Photoacoustic Analysis of Illuminated Si-TiO2 Sample Bending Along the Heat-Flow Axes

Photoacoustic Characterization of TiO2 Thin-Films Deposited on Silicon Substrate Using Neural Networks

“…In order to avoid additional normalizations and the calculation of effective values, we resorted to the use of the two-layer model for determining thin-film parameters where the properties of the silicon substrate are known [ 21 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 ]. Neural networks were formed for the analysis of photoacoustic signals generated from the Si substrate and the TiO 2 thin-film system.…”

“…Temperature Distributions in Two-Layer Sample Periodic temperature distributions in the thin-film (label 1 forTiO 2 ) and substrate (label 2 for Si) illuminated by the modulated light source ( Figure 1 and Figure 3 ) can be obtained by solving the thermal-diffusion equations in the form [ 21 , 31 , 59 , 62 ]: and where ω = 2 πf , f is the modulation frequency, I 0 is the incident light intensity, , R 1 is the film reflection coefficient, R 2 is the substrate reflection coefficient, is the film complex thermal diffusivity , D T 1 is the film thermal diffusion coefficient, is the substrate complex thermal diffusivity , D T 2 is the substrate thermal diffusion coefficient, k 1 is the thin-film heat conduction coefficient, k 2 is the substrate heat conduction coefficient, β 1 is the film absorption coefficient, β 2 is the substrate absorption coefficient, and δn p 2 ( z,f ) is the substrate photo-generated minority carrier dynamic density component (Equation (A2)). The general solutions of Equations (A1) and (A2) can be written in the form [ 21 , 31 , 59 , 62 ]: and where the constants A 3 , B 3 and B 4 are given as: Here is the complex minority carrier diffusion length, D p 2 is the diffusion coefficient of minority carriers (holes p in the n -type substrate), and τ p 2 is the bulk minority carrier lifetime. Constants A 1 , A 2 , B 1 and B 2 can be found solving the boundary conditions [ 21 , 31 , …”

“…The general solutions of Equations (A1) and (A2) can be written in the form [ 21 , 31 , 59 , 62 ]: and where the constants A 3 , B 3 and B 4 are given as: Here is the complex minority carrier diffusion length, D p 2 is the diffusion coefficient of minority carriers (holes p in the n -type substrate), and τ p 2 is the bulk minority carrier lifetime. Constants A 1 , A 2 , B 1 and B 2 can be found solving the boundary conditions [ 21 , 31 , 59 , 62 ]: where s F and s R are the substrate surface recombination speeds at the front ( z = 0) and rear ( z = l 2 ) surfaces, respectively. Based on our previous investigations, the analysis of the two-layer optical properties shows that the multiple optical reflections can be neglected in the Si substrate [ 31 ], but must be taken into account in the case of thin TiO 2 film.…”

“…Periodic temperature distributions in the thin-film (label 1 forTiO 2 ) and substrate (label 2 for Si) illuminated by the modulated light source ( Figure 1 and Figure 3 ) can be obtained by solving the thermal-diffusion equations in the form [ 21 , 31 , 59 , 62 ]: and where ω = 2 πf , f is the modulation frequency, I 0 is the incident light intensity, , R 1 is the film reflection coefficient, R 2 is the substrate reflection coefficient, is the film complex thermal diffusivity , D T 1 is the film thermal diffusion coefficient, is the substrate complex thermal diffusivity , D T 2 is the substrate thermal diffusion coefficient, k 1 is the thin-film heat conduction coefficient, k 2 is the substrate heat conduction coefficient, β 1 is the film absorption coefficient, β 2 is the substrate absorption coefficient, and δn p 2 ( z,f ) is the substrate photo-generated minority carrier dynamic density component (Equation (A2)).…”

Influence of non-irradiated surface optical absorber on temperature gradient induced by photothermal effect in a thin film

“…Photothermal (PT), and consequently photoacoustic (PA) techniques, are based on direct or indirect measurement of phenomena resulting from heat transfer processes in the examined material, whereas the most straightforward approach considers the examination of surface temperature variations of the sample (Popovic et al, 2018(Popovic et al, , 2021. Since these experimental techniques are considered model-dependent, their development largely involves the development and the analysis of theoretical-mathematical models which link physical processes in the examined material and the measured signal (Dramićanin et al, 2000;Galovic et al, , 2014Galović and Dramićanin, 1999;Markushev et al, 2019;Nesic et al, 2016;Nesic, Galovic, et al, 2012;Nesic, Gusavac, et al, 2012;Popovic et al, 2021) (Aleksić et al, 2022;Djordjevic et al, 2022;Markushev et al, 2018Markushev et al, , 2020Popovic et al, 2009;Somer et al, 2013;Soskic et al, 2012Soskic et al, , 2016Todorović, 2003;Todorović and Nikolic, 2000).…”