_{2}Thin Film Deposition Using Multiple Linear Regressions

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A nanocrystalline SnO_{2} thin film was synthesized by a chemical bath method. The parameters affecting the energy band gap and surface morphology of the deposited SnO_{2} thin film were optimized using a semi-empirical method. Four parameters, including deposition time, pH, bath temperature and tin chloride (SnCl_{2}·2H_{2}O) concentration were optimized by a factorial method. The factorial used a Taguchi OA (TOA) design method to estimate certain interactions and obtain the actual responses. Statistical evidences in analysis of variance including high F-value (4,112.2 and 20.27), very low P-value (<0.012 and 0.0478), non-significant lack of fit, the determination coefficient (R^{2} equal to 0.978 and 0.977) and the adequate precision (170.96 and 12.57) validated the suggested model. The optima of the suggested model were verified in the laboratory and results were quite close to the predicted values, indicating that the model successfully simulated the optimum conditions of SnO_{2} thin film synthesis.

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Metal oxide semiconductors with wide band gaps have many important applications in the optics, electric and electronic industries. Transparent SnO_{2} thin films have been widely used in the production of transparent electrodes, far-infrared detectors, solar cells and gas sensors [_{2} thin films have also garnered attention since higher quality synthesis of SnO_{2} thin films was achieved.

A variety of methods, such as magnetron sputtering [_{2} thin films. Among all the methods, the chemical bath deposition technique is very attractive because it is easy to control the growth factors, and crystal quality [

Since in the CBD method several effective parameters such as concentration, time, temperature and the pH of the solution exist, too many experiments must be performed for finding the optimum conditions. Besides laborious experimental management, this also requires more chemicals, instruments and labor time. Furthermore, the preparation conditions are critical factors that affect the shape and size of the resulting nanomaterials [

The Taguchi method is a statistical technique used in empirical studies. It is an conomical way to characterize complicated processes, and it requires fewer experiments to optimize reactions. In the methodology, a factorial design was used for experimental design and fitting the performed results with a polynomial equation in the vicinity of the optimum conditions to make a model [

Glass slides of 76 × 25 mm^{2} were used as the substrate. SnCl_{2}·2H_{2}O (Merck, Darmstadt, Germany, 98.1%), Ethylenediaminetetraacetic acid and triethanolamine (Sigma Aldrich, St Louis, MO, USA) were used as the complexing agents. Ethanol, HCl and H_{2}O_{2} used in this study were of analytical reagent grade.

The reactions were performed in 100 mL flasks and specified volumes of deionized water were added as the solvent. Different concentrations of tin chloride were mixed with the complexing agents, while different amounts of H_{2}O_{2}, HCl and ethanol were subsequently added to adjust the pH. The reaction was performed in a water bath at different temperatures and for different deposition times, as shown in

To find the optimum deposition conditions, the experiments were designed by factorial and TOA as shown in

The total number of performed runs was nine. The designed actual responses were fitted to the quadratic cubic models by orthogonal array TOA. The fitting was based on a second order polynomial model by a multiple regression analysis [_{d}^{2}), adjusted R-squared (R_{Adj}^{2}), and predicted R-squared (R_{Pred}^{2}) and adequate precision of Predicted Residual Error of Sum of Squares (PRESS). Most of these parameters are clearly defined in experimental design texts. R_{Adj}^{2} and the R_{Pred}^{2} are the measurement of the amount of variation around the mean and the new explained data, respectively. F-value is a statistically valid measure of how well the factors described the variation in the data about its meaning while P-value represents the degree of significance of each variable [

The model fitting technique showed sufficient correlation between the predicted values to the observed values. The fitting of the data to various models (_{2}. ^{2}) obtained for the energy band gap and RMS were 0.978 and 0.977, respectively.

