Nanoscale Charge Accumulation and Its Effect on Carrier Dynamics in Tri-cation Perovskite Structures

Nanoscale investigations by scanning probe microscopy have provided major contributions to the rapid development of organic–inorganic halide perovskites (OIHP) as optoelectronic devices. Further improvement of device level properties requires a deeper understanding of the performance-limiting mechanisms such as ion migration, phase segregation, and their effects on charge extraction both at the nano- and macroscale. Here, we have studied the dynamic electrical response of Cs0.05(FA0.83MA0.17)0.95PbI3–xBrx perovskite structures by employing conventional and microsecond time-resolved open-loop Kelvin probe force microscopy (KPFM). Our results indicate strong negative charge carrier trapping upon illumination and very slow (>1 s) relaxation of charges at the grain boundaries. The fast electronic recombination and transport dynamics on the microsecond scale probed by time-resolved open-loop KPFM show diffusion of charge carriers toward grain boundaries and indicate locally higher recombination rates because of intrinsic compositional heterogeneity. The nanoscale electrostatic effects revealed are summarized in a collective model for mixed-halide CsFAMA. Results on multilayer solar cell structures draw direct relations between nanoscale ionic transport, charge accumulation, recombination properties, and the final device performance. Our findings extend the current understanding of complex charge carrier dynamics in stable multication OIHP structures.

S-3 recorded at different lift heights. The line profile was extrapolated for 0.1 nm distance using the fit. The clear contrast between grains and GBs shows that it is due to local variation of the Vcpd, rather than of purely capacitive origin.

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Table S1. Extracted time constants and adjusted R2 resulting from ( ) = 0 + ( / ) fit to separate parts of the first harmonic electrostatic response.

Open-loop pump-probe Kelvin probe force microscopy and its application
In Kelvin probe force microscopy (KPFM) a sinusoidal electrical signal is applied between the AFM tip and the sample at a fixed frequency which gives rise to an electrostatic force: where is the overall electrostatic force, , and 2 are the DC, first harmonic and second harmonic components of the total electrostatic force. In KPFM, the first harmonic ( ) of the electrostatic force is nullified by applying a DC voltage ( ) to the tip or the sample: where z is the tip sample distance, t is time, C is the capacitance, is the applied AC voltage to the tip, is the angular frequency, VDC the applied DC voltage, is the tip-sample contact potential difference. The contact potential difference can be expressed as: where 0 is the applied pump voltage amplitude to drive the laser, is the repetition period and k is an integer. The probing signal in this case is: S-11 where is the applied pulse voltage, is the angular modulation frequency, is the time delay between the pump and probe pulses, k is an integer and 0 = is the duty cycle of the probe signal. With a sampling time, this results in integration over number of periods of the electrostatic force response of the tip-sample system. Every recorded data point with spacing is going to be the sum of integrals at the selected . Increasing continuously by where ∆ = − is the frequency difference between pumping and probing signals, the recorded integrals at each point. Note that the sampling rate is completely independent from the pump frequency, thus the temporal resolution is limited by the minimum pulse width of the waveform-generator. We note that the pulsed probe signal is additionally amplitude modulated (AM) and the probe response is detected at the modulation frequency with a lock-in amplifier.
Firstly, this is more sensitive (especially if a cantilever Eigenmode is chosen for the envelope frequency), secondly, it removes any spurious drift of the static cantilever bending. Another implementation of the pump-probe sampling can be realized by using pulse-width modulation (PWM) of the probing signal, where the duty cycle changes periodically with the modulation frequency: where ℎ is the modulation depth. Here the time resolution is no longer limited by the pulse duty cycle ( 0 ) but rather the modulation depth ( ℎ ), which normally is set to be ℎ < 0 , and thus can result in superior temporal sensitivity and signal-to-noise ratio The reciprocal of the exponential factor multiplied by the repetition time and the frequency difference between the pulses gives the time constant on the correct timescale: where is the repetition period and is the frequency difference between pump and probe pulse. A repetition frequency of 50-150 kHz was selected for the pulses as it allows monitoring of microsecond timescale effects but can still be modulated by a sinusoidal waveform at the cantilever resonance frequency which improves sensitivity. The temporal resolution in a pumpprobe configuration is defined by the duty cycle (pulse-width) of the probing signal. We note that although higher duty cycles (pulse-widths) lead to higher signal to noise ratios (SNR) (see Figure S4b inset), the overall temporal resolution of the measurement decreases as can be seen S-13 in Figure S4b, where we show the measured and fitted time constants versus the probing pulse duty cycle in an amplitude modulated probe pulse measurement. The results show that the extracted time constant decreases with decreasing probe duty cycle. Once the pulse-width that matches or is lower than the time constant under investigation is reached a minimum appears and persists until the measured signal drops below the noise level. We note that at the 2 μs pulsewidth the extracted response is still a convolution of the system response and the averaging effect of the probing pulse-width, leading to an error in the exponential fit. In contrast, the asymmetry seen in Figure S4b. indicates that the slow relaxation is defined by the system response rather than by the applied pulse-width. In case of the map shown in Figure 4., although, depending on the employed scanning speed the integration time changes for each pixel, as mapping was done at a constant phase-offset between the pulses, the contrast between pixels and the resulting maps is independent of the interplay of applied pulse and scanning frequencies.
Optimum conditions for our measurements were reached at 1 μs pulse width.