Solution Processing and Self-Organization of PbS Quantum Dots Passivated with Formamidinium Lead Iodide (FAPbI3).

Solution-processed lead sulfide quantum dots (PbS QDs) are very attractive as NIR-active semiconductors for the fabrication of cost-efficient optoelectronic devices. To control the thin film carrier transport, as well as stability, surface passivation is of crucial importance. Here, we present the successful surface passivation of PbS QDs by the formamidinium lead iodide (FAPbI3) ligand. An effective procedure for the fabrication of FAPbI3-passivated PbS QDs through a binary-phase ligand exchange protocol in hexane and n-methylformamide is demonstrated. It is shown that this solution-processed ligand exchange drastically changes the photoluminescence intensity, exciton recombination dynamics, and carrier lifetime of the nanocrystals. The solution casting of the ligand-exchanged nanocrystals into thin films results in the periodic ordering of QDs in a square superlattice with close contacts. Planar graphene/QD photodetectors fabricated with PbS QDs passivated with FAPbI3 show substantially increased thermal stability as compared to similar devices using PbS QDs passivated with commonly used methylammonium lead iodide.

Introduction

During the past decade, band-gap tunability, simple and low-cost synthesis, high charge carrier mobility, and special optoelectronic properties of semiconductor quantum dots (QDs) have attracted tremendous interest for solution-processed optoelectronic devices.[1] Of particular interest, monodispersed PbS QDs can easily be processed from earth-abundant materials, exhibiting size-tuned band gaps over a broad spectral range extending to the near-infrared.[2,3] Owing to their useful properties, particularly large Bohr radius (20 nm) and high charge carrier mobility rendered possible by short conjugated ligands, applications of PbS QDs in optoelectronic devices have surged up.[4−6] Due to the high surface-to-volume ratio of PbS QDs, the electronic properties are highly affected by the surface characteristics because the surface states dictate the position and the number of states near the band gap.[7] Accordingly, using these QDs in optoelectronic devices requires surface treatments to improve the electronic coupling and electron transport between QDs.[8−10] To enhance the stability of QDs, long ligands are commonly used for surface passivation. However, the steric hindrance prevents long organic ligands from penetrating the intercation trenches on the surface of QDs, resulting in incomplete surface passivation. Unpassivated surface sites are susceptible to attack by oxygen and/or water, leading to instability of the QDs in air.[11] Furthermore, surface passivation by short ligands is not only more effective but also improves the conductivity of QD films. In fact, the charge carrier mobility in QD thin films is enhanced by several orders of magnitude through conjugating with short ligands. Therefore, complete surface passivation by short ligands is necessary to make them stable and to prevent their degradation. Various approaches and different types of ligands have been employed for the surface treatment of QDs to form highly conductive arrays and films.[1,12−17] Solution and solid-state ligand exchange methods have widely been used.[1] The former works are based on the transferring of long alkyl-capped PbS QDs (e.g., oleic acid (OA)-PbS) from a nonpolar solvent to a polar solvent through ligand exchange with shorter capping molecules (e.g., mercaptopropionic acid, MPA, or 2-ethanedithiol). In the latter procedure, the washing of deposited films with an organic solution containing short ligands is performed for the ligand exchange. The great advantages of the former over the latter method are the possibility of ink-printing as the one-step film fabrication process and complete passivation of the QD surfaces.[1,18]

All-inorganic perovskite structures in the form of CsPbX3 (X = I, Br, Cl) have a similar crystal structure and low lattice mismatch with PbS.[19] Organic–inorganic perovskites, for example, methylammonium lead halides (CH3NH3PbX3 or MAPbX3), are intensively used in thin film solar cells because of their superior properties like high charge carrier diffusion lengths, high charge carrier mobility, and broad absorption range. Another interesting point is their perfect lattice matching with PbS QDs.[20] Recently, CH3NH3PbX3 perovskites have successfully been employed as stable capping ligands for a variety of QDs like PbS, CdS, InP, and CdSe.[21] As a result, efficient electronic passivation and highly luminescent QDs have been attained. The solid-state ligand exchange method has also been employed for the replacement of oleate and oleylamine to achieve PbS–CH3NH3PbX3.[20] As compared to PbS QDs, PbS–CH3NH3PbI3 QDs exhibit complementary optical absorption spectra, facile charge separation, high conductivities, and efficient charge transport. Choi et al.[22] prepared a high-quality PbS QD ink through the solution ligand exchange process by the use of MAPbI3 as the capping material. The PbS nanocrystals were stabilized by PbI3 anions and MA cations as an electrical double layer. By using this ink, they attained solar cells with a power conversion efficiency of 3.7%.

