Markov Chain Monte Carlo Sampling for Target Analysis of Transient Absorption Spectra

Abstract

Global and target analysis techniques are ubiquitous tools for interpreting transient absorption (TA) spectra. However, characterizing uncertainty in the kinetic parameters and component spectra derived from these fitting procedures can be challenging. Furthermore, fitting TA spectra of inorganic nanomaterials where the component spectra of different excited states are nearly or completely overlapped is particularly problematic. Here, we present a target analysis model for extracting excited-state spectra and dynamics from TA data using a Markov chain Monte Carlo (MCMC) sampler to visualize and understand uncertainty in the model fits. We demonstrate the utility of this approach by extracting the overlapping component spectra and dynamics of single- and biexciton states in CsPbBr3 nanocrystals. Significantly, refinement of the component spectra is accomplished by fitting the entire fluence-dependent series of ensemble TA data using the Poisson statistics of photon absorption, providing multiple checks for internal consistency. The MCMC method itself is highly general and can be applied to any data set or model framework to accurately characterize uncertainty in the fit and aid model selection when choosing between different models.

Size-Dependent Biexciton Spectrum in CsPbBr3 Perovskite Nanocrystals

“…We propose a simple kinetic model (eq ) consisting of biexciton and exciton populations (BX and X, respectively) that decay in series with the decay time constants as two of the fit parameters (τ BX and τ X )­ The justification of this model is based, in part, on the observation that the TA spectral shape at long pump–probe delays (>200 ps) does not depend on the initial excitation fluence. Under the experimental conditions used here, we observed no evidence of a separate fast-decay channel attributable to trion formation and decay. , …”

“…The full multidimensional fluence-dependent data set is fit to a simple first-order kinetic model in which biexcitons decay into excitons while simultaneously solving for the underlying component spectra associated with each of these states. We combine this approach with a Markov chain Monte Carlo sampler to carefully examine the statistical certainty of the fits and verify the model assumptions . By applying this method and comparing the separate exciton and biexciton spectra as a function of NC size, we are able to more thoroughly characterize exciton–exciton interactions in perovskite materials.…”

Energy Transport in CsPbBr3 Perovskite Nanocrystal Solids

“…Energy transfer processes in quantum dot solids are usually characterized using transient absorption/time-resolved PL microscopy and other spectroscopy methods, ,,,− which allow determining both the spatial extent of the energy migration (exciton diffusion length, l diff ) and the rate of energy transfer between neighboring nanocrystals ( k hop ). An important benefit of the present fluorescence-quenching approach lies in the ability to study solids with a flat energy landscape.…”

A theoretical study of correlation effects of N electrons in semiconductor nanocrystals : applications to optoelectronic properties of perovskite nanocrystals

“…− + The Coulomb reduced matrix element X k (ab, cd) was defined in (3.3.9). 6 The k-pole angular diagrams of the direct and exchange interactions can be found in Fig. 4.2.3.…”

“…In a recent publication by Ashner et al [5], the biexciton shifts were determined to be some small blue shifts on the order of a few meV by using some novel fitting method published in Ref. [6]. While the experimental Δ XX values are in contradiction with one another, we would like to note that the extraction of the biexciton shifts from the transient absorption (TA) or time-resolved photoluminescence (TRPL) spectra relies heavily on post-measurement fitting methods.…”