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Dutta R, Tian SIP, Liu Z, Lakshminarayanan M, Venkataraj S, Cheng Y, Bash D, Chellappan V, Buonassisi T, Jayavelu S. Extracting film thickness and optical constants from spectrophotometric data by evolutionary optimization. PLoS One 2022; 17:e0276555. [PMID: 36449457 PMCID: PMC9710797 DOI: 10.1371/journal.pone.0276555] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Accepted: 10/09/2022] [Indexed: 12/04/2022] Open
Abstract
In this paper, we propose a simple and elegant method to extract the thickness and the optical constants of various films from the reflectance and transmittance spectra in the wavelength range of 350 - 1000 nm. The underlying inverse problem is posed here as an optimization problem. To find unique solutions to this problem, we adopt an evolutionary optimization approach that drives a population of candidate solutions towards the global optimum. An ensemble of Tauc-Lorentz Oscillators (TLOs) and an ensemble of Gaussian Oscillators (GOs), are leveraged to compute the reflectance and transmittance spectra for different candidate thickness values and refractive index profiles. This model-based optimization is solved using two efficient evolutionary algorithms (EAs), namely genetic algorithm (GA) and covariance matrix adaptation evolution strategy (CMAES), such that the resulting spectra simultaneously fit all the given data points in the admissible wavelength range. Numerical results validate the effectiveness of the proposed approach in estimating the optical parameters of interest.
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Affiliation(s)
- Rajdeep Dutta
- Institute for Infocomm Research (IR), Agency for Science, Technology and Research (A*STAR), Singapore, Singapore
- * E-mail: (RD); (VC); (TB); (SJ)
| | - Siyu Isaac Parker Tian
- Low Energy Electronic Systems (LEES), Singapore-MIT Alliance for Research and Technology (SMART), Singapore, Singapore
- Solar Energy Research Institute of Singapore (SERIS), National University of Singapore, Singapore, Singapore
| | - Zhe Liu
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States of America
| | | | - Selvaraj Venkataraj
- Solar Energy Research Institute of Singapore (SERIS), National University of Singapore, Singapore, Singapore
| | - Yuanhang Cheng
- Solar Energy Research Institute of Singapore (SERIS), National University of Singapore, Singapore, Singapore
| | - Daniil Bash
- Institute of Materials Research and Engineering (IMRE), Agency for Science, Technology and Research (A*STAR), Singapore, Singapore
| | - Vijila Chellappan
- Institute of Materials Research and Engineering (IMRE), Agency for Science, Technology and Research (A*STAR), Singapore, Singapore
- * E-mail: (RD); (VC); (TB); (SJ)
| | - Tonio Buonassisi
- Low Energy Electronic Systems (LEES), Singapore-MIT Alliance for Research and Technology (SMART), Singapore, Singapore
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States of America
- * E-mail: (RD); (VC); (TB); (SJ)
| | - Senthilnath Jayavelu
- Institute for Infocomm Research (IR), Agency for Science, Technology and Research (A*STAR), Singapore, Singapore
- Artificial Intelligence, Analytics And Informatics (AI), A*STAR, Singapore, Singapore
- * E-mail: (RD); (VC); (TB); (SJ)
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