To the best of our knowledge, MAPbX3 are the only organic–inorganic capping materials, which have been used so far to enhance the absorption region and improve the electron transport of PbS QD films. Unfortunately, the weak stability of methylammonium lead iodide[23,24] is limiting their optoelectronic applications. To improve the stability of the perovskite, formamidinium (FA) was used to replace methylammonium (MA) cations.[25] Formamidinium lead halide perovskites (CH(NH2)2PbX3 or FAPbX3) have recently been considered as a promising alternative for the thermodynamically less stable MA perovskites. The FA cation is larger (1.9–2.2 Å) than the MA cation (1.8 Å), thus narrowing the band-gap energy of FAPbI3.[26] The higher stability of the FAPbI3 structure is attributed to the higher number of hydrogen bonds between the hydrogen atoms of the ammonium cations and iodine ions in the inorganic cage.[27]

In this paper, we introduce FAPbI3 as a more effective organic–inorganic ligand for the surface passivation of PbS QDs. Drastic changes in the photoluminescence (PL) properties and exciton recombination dynamics of PbS QDs are demonstrated. The lifetime of charge carriers is significantly reduced as compared with that of OA-capped PbS QDs. In addition, the formation of nanocrystal superlattices during film formation is shown. Also, by using PbS–FAPbI3 QDs in photodetectors, we obtain an improvement in both response amplitude and thermal stability with respect to a similar device where the active layer consists of PbS–MAPbI3.

Results and Discussion

A schematic illustration of the solution-processed ligand exchange via FAPbI3 is shown in Figure a. We also observed an increased solubility of PbS–FAPbI3 as compared to that of PbS–MAPbI3 as precipitation of the suspended particles in NMF by centrifugation at 14 000 rpm was much harder in the case of PbS–FAPbI3 (see SI, Figure S2). The absorption spectra of the PbS QD solution before and after ligand exchange with FAPbI3 are illustrated in Figure b. Two distinct absorption peaks in the NIR region are visible. The main absorption peaks before the ligand exchange are located at 914 and 1292 nm. These peaks shifted to about 894 and 1390 nm after the treatment. Therefore, the exchanged QDs absorb a broader range of the spectrum from visible to NIR, which makes them more suitable for photodetector devices.

Figure 1

(a) Schematic presentation and photographic images of colloidal PbS QDs processed by the solution ligand exchange protocol. The effect of ligand exchange treatment on (b) absorption, (c) steady-state PL, (d) time decay PL, and (e) FTIR spectrum of PbS QDs. PL and FTIR were measured in colloidal hexane and N-methylformamide solutions for OA and FAPbI3, respectively. Absorption spectra were measured on spin-coated films.

The PL spectra in the solution of OA–PbS QDs and after ligand exchange with FAPbI3 are shown in Figure c. The emission peaks are located at 1350 nm for OA and 1480 nm for FA. Such large red shifts upon replacing oleate ligands by iodide salts have been reported and attributed to the decrease in wavefunction confinement due to a shallower HOMO level of the adsorbed iodide.[28] Additionally, a change in the absorption peak position can occur upon aggregation when using short capping ligands.[29] This is accompanied by a drastic change in the luminescence quantum efficiency and a much-reduced exciton lifetime (typically 1 ns) due to defect state quenching. Although we do observe a reduced quantum efficiency and lifetime, the values obtained in this work are higher than for the bare aggregated PbS QDs. Red shifts in the excitonic absorption and emission peaks can also be induced via interparticle coupling between the QDs.[29−31] Such coupling leads to both a significant red shift and a reduction in the quantum efficiency of luminescence via exciton dissociation due to charge carrier tunneling from dot to dot. While this process is expected in solid films, it is less expected to occur in solution. In the case of large QD size distributions, however, the unexpected large Stokes shifts of up to 200 meV could be attributed to aggregation in solution.[32] It is noteworthy that the Stokes shift in our case is around 50 meV. We therefore rather exclude the possibility of aggregation. Observation of a blue shift from 914 to 894 nm in the first absorption peak after ligand exchange can be ascribed to the formation of minibands induced by electron coupling between adjacent nanocrystals.[33,34] The formation of the minibands is very important for efficient carrier collection in optoelectronic devices.[33,34]

