Artificial Neural Networks to Predict Sheet Resistance of Indium-Doped Zinc Oxide Thin Films Deposited via Plasma Deposition
Abstract
:1. Introduction
2. Modelling Background
- 1.
- Analytical models rely on simple analytical formulae to describe the behaviour of the glow discharge parameters, such as the current and voltage. They are simple and easy to calculate; however, they suffer from accuracy and are only applicable for limited ranges of deposition conditions [16].
- 2.
- Pathway models are based on a simple approach of following the sputtered and working gas species within the discharge to gain understanding of the discharge processes in pulsed magnetron sputtering discharges. It was originally developed to determine the ionized fraction of the film-forming material arriving at the substrate and to explain the low deposition rate observed in some discharges [17].
- 3.
- Fluid models define the plasma as a continuum and are based on continuity and transport equations for the various discharge species, along with the Poisson equation, in order to obtain a self-consistent electric field distribution. The fluid model has an advantage in terms of easy computing. However, the validity of using a fluid model to describe a magnetron sputtering discharge has been questioned [18].
- 4.
- Ionization region models are based on defining an ionization region which is volume-averaged and time dependent. The region is the visually observed bright glowing plasma near the surface of the target. Via this model, the time evolution of neutral and charged species and the electron temperature in pulsed magnetron sputtering discharges can be calculated. The model is constrained by experimental parameter inputs—such as the geometry and the working gas pressure, the working gas, sputter yields and target species—and a reaction system setup for these species, in the sense that it first needs to be adapted to an existing discharge and then fitted using two or three parameters to reproduce the measured discharge current and voltage waveforms [19,20].
- 5.
- Hybrid models, as the name suggests, intend to combine the precision of kinetic models with the computational simplicity of the fluid model. In the magnetron sputtering discharge, the secondary electrons are emitted from the cathode target surface and accelerated to high energies within the cathode sheath. Often, the electrons are split up into two groups: the so-called fast electrons, with energy above the threshold for inelastic collisions, which are treated with a kinetic Monte Carlo model, and slower electrons that are described with a fluid model. In the hybrid approach, the ions and bulk electrons are treated by the fluid description and the fast electrons are treated by the particle model [21]. However, this approach has been criticised by Kolev and Bogaerts [22].
- 6.
- In Direct Monte Carlo simulations, several test particles, representing many plasma species, are followed. The movement of the test particles is influenced by applied forces and collisions with other particles. Direct Monte Carlo simulations have been used to predict the spatial distribution of the ionization [23] and ion trajectories [24] in a planar magnetron sputtering discharge.
- 7.
- Boltzmann solver is based on numerically solving the Boltzmann equation to obtain the electron energy distribution within the discharge. This is an accurate and widely implemented model in discharge physics. However, in the magnetron sputtering discharge, the Boltzmann equation includes a Lorentz force term that leads to mathematical complexity. Therefore, this approach has only been applied successfully in the case of a cylindrical magnetron sputtering discharge that consisted of a coaxial inner cathode and an outer anode [25,26,27,28].
- 8.
- Monte Carlo collisional simulations are based on the same principle as the discussed Monte Carlo simulations. The trajectories of many individual species are calculated applying Newton’s laws, and their collisions are treated by assigning random numbers [29]. Furthermore, the electric field distribution is also calculated self-consistently from the positions of the charged species using the Poisson equation. This approach provides spatial distribution of the charged particles projected onto a grid, along with the electric field across the discharge, illustrating charge density distribution, from which the electric field distribution can be calculated. It is the most powerful numerical method to explore the magnetron sputtering discharge. However, it relies on significant computational power as it tries to describe the detailed behaviour of charged species along with solving the Poisson equation [30].
2.1. A New Approach
2.2. ANN Modelling
2.3. CNN Modelling
3. Experimental
3.1. The Instruments
3.2. The Experiments and Results
3.2.1. The Integral Approach
3.2.2. The Spectral Approach
3.2.3. The Image Recognition Approach
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Predicted | Real | Relative Error |
---|---|---|
7.598 | 7.5 | 1.31 |
13.955 | 13.5 | 3.37 |
7.360 | 7.5 | 1.87 |
10.832 | 11.4 | 4.98 |
9.967 | 9.6 | 3.82 |
7.487 | 7.5 | 0.18 |
10.893 | 11 | 0.97 |
10.255 | 9.6 | 6.82 |
9.377 | 9.6 | 2.32 |
10.996 | 10.7 | 2.77 |
10.518 | 10.7 | 1.71 |
10.457 | 10.7 | 2.27 |
7.467 | 7.5 | 0.45 |
13.073 | 13.5 | 3.16 |
11.098 | 11.4 | 2.65 |
9.937 | 10 | 0.63 |
7.329 | 7.5 | 2.27 |
10.551 | 11.4 | 7.44 |
10.290 | 10.7 | 3.83 |
10.045 | 9.8 | 2.50 |
11.811 | 10.7 | 10.38 |
11.475 | 11 | 4.32 |
10.474 | 10 | 4.74 |
Modelling Approach and Data | R2 | Stability |
---|---|---|
ANN model, Integral approach | 0.795 | Poor |
ANN model, Spectral approach | 0.153 | poor |
ANN model, Spectral approach with PCA dimensionality reduction | 0.883 | Moderate |
CNN model, Standard Scaled | 0.642 | Moderate |
CNN model, Min Max scaled | 0.897 | Moderate |
CNN model, Standard Scaled, SVD first layer | 0.934 | Good |
CNN model, Min Max Scaled, SVD first layer | 0.741 | Good |
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Salimian, A.; Aminishahsavarani, A.; Upadhyaya, H. Artificial Neural Networks to Predict Sheet Resistance of Indium-Doped Zinc Oxide Thin Films Deposited via Plasma Deposition. Coatings 2022, 12, 225. https://doi.org/10.3390/coatings12020225
Salimian A, Aminishahsavarani A, Upadhyaya H. Artificial Neural Networks to Predict Sheet Resistance of Indium-Doped Zinc Oxide Thin Films Deposited via Plasma Deposition. Coatings. 2022; 12(2):225. https://doi.org/10.3390/coatings12020225
Chicago/Turabian StyleSalimian, Ali, Arjang Aminishahsavarani, and Hari Upadhyaya. 2022. "Artificial Neural Networks to Predict Sheet Resistance of Indium-Doped Zinc Oxide Thin Films Deposited via Plasma Deposition" Coatings 12, no. 2: 225. https://doi.org/10.3390/coatings12020225
APA StyleSalimian, A., Aminishahsavarani, A., & Upadhyaya, H. (2022). Artificial Neural Networks to Predict Sheet Resistance of Indium-Doped Zinc Oxide Thin Films Deposited via Plasma Deposition. Coatings, 12(2), 225. https://doi.org/10.3390/coatings12020225