The S/N ratio is a logarithmic function used to optimize the process or product design and minimize the variability. The maximization of S/N ratio allows reduction of variability of the process against undesirable changes in the neighboring environment or uncontrollable factors. To minimize variability, the level of factor which produces the higher value of S/N ratio must be chosen. The S/N ratios were calculated using _{i}

The ANOVA results of the quadratic model for the deposition of SnO_{2} thin film are presented in

The coefficients of determination (R^{2}) of the model were 0.9838 and 0.9937, which indicated 98.38% and 99.37% of variability in the response could be explained by the model. Therefore, the present R^{2}-values reflected a very good fit (>0.9) between the experimental and predicted values [

In addition, the R^{2}_{Adj} (0.9353 and 0.9997) were satisfactory, which confirms the aptness of the model. Moreover, the adequate precision (12.57 and 170.96) shows remarkable signal (≫4). This ensured model (quadratic) was suitable to navigate the design space and provide a satisfactory match of the polynomial model to the experimental data.

It is normal to describe experimental data by forming a mathematical relationship between the factors (independent variables) and responses (dependent variables). The final model to describe the relationship of the energy band gap and surface roughness with control factors is shown in _{1}, X_{2}, X_{3} and X_{4} are demonstrated in _{1}, X_{2}, X_{3} and X_{4}) shows a direct relationship between the response and the effective factors. Quadratic terms of equation include (X_{1}^{2} and X_{3}^{2}), are one way of obtaining the maximum or minimum value and show the optimum performance at a particular factor. The interaction term (X_{1}X_{3}, X_{1}X_{2}) implies the dependent influence of two factors on the response. Negative values of coefficient estimates denote negative influence of parameters on the responses. It was observed that all the linear coefficients of the model gave a negative effect, except the coefficient estimated for concentration (C). This indicates that the energy band gap and surface roughness were negatively affected by pH, temperature and time. Besides, it was also observed that concentration had a significant effect on responses. Therefore the surface morphology and energy band gap of deposited SnO_{2} thin film improve by decreasing the pH, temperature and time to minimum levels, and increasing the concentration to the maximum level of the design.

Based on the validated model, the 3D plots present the numerous predicted (simulated) responses with the four variables and one response (_{2} concentration on chemical synthesis of SnO_{2} thin film was investigated during the deposition as a preliminary study, while two variables in each case were held constant (e.g., _{2} concentration.

^{+} ions increases in the solution (_{2}O (

Thus, the nucleation occurs by multiple growths and reduces the size and surface roughness of the film:

A decrease in RMS roughness was observed above the optimum. The reduction may be due to the prolonged deposition time which destroys the film.

^{2+} ions in the reaction solution (^{2+} ions would not have the opportunity to react with the OH^{−} ions resulting in cluster growth of the film.

The same trend was observed in

_{2} (_{2} thin film. Further increases again increase the energy band gap value.

As a result, the optimum conditions for energy band gap and surface roughness are somewhat different. Simultaneous optimization led by the model allowed us to evaluate the optimum conditions for both responses. As a result the optimum point for energy band gap and surface roughness were 3.40 eV (average) and 50 nm under the conditions of pH of 6 and tin chloride concentration 0.14 M with 78 min of deposition time and 45 °C bath temperature. The optimum was validated by performing confirmatory experiments.

Once the optimum level of the design parameters had been selected, the final step was to predict and verify the improvement of the quality characteristic using the optimum level of the design parameters. _{2} thin film at the optimum conditions predicted by TOA. As observed, the experimental values were reasonably close to the simulated values, which indicated the high validity and adequacy of the model. The grain size of the deposited SnO_{2} film under the optimum conditions according to SEM observation was about 45 nm.

Nanocrystalline SnO_{2} thin film synthesis was optimized and modeled using a Taguchi robust design method with multiple linear regression analysis. The experiments were designed with four effective factors including concentration, pH value, and deposition time and bath temperature. To suggest a model for the deposition, the responses were fitted with a quadratic model. The ANOVA confirmed the high validity of the model as evidenced of the high F-value (20.27 and 4,112.2), non-significant lack of fit, the R^{2} (98.38% and 99.37%), and the adequate precision (12.57 and 170.96). The results of simulated 3D plots and predicted model for the SnO_{2} nanocrytalline synthesis were in agreement with the experimental results of a confirmation test. This study indicates the success of an orthogonal array to simulate the optimum condition of SnO_{2} nanocrytalline synthesis using the chemical bath method.

