Study of the Enhanced Efficiency of Crystalline Silicon Solar Cells by Optimizing Anti Reflecting Coating using PC1D Simulation

Mohnish Kumar Sahu, Naman Shukla*, Sanjay Tiwari

School of Studies in Electronics and Photonics, Pt. Ravishankar Shukla University, Raipur

Abstract:

In this paper, simulation of a mono crystalline silicon solar cell was done using PC1D software. The impact of different solar cell parameters, with their effects on power and efficiency, has been investigated. It is seen that the textured surface reduces reflection and increases the efficiency of the solar cell at least 2–3%. From the simulation, it is seen that the optimum value of p-type doping concentration 1 × 10¹⁶ cm⁻³, n-type doping concentration 5 × 10¹⁸ cm with pyramid height of 2–3 μm and equal angles of 54.74 degrees produces the best result in simulation. An anti-reflective coating with a refractive index of 1.38 and a thickness of 84 nm is considered optimal. By optimizing the effective parameters, a solar cell with an efficiency of 24.45% was achieved through simulation. For a p-type mono crystalline silicon wafer, with an area of 10 × 10 cm² and a thickness of 200 μm, initial simulation shows a 24.45% efficient solar cell.

Keywords: Anti reflection coating, c-Si Solar Cell, Doping Concentration, Efficiency, PC1D.

Introduction

Anti-reflection coatings minimize the reflection of one or many wavelengths and are typically used on the surface of lenses so that small amount of light is lost. A simple coating can be designed to minimize the reflection on an interface between two materials by providing an extra material for light to interact with absorption layer. This can reduce the total reflection coefficient of the system by having light reflect from two interfaces where each interface has a smaller difference in refraction indices than the original interface. This type of coating is an anti-reflection coating, and the optimum refractive index of the coating (n_c) to minimize the total reflection coefficient is given by the geometric mean of the two materials that made up the original interface. In the case of air and glass, the optimum antireflective coating would have a refractive index of approximately 1.23. No real material has this ideal index, but magnesium fluoride (MgF₂) is often used because of its refractive index (1.38) which is close to the ideal value.

Nowadays, not only the solar cells have an anti-reflective coating, but such a coating can also be used on the glass surface (substrate) of solar modules. Anti-reflective coatings on the glass of the solar modules improve light transmission and thus increase the overall efficiency of the PV module. Another advantage is that the glare from the glass will get reduced. This allows the panels to blend in more easily with its surrounding. Also, it clears the path for installations nears airports (a panel without anti-reflective coating might blind a pilot). PC1D is commercially available software most commonly used for solar cell modeling (PVEducation, 2009). This software is currently used by many companies and universities such as the University of New South Wales, Australia. Here the PC1D version 5.9 has been used to simulate an energy efficient mono crystalline silicon solar cell. The simulation also gives insight about the range and impact of doping concentration, diffusion length, texturing and anti-reflection coating the simulation of PSC. This software tool has executed the semiconductor equation, the continuity equation of carrier, poisson equation, carrier transport equations etc..

Theory

Efficient and accurate modeling requires all the parameters of the solar cell to be involved, but for simplicity and to understand the impact of the parameters, some of the parameters like texturing and anti-reflection coating are not considered at first. Typically, a solar cell as shown in Figure 1, thickness varies from 100 to 500 nm and normally the area is of 10×10 cm² or. So, a p-type silicon wafer, with an area of 10 × 10 cm² and thickness of 200 μm was selected for solar cell simulation. The doping concentration of a mono crystalline silicon wafer varies from 5 × 10¹² cm⁻³ to 5 × 10¹⁸ cm⁻³. High doping concentration in a p-type wafer increases V_oc (open circuit voltage) but at the cost of damaging the crystal. So, moderate doping is generally used in a p-type silicon wafer. Thus, the doping concentration of the p-type silicon wafer has been randomly adjusted to 5 × 10¹⁶ cm⁻³ at first.

By using a four-point probe instrument it is seen that normally p-type wafer sheet resistivity varies from 0.01 to 10 cm. Because of variation in doping concentration, the sheet resistivity varies. The sheet resistivity decreases with the increase of doping concentration. For doping concentration 5 × 10¹⁶ cm⁻³, the p-type wafer sheet resistivity is 0.3441.cm. So, 0.3441 .cm was considered at first for simulation. The doping level of the emitter (n type) has been randomly adjusted to 5×10¹⁸ cm⁻³ to form a p-n junction. For 5 ×10¹⁸cm⁻³ the emitter (n-type) sheet resistance is 26.11 / (ohms/square). 26.11 / was considered as the sheet resistance of the emitter. Normally the thickness of the emitter (n-type) varies from 1–2 μm.

So in this simulation, the thickness of the emitter was adjusted to 2 μm and uniform doping profile condition has been assumed. Diffusion length must be less than the thickness of the p-type material. The thickness of the p-type wafer is selected as 300 μm and, at first, diffusion length was randomly considered, 144.3 μm. To observe the impact of the anti-reflection coating (ARC), ARC was not applied at first. To emulate the sun, AM (Air Mass) −1.5 G condition was selected. Also, to see the time progression, the number of time steps was selected as 50. After running the simulation, it is seen that the efficiency of the solar cell is 12.10%. Doping Concentration [cm^-3] Low doping moderate doping heavy doping.

  Figure 1. c-Si Solar Cell with ARC Coating.

Simulation of c-Si Solar cell with arc

Figure 2. PC1D simulator Front Panel

The anti-reflection coating (ARC) shows the most significant change in efficiency in this simulation. To design the ARC layer the following equations were used to determine, the thickness and refractive index of the ARC layer.

Refractive index of ARC is

η_AR = √ η_air× η_si(λ )

And the thickness of ARC is

d = 

Using both equations, thickness and refractive index of the ARC layer are tabulated in Table 1. Varying the refractive index and thickness the simulation efficiency of the solar cell was calculated and tabulated. It is seen that if the thickness of the ARC layer is 84 nm then the maximum efficiency of 24.45% can be achieved. If the thickness of the ARC layer is higher (e.g. 100 nm) than or lower than (e.g. 68 nm) 84 nm then the efficiency decreases. That is for 84 nm thickness the solar spectrum is absorbed more effectively.

In the PC1D simulation tool, crystalline Si (c − Si) solar cell device simulations are carried out using the following numerical equations representing the quasi-one-dimensional transportation of electrons and holes of a semiconductor material (Solar cells). Equations gives us a clear-cut idea of creating a model of a silicon cell and optimizing various process parameters including the ARC coating layer properties (Hashmi, 2018)

Jn = µn · n ·EFn                                                           (1)

Jp = µp · p · EFp                                                           (2)

The current densities of the electrons and the holes are represented as J_n and J_p respectively and they are numerically formulated as indicated in Equations (1) and (2). In which, the parameters n and p are the electron    and hole density, µn and µp is the mobility of the electron and holes. The 5 EF_n and 5 EF_p are the diffusion coefficients that represents the difference in electron and hole quasi-Fermi energies EFn and EFp. (Hashmi, 2018) 

= 5 · J_nq + G_L − Un                                                (3)

= 5 · J_pq + G_L – Up                                                 (4)

∆2φ = qe_x0010_ n − p + N_−acc − N_+donar           (5)

Equations (3) and (4) are derived from the law of conservation of charge or the continuity equation. where GL and Un are generation rate and recombination rate. Equation (5) represents Poisson’s equation for solving the electrostatic field problems.

where N_−acc and N_+don are acceptor and donor doping concentrations.

                        n = NCF1/2qψ + Vn − qφ

Here N_c and N_v are the effective density of states in the conduction and valence bands. To describe the type of material used, Fermi-Dirac statistics directly related to the band edges and N_c and N_v carrier densities are expressed. The infinite element approach is used to solve the three basic equations that assist in simulating the solar cell behaviors using the PC1D modelling tool.

Figure 3.  Current density of ARC (MgF₂)

Many other process parameters are optimized using the PC1D simulation tool in the literature, but the proposed research aims to optimize the design process characteristics of the ARC layer used in the fabrication of the c − Si solar cells as shown in figure 3. Finally, the efficiency of c- Si solar cells is calculated using the following equations-

η =

where, η represents the efficiency of the solar cell which is calculated using P_max, I_in, J_mpp, V_mpp, J_SC, V_OC and FF that indicates the maximum power, incident power, current at maximum power point, voltage at maximum power point, saturation current density, Open circuit voltage and fill factor. In this present study, we have considered p-type wafer with resistivity of 1 Ω − cm (doping of 5 × 10¹⁶ cm), device area of 100 cm², front surface textured with 3 µm depth. The n+ emitter and p+ back surface field was formed with doping concentration of 5 × 10¹⁶ cm⁻³ and 5× 10¹⁸ cm⁻³ respectively. Bulk lifetime of 1000 µs and front and rear surface recombination velocity of 10,000 cm/s were considered for solar cell simulation by PC1D. Numerous simulations were performed to study the impact of different parameters on the solar cell device performance. Base resistance (0.015 Ω), internal conductance (0.3 S), light intensity (0.1 W/cm²) used in this modelling.

Table.1 Parameter of PC1D Simulation

Result and Discussion

ARC is one of the important parameters to enhance the efficiency of PV module. The increasing demand of efficient solar panel makes the researchers to explore the best ways to improve light traction. Many researchers proved experimentally the performance of material and their impact in enhancing the transmittance in wide range of wavelength spectrum. This review paper has given the investigation about ARC, which can be well suited with silicon solar cell and glass substrate in order to reduce reflection.

 Maximum efficiency of 24.45% is achieved with p-type doping concentrations of 5×10¹⁶cm⁻³ and 5×10¹⁸ cm⁻³, diffusion lengths of 200.3 μm, both sides of textured wafers (pyramid height of 2-3 m and equal angle of 54.74), anti-reflection coating thicknesses of 74 nm, and refractive indices of 1.38, as shown in the figure 4. Figure 5 shows a band diagram for the Nc and Nv energy levels. These optimum parameters are compared with published literature and it is found that the values are feasible as shown in result section.

 Figure.4- V-I plot of output of c-Si solar cell         Figure.5- band diagram of Nc and Nv         

 Conclusion

Simulation of a mono crystalline silicon solar cell has been done by PC1D software. All the optimum solar cell parameters used in the simulation are compared with published literature and it is found that the values are feasible. With the assist of experimentally obtained values, the all process has been thoroughly investigated in the PC1D simulation. The most significant accomplishment, it may be said, was the development of a solar cell with an efficiency of more than 20% through careful examination of another process, specifically through the optimization of several parameters in the PC1D simulation. It is adequate to say that by applying the Doping effect on the solar cell at least 1–2% increase in efficiency is to be expected in a real-world solar cell fabrication scenario Simulation facilitates us by making better decisions, thus it is one of the cost saving strategies for engineering. Promoting simulation of the solar cell before actual fabrication may minimize a cost and gives an in-depth reason of what to expect by changing the parameters.

Acknowledgements

I am thankful for research facilities provided by Photonics Research Laboratory, School of Studies in Electronics and Photonics, Pt. Ravishankar Shukla University, Raipur, Chhattisgarh, India.

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