Reduced Artifact Approach for Determining Diffusion Coefficients in Time-Resolved Microscopy

Abstract

Ultrafast microscopy methods traditionally assume a Gaussian profile to extract excited state diffusivities from transport measurements. Although this fitting method recovers accurate diffusion coefficients when the point spread function is well-represented by a Gaussian, even minor spatial aberrations introduced by the imaging system cause significant errors in the determined value. To provide a more accurate measure of excited state transport in nano-and microscale materials systems, an alternative analysis protocol is proposed that numerically convolves the Green's function solution to the diffusion equation with the experimentally measured point spread function. In contrast to the Gaussian fitting approach, the numerical convolution is shown to be robust against artifacts caused by nonideal point spread functions. Furthermore, the numerical convolution approach is highly effective at resolving anisotropic diffusion in modeled data.

Direct Correlation of Charge Carrier Transport to Local Crystal Quality in Lead Halide Perovskites

“…The resulting 1D profile is fit while only weighting data points on the right side of the profile. The reported diffusion coefficients are an average of eight angle-resolved fits performed at intervals of π/4 …”

“…The reported diffusion coefficients are an average of eight angle-resolved fits performed at intervals of π/4. 31 EBSD patterns were collected using a Physical Electronics 710 scanning Auger nanoprobe with a 20 keV electron beam. Patterns were collected on a 250 nm square sampling grid.…”

“…Figure (a) shows representative profiles from Δ t = 1 ps (black) to Δ t = 200 ps (blue) at two locations (I and II) marked on Figure (a). To extract the diffusion coefficient, time-dependent profiles are fit to a numerical convolution of the experimental point spread function with the Green’s function solution to the diffusion equation Figure (b) shows a histogram of the diffusion coefficients measured from nine separate locations on the domain.…”

“…To extract the diffusion coefficient, time-dependent profiles are fit to a numerical convolution of the experimental point spread function with the Green's function solution to the diffusion equation. 31 Figure 2(b) shows a histogram of the diffusion coefficients measured from nine separate locations on the domain. The smallest value measured was 0.60 cm 2 /s, and the largest was 2.61 cm 2 /s.…”

Leaving the Limits of Linearity for Light Microscopy

“…A disadvantage of these studies, however, is that they require yet another dimension of information to be collected, slowing imaging times. Finally, note that, as more information is collected from the expansion of all of these techniques, new computational techniques will be needed in order to quickly and accurately analyze the resulting large, complex, and coupled data sets. − The body of work in this area is worthy of its own perspective.…”