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Electric force microscopy was used to record the light-dependent impedancespectrum and the probe transient photoconductivity of a film of butylammoniumlead iodide, BA$_{2}$PbI$_{4}$, a 2D Ruddlesden--Popper perovskitesemiconductor. The impedance spectrum of BA$_{2}$PbI$_{4}$ showed modestchanges as the illumination intensity was varied up to 1400 mW/cm$^{2}$, incontrast with the comparatively dramatic changes seen for 3D lead-halideperovskites under similar conditions. BA$_{2}$PbI$_{4}$'s light-inducedconductivity had a rise time and decay time of $\sim$ 100 $\mu$s, 10$^{4}$slower than expected from direct electron-hole recombination and yet 10$^{5}$faster than the conductivity-recovery times recently observed in 3D lead-halideperovskites and attributed to the relaxation of photogenerated vacancies. Whatsample properties are probed by electric force microscope measurements remainsan open question. A Lagrangian-mechanics treatment of the electric forcemicroscope experiment was recently introduced by Dwyer, Harrell, and Marohnwhich enabled the calculation of steady-state electric force microscope signalsin terms of a complex sample impedance. Here this impedance treatment of thetip-sample interaction is extended, through the introduction of atime-dependent transfer function, to include time-resolved electrical scannedprobe measurements. It is shown that the signal in a phase-kick electric forcemicroscope experiment, and therefore also the signal in a time-resolvedelectrostatic force microscope experiment, can be written explicitly in termsof the sample's time-dependent resistance (i.e., conductivity).

journal of physical chemistry. c./journal of physical chemistry. c

Light-dependent Impedance Spectra and Transient Photoconductivity in a  Ruddlesden-Popper 2D Lead-halide Perovskite Revealed by Electrical Scanned  Probe Microscopy and Accompanying Theory