The ligand exchange treatment not only induced a red shift in the emission peak but also significantly quenched the PL intensity. At the excitation wavelength of 565 nm, PLQY values of 15 and 1.5% were determined before and after ligand exchange, respectively. The result of time-resolved PL (TRPL) spectroscopy is shown in Figure d. We employed a biexponential model to fit the experimental data,[29] and the extracted parameters are compiled in Table .

Table 1

TRPL Fitting Results for PbS QDs Passivated with OA and FAPbI3 Ligands

sample	A1	τ1 (ns)	A2	τ2 (ns)
PbS–OA	0.88	1076	0.88	1076
PbS–FAPbI3	0.41	10.3	0.20	1777

τ1 and τ2 show the fast and slow decay components, where A1 and A2 represent their amplitudes. The results display that the ligand exchange treatment reduces the exciton lifetime and changes the relaxation mechanisms. A long organic ligand can interrupt the charge transfer between QDs and lead to the slow radiative recombination process. Formamidinium lead iodide decreases the interparticle distances between QDs so that the nonradiative recombination becomes prominent.[29,35]

Figure e depicts the FTIR spectra of PbS QDs before and after ligand exchange. Four characteristic peaks of OA are observed at 2925, 2852, 1542, and 1400 cm–1.[36] These peaks disappear after the ligand exchange treatment, which indicates removing of OA upon the exchange process. The peaks of N–H and C=N bonds are visible at 3359 and 1712 cm–1, respectively.[37,38] This observation indicates the existence of the perovskite phase on the surface of PbS QDs. Apart from these peaks, all other peaks are related to the solvent.

Figure exhibits the full survey and high-resolution XPS spectra of PbS–OA and PbS–FAPbI3 QD films that were spin-cast on gold-coated substrates. Table lists the atomic composition of the samples for the relevant elements. The XPS analysis corroborates the successful exchange of ligands. Evidence comes from the fact that the oxygen signal in PbS–FAPbI3 QD is missing, while it is clearly present in the PbS–OA sample, confirming the presence of oleic acid (Figure d). Albeit the carbon/oxygen ratio of 11.8 is somewhat higher than its theoretical value of 9, the relative atomic concentration confirms the presence of oleic acid since carbon contamination from the atmosphere during sample transfer and mounting cannot be excluded. Further evidence for the ligand exchange comes from the presence of iodide for the PbS–FAPbI3 QD samples (Figure c). From Table , we infer an iodide/lead ratio of 0.61, which is substantially lower than the value of 3 expected for PbI3–. Also, in the case of PbS–FAPbI3 QD samples, we observe double peak features for the Pb 4f7/2 and Pb 4f5/2 peaks with a separation energy of 1 eV, respectively (Figure e). This separation energy corresponds well to the chemical shift observed between the Pb 4f7/2 peak of PbS (137.7 eV)[39] and FAPbI3 (138.6 eV).[40] Transmission electron microscopy (TEM) analysis indicates that the FAPbI3 ligand is thinner than 1 nm (Figure ), and therefore a strong lead signal from the PbS core is indeed expected. An alternative interpretation of the shoulder on the low-energy side of the Pb 4f7/2 peak has previously been attributed to the metallic Pb0 present on organo-metal halide-capped PbS nanoparticles after ligand exchange.[22] However, the expected chemical shift between FAPbI3 and Pb0 (136.9 eV)[41] would be 1.7 eV, which is significantly larger than the peak-to-peak separation of 1.0 eV observed here. Another argument against the assignment to metallic lead is the very low I/Pb = 0.6 ratio, meaning that the concentration of Pb0 would be about twice that of PbI3–. This would contradict the very similar intensity we observe for the double Pb 4f7/2 peak. We note that there is a considerable shift of the PbS–FAPbI3 XPS peaks to lower binding energies. This could arise from charging effects and from the interface dipole induced by the ligand.[42] An in-depth investigation of these effects, however, is beyond the scope of this work.

