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Inverse problem solving in semiconductor photoacoustics by neural networks. (English) Zbl 1470.82037

Summary: We developed a method of inverse problem solving in semiconductor photoacoustics based on neural networks application. Simple structured neural networks, trained on a large set of data obtained by the well-known theoretical models in the 20 Hz-20 kHz modulation frequency range, are applied to determine thermal diffusivity, coefficient of linear expansion and thickness of n-type silicon samples, using undistorted experimental photoacoustic signals. The efficiency of the neural networks was tested depending on the type of input data, showing the best performances in the case when signal amplitudes and phases are simultaneously presented to the network. Real-time parameter prediction is achieved together with high accuracy and reliability allowing one to perform the full characterization of a sample in the frequency domain.

MSC:

82D37 Statistical mechanics of semiconductors
68T07 Artificial neural networks and deep learning
Full Text: DOI

References:

[1] Mandelis A, editor. Photoacoustic and thermal wave phenomena in semiconductors. New York (NY): Elsevier, 1987. ISBN-10: 0444012265
[2] Mandelis A, Hess P, editors. Semiconductors and electronic materials. Vol. IV in the Series: Progress in photothermal and photoacoustic science and technology. Bellingham: SPIE Press, 2000. p. 271-315. ISBN: 9780819435064
[3] Rosencwaig A, Gersho A. Theory of the photoacoustic effect with solids. J Appl Phys. 1976;47:64. doi: 10.1063/1.322296 · doi:10.1063/1.322296
[4] McDonald F, Wetsel G. Generalized theory of the photoacoustic effect. J Appl Phys. 1978;49:2313. doi: 10.1063/1.325116 · doi:10.1063/1.325116
[5] Da Silva MD, Bandeira IN, Miranda LCM. Open-cell photoacoustic radiation detector. J Phys E, Sci Instrum. 1987;20:12. doi: 10.1088/0022-3735/20/12/009 · doi:10.1088/0022-3735/20/12/009
[6] Perondi LF, Miranda LCM. Minimal-volume photoacoustic cell measurement of thermal diffusivity: effect of the thermoelastic sample bending. J Appl Phys. 1987;62:2955. doi: 10.1063/1.339380 · doi:10.1063/1.339380
[7] Balderas-Lopez JA, Mandelis A. Thermal diffusivity measurements in the photoacoustic open-cell configuration using simple signal normalization techniques. J Appl Phys. 2001;90:2273. doi: 10.1063/1.1391224 · doi:10.1063/1.1391224
[8] Todorovic DM, Nikolic PM, Bojicic AI, et al. Thermoelastic and electronic strain contribution to the frequency transmission photoacoustic effect in semiconductors. Phys Rev B. 1997;55:15631-15642. doi: 10.1103/PhysRevB.55.15631 · doi:10.1103/PhysRevB.55.15631
[9] Duch W, Diercksen GHF. Neural networks as tools to solve problems in physics and chemistry. Comput Phys Commun. 1994;82(2-3):91-103. doi: 10.1016/0010-4655(94)90158-9 · doi:10.1016/0010-4655(94)90158-9
[10] Artrith N, Urban A. An implementation of artificial neural-network potentials for atomistic materials simulations: performance for \(TiO_2\). Comput Mater Sci. 2016;114:135-150. doi: 10.1016/j.commatsci.2015.11.047 · doi:10.1016/j.commatsci.2015.11.047
[11] Ćojbašić Z, Nikolić V, Ćirić I, et al. Computationally intelligent modelling and control of fluidized bed combustion process. Therm Sci. 2011;15:321. doi: 10.2298/TSCI101205031C · doi:10.2298/TSCI101205031C
[12] Markushev DD, Rabasovic MD, Todorovic DM, et al. Photoacoustic signal and noise analysis for Si thin plate: signal correction in frequency domain. Rev Sci Instrum. 2015;86:035110. doi: 10.1063/1.4914894 · doi:10.1063/1.4914894
[13] Aleksić SM, Markushev DK, Pantić DS, et al. Electro-acoustic influence of the measuring system on the photoacoustic signal amplitude and phase in frequency domain. Facta Universitatis Ser: Phys Chem Technol. 2016;14(1):9-20. doi: 10.2298/FUPCT1601009A · doi:10.2298/FUPCT1601009A
[14] Lukić M, Ćojbašić Ž, Rabasović MD, et al. Computationally intelligent pulsed photoacoustics. Meas Sci Technol. 2014;25:12. doi:10.1088/0957- 0233/25/12/125203 doi: 10.1088/0957-0233/25/12/125203 · doi:10.1088/0957-0233/25/12/125203
[15] Lukić M, Ćojbašić Ž, Rabasović MD, et al. Neural networks-based real-time determination of laser beam spatial profile and vibrational-to translational relaxation time within pulsed photoacoustics. Int J Thermophys. 2013;34(8-9):1795-1802. doi: 10.1007/s10765-013-1507-y · doi:10.1007/s10765-013-1507-y
