Mapping Transport Properties of Halide Perovskites via Short-Time-Dynamics Scaling Laws and Subnanosecond-Time-Resolution Imaging

The excellent optoelectronic and transport properties of halide perovskites have led to the rapid development of perovskite-based optoelectronic devices. A fundamental understanding of charge-carrier dynamics, as well as the implementation of physical models able to accurately describe their behaviour, is essential for further improvements in the field. Here, combining advanced modeling and characterization, a method for analyzing the short time dynamics of time-resolved fluorescence imaging (TRFLIM) decays is demonstrated. A theoretical scaling law for the time derivative of transient photoluminescence decays as a function of excitation power is extracted. This scaling law, computed from classical drift-diffusion equations, defines an innovative and simple way to extract quantitative values for several transport parameters, including the external radiative-recombination coefficient. The model is notably applied on a set of images acquired with a temporal shift of 250 ps to map the top-surface recombination velocity of a triple-cation mixed-halide perovskite thin film at the microscale. The development of high-time-resolution imaging techniques coupled with a scaling method for analyzing short time dynamics provides a solid platform for the investigation of local heterogeneities in semiconductor materials and the accurate determination of the main parameters governing their carrier transport.

Figure 1

Experiments on triple-cation perovskite [${\mathrm{Cs}}_{0.05}$(${\mathrm{MA}}_{0.17}{\mathrm{FA}}_{0.83}$)${}_{0.95}\mathrm{Pb}$-(${\mathrm{Br}}_{0.17}{\mathrm{I}}_{0.83}$)${}_3$] thin films under an inert atmosphere. (a) Scheme of subnanosecond-resolved TRFLIM acquisitions. The 3-ns-long gates slide in time with an interval of 250 ps. For each gate, an image is acquired. Temporal convolution of the signal with the gates results in a delay between the laser pulse (a few tens of picoseconds long) and the center of the maximal frame. Top right is the obtained decay averaged over the images. All images share the same color scale (from $3.5\times {10}^4$ to $6\times {10}^4$ counts). (b) TRPL intensity, computed as the space integration of the TRFLIM signal, as a function of time for different fluences acquired with a time shift of $250$ ps. Dark curves correspond to lower fluences (down to $4\times {10}^{11}{\mathrm{ph\; cm}}^{-2}$) and red curves to higher fluences (up to ${10}^{13}{\mathrm{ph\; cm}}^{-2}$). Inset, comparison of subnanosecond-resolved curves (open circles) with regular decays resolved at 3 ns (line). Only the first 150 ns of the regular and longer decay (that lasts up to $t=879\mathrm{ns}$) are shown. (c) Relative slope fitted on the decays between 0.5 and $2.5\mathrm{ns}$ as a function of laser fluence: blue, measured on raw decays; yellow, measured on deconvoluted decays. Error bars are given by the fitting function; see Sec. 2 on numerical uncertainty within the Supplemental Material [34]. Curves are fitted by using a linear function (dotted line): $y=ax+b$. Parameters found for the raw scaling are $a=-(5.7\pm 0.6)\times {10}^{-6}{\mathrm{cm}}^2{\mathrm{s}}^{-1}$ and $b=-(1.24\pm 0.03)\times {10}^8{\mathrm{s}}^{-1}$. Parameters found from scalings from deconvoluted decays are $a=-(1.07\pm 0.15)\times {10}^{-5}{\mathrm{cm}}^2{\mathrm{s}}^{-1}$ and $b=-(2.06\pm 0.08)\times {10}^8{\mathrm{s}}^{-1}$.

Figure 2

Local determination of parameters. (a) Map of top-surface recombination velocity from fitted local intercepts of local scalings. Seven fluence acquisitons of Fig. 1 are used at a local scale. Binning of $10$ pixels is applied, meaning that all pixels are averaged out over a square of $10\times 10$ pixels. For each pixel, seven decays are obtained, corresponding to seven fluences. Derivative of deconvoluted decays are computed between 0.5 and 2.5 ns. Derivatives are assembled to form the scaling, from which the intercept is fitted. Slope for all points is set to $a=-1.07\times {10}^{-5}{\mathrm{cm}}^2{\mathrm{s}}^{-1}$. To obtain the map of local intercept, we compute locally the average of the ensemble, $E=(\mathrm{derivative}-a\times \mathrm{fluence})$. For the uncertainty, we compute $\mathrm{std}(E)/\sqrt{E_n}$, with $E_n$ as the number of elements in $E$. Then, we use Eq. (7) and the assumed values for the other parameters to compute the map of $S_{\mathrm{top}}$ from the map of the intercept. Parameters are estimated to be $D=3.54\times {10}^{-3}{\mathrm{cm}}^2{\mathrm{s}}^{-1}$, $k_1=9.23\times {10}^6{\mathrm{s}}^{-1}$, and $\alpha =6.5\times {10}^4{\mathrm{cm}}^{-1}$. (b) Vertical cross section of map (a) at $x=6.5\mu \mathrm{m}$.