Mathematical Modeling of Photovoltaic Properties of Nipc/P-Si (Organic/Inorganic) Heterojunction by Using Artificial Neural Networks Model

In this research, the artificial neural network (ANN) and resilient back propagation (R-prop) training algorithm are utilized to model the photovoltaic properties of Nickel – phthalocyanine (NiPc/p-Si) heterojunction. The experimental data are extracted from experimental studies. Experimental data are utilized as inputs in the ANN Eight the minimum value of error. approach ANN is processed to the model. Training of different structures of artificial neural networks are trained to get a better mean square error (MSE) and best execution for the The ). 3- investigated and their values are very small (MSE < 10 also are The ANN performances networks. excellent d voltage characteristics of NiPc films are produced and provide - mulation results of the current si also processed is ictions matching with the corresponding experimental data. Utilization of ANN model for pred is between the inputs and outputs the relation s which describe uation The eq accurate results. s and give appeared in the major guessing power and the ability has obtained. The high accuracy of the ANN model ding on the obtained equations. eneralization depen

investigated and their values are very small (MSE < 10 also are The ANN performances networks. excellent d voltage characteristics of NiPc films are produced and provide -mulation results of the current si also processed is ictions matching with the corresponding experimental data. Utilization of ANN model for pred is between the inputs and outputs the relation s which describe uation The eq accurate results. s and give appeared in the major guessing power and the ability has obtained. The high accuracy of the ANN model ding on the obtained equations. eneralization depen g of (Organic/Inorganic) -Properties Photovoltaic -) Model

Introduction
Organic semiconductors are hopeful candidates due to their role and diversity. Phthalocyannines are prototype organic semiconductors and are recognized by their high thermal and chemical stability. They form large groups of organic compounds which have been essential for the search because of their active properties for more than 40 years Linstead (1934). Organic semiconductors have many potential applications so that the researches on this field have been enlarged rapidly. Examples of these applications are the use of organic semiconductors in photovoltaic cells Wohrle and Meissner (1991), laser printers Gregory (1991), dyes, pigments, photocopying agents Haisch et. al. (1997), gas sensors Gardner et. al. (1992) and Mrwa et. al. (1995), optical data storage systems Ao et. al. (1995), solar cells Kerp and Faasen (2000), light emitting diodes Lee et. al. (1999), and also in nuclear reactor systems. In recent years an important jump of organic photovoltaic (PV) solar cells are achieved Reycroft and Ullai (1980), Ghosh et. al. (2001), Khelifi et. al. (1985), Mahapatro and Ghosh (2001), Tang (1986) and El-Nahass et. al. (2005).
Numerous studies have demonstrated the bio-inspired computing techniques such as artificial neural networks (ANNs) and evolutionary computing techniques can be alternative methods have long applied. ANNs are biologically inspired computer programs designed to simulate the way in which the human brain processes  Mohamed and Habashy (2018). Artificial neural network (ANN) model is proceeding quickly, and it is applied in different fields. It is an approach which imitates the human mental processes, where it holds computationa l power, ability of learning, generalization and prediction of acceptable outputs for the inputs that have not exist during a training step Nada et. al. (2013). Developments in ANNs and their applications to physics have made it feasible to model enormous characteristics in different areas in physics. Many investigations have been presented on utilizing ANN in modeling different properties of semiconductors. Darwish. et. al (2015) studied Optoelectronic performance and artificial neural networks (ANNs) modeling of n-InSe/p-Si solar cell. They found that the uses of an artificial neural network and R-prop training algorithm succeeded in predicting the optical constants of 30 70 − (0≤x≤3). Ali and Mohamed (2018) utilized the artificial neural network in modeling the electrical impedance spectroscopy of (4E)-2-amino-3cyanobenzo[b]oxocin-6-one. They found that ANN simulated the experimental data with a very high accuracy and predicted new values that were unmeasured experimentally. Also, they showed that artificial neural network model is a very e ffective tool in modeling and able to follow the patterns of the experimental data with a high precision. El-Barry and Habashy (2019) studied the Optical characterization of casting (Adamantan Fulgide) thin films using (CTANNs) approach. They found that modeling of optical characterizations of casting (Admantan-Fulgide) thin films with different concentrations by using ANN provided accurate results and low error rates. El-Barry and Mohamed (2019) studied of photovoltaic characteristics of pyronine thin film/p-Si single crystal experimentally and theoretically by using ANN model. They found that the ANN trained results are in excellent matching with the experimental data and the generalization process provided accurate predicted results . Mohamed (2019) utilities ANN model to predict of alternating current (AC) conductivity for different samples of organic semiconductors. He found that using of ANN model is considered a very successful tool to predict the AC conductivity for organic semiconductors. Also he concluded a generalized equation to predict AC conductivity for a ny other organic semiconductor.
In this paper, ANN is used to model the photovoltaic properties of NiPc/p-Si (organic/inorganic) heterojunction. We will try to use ANN model to simulate the experimental data, predict values are in the experimental data range as a testing step, make predictions for values are not exist in the experimental data range as an application for the generalization process and finally we will introduce the equation which describes the physical behavior under study. In this respect, the paper organized in five sections, the first section gives a brief introduction and showed some important researches from literatures, the second displays the experimental procedures, the third introduces brief notes on ANN model, the fourth discusses the results, the last section displays our conclusi ons.

