Photoinduced Current Transient Spectroscopy on Metal Halide Perovskites: Electron Trapping and Ion Drift

Metal halide perovskites (MHPs) are disruptive materials for a vast class of optoelectronic devices. The presence of electronic trap states has been a tough challenge in terms of characterization and thus mitigation. Many attempts based on electronic spectroscopies have been tested, but due to the mixed electronic–ionic nature of MHP conductivity, many experimental results retain a large ambiguity in resolving electronic and ionic charge contributions. Here we adapt a method, previously used in highly resistive inorganic semiconductors, called photoinduced current transient spectroscopy (PICTS) on lead bromide 2D-like ((PEA)2PbBr4) and standard “3D” (MAPbBr3) MHP single crystals. We present two conceptually different outcomes of the PICTS measurements, distinguishing the different electronic and ionic contributions to the photocurrents based on the different ion drift of the two materials. Our experiments unveil deep level trap states on the 2D, “ion-frozen” (PEA)2PbBr4 and set new boundaries for the applicability of PICTS on 3D MHPs.


Table of contents
(PEA)2PbBr4 and MAPbBr3 atomistic representation and samples' photographs

Figure S4
Intensity modulated photocurrent spectroscopy (IMPS) on MHPs: data and setup

Figure S6
MAPbBr3 current transients, highlighting reverse current spikes

Figure S7
Charge transport model for positive bias and experimental transients

Figure S9
Stability of the photocurrent transients

Figure S10
Repeatability of the PICTS measurements

Figure S11
PICTS measurements stress test and signal drift assessment

Ion drift calculation from impedance spectroscopy (IS)
Based on the experimental data reported in the main text Figure 2a,b, we derived the following calculations for describing the time evolution of the sample impedance, correlating the value to the ion diffusivity.We argue that the photoinduced mobile ions slowly drift across the entire crystal of thickness , under the external potential bias (+5 ) applied such that:  = 1 ;  = / = 5 /.Therefore, the ion diffuses according to the Einstein-Smoluchowski equation:

𝑘 𝐵 𝑇 𝑞
Here  is the ion diffusion coefficient,  is the ion mobility,   is the Boltzmann constant,  is the temperature,  is the elementary charge.The ion mobility  can be rewritten as drift velocity   over the electric field  imposed by an external bias.The drift velocity can be further decomposed considering the crystal thickness separating the electrodes  and the transient time .While all the other parameters' values are known, we retrieved the transient time value of  = 3000 ± 1500  by the exponential fitting displayed in Figure 2a  Therefore, due the external bias and continuous illumination, ions drift across the entire crystal with a high time constant, that corresponds to an average diffusivity value for all the ionic species falling in the 10 −8 cm 2 /s range.

