Photoacoustic Measurements of the Thermal and Elastic Properties of n-Type Silicon Using Neural Networks
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ORIGINAL PAPER
Photoacoustic Measurements of the Thermal and Elastic Properties of n-Type Silicon Using Neural Networks Кatarina Lj. Djordjevic 1
&
Dragan D. Markushev 2 & Žarko М. Ćojbašić 3 & Katarina Lj. Djordjevic 4
Received: 11 February 2019 / Accepted: 13 June 2019 # Springer Nature B.V. 2019
Abstract In this paper, a simple multilayer perceptron neural network with forward signal propagation was designed and used to simultaneously determine the main physical parameters, such as: the thermal diffusivity, thermal expansion coefficient and thickness, from the transmission, frequency-modulated photoacoustic response of the sample. The amplitude and phase responses of the transmission open-cell photoacoustic signals were calculated in n-type silicon plates using a theoretical model and were used to train and test a neural network. The simulation was done in the modulation frequency range from 20 Hz to 20 kHz and using a wide range of expected values of thermal diffusivity and the thermal coefficient of expansion for semiconductor samples as well as their thickness. The advantages and disadvantages of neural networks utilization as an appropriate mathematical tool designated for semiconductor measurement-oriented purposes are analyzed. Network reliability, precision, and the possibility of operation in real time have been verified on an independent set of signals, establishing photoacoustics as a competitive and powerful technique assigned for material characterization. Keywords Photoacoustic . Semiconductors . Thermal diffusion . Thermal expansion . Artificial neural networks
1 Introduction The frequency modulated photoacoustics of semiconductors has been the focus of numerous explorations for many years due to their simple and reliable thermal and mechanical characterization by this experimental technique [1–6]. Photoacoustic is a non-destructive and precise non-contact technique based on the effect of sound generation due to light-matter interaction [7–9]. According to the theory of a composite piston in solid semiconductors, illuminated by a modulated light source, three different acoustic signals are generated in the cell: thermodiffusion, thermoelastic and plasmaelastic ones [10–12]. Thermodiffusion (TD) sound waves carry the information about the thermal conductivity
* Katarina Lj. Djordjevic [email protected] 1
Faculty of Physics, University of Belgrade, Belgrade, Serbia
2
Institute of Physics, University of Belgrade, Belgrade-Zemun, Serbia
3
Mechanical Engineering Faculty, University of Niš, Niš, Serbia
4
Vinca Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
of the sample, its density and its specific heat, described by one common coefficient of heat transfer - thermal diffusivity DT. Thermoelastic (TE) sound waves carry the information on the geometric characteristics of the sample through its thickness l and radius Rs, and on sample expansion due to heating through the coefficient of linear expansion α. Plasma elastic (PE) waves carry the information
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