Experimental data
The NiPc powder utilized in this study is acquired from Kodak, UK. pieces of p-silicon of 1 cm² each and 450 µm thick were scrubbed and treated with etching solution of CP4 (HF: HNO₃:CH3COOH in ratio 1:6:1). After etching , the Si wafers were solved in distilled water and then with ethyl alcohol. After the Si-substrate cleaning and etching, Nipc thin film with different thicknesses were deposited on the front side of the substrate by conventional thermal evaporation technique, and then the NiPc layer was covered by an Au mesh to be applied as an ohmic electrode. The back side of Si was coated by a thick layer of aluminum electrode. The fabricated NiPC/P-Si heterojunction was annealed at 373 for 2 hours to enhancement the performance of heterojunctio n under investigation. Measurements of dark current-voltage characteristics within the temperature range 298-373 K were produced in air. A stabilized power supply and a Keithley were used to determine the current abundance through the cell by 617 an electrometer. Mean of Pt-PtRh thermocouple with monitor (philips thermostat PT 2282 A) was utilized to determine the temperature directly. A proportional temperature controller (Euro-therm. model no. 390-200) was hired to shun the sudden drop in the heater temperature. the cells illuminated by light coming from a light source (white light) with an intensity for incident power of 6 mW/cm². The dark C-V characteristics were determined at 1 MHz using Model 410 CV Meter El-Nahass et. al. (2005).

Artificial neural network model
Artificial neural network contains of simple processing units which operate by transmitting signals to each other over a huge number of weighted connections. Neurons are the "building blocks" of neural networks as units or nodes. Basically, inputs are received from many other neurons counting on the processing function of the neuron, the current input is used to change its internal state (activation), sends one output signal to many other neurons. Forward networks supply the most popular neural network. During the training process, the networ k detects its weights and bias to reach to the least error and the best performance of networks. In this research, resilient back-propagation algorithm (R-prop.) is the training algorithm used in artificial neural networks model. R-prop is utilized to eliminate the failed effects during training. These effects caused by the values of partial derivatives that yield from applying the transfer functions (the sigmoid functions) to the outputs. Fig 1 introduces a Simple neuron model. It consists of inputs, the activation function and output. Each input is weighted by a factor . The sum of all inputs is calculated. Then an activation function ƒ is applied to the resultant to produce the neural output ƒ( ). As shown in the following equations: The sum of weighted inputs = ( ∑ ) Where n is the number of inputs. Mohamed (2019).

Figure 1a Simple neuron model
In this research, the artificial multilayer neural network is utilized for modelling the experimental data. It consists of three types of layers. The first type of layers; the input layer contains the inputs. While the second type of layers is the hidden layers where the neurons organized. The last type of layers includes the neuron output called output layer. Figure1b demonstrates a schematic presentation of an artificial multilayer neural network structure. The network follows the supervised learning rule. During the training process, the network iteratively adjusts connection weights and biases until the network results simulate the targets with high precision. In this approach, backpropagation error adjustment (BPE) is the utilized modification technique.

Figure 1b. Schematic diagram for the artificial multilayer neural network
The ANN performances calculated using the mean squared error (MSE) for the training dataset. It can be calculated using the following equation.
Where . is the experimental data, . is the ANN predicted results, is the average and n is number of inputs.