We would like to express acknowledgement with thanks to the Physic department of Faculty Science and atomic force microscopy laboratory.

The authors declare that there is no conflict of interest.

_{2}transparent electrodes by thermal annealing dependent structural changes for photovoltaic applications

_{2}nanoparticles synthesized by seed-mediated growth: Design of highly sensitive gas sensors

_{2}nanoparticles by sol-gel method

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_{x}(x = 1 – 2) thin film using a chemical bath deposition method with improved deposition time, temperature and pH

Scatter plot of coded predicted energy band gap value

Scatter plot of coded predicted RMS roughness value

Analysis of effects of control parameters and interaction on S/N for energy band gap.

Analysis of effects of control parameters and interaction on S/N for surface roughness.

Response surface plots indicating the effect of interaction between process variables on synthesis of nanocrystalline SnO_{2} thin film (

Surface morphology of nanocrystalline tin oxide thin film at the optimum conditions.

Energy band gap of nanocrystalline tin oxide thin film at the optimum conditions.

Experimental design of SnO_{2} nanocrystalline thin film deposition

_{1} |
_{2} |
_{3} |
_{4} |
|||
---|---|---|---|---|---|---|

1 | 0 | 1 | −1 | - | ||

0 | −1 | 0 | −1 | - | ||

0 | 1 | 1 | 0 | - | ||

1 | 1 | 0 | 1 | - | ||

1 | −1 | −1 | 0 | - | ||

−1 | −1 | 1 | 1 | - | ||

0 | 0 | −1 | 1 | - | ||

−1 | 1 | −1 | −1 | - | ||

−1 | 0 | 0 | 0 | - |

BG: (energy band gap); SR: (surface roughness).

Independent variables and their levels employed in the factorial design.

| ||||
---|---|---|---|---|

_{1} |
pH | - | 4 | 6 |

_{2} |
Deposition time | Min | 30 | 90 |

_{3} |
Concentration | Mol/L | 0.05 | 0.15 |

_{4} |
Temperature | °C | 30 | 50 |

Analysis of variance for energy band gap of SnO_{2} nanocrystalline deposition parameters.

0.022268 | 7 | 0.003181 | 4112.205 | 0.0120 | |

_{1} |
0.000131 | 1 | 0.000131 | 169.2554 | 0.0488 |

_{2} |
0.002863 | 1 | 0.002863 | 3701.516 | 0.0105 |

_{3} |
0.001045 | 1 | 0.001045 | 1350.768 | 0.0173 |

_{4} |
0.000159 | 1 | 0.000159 | 205.9534 | 0.0443 |

_{1}^{2} |
0.008121 | 1 | 0.008121 | 10497.36 | 0.0062 |

_{3}^{2} |
0.005415 | 1 | 0.005415 | 6999.376 | 0.0076 |

_{1} X_{3} |
0.001567 | 1 | 0.001567 | 2026.150 | 0.0141 |

0.0000007 | 1 | 0.0000007 | - | - | |

0.022 | 8 | - | - | - | |

| |||||

0.9937 | 0.00088 | ||||

^{2} |
0.9997 | 0.18 | |||

170.96 | 14 |

Analysis of variance for surface roughness of SnO_{2} nanocrystalline deposition parameters.

0.00055 | 6 | 0.00055 | 20.27 | 0.0478 | |

0.00021 | 1 | 0.00021 | 47.17 | 0.0205 | |

_{2} |
0.00005 | 1 | 0.00005 | 10.41 | 0.0841 |

_{3} |
0.00006 | 1 | 0.00006 | 13.26 | 0.0678 |

_{4} |
0.00004 | 1 | 0.00004 | 9.53 | 0.0909 |

_{1}^{2} |
0.00022 | 1 | 0.00022 | 49.86 | 0.0195 |

_{1} X_{4} |
0.00006 | 1 | 0.00006 | 12.18 | 0.0732 |

0.000009 | 2 | 0.000006 | - | - | |

0.0006 | 8 | - | - | - | |

| |||||

0.9838 | 0.0021 | ||||

^{2} |
0.9353 | 1.34 | |||

12.57 | 35 |