(698e) Enhanced Bayesian Parameter Estimation from Time-Resolved Photoluminescence Data through an Adaptive Metropolis Sampler

Optoelectronic characterization through methods such as terahertz spectroscopy, current-voltage profiling, and time-resolved photoluminescence (TRPL) deliver critical information regarding the performance of novel semiconductors, with material parameters such as the carrier mobilities, doping level, and relative rates of radiative versus nonradiative recombination mechanisms commonly of interest. Much of this information is contained within the ubiquitous drift-diffusion-recombination model [1] for time-resolved photoluminescence and the underlying carrier transport, but deconvoluting the individual mechanisms governed by each material parameter from photoluminescence curves has proven challenging. In this work, we introduce an adaptive Metropolis algorithm for the efficient acquisition of material parameter values from TRPL datasets. We demonstrate that up to eight material parameters are recoverable: the electron (μ­_n) and hole (μ­_p) mobilities, the doping concentration (p₀), the external radiative recombination coefficient (­k*), the front (S_F) and back (S_B) surface recombination velocities, and the electron (Ï„_n) and hole (Ï„_p) bulk Shockley-Reed-Hall recombination lifetimes. Where the recovery fails, identification of inter-parameter correlations guides the development of more informative measurement suites.

The Metropolis sampler is initialized with a randomly selected candidate parameter vector X₀ and specified covariance matrix C₀ and performs state updates according to the Metropolis-Hastings algorithm. A multivariate Gaussian proposal distribution N(X_t-1, C_t-1) supplies candidates X_t whose posterior probability values are determined by comparison of experimentally observed TRPL datapoints with simulated TRPL resulting from X_t. New candidates are accepted or rejected according to the ratio of their probability versus that of previously accepted candidates, allowing the sampler to move gradually toward more probable regions of parameter space. We apply several modifications to the base Metropolis-Hastings algorithm for improved performance when handling TRPL datasets: (1) a delayed acceptance procedure [2], where simulations are terminated early (and candidates discarded) if their probability is low, (2) adaptive recalculation of the covariance matrix [3] to optimize the acceptance rate of new candidates, and (3) parallel computation of up to 16 Markov subchains with differing initial X₀ for faster detection of inter-parameter correlations.

Through testing of this sampler with various simulated TRPL observations drawn from a methylammonium lead iodide absorber [4], we establish measurement schemes for the identification of the eight material parameters. We identify the power scan as a useful, informationally dense measurement suite from which four of these parameters or lumped combinations thereof are recoverable: the ambipolar mobility μ’, p₀, ­k*, and an effective carrier lifetime τ’ for nonradiative recombination. Combining power scans drawn from at least two sample thicknesses allows for differentiation of τ’ into bulk recombination lifetimes (Ï„_n, Ï„_p) and a combined surface recombination velocity (S_F + S_B). For absorbers in which surface recombination occurs at a timescale comparable to diffusion, we find that S_F and S_B are individually recoverable owing to the finite activation time needed for carriers to reach the back surface while μ­_n and μ­_p are individually recoverable when carrier densities are insufficient to sustain ambipolar diffusion.

[1] R. K. Ahrenkiel, "Minority-Carrier Lifetime in III-V Semiconductors," in Minority Carriers In III-V Semiconductors: Physics and Applications, Academic Press, Inc, 1993, pp. 39-150.

[2] M. Banterle, C. Grazian, A. Lee and C. P. Robert, "Accelerating Metropolis-Hastings algorithms by Delayed Acceptance," Foundations of Data Science, vol. 1, no. 2, pp. 103-128, 2019.

[3] H. Haario, E. Saksman and J. Tamminen, "An adaptive Metropolis algorithm," Bernoulli, vol. 7, no. 2, pp. 223-242, 2001.

[4] F. Staub, H. Hempel, J.-C. Hebig, J. Mock, U. W. Paetzold, U. Rau, T. Unold and T. Kirchartz, "Beyond Bulk Lifetimes: Insights into Lead Halide Perovskite Films froms Time-Resolved Photoluminescence," Physical Review Applied, vol. 6, no. 4, 2016.