(274h) Deconvoluting Ultrafast Carrier Phenomena through Bayesian Inference of Time-Resolved Terahertz Spectroscopy Data

The development of high-efficiency absorber materials for photovoltaic devices requires knowledge of material parameters that characterize the transport of charge carriers through the absorber, such as the carrier mobility, the doping concentration, and the rates of radiative, defect-assisted, and other nonradiative recombination mechanisms. However, the assembly of this body of information for novel materials is typically piecemeal, in which disparate measurements along different stages in the development cycle, from simple absorber to functional device, contribute one or two parameters at a time to the overall material profile. The characterization process is particularly complex when early-stage or nonideal materials are involved, in which a multitude of competing carrier phenomena can mask the true physical origins of observed responses. In a time-resolved photoluminescence (TRPL) measurement, for example, the universally reported carrier lifetime can originate from a combination of not only defect-assisted recombination in the bulk, but also recombination at surface defects, carrier trapping and detrapping, and device field effects. This ambiguity limits the effectiveness of characterization techniques alone at pinpointing specific areas of improvement for novel materials development.

More material information can be recovered when characterization experiments are paired with physics-driven simulations of the carrier dynamics. Charge carrier evolution is described by the drift-diffusion model, in which the transient charge carrier density is computed in terms of diffusion, electronic drift, and recombination. These mechanisms are controlled by parameters that correspond directly to the parameters targeted by characterization techniques. The carrier density can then be used to model an observed transient response. In TRPL, for instance, the intensity is proportional to the radiative recombination term. Limiting cases of the model can be used to estimate some parameters, while global fitting techniques have been employed to determine combinations of parameters whose simulated transients match experimental data. This has allowed some groups to differentiate first-, second-, and third-order recombination mechanisms from TRPL alone. However, the size of the parameter space, the overlaps between how different carrier mechanisms affect the transient, and the computational expense of simulations have historically precluded more complete recovery of the material parameter set.

We have recently proposed a Bayesian inference method employing Metropolis Monte Carlo (MMC) sampling to extract material parameters more efficiently from TRPL measurements. We have successfully recovered the ambipolar mobility, doping concentration, bulk carrier lifetime, surface recombination velocity, radiative recombination rate, and Auger recombination rate simultaneously from TRPL measurements of methylammonium lead iodide absorbers. The MMC-based method locates parameter space regions with high likelihood (goodness-of-fit) within a few thousand simulations completable within hours on an ordinary desktop computer. In contrast to global fitting routines, the ability of MMC samplers to oscillate between parameter spaces with similarly high likelihoods allows us to visualize any between-parameter covariances that identify carrier mechanisms which are indistinguishable from the available data and guide the development of more informative characterization experiments.

While the introduction of MMC sampling can greatly enhance the information content of TRPL experiments, TRPL has only a limited ability to capture carrier dynamics at picosecond time scales. In particular, the carrier mobilities cannot be resolved if carrier diffusion is fast enough to overlap with the instrument response function of the TRPL setup. Time-resolved terahertz spectroscopy (TRTS), on the other hand, is easily capable of probing this ultrafast time range. TRTS and TRPL share many characteristics and advantages: they are contact-free and nondestructive measurements that can be applied to early-stage materials, and the photoexcited carriers generated by each measurement are governed by the same drift-diffusion model. The similar parameter space also results in TRTS data analysis having the same challenges as TRPL analysis—global fitting methods have been used to estimate the electron and hole mobilities, surface recombination velocities, bulk lifetime, and doping concentrations of Cu₂ZnSnSe₄ and CdTe from TRTS data, but a comprehensive treatment of the parameter space from the lens of TRTS can maximize the number of recoverable parameters from this method, identify limitations of specific TRTS experiments, and evaluate the informativeness of complementary TRTS/TRPL analyses.

In this work, we aim to provide a detailed analysis of the optoelectronic parameter space from the perspective of TRTS measurements; namely, we will identify sufficient conditions and qualities needed in TRTS data sets to isolate each optoelectronic parameter or parameter covariance from a material, and then demonstrate that all such parameters can be recovered simultaneously by applying the MMC sampling method to a simulated data set containing the requisite conditions. We created a set of 12 simulated TRTS decays for a uniform, p-doped, 3 μm CdTe absorber with one face passivated with Al₂O₃. Initial excitations for the decays spanned three fluences: 10¹³, 10¹², 10¹¹ cm^-2 pulse^-1 and two wavelengths: 400 nm and 800 nm. Furthermore, we considered illumination from both the passivated and unpassivated faces of the absorber. We added relative Gaussian noise with a standard deviation of 5% of the signal to model typical variance observed in previous measurements with our setup. Selected TRTS decays and input parameter values for this absorber are shown in Figure 1a.

We initialized three random walks with initial states randomly selected within +/- 1 order of magnitude of the input values and computed 10,000 MMC samples per walk over 6 hours. The first 5,000 states, in which the random walk is moving toward the region of high likelihood, were discarded; the mean and variance of the remaining states were reported as the prediction and its uncertainty. Trace plots illustrating the path taken by each walk along the directions of selected parameters are shown in Figure 1b. Regardless of initial state, all three walks rapidly identified the correct values of the electron and hole mobilities and , the doping concentration , the unpassivated surface recombination velocity , and the electron and hole bulk lifetimes and .

Insights into specific features of the TRTS data set that yield specific parameters can be gained by repeating the MMC method with subsets of the data. We find that by considering a power scan with only the 800 nm wavelength and unpassivated-side illumination, the ambipolar mobility is identified but not the individual and . It is likely that the inclusion of data from additional wavelengths and illumination faces increases the sensitivity of the method to carrier diffusion because the method must find a state that correctly replicates diffusion from many different initial carrier density profiles. Similarly, the accuracy in is increased when multiple wavelengths or illumination faces are involved, because the surface recombination is strongly affected by the concentration of carriers at the relevant surface. We did not successfully identify because the passivated surface makes a negligible contribution compared to the unpassivated surface, but the MMC method did correctly identify the surface with higher recombination. The doping concentration is identifiable only when the data set includes fluences which generate carrier densities that cross . As the carrier density shifts from > (high injection) to < (low injection), the functional form of each recombination mechanism also shifts. For instance, bulk recombination is governed by the effective lifetime in high injection and by in low injection. The presence of these two regimes in the data allows the method to differentiate between and , whereas this determination will likely be difficult for a material with lower or a setup with narrower dynamic range. We do not identify the radiative recombination rate or the Auger recombination rates because the excitation powers considered do not generate sufficient carrier densities for these higher-order mechanisms to have a significant effect; the lifetime for these mechanisms at the largest carrier density is c.a. 600 ns.

The ability to identify carrier mobilities from inferences of TRTS data while also identifying the most relevant recombination mechanisms is a significant advantage over inferences of TRPL data. However, the fact that these recombination mechanisms were identified is dependent on their lifetimes being observable within the 10-nanosecond time range of the TRTS data set, which is not universal across materials and may not be known a priori for particularly early-stage materials. For instance, recombination lifetimes exceeding 100 ns are common among perovskites, and it is unlikely that TRTS alone will resolve these. An inference of combined TRTS and TRPL data could identify these parameters regardless of the time range they are observable in, but it will ultimately be necessary to verify these conclusions with simulated measurements from absorbers across broader ranges of input parameter values as well as experimental measurements of real materials.