PICTS Discussion
In addition to the electric field imposed by the external bias, light absorption at the MHP surface causes a transient variation of the fixed charges screening, thus a modification of an additional local electric filed.This, in turn, causes a local drift of ionic species.Thanks to different light modulation frequencies we can select different ionic species that move at different speeds, or in other terms, ions having different diffusion coefficients (due to the link between mobility and diffusion).
From the impedance spectroscopy measurements under illumination we obtained an impedance evolving with time constant ~3000 , in line with reported values in literature, 3,4 which is orders of magnitude higher than the maximum probed time of 2.5  in our photocurrent transients.This means that during the single PICTS transients, the overall ionic current flowing from one metal contact to another is not affecting the extracted photocurrent.In fact, by considering the longest 2.5  light pulse (Figure S8), we can calculate an upper limit for the ion drift length (in addition to the already drifting ions under bias in dark condition) of ~30 . 5The spatial extend of such drift does not significantly alter the sample global ion distribution during the single measurement time-span (see stability and repeatability checks in Figures S9, S10) , but it does induce a reversible ion accumulation on the hour time-scale if the bias voltage (and/or illumination) is held constant (Figure S11).The bias voltage we set was chosen to maximize the current without excessively affecting the baseline.The architectural configuration of the topbottom contacts had no influence on the value of the photocurrent transient time constants as demonstrated by a comparison with photocurrent transients obtained from a coplanar architecture reported in Figure S12.
[8][9] Such motion induces a transient impedance change of the form  =  0 exp (−   ), where  0 is the space charge region (SCR) impedance when light is turned off, and  is the characteristic time of ionic motion.Considering the relation   = , and the Einstein-Smoluchowski equation for the diffusion of charged particles ( =   /) in the depletion layer, the migration rate of ions during the drift process can be written as: 6,7,10 where  is the temperature,   is the depletion layer (or space charge region) width,  is the elementary charge,  is the electric field in the SCR,   is the Boltzmann constant,  0 is the ion diffusion coefficient at  = ∞, and   is the diffusion activation energy.The change in the ionic impedance at the contact has a direct influence on the electronic motion in the material.Therefore, the ion migration rate is found also in the expression of the electronic photocurrent decay: where   is the dark current value,  0 is the photocurrent amplitude at steady state, and   is the ion migration rate from Eq. ( 1).The latter describes an Arrhenius-type dependence of   as a function of temperature, which resembles the one obtained in classical PICTS due to emission of charge carriers from deep traps.Because of this, PICTS signals in MHPs arising from ionic motion can easily be misinterpreted as coming from deep electronic states.Therefore, determining if ions play a major role the photocurrent transients become pivotal for discriminating two different physical processes that lead to a description of different quantities using PICTS experiments: trap state energies or ion diffusion activation energies.
Table 1 in the main text, reports the activation energies and diffusion coefficients at room temperature obtained by a linear fitting of the Arrhenius plots in Figure 4e by Eq. (1).While the activation energy is easily obtainable by the fit slope, the diffusion coefficient requires the knowledge of  and   which are parameters difficult to assess experimentally.Thus, the reported  300 values are a rough estimate, based on the values of  = 0.3 /µ, and   = 1 µ.The former is based on the value measured by kelvin probe force microscopy. 11The latter is derived from values reported in ref. [11] and ref. [12], where the band bending at the MHP−metal interface for both MAPbI3, and MAPbBr3 is characterized to be in the microns range and we consider a conservative estimate based on the partial compensation of the interfacial charges responsible for the SCR by the photogenerated charge carriers.

Ion's assignment
We provide a tentative assignment of the reported PICTS maxima (traces) to migrating ionic species in MAPbBr3, that are reported in Table 1, main text.We assign the traces measured with negative bias to positively charged ions, and features measured with positive bias to negatively charged ones.Therefore, the traces reported in Figure 4, main text, LN and MN should correspond to positively charged species.The most mobile charged ionic species in MHPs are MA • , and V Br • , i.e. methylammonium interstitials and bromine vacancies, while Pb i •• is expected to be rather immobile in the lattice. 13Reichert et al. assigned the  trace to MA  • , 7 and, given the good overlap of LN with , we assign LN to this ionic species.We associate the higher activation energy that we measured with respect to the one reported for  to the absence of grain boundaries in the single crystal samples.By exclusion, we assign MN to V Br • migration.Given the vicinity of MP and HP1 in the Arrhenius space, we assign them to the same negatively charged ionic species.Given the good overlap with the  trace reported in ref. [7], which was assigned to halide interstitials, 7 we them to Br i ′ migration.The difference in activation energy of around 0.2 eV between MP and HP1 might be related to the presence of the second HP2 trace in the high frequency PICTS map.Indeed, the presence of several features in the spectra can lead to convolutions between the peaks, that mask the real activation energy of the underlying phenomena.The HP2 feature shows a good overlap with the  trace, 7 which was assigned to V MA ′ , in good agreement with the negative charge expected for this defect.However, as discussed above, the estimated diffusion coefficient of HP2 is not compatible with an ionic migrating species.Therefore, this trace needs further investigation to assess its nature.It is important to note the difficulty of assigning traces from defect spectroscopy to the underlying ionic migrating species.This task has proven to be difficult not only by the experimental challenges of these measurements, but also to the intrinsically complex nature of ion migration in MHPs.As an example, as discussed above the  trace was assigned to V MA ′ , 7 but recently the same group reassigned it to V I • , 14 thus changing not only the moving chemical specie, but also its charge.
However,  was also observed by the same group in MHPs without iodine, like CsFAPbBr1-xClx, 15 and, on the other hand, it was not observed in a iodine-based MHP like FAPbI3. 16This exemplifies how difficult is the task of assigning defect spectroscopy traces to their related ionic species.Therefore, we note that the assignments reported above should be taken with caution and may be changed in the future upon further investigation.

