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\title{Effect of Band Gap Difference and Doping Concentration on the Performance of an InxGa1-XN based Multi Quantum Well Solar Cell}
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             \author[1]{Md. Nasmus Sakib Khan  Shabbir}

             \author[2]{Nezam  Uddin}

             \affil[1]{  }

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\date{\small \em Received: 8 December 2013 Accepted: 3 January 2014 Published: 15 January 2014}

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\begin{abstract}
        


Increasing the efficiency of solar cell is the prime concern in the field of photovoltaic technology as solar cell has become the promising source of renewable energy in recent years. This paper presents InxGa1-xN based multi quantum well solar cell for higher efficiency. In this paper the performance of the solar cell i