Figure 2

Survey spectrum of passivated PbS QDs with (a) oleic acid and (b) FAPbI3. High-resolution XPS spectra of (c) I 3d5, (d) O 1s, (e) Pb 4f, and (f) C 1s.

Table 2

Concentration of Components (atom %) Determined by XPS

sample	C 1s	O 1s	I 3d5	Pb 4f
PbS–OA	69.75	5.93	0	8.36
PbS–FAPbI3	25.08	0.56	5.01	8.17

Figure 4

Low-magnification zero-loss filtered TEM images of PbS QDs capped with (a) OA and (b) FAPbI3. The insets are FT patterns extracted from the areas indicated by the red squares. Self-organization of QDs in hexagonal- and square-packed fashions is visible. HRTEM images of (c) PbS–OA and (d) PbS–FAPbI3 QDs.

The crystallinity of QDs was assessed by electron diffraction (ED). The ED pattern in Figure a shows well-defined diffraction rings corresponding to the rock-salt structure of PbS. The simulated diffraction rings calculated using the Fm3̅m space group and lattice parameter a = 0.5934 nm[43] confirm an excellent agreement with the experimental data. Figure b shows a high-resolution transmission electron microscopy (HRTEM) image of a PbS nanocrystal oriented with its [001] zone axis perpendicular to the image plane. HRTEM studies showed that monodispersed nanocrystals with an average size of 4.7 ± 0.2 nm were synthesized. The nanoparticles have a truncated octahedron or rhombicuboctahedron shape with (100)-, (110)-, and (111)-type facets. The Fourier transform (FT) of the nanocrystal (Figure c) and a line profile extracted along the [100] direction (marked with a red rectangle in Figure d) confirm the lead sulfide rock-salt structure.

Figure 3

(a) ED pattern of PbS–OA QDs with overlaid simulated diffraction rings. (b) HRTEM image of a PbS QD and (c) corresponding FT pattern. (d) Line profile obtained along the [100] direction of the FT in panel (c) (indicated by the red rectangle).

Overview zero-loss filtered TEM images of the films prepared from PbS–OA and PbS–FAPbI3 QDs are shown in Figure . In Figure a, large domains of QDs organized in a hexagonal close-packed fashion are visible. Figure b reveals much smaller domains of QDs organized in a square-packed fashion. FT patterns extracted from the selected areas (indicated by the red squares) are shown as insets. The FT spots reveal the self-organization of the nanocrystals during film formation. The reciprocal distances were used to extract the superlattice spacing. The FT pattern shown in Figure a reveals that the PbS QDs are organized in a hexagonal close-packed fashion and are spaced by 0.18 nm–1, i.e., 5.6 nm. The FT image presented in Figure b shows that, at the studied region of the film, the nanocrystals are organized in a square-packed fashion and are separated by 0.21 nm–1, i.e., 4.8 nm. HRTEM studies at higher magnifications reveal that the nanocrystals organized in a hexagonal close-packed fashion are not fused together but separated about 1 nm (Figure c). In contrast, the exchanged QDs arranged in a square-packed fashion often appear to have necking points along the (100)-type facets (Figure d), in line with the previous reports.[44] These results reveal a reduction of the interparticle spacing of the nanocrystals in the thin film after the ligand exchange.

As the PbS nanocrystals present a truncated octahedron or rhombicuboctahedron shape, three different facets, including (100), (110), and (111) orientations, are exposed to the ligands. The (100)-type facets are the least acidic ones having a lead coordination number of 5.[45] The (110) and (111) facets have lead coordination numbers of 4 and 3, respectively, with a higher affinity toward anionic ligands.[44] However, due to the lower surface energy of the 100-type facets as compared to that of the (111)-type ones, ligands can more easily be removed from (100).[44] During the ligand exchange, anionic perovskite ligands prefer (110) and (111) facets, while neighboring QDs are connected along the 100-type facets resulting in the square-packed nanocrystals.[21,44]