[16] Djordjevic KL, Markushev DD, Ćojbašić ŽM, et al. Photoacoustic measurements of the thermal and elastic properties of n-type silicon using neural networks. Silicon. 2019 doi: 10.1007/s12633-019-00213-6 · doi:10.1007/s12633-019-00213-6
[17] Todorović DM, Nikolić PM, Dramićanin MD, et al. Photoacoustic frequency heat-transmission technique: thermal and carrier transport parameters measurements in silicon. J Appl Phys. 1995;78(9):5750. mailto:10.1063@1.359637.pdf doi: 10.1063/1.359637 · doi:10.1063/1.359637
[18] Todorović DM, Nikolić PM. Semiconductors and electronic materials progress in photothermal and photoacoustic, science and technology Chap. 9. New York (NY): Optical Engineering Press 2000. p. 273-318.
[19] Dramićanin MD, Nikolić PM, Ristovski ZD, et al. Photoacoustic investigation of transport in semiconductors: theoretical and experimental study of a Ge single crystal. Phys Rev B. 1995;51:4226. doi: 10.1103/PhysRevB.51.14226 · doi:10.1103/PhysRevB.51.14226
[20] Gurevich YG, Lashkevych II. Sources of Fluxes of energy, heat, and diffusion heat in a bipolar semiconductor: influence of nonequilibrium charge carriers. Int J Thermophys. 2013;34:341. doi: 10.1007/s10765-013-1416-0 · doi:10.1007/s10765-013-1416-0
[21] De la Cruz GG, Gurevich YG. Electron and phonon thermal waves in semiconductors: an application to photothermal effects. J Appl Phys. 1996;80:1726. mailto:10.1063@1.362971.pdf doi: 10.1063/1.362971 · doi:10.1063/1.362971
[22] Marin E, Vargas H, Diaz P, et al. On the photoacoustic characterization of semiconductors: influence of carrier recombination on the thermodiffusion, thermoelastic and electronic strain signal generation mechanisms. Phys Status Solidi A-Appl. 2000;179:387. doi:10.1002/1521-396X(200006)179:23.0.CO;2-Y doi: 10.1002/1521-396X(200006)179:2<387::AID-PSSA387>3.0.CO;2-Y · doi:10.1002/1521-396X(200006)179:2<387::AID-PSSA387>3.0.CO;2-Y
[23] Markushev DK, Markushev DD, Galović S, et al. The surface recombination velocity and bulk lifetime influences on photogenerated excess carrier density and temperature distributions in n-type silicon excited by a frequency-modulated light source. Facta Universitatis Ser: Electron Energ. 2018;31(2):313-328. doi: 10.2298/FUEE1802313M · doi:10.2298/FUEE1802313M
[24] Markushev DK, Markushev DD, Aleksic SM, et al. Effects of the photogenerated excess carriers on the thermal and elastic properties of n-type silicon excited with a modulated light source: theoretical analysis. J Appl Phys. 2019;126:185102. doi: 10.1063/1.5100837 · doi:10.1063/1.5100837
[25] Popović MN, Nešić MV, Cirić-Kostić S, et al. Helmholtz resonances in photoacoustic experiment with laser-sintered polyamide including thermal memory of samples. Int J Thermophys. 2016;37:116. doi: 10.1007/s10765-016-2124-3 · doi:10.1007/s10765-016-2124-3
[26] Sola J, Sevilla J. Importance of input data normalization for the application of neural networks to complex industrial problems. IEEE Trans Nucl Sci. 1997;44(3):1464-1468. doi: 10.1109/23.589532 · doi:10.1109/23.589532
[27] Wang LY, Yin GG, Zhao Y, et al. Identification input design for consistent parameter estimation of linear systems with binary-valued output observations. IEEE Trans Automat Contr. 2008;53(4):867-880. doi: 10.1109/TAC.2008.920222 · Zbl 1367.93154 · doi:10.1109/TAC.2008.920222
[28] Marquard DW. An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math. 11(2):431-441. doi: 10.1137/0111030 · Zbl 0112.10505 · doi:10.1137/0111030
[29] Rabasović MD, Nikolić MG, Dramićanin MD, et al. Low-cost, portable photoacoustic setup for solid state. Meas Sci Technol. 2009;20:9. doi: 10.1088/0957-0233/20/9/095902 · doi:10.1088/0957-0233/20/9/095902
[30] Glorieux C, Thoen J. Thermal depth profile reconstruction by neural network recognition of the photothermal frequency spectrum. J App Phys. 1996;80(11):6510-6514. doi: 10.1063/1.363670 · doi:10.1063/1.363670
[31] Glorieux C, Li Voti R, Thoen J, et al. Depth profiling of thermally inhomogenous materials by neural network recognition of photothermal time domain data. J App Phys. 1999;85(10):7059-7063. doi: 10.1063/1.370512 · doi:10.1063/1.370512
[32] Popovic MN, Furundzic D, Galovic SP. Photothermal depth profiling of optical gradient materials by neural network. Publ Astron Obs Belgrade. 2010;89:2015.
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