can be expressed by equation (7) t bi V bi is the built-in potential (which has been obtained by C-V measurements above), W is depletion width, ω is angular frequency. The method consists of calculating the derivative of the frequency dependence of the capacitance and scaling the frequency into an energy axis. C(ω) can be written as 34 : 2 2 from which C(ω) data can be obtained from the measured impedance data Z(ω). Thus, the differential capacitance ωdC/dω versus ω can be calculated and the result is depicted in Fig. 4(b). It is seen that the differential capacitance has a peak for each temperature, which corresponds to the characteristic frequency ω 0 . Moreover, the peak shifts to low angular frequency as the temperature decreases. The relationship between the angular frequency ω and the energy E ω can be described by equation (9) and equation (10) 35,36 : 2 where ξ corresponds to the emission prefactor. According the equation (10), the active energy of trap states (E ω = E t ) was extracted from an Arrhenius plot of maxima ln(ω 0 /T 2 ) vs 1000/T as shown in Fig. 4(c). The value of E t is 0.36 eV which is similar to the reported value 20,23 . A attempt frequency ν 0 = 2.88 × 10 12 s −1 (300 K) is also obtained from which capture cross section and capture radius can be calculated to be σ = 1.03 × 10 −13 cm 2 and r = 1.81 nm, respectively. The depletion width can be obtained by equation (11): 0 bi a Therefore, the defect distribution can be determined by calculating the derivative in a C(ω) measurement and the results was depicted in Fig. 4(d). The density of defect states has a Gaussian distribution, and the width of these Gaussian distributions is on the order of thermal energy (about 26 to 35 meV). The peak with activation energy at about 0.34 eV is quite consistent with the value of E t . The density of defects at the peak is around 3.2 × 10 16 cm −3 eV −1 at 193 K (the overall trap density is 1.12 × 10 16 cm −3 ), and as the temperature increases, the density is reduced. The value and the phenomenon are in agreement with the previously reported 37 In summary, we investigated trap states in short-circuited planar PbS QDPVs with the planar architecture of ITO/ZnO/PbS-TBAI/PbS-EDT/Au. A defect trap state of about 0.34 eV with a density of 3.2 × 10 16 cm −3 eV −1 is determined. Temperature dependent J-V and C-V measurements consistently indicate that trap states greatly influence the diode ideality factor n and saturation dark current density J 0 and build-in voltage V bi , which translates into large open-circuit voltage loss, photocurrent reduction and fill factor cut. Hence significantly reducing/ illuminating trap states in the QD layer is the key to largely improving the device performance of QDPVs.

Experimental
Material Preparation. PbS and ZnO colloidal quantum dots were synthesized using previously reported methods 44,45 . The concentrations of the PbS dispersed in octane and the ZnO dispersed in chloroform were both 50 mg/ml. The TBAI solution (10 mg/ml in methanol) and EDT solution (0.02 vol% in acetonitrile) were stirred rigorously for ca. 24 h at room temperature before use.
Device Fabrication. The ZnO layer was spin-coated on the cleaned ITO substrate, PbS QD layers were then spin-coated (at 2500 rpm for 15 s) by layer-by-layer process on the ZnO film. To form the PbS-TBAI layer, a TBAI solution was applied to the prepared PbS layer for 60 s, followed by two rinse-spin steps with methanol. To form the PbS-EDT layer, an EDT solution and acetonitrile were used. All the spin-coating steps were performed under ambient condition at room temperature. The films were stored in air overnight and then Au electrodes (100 nm thick) were thermally evaporated onto the films through shadow masks. Before measurement the unencapsulated devices were stored in air for another day. J-V Characterization and EQE. J-V characteristics of the devices were measured with a computer-controlled Keithley 2400 source meter at a speed of 0.01 V/s and Newport solar simulator with 100 mW/cm 2 illumination. EQE spectra were collected using Oriel IQE-200 ™ in the atmosphere. Prior to the use of the light, the spectral response and the light intensity were calibrated using a mono-silicon detector produced by the National Renewable Energy Laboratory.
Low-temperature Measurements. The sample was mounted onto a LN 2 -coolable sample stage inside a vacuum chamber and the closed-cycle cryostat Janis CCS-150 was allowed conducting experiments in the 33-293 K temperature range with a step of 20 K by providing high-pressure helium gas to the cold head with compressor. The temperature changed at a speed of 5 K/min. Before measurement, the device was stored at each setting temperature for 10 min. IS Measurements. The impedance spectroscopy (IS) measurements were performed using a Zahner Zennium electrochemical workstation. The impedance spectra were recorded by applying varied AC signal from 1 Hz to 4 MHz. All the AC oscillating amplitudes were set as low as 20 mV (rms) to maintain the linearity of the response.
CV Measurements. The capacitance-voltage (C-V) measurements were performed using a Zahner Zennium electrochemical workstation. They were recorded at a frequency of 1 kHz for extracting V bi . The AC oscillating amplitudes were set as low as 20 mV (rms) to maintain the linearity of the response.