To assess the stability of the different QD ligands, we chose the planar graphene/QD photodetector architecture (SI, Figure S1), since the latter is less sensitive to the morphology of the QD film. Figure a,b shows the current response of the graphene/QD photodetectors at an applied source–drain voltage of 3 V during alternating irradiation (ON) and dark (OFF) periods. Devices using QDs with a MAPbI3 ligand and QDs with a FAPbI3 ligand show photocurrents of 0.6–0.7 μA, respectively. The mechanism of photoconduction in channels with graphene/PbS quantum dot heterostructures has been elucidated.[46] Upon irradiation, electron–hole pairs are induced in the PbS QDs, which can both be transferred to graphene with an extremely high carrier mobility of up to 200 000 cm2/Vs,[46] given the fact that the Fermi level of graphene lies in the band gap of PbS. However, the rates of electron and hole transfers differ, which induces a net electronic charge on the QDs and a compensating positive charge on graphene. By this photodoping effect, the conductivity of graphene is changed, which gives rise to the observed photocurrent response (see Figure c).[46] This principle was shown to lead to high optical gain and enhanced optical response.[47] Numerous studies in the literature indicate that MAPbI3 is thermodynamically unstable with respect to decomposition forming lead iodide, hydroiodic acid, and methylamine gas in the absence of air.[48] Heat accelerates this process as can be clearly seen in the shortened lifetime of solar cell devices.[48] Therefore, perovskite layers with increased stability have been developed by replacing MA by the larger organic cation FA. Here, we have investigated whether the stability of perovskite ligands on PbS QDs also follows this trend. For this purpose, we have investigated the aging of thin film graphene/QD photodiode layers at 130 °C for 1 h (Figure b). While the photocurrent decrease in the case of FA was only 4%, the decrease in the case of MA was 40% and therefore significantly higher. We attribute the deterioration of the devices upon annealing to the accumulation of decomposition products at the graphene interface, reducing the photoinduced charge transfer and due to the agglomeration of QDs, reducing the absorption coefficient of the latter.[49]

Figure 5

Current response of graphene/PbS–FAPbI3 and PbS–MAPbI3 QD phototransistors under white light illumination (a) before and (b) after maintaining at 130 °C for 1 h, and (c) schematic illustration of the photodoping effect in graphene/PbS QDs.

Conclusions

In summary, we have employed a facile and solution-based procedure at room temperature to exchange long alkyl ligands (such as OA) with an organic–inorganic ligand (FAPbI3 perovskite) for PbS QDs. High-resolution transmission electron microscopy characterizations revealed self-organization of the nanocrystals in superlattices during thin film formation. The ligand-exchanged QDs organized in square-packed lattices instead of hexagonal-packed structures with shorter interparticle distances. The ligand exchange produced a red shift in the absorption and emission spectrum and promoted additional exciton-quenching channels. Also, the FAPbI3 ligand showed superior thermal stability in graphene/QD photodetectors as compared to similar devices using QDs using the MAPbI3 ligand. The proposed approach for the passivation of PbS QDs with a formamidinium-based organic–inorganic perovskite may pave a new way for the development of optoelectronic devices.

Experimental Section

Materials

Lead(II) acetate trihydrate (Pb(CH3COO)2·3H2O, 99.99%, Sigma-Aldrich), bis(trimethylsilyl)sulfide (TMS2S, Sigma-Aldrich), lead(II) iodide (PbI2, 99%, Sigma-Aldrich), formamidinium iodide (FAI, 99%, Sigma-Aldrich), 1-octadecene (ODE, 90%, Sigma-Aldrich), oleic acid (OA, 90%, Sigma-Aldrich), N-methylformamide (NMF, HCONHCH3, 99%, Sigma-Aldrich), ethanol (Fluka), hexane (95%, Sigma-Aldrich), acetone (99.5%, Sigma-Aldrich), titanium(IV) isopropoxide (TTIP, 97%, Sigma-Aldrich), hydrochloric acid (HCL, Sigma-Aldrich), and methylammonium iodide (MAI, 98%, Sigma-Aldrich) were used without further purification. Si/SiO2/graphene substrates (Graphenea, Spain) were utilized for device fabrication.

Synthesis of PbS QDs

The synthesis of PbS QDs was performed by using a hot-injection method according to the protocol reported by Hines and co-workers.[2] Briefly, 1.5 g Pb(CH3COO)3·3H2O, 35 mL 1-octadecene (ODE), and 15 mL OA were mixed in a three-neck flask. The resulting solution was degassed under vacuum for 2 h at 120 °C followed by stirring at 143 °C under a nitrogen atmosphere. In another container, 0.42 mL TMS2S was mixed with 10 mL of dried ODE. The second solution was injected into the first one at 143 °C. The growth time was 3 min. The reaction mixture was then cooled to room temperature. The washing process was performed with hexane/ethanol (solvent/nonsolvent) three times, redissolved in hexane, and finally filtered through a 0.2 μm PTFE filter.