a-Dark current -voltage characteristics
Eight individual neural networks are trained separately to model the experimental data. Table 1. Summarizes the main features of the eight networks. It includes the number of hidden layers (HLS), the number of nodes (ANs), inputs, the number of epochs, the best (MSE) performance and outputs for modelling of the photovoltaic characteristic of NiPc/p-Si heterojunction.  Figure   Figure 3a. shows the training procedure which reveals that the mean squared error of the network starting at a large value and diminishing to reach the best (MSE) performance value at 0.0034345 after 500 epochs. The number of epochs represent the number of neural network iterations. It is clear from the performance curve that it Starts with a large value of (MSE) then by iterations the (MSE) reaches to a very small value that confirms a successful ANN learning process. Figure 3 b. shows the current-voltage characteristics simulation results of NiPc films together with the corresponding experimental data for temperature range 298-373 K and the predicted results for 273, 298 and 340 K. It is clearly observed that ANN gives high precision results. The Second artificial neural network contains one input (the junction resistance) and one output (the voltage) as shown in Table 1. figure 4. shows schematic diagram for the construction of the second artificial neural network. Figure 5a. shows the training procedure which reveals that the best mean squared error value 2.4781 × 10 −21 at 988 epochs. Figure 5b. shows the ANN simulation results for junction resistance ,versus V for NiPc /p-Si together with the corresponding experimental data. It is clearly observed that The ANN results and the experimental data are in good agreement. The third artificial neural network contains two inputs (the voltage and the temperature) and one output (the current) as shown in Table 1. figure 6. demonstrates the construction of the third artificial neural network.   The fourth artificial neural network contains two inputs (log v and temperature) and one output (log I) as shown in Table 1 and Fig. 8.  Figure 9a shows the training performance and the mean squared error for the forth network starting at a large value and diminishing to reach a best value of 6.0149 x 10 -9 after 500 epochs. Figure.9b shows the ANN simulation results of the current-voltage characteristics of NiPc films together with the corresponding experimental data for temperature range 298-373 K and the predicted current at 273, 373, 360 and 380 K. It is clearly observed that ANN trained results is very precise. The fifth artificial neural network contains two inputs (voltage and temperature) and one output reverse current) as shown in Table and  at 1219 × 10 −15 equal to 9.7026 is MSE he best ifth neural network. T the MSE for the f Figure 11a. shows V -I logarithmic plots of the reverse bias of -epochs. Figure 11b. shows the simulation results of semi temperature range 298 for characteristics of NiPc films together with the corresponding experimental data 373 K. It is clearly observed that the trained ANN results and the experimental data are in good agreement. . heterojunction Figure.13a. shows the ANN performance and the best mean squared error for the sixth network that equal to 2.2087 × 10 −8 at 307 epochs. Figure 13 b. shows the ANN simulation results for −2 -V characteristics of NiPc films together with the corresponding experimental. It is clearly observed that ANN simulated curve completely coincides with the experimental data points and that introduces excellent performance for the ANN model. The seventh artificial neural network contains one input (voltage) and one output (width of the depletion region) as shown in Table 1.  Figure15a shows the ANN performance for the seventh network and the mean squared error starting at a large value and diminishing to reach a best value at 1.0784 × 10 −11 after 90 epochs. The best MSE confirms that the learning process is carried out successfully. Figure 15b shows the ANN simulation results for the 2 -V characteristics of of NiPc films together with the corresponding experimental. The eighth artificial neural networ k contains one input (voltage) and one output (current for illumination and dark) as shown in Table 1. Figure 16 shows the construction for the eighth network. Si heterojunction. -under illumination and dark for NiPc/p Figure 17a introduces the performance containing the learning curve and the best value using the mean squared error function. The best MSE is 6.2653 × 10 −13 at 308 epochs. Figure17b represents the ANN simulation results for − characteristics under illumination and dark for NiPc films together with the experimental data. It is clearly observed that the trained ANN results and the measured curves (experimental data) are in good agreement. The equation which describes the physical behavior of the photovoltaic properties of NiPc/p-Si heterojunction is given in Appendix A.

Conclusion
In this research, ANN model used to model the photovoltaic properties of NiPc/p-Si (organic/inorganic) heterojunction. The experimental data extracted from previous practical studies. These data used as inputs in the ANN model. The model has been trained in different topologies in order to obtain the best neural networ k structure providing the least error. Eight neural networks were trained to model the experimental d ata their constructions introduced in the discussion. They consist of three hidden layers containing different numbers of neurons in each layer. The R-Prop train function (trainrp) and log-sigmoid (logsig) utilized as the training algorithm and transfer function, respectively. The best performance achieved for all networks did not exceed 10 3 by using the mean squared error MSE function. The ANN predicted results at values of 298 K for dark currentvoltage characteristics and 373 K for variation of log I with log V of NiPc/p-Si heterojunction which measured experimentally introduce an excellent accordance with the experimental data . Also, the predicted ANN results at 273 and 340 K for dark current-voltage characteristics and at 273 ,360 and 380 K for variation of log I with log V of NiPc/p-Si heterojunction which are not measured. The most important result presented in the research is the mathematical relation which describes the behavior of the photovoltaic properties of NiPc/p-Si (organic/inorganic) heterojunction. It is clear from the trained results that the ANN model was able to follow the target patterns very efficiently and was even able to predict values which had not been measured in practice. Therefore, ANN can be considered a powerful tool for estimating photovoltaic properties of NiPc/p-Si (organic/inorganic) heterojunction.