Study of the Influence of the Diode Ideality Factor on the Si Solar Cell

Abstract: This paper studies the influence of the Diode Ideality Factor n values on the characteristics of a Si solar cell. It focuses on the influence of different n values on the output result respectively in a standard and different environments. Based on the I-V and P-V curves obtained from the simulation using MATLAB software, a mathematical model of solar cells is obtained. It is found that n value is linearly related to the maximum output power and the influence of difference n value on maximum output power is significant under the different illumination and temperature.


Introduction
The solar cell has been greatly developed as a clean and renewable energy technology in recent years.Due to the effect of temperature and light intensity on power generation, its curves of I-V and P-V both present nonlinear variations.Under the condition without considering the environment, the factors influencing the output characteristic curve also include solar cell materials, equivalent series-parallel resistance and diode ideality factor and etc.In the literature [1][2][3], all of the simulations of solar cells ignore the influence of solar cells' characteristics on the output power and just focus on the influence of external temperature and illumination on the I-V and P-V curves.In the literature [6], the photo-generated electromotive force in solar cells is mentioned to cause the forward bias for a PN junction and then generate a leakage current flowing through the diode.It also found that the size of the diode-ideality-factor n depends on the size of the leakage current.However, the value of n is often an artificially fixed value in the above literatures.Because n influences the simulation process and its different value should lead to the different simulation results.So it is necessary to study the influence of n on the output results of the simulation.
This paper investigates the influence of n on the simulation for solar cells in MATLAB/Simulink environment.Under different n values, the simulation of I-V and P-V output curves of solar cells are simulated.More details are shown in the following sections.

Classical I-V model of solar cells and ideal factor n
The I-V equation of solar cell can be given according to the equivalent circuit [3].
Where, R S means the equivalent series resistance and R P is the equivalent parallel resistance.n is the diode ideality factor and k is the Boltzmann constant.q is the charge constant.N s and T are the number of series unit and the battery temperature(°F), respectively.
From the I-V equation, it can be concluded that the values of I L , I S , R S , R P , N S must be obtained at first in order to get the I-V curve.However, those values are all sensitive to specific environment, battery temperature and illumination intensity.Generally speaking, their values under the specific circumstances can be calculated via the equations in the [1,2,7].
The simulation model built in the MATLAB/SIMULINK can be obtained under the condition of corresponding solar cells I-V, P-V curves.
It can be concluded from (1) that the diode ideality factor n is another reference which can influence the I-V characteristic.However, in most cases the value of n given in the simulation does not regard to its influence on the simulation result.And this thesis will give analysis to the different values of diode ideality factor.
There is a leak current in the real solar cell due to the forward bias of PN junction caused by photo-induced voltage, which flows in the opposite direction of the lightgenerated current, offsetting part of light-generated current.At the time of I-V curve fitting, superposition is conducted to two diodes to simulate the dark features of solar cell.I S1 is used to denote the recombination saturation current flowing through the body area or the surface trap level, and the corresponding n=1; I S2 is made to denote recombination saturation current flowing through PN junction or crystal boundary depletion region, and the corresponding n=2.Thus the I-V curve can be interpreted as [6]: It can be seen from ( 2) that different n values lead to different maximum power output.Thus it is important to choose a reasonable value of n for carrying out simulation to solar cell.

Simulation and analysis of ideality factor n
According to the aforementioned mathematical modeling, the simulation modeling on solar cell can be carried out in the MATLAB/Simulink environment.This thesis hereby simulates the solar panel.Detailed references of the panel are available in table (1) below: Through the simulation, the I-V and P-V output characteristic curves under the different n values are all in standard environment (T = 25°C, illumination intensity S = 1000W/m 2 ).The results are shown in the Figure 1 and Figure 2.
From the Figure 1 and Figure 2, it can be seen that in a standard environment, the curvature degree of I-V curve decreases with the increase of n value.The smaller the n value is, the more similar the curve is to a rectangle.And the greater the n value is, the more similar the curve is to a triangle.It can see from Figure 1, the P-V curve approaches its maximum power point when n=1, and the maximum output power decreases linearly with increasing n. Figure 3 abstracts the total maximum powers under the different n from Figure 1 through integration, as shown in Figure 3.Under the standard environment, the n value should influence the I-V and P-V curves of solar cells.But the temperature and illumination intensity are changing all the time in an actual environment.So the maximum output power of different n value at 25°C under the different illumination intensity is as shown in Figure 4.It can be seen from Figure 4 that the illumination intensity influences the output power much more than n.But to maximize the conversion efficiency of solar cells, the selection of n value is very important.From Figure 4, it can be also seen that the growth rate of maximum output power corresponding to the illumination intensity in the case of n between 1 and 1.3 is maximum.5, it can be seen that when the temperature and n value influence the maximum output power under certain illumination intensity, the temperature plays the leading role.The lower the temperature is, the larger the maximum output power will be.However, it can also be seen that the growth rate of maximum output power corresponding to the temperature under the n between 1 and 1.3 should be the maximum.
Combined with the results of Figure 4 and Figure 5, an important conclusion about the influence on the output characteristics of solar cells is given as following: Illumination-intensity > temperature > n On the basis of the analysis of actual situation and simulation results, it can be seen that the diode ideality factor n cannot be 1 when the recombination saturation current flowing through the body area or the surface trap level and recombination saturation current flowing through PN junction or crystal boundary depletion region exist together.Therefore, in the actual situation, it is necessary to improve the illumination intensity and make the n value between 1.1 and 1.3 in order to achieve the maximum conversion efficiency of PV cells.

Conclusion
This paper discusses the influence of different n on the output characteristics.It set up a model and do the simulation under the MATLAB/SIMULINK environment.The simulation results shows that n values influence the I-V and P-V output characteristics of solar cells.Further, it is found that n value is linearly related to the maximum output power and the slope is -1.77, and the influence of difference n value on maximum output power is significant under different illumination and temperature.
The results of this paper should be helpful for the studies of characteristics of a Si solar cell.

Figure 4 .
Figure 4. Maximum power of different n value at 25 °C under the different illumination intensity

Figure 5 .
Figure 5.The maximum output power of different n value under the illumination intensity of S=1000W/m 2 at different temperature

Table 1 .
Detailed references of solarex msx60 solar panel