Solution Ligand Exchange

The method developed by Dirin and co-workers[21] was utilized for the ligand exchange in the solution phase. Formamidinium (methylammonium) iodide (50 μmol) and 50 μmol of lead iodide were dissolved in NMF. This ligand solution was mixed with 5 mg PbS QDs in 1 mL hexane. The biphasic system was stirred for 4.5 h (1 h) until complete migration of QDs occurs. Afterward, the nonpolar phase was removed, and the nanocrystals were washed three times with 1 mL hexane. The FA-passivated QDs were then precipitated by adding an appropriate amount of acetone followed by dispersion in NMF. For comparison, PbS QDs were also passivated with MAPbI3 ligands according to a previously published procedure.[21]

Device Fabrication

The purchased Si/SiO2/graphene substrate (SiO2 thickness of 300 nm coated with a graphene monolayer) was cut to 2 × 2 cm2 pieces inside the glovebox (see SI, Figure S1a). Thereafter, interdigitated source and drain gold electrodes with a channel length of 250 μm and a width of 5 mm were deposited by physical vapor deposition (PVD). To compare the effect of the perovskite ligands, 10 μL of QD solutions (before and after ligand exchange with MAPbI3 or FAPbI3) were deposited on graphene via drop-casting (80 nm). Then, the samples were placed on a hot plate at 70 °C for 10 min to dry the active layer. After fabrication, the devices were either directly characterized or placed in an oven at 130 °C for 1 h to test their thermal stability. The device architecture and a photograph of the devices are given in the SI (Figure S1).

Characterizations

Microscopy

The size and morphology of the nanocrystals were observed by a JEOL 2200FS TEM equipped with an in-column Omega-type energy filter. The instrument was operated at 200 keV and used for electron diffraction (ED), HRTEM, and energy-filtered transmission electron microscopy (EFTEM). A multifunctional field-emission scanning electron microscope (NanoSEM 230) was employed for observation of the prepared thin films.

Spectroscopy

The absorption spectrum of the as-synthesized and ligand-exchanged colloidal PbS QDs was recorded on a Shimadzu UV-3600 UV–vis–IR spectrophotometer. Steady-state and time-resolved PL measurements were conducted on a Fluorolog Horiba Jobin Yvon and a NanoLog FL3 Horiba spectrofluorimeter, respectively. A Vector Bruker 22/DigilabBioRad FTS 6000 FT-IR Spectrometer was used for the FTIR measurement. XPS spectra were acquired on a Physical Electronics (PHI) Quantum 2000 Scanning ESCA Microprobe System using monochromated Al Kα radiation (hν = 1486.7 eV) and a hemispherical capacitor electron-energy analyzer equipped with a channel plate and a position-sensitive detector. The electron take-off angle was 45°, and the analyzer was operated in the constant pass energy mode at 23.5 eV for the detailed spectra of the Cu 2p3/2, O 1s, C 1s, and N 1s peaks, and a step size of 0.20 eV was used. The beam diameter was typically 150 μm. The binding energy is calibrated using Cu 2p3/2, Ag 3d5/2, and Au 4f7/2 at 932.62, 368.21, and 83.96 eV, respectively, to within ±0.1 eV (see ISO.15472; 2010-05). To compensate for possible surface charging, built-in electron and argon ion neutralizers were used. The base pressure of the system was below 5 × 10–7 Pa. The spectra were analyzed using the software MultiPak 8.2B, and the peaks are shown after a Shirley background subtraction. The atomic concentrations were calculated using the corrected relative sensitivity factors, as given by the manufacturer, and normalized to 100 atom %. The relative uncertainty is around 10%.

Device Performance

Current versus time curves were measured by a Keithley 4200 SCS parametric analyzer, equipped with a SuperK compact supercontinuum white pulsed laser unit (NKT Photonics, 450–2400 nm range). The pulse width of the laser source was 2 ns at a repetition rate of 1 kHz with a total output power of 110 mW. Devices were alternatively measured in the dark and under laser irradiation for time periods of several seconds each. A constant bias VSD of 3 V was applied to the source contact during the photocurrent transients and the source–gate voltage was set to 0 V.