Abstract
The detection of weak features in spectra remains a challenge. Differentiation remains a standard method, but maximum-entropy filters provide an alternative. Using dielectric-function data for MoSe2 as a test case, we compare the capabilities of two maximum-entropy filters, the original Burg version and its corrected offshoot, to detect the biexciton and determine its energy. In contrast to differentiation, both approaches detect the biexciton. However, neither provides accurate values of the excitonic transition energies in this spectral range, although the Burg version is somewhat better.
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References
A. Savitzky, M.J.E. Golay, Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, 1627 (1964)
K.J. Kim, M.H. Lee, J.H. Bahng, K. Shim, B.D. Choe, Optical constants and electronic interband transitions of disordered GaAs1−xPx alloys. J. Appl. Phys. 84, 3696 (1998)
M.R. Buckley, F.C. Peiris, O. Maksimov, M. Muñoz, M.C. Tamargo, Dielectric functions and critical points of BexZn1−xTe alloys measured by spectroscopic ellipsometry. Appl. Phys. Lett. 81, 5156 (2002)
T.J. Kim, J.J. Yoon, S.Y. Hwang, Y.W. Jung, T.H. Ghong, Y.D. Kim, H. Kim, Y.-C. Chang, InAs critical-point energies at 22 K from spectroscopic ellipsometry. Appl. Phys. Lett. 97, 171912 (2010)
H.G. Park, T.J. Kim, F. Ullah, V.L. Le, H.T. Nguyen, Y.S. Kim, Y.D. Kim, Temperature dependence of the dielectric function of monolayer MoSe2. Sci. Rep. 8, 3173 (2018)
V.L. Le, T.J. Kim, Y.D. Kim, D.E. Aspnes, Combined interpolation, scale change, and noise reduction in spectral analysis. J. Vac. Sci. Technol. B 37, 52903 (2019)
H.T. Nguyen, T.J. Kim, H.G. Park, V.L. Le, X.A. Nguyen, D. Koo, C.-H. Lee, D.D. Cuong, S.C. Hong, Y.D. Kim, Temperature dependence of optical properties of monolayer WS2 by spectroscopic ellipsometry. Appl. Surf. Sci. 511, 145503 (2020)
L.V. Le, T.J. Kim, Y.D. Kim, D.E. Aspnes, Reducing or eliminating noise in ellipsometric spectra. J. Korean Phys. Soc. 81, 403 (2022)
L.V. Le, T.J. Kim, Y.D. Kim, D.E. Aspnes, Maximum-entropy revisited: optimal filtering of spectra. J. Appl. Phys. 129, 224902 (2021)
L.V. Le, Y.D. Kim, D.E. Aspnes, Eliminating white noise in spectra: a generalized maximum-entropy approach. J. Appl. Phys. 132, 74903 (2022)
L.V. Le, T.J. Kim, Y.D. Kim, D.E. Aspnes, Detection of the biexciton of monolayer WS2 in ellipsometric data: a maximum-entropy success. Phys. Status Solidi 260, 2200271 (2023)
J. P. Burg, Maximum Entropy Spectral Analysis (Stanford University, 1975).
L.V. Le, T.J. Kim, Y.D. Kim, D.E. Aspnes, Decoding “Maximum entropy” deconvolution. Entropy 24, 1238 (2022)
V.L. Le, T.J. Kim, Y.D. Kim, D.E. Aspnes, External removal of endpoint-discontinuity artifacts in the reciprocal-space analysis of spectra. Curr. Appl. Phys.. Appl. Phys. 20, 232 (2019)
L.V. Le, Y.D. Kim, D.E. Aspnes, Quantitative assessment of linear noise-reduction filters for spectroscopy. Opt. Express 28, 38917 (2020)
J. Pei et al., Excited state biexcitons in atomically thin MoSe2. ACS Nano 11, 7468 (2017)
Acknowledgements
L.V.L. acknowledges the support of this work by the Vingroup Innovation Foundation (VinIF) (Grant No. VINIF.2022.STS.46) and the Vietnam Academy of Science and Technology (Grant No.THTEXS.01/21-24). T.J.K. acknowledges the support by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (NRF-2021R1A2C1005359 and NRF-2020R1A5A1016518).
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Le, L.V., Kim, T.J., Kim, Y.D. et al. Deconvolution of the biexciton structure of monolayer MoSe2 in spectroscopic ellipsometric data: a comparison of maximum-entropy methods. J. Korean Phys. Soc. (2024). https://doi.org/10.1007/s40042-024-01123-6
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DOI: https://doi.org/10.1007/s40042-024-01123-6