Figure S12
Figure S12PICTS with coplanar electrodes configuration for MAPbBr3

Figure S2 .
Figure S2.PICTS data analysis layout.(a) Simulated current transients for a single defect state with   = 0.5  and  = 10 −19  2 in the 350 − 500  temperature range.Here   is the activation energy of the trapped charge carrier,  is the trap's capture cross-section.For the complete description of the classic PITCS parameters see refs.[1,2].(b) Selected transients from (a) at three different temperatures.For all three, the same rate window is selected, with  1 = 0.1  and  2 = 0.2 .The corresponding Δ values are indicated by two-sided arrows.(c) The PICTS spectrum consists of a plot of the Δ values as a function of temperature.Coloured dots indicate the specific Δ values calculated from the transients in (b).This spectrum is related to the rate window   = 14.4 Hz, determined by the  1 and  2 values.

Figure S3 .
Figure S3.Impedance spectroscopy (IS) extended data.(a) IS experimental setup: a LED driver connected to either a 470  or 365  LED (for MAPbBr3 and (PEA)2PbBr4 respectively) shines light onto the sample, inducing a photocurrent.The sample is polarized with a +5  external bias applied through a lock-in amplifier.The frequency response analyzer (FRA) module of the lock-in amplifier was used to induce an AC voltage perturbation of amplitude 200 , with frequency

Figure S4 .
Figure S4.Intensity modulated photocurrent spectroscopy (IMPS) extended data.(a) IMPS setup schematic.The sample is mounted in a vacuum chamber (Nextron) and electrically connected to

Figure S5 .
Figure S5.(PEA)2PbBr4 (a,b) and MAPbBr3 (c,d) current versus voltage plots over temperature in logarithmic scale (a,c) and linear scale (b,d) used to calculate the ion conductivity activation energy, and showing Ohmic behavior.

Figure S6 .
Figure S6.MAPbBr3 photocurrent transient measured at a 70  excitation time.The insets highlight the reverse current spikes when the light is turned on (first spike from the left) and turned off (second spike from the left).Bias voltage −5 , illumination 470 , 5 / 2 .

Figure S7 .
Figure S7.(a) Normalized photocurrent transient at room temperature for +5  bias and illumination pulse duration 2.5 .(b-d) Band diagram models for illustrating the effect of intermittent illumination over time at the semitransparent electrode, where a positive bias is applied.

Figure S8 .
Figure S8.Complete photocurrent transient dataset used to derive the Arrhenius plots reported in main text Figure 4e.Positive (a-b) and negative (c-e) bias and slow (a,c) medium, (b,d) and high (e) light modulation frequencies are used to distinguish ionic charge sign and ion species, respectively.Note: no readable signal was observed for positive bias and high frequency.

Figure S9 .
Figure S9.Stability of the photocurrent transients used to carry out PICTS analysis.The MAPbBr3 sample was loaded in the cryostat at room temperature in vacuum and the current flowing through

Figure S10 .
Figure S10.PICTS measurements repeatability test.(a-d) PICTS maps corresponding to measurements carried out at different voltages: −5  (a,b), +5  (c,d), at subsequent times, i.e. measurements reported in (a,c) preceded the measurements (c,d) carried out on the same sample.e, Arrhenius plots of the maxima displayed in (a,b,c,d) in red versus inverse temperature showing good repeatability.

Figure S11 .
Figure S11.PICTS measurements stress test and signal drift assessment under vacuum, applied external bias and intermittent illumination over a time span of hours.(a-c) PICTS maps corresponding to measurements carried out at different times:  = 0 ℎ (a),  = 1.5 ℎ (b), and  = 3 ℎ (c).(d) Arrhenius plots of maxima displayed in (a,b,c) in red versus inverse temperature, showing a good signal reproducibility.

Figure S12 .
Figure S12.Comparison of photocurrent transients for the coplanar and the top-bottom contacts architecture on the MAPbBr3 single crystal.(a) Normalized photocurrent transients for the coplanar (green) and the top-bottom (orange) contacts, scattered dots, fitted in the photocurrent decay region with double exponential decays (lines).(b) Time constants of the decays retrieved from the fitting of data displayed in (a) demonstrating very similar decay behavior.
inset, main text.By plugging in the values, we get: