Hybrid Lateral Multi-junction Solar Cell Using Nonpolar InxGa(1-x)N Material

The efficiency of nonpolar InxGa(1-x)N material based hybrid lateral multi-junction solar cells was simulated using finite element approach. In this work we have used p-i-n and p-n structures for designing the sub-cells of hybrid lateral multi-junction solar cells. We have optimized both the subcell structures separately at different values of indium composition (x) for maximum efficiency. We have proposed fourteen sub-cells for our hybrid lateral multi-junction solar cell device through which it absorbs solar spectrum from 0.3 to 1.7 μm wavelength range. Results of simulation are presented here, which predict 37.08% average efficiency for lateral multi-junction solar cell based on p-i-n sub-cells while 40.21% average efficiency for lateral multi-junction solar cell based on p-n sub-cells. But the proper hybrid combination of p-i-n and p-n sub-cells provided 41.5% average efficiency.


INTRODUCTION
A multi-junction solar cell facilitates us to absorb complete solar spectrum from ultra-violet to infrared region [1][2][3][4]. It contains multiple p-n junctions of different materials. These p-n junctions are called sub-cells. These sub-cells are connected in such a way, that they can absorb maximum range of solar spectrum and convert it into electrical power [5][6][7]. In VMJ solar cells, spectrum splitting is performed by the sub-cells as shown in Fig. 1.

Fig. 1. Basic arrangement of sub-cells in VMJ solar cell
In VMJ solar cells, the sub-cells are arranged vertically one on one with ascending order of their energy band gap. When solar radiations are incident on the top surface of the solar cell, every sub-cell absorbs the radiation of energy greater than energy band gap and passes the remaining radiations to the next sub-cell just below it [6,8].
In such a way, maximum radiations are absorbed by VMJ solar cell. VMJ solar cells are grown monolithically [9,10]. In general VMJ solar cells are more expensive compare to single junction solar cells due to the expensive fabrication steps involved in growing layers of materials with lattice mismatch. Moreover, strain and interface defects significantly affect the performance of VMJ solar cells [9,11]. The highest 40.7% efficiency has been achieved by using this structure [9,12].
The LMJ solar cell works as an important solution for the problems associated with VMJ solar cell. In LMJ solar cells, the optical beam splitter is used for splitting the solar spectrum into the desired bandwidth [13][14][15]. The basic arrangements of sub-cells in LMJ solar cell is shown in Fig. 2.

Fig. 2. Basic arrangements of sub-cells in LMJ solar cell
The sub-cells of LMJ solar cell are connected externally, therefore it provides greater flexibility in terms of interconnections of sub-cells and material choice issues and yield higher efficiency [16,17]. Further improvement in LMJ solar cell will be possible by utilizing the flexibility of choosing the sub-cells independently. In present work we have optimized the sub-cells of p-i-n and p-n structures. Results show that proper combination of these sub-cells offer a chance to achieve better efficient Hybrid Lateral Multi-Junction (HLMJ) solar cell.
Nonpolar In x Ga (1-x) N alloy is the most suitable material for photovoltaic applications. This alloy has direct band gap property at entire energy band gap range, which makes this material suitable for generating and absorbing light [18], [19]. In x Ga (1-x) N material can absorb solar spectrum from 0.3 to 1.7 µm wavelength by changing indium composition (x) from 0 to 1 [18], [19]. Therefore nonpolar In x Ga (1-x) N material is capable of absorbing more than 80% radiations of AM1.5D spectrum of the sun.

METHOD
The energy band gap of nonpolar In x Ga (1-x) N material has controlled by varying indium composition (x) from 0 to 1. This material can  Table 2.
We have started the simulation process with a p-In x Ga (1-x) N/n-In x Ga (1-x) N solar cell structure by using PC1D (version 5.9) simulation software.
Here we have considered that solar radiations of AM1.5D spectrum are entering from n-In x Ga (1-x) N region. We have used untextured upper surface with good quality passivation layer. We have optimized the thickness of n-In x Ga (1-x)

RESULTS AND DISCUSSION
The carrier life time is the direct indicator of material quality [23]. Study of In x Ga (1-x) N material shows that the carrier lifetime for considerable quality of the material should be 1ns. For In x Ga (1-x) N material, as we increase the value of indium composition (x), the quality of the material is degraded. This reduction in quality of In x Ga (1x) N material is due to the size difference between the indium and gallium atoms. This difference generates the lattice defects and also changes the internal polarization field. The devices fabricated by using nonpolar In x Ga (1-x) N material is free from the polarization effect, but exaggerated by the lattice defects like trapping centers and dislocation density [18,[23][24][25]. It is well known that for good quality material, the p-n structure of solar cell is more efficient than p-i-n structure solar cell [21]. In this work we have considered 1ns lifetime of carriers for the In x Ga (1x) N material. Here we have used the p-i-n hetrostructure for designing the sub-cells of LMJ solar cell. In this structure p and n regions are made by GaN material while i-layer is formed by using In x Ga (1-x) N material. We have got 100nm thick n-GaN and 400 nm thick p-GaN layer for designing the p-i-n hetrostructure sub-cells through the simulation. The thickness of n-GaN layer plays a vital role in device efficiency. Large thickness of n-GaN layer makes the device bulky and less transparent for light. But small thickness of n-GaN layer should be problematic in fabricating ohmic contacts for the device. An i-In x Ga (1-x) N layer is inserted between them and optimized the thickness of this layer for maximum efficiency. Fig. 3 shows the required thickness of i-In x Ga (1-x) N layer for maximum efficiency at different indium composition (x).

Fig. 4. Optimized p-doping in i-In x Ga (1-x) N layer
It is well known that the p-i-n hetrostructure solar cell provides better results with large energy difference between i-layer and n or p layer [23]. But the pattern of results are reversed after 45% of indium composition (x) in i-In x Ga (1-x) N layer. This change of pattern is due to the poor quality of In x Ga (1-x) N material at higher indium composition (x). The lattice mismatch generates the trapping centers at the interface of two layers. These trapping centers trap the photo carriers pass through it [23,26,27]. But the conduction band offset plays a vital role in degrading the performance of p-i-n hetrostructure sub-cells. This conduction band offset works as a barrier for those photo electrons which passes the n-GaN/i-In x Ga (1-x) N interface [26]. Finally one

Fig. 5. The external efficiency of p-i-n and p-n sub-cells at different values of indium composition (x)
got better results for p-n sub-cells for higher values of indium composition (x) in sub-cells.
Results shows that the performance of p-i-n subcells are better than p-n sub-cells up to 45% of indium composition and after that results are reversed. For designing HLMJ solar cell, it is suggested that p-i-n sub-cells can used up to 45% indium composition and remaining from p-n sub-cells for higher indium composition. The average efficiency of LMJ solar cell based on p-in sub-cells was 37.08% and 40.21% for p-n subcells while through the proposed model of HLMJ solar cell one can achieve the 41.5% average efficiency.

CONCLUSION
Results of simulation, study and proposed design of HLMJ solar cell indicates that the flexibility of choosing the sub-cells in LMJ solar cell improve the performance. The efficiency of LMJ solar cell with p-i-n sub-cells was 37.08%. This efficiency improved further by 8.44% using p-n sub-cells. But finally the use of proper combination of p-i-n and p-n sub-cells in the proposed HLMJ solar cell provided 41.5% efficiency. This efficiency is greater than 11.92% from LMJ solar cell using pi-n sub-cells and 3.2% of using p-n sub-cells.