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Journals >Opto-Electronic Advances >Volume 4 >Issue 10 >Page 210039-1 > Article

Opto-Electronic Advances
Vol. 4, Issue 10, 210039-1 (2021)

Hybrid artificial neural networks and analytical model for prediction of optical constants and bandgap energy of 3D nanonetwork silicon structures

Shreeniket Joshi and Amirkianoosh Kiani^*

Author Affiliations

Silicon Hall: Micro/Nano Manufacturing Facility, Faculty of Engineering and Applied Science, Ontario Tech University, 2000 Simcoe St N, Oshawa, Ontario L1G 0C5, Canada

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DOI: 10.29026/oea.2021.210039 Cite this Article

Shreeniket Joshi, Amirkianoosh Kiani. Hybrid artificial neural networks and analytical model for prediction of optical constants and bandgap energy of 3D nanonetwork silicon structures[J]. Opto-Electronic Advances, 2021, 4(10): 210039-1 Copy Citation Text

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Abstract

The aim of this study is to develop a reliable method to determine optical constants for 3D-nanonetwork Si thin films manufactured using a pulsed-laser ablation technique that can be applied to other materials synthesized by this technique. An analytical method was introduced to calculate optical constants from reflectance and transmittance spectra. Optical band gaps for this novel material and other important insights on the physical properties were derived from the optical constants. The existing optimization methods described in the literature were found to be complex and prone to errors while determining optical constants of opaque materials where only reflectance data is available. A supervised Deep Learning Algorithm was developed to accurately predict optical constants from the reflectance spectrum alone. The hybrid method introduced in this study was proved to be effective with an accuracy of 95%.

$N = n - {\rm{i}}k\;{\rm{with}}\;{\rm{i}} \approx \sqrt { - 1}\;. $

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$\begin{split} T =\;& \frac{{Ax}}{{B - Cx{\rm{cos}} \varphi + D{x^2}}}\;,\\ A =\;& 16{n^2}s,B = {\left( {n + 1} \right)^3}\left( {n + {s^2}} \right),\\ C = \;&2\left( {{n^2} - 1} \right)\left( {{n^2} - {s^2}} \right),\\ D =\;& {\left( {n - 1} \right)^3}\left( {n - {s^2}} \right),\\ \varphi =\;& \frac{{4 {\rm{\pi}} nd}}{\lambda },x = {\rm{\exp}} \left( { - \alpha d} \right),\alpha = \frac{{4{\rm{\pi}} k}}{\lambda }\;. \end{split} $

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$ {T_{\rm{M}}} = \frac{{Ax}}{{B - Cx + D{x^2}}}\;,$

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$ {T_{\rm{m}}} = \frac{{Ax}}{{B + Cx + D{x^2}}}\;.$

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$ n\left( \lambda \right) = {A_n} + \frac{{{B_n}}}{{{\lambda ^2}}} + \frac{{{C_n}}}{{{\lambda ^4}}}\;.$

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$ k\left( n \right) = {A_k} + \frac{{{B_k}}}{{{\lambda ^2}}} + \frac{{{C_k}}}{{{\lambda ^4}}}\;.$

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$ k\left( E \right) = \mathop \sum \limits_i^q \frac{{{A_i}{{\left( {E - E_{\rm{g}}} \right)}^2}}}{{{E^2} - {B_i}E + {C_i}}}\;.$

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$ n\left( E \right) = n\left( \infty \right) + \mathop \sum \limits_i^q \frac{{{B_{0i}}E + {C_{0i}}}}{{{E^2} - {B_i}E + {C_i}}}\;.$

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$ {T \left( {\lambda ,{\rm{ }}s\left( \lambda \right),{\rm{ }}d,{\rm{ }}n\left( \lambda \right),{\rm{ }}\kappa (\lambda )} \right){\rm{ }} = {\rm{ }}T\;{\rm{ experimental}}\left( \lambda \right)} \;.$

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$ {R \left( {\lambda ,{\rm{ }}s\left( \lambda \right),{\rm{ }}d,{\rm{ }}n\left( \lambda \right),{\rm{ }}\kappa (\lambda )} \right){\rm{ }} = {\rm{ }}R\;{\rm{ experimental}}\left( \lambda \right)} \;.$

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$ \alpha = \frac{1}{d}\ln \left[ {\frac{{{{\left( {1 - R} \right)}^2} + \left[ {{{\left( {1 - R} \right)}^4} + 4{R^2}{T^2}} \right]{^{1/2}}}}{{2T}}} \right]\;.$

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$ \alpha = \frac{1}{d}\ln \left( {\frac{{1 - R}}{T}} \right)\;.$

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$ k = \frac{{\alpha \lambda }}{{4{\rm{\pi}} }}\;.$

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$ n={{\left[ \frac{4R}{{{\left( R-1 \right)}^{2}}}-{{k}^{2}} \right]}^{1/2}}-\left( \frac{R+1}{R-1} \right)\;. $

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$ \begin{split} \;&T = \frac{{{n_2}}}{{{n_0}}}\\ &\cdot\frac{{\left\{ {{{\left( {1 + {g_1}} \right)}^2} + h_1^2} \right\}\left\{ {{{\left( {1 + g_2^2} \right)}^2} + h_2^2} \right\}}}{{{\rm{exp}} \left( {2{\alpha _1}} \right) + \left( {g_1^2 + h_1^2} \right)\left( {g_2^2 + h_2^2} \right){\rm{exp}} \left( { - 2{\alpha _1}} \right) + C\cos 2{\gamma _1} + D\sin 2{\gamma _1}}}\\ \;&C = 2\left( {{g_1}{g_2} - {h_1}{h_2}} \right)\\ \;&D = 2\left( {{g_1}{h_2} + {g_2}{h_1}} \right)\\ \;&{g_1} = \frac{{n_0^2 - n_1^2 - {k^2}}}{{{{\left( {{n_0} + {n_1}} \right)}^2} + {k^2}}}\;\& \;\;{g_2} = \frac{{n_1^2 - n_2^2 + {k^2}}}{{{{\left( {{n_1} + {n_2}} \right)}^2} + {k^2}}}\\ \;&{h_1} = \frac{{2{n_0}{k_1}}}{{{{\left( {{n_0} + {n_1}} \right)}^2} + k_1^2}}\;\& \;\;{h_2} = \frac{{2\left( {{n_1}k - {n_2}{k_1}} \right)}}{{{{\left( {{n_1} + {n_2}} \right)}^2} + {{\left( {{k_1} + {k_2}} \right)}^2}}}\\ \;&{\alpha _1} = \frac{{2{\rm{\pi}} kd}}{\lambda }\;\& \;\;{\gamma _1} = \frac{{2{\rm{\pi}} {n_1}d}}{\lambda }\;, \end{split} $

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Shreeniket Joshi, Amirkianoosh Kiani. Hybrid artificial neural networks and analytical model for prediction of optical constants and bandgap energy of 3D nanonetwork silicon structures[J]. Opto-Electronic Advances, 2021, 4(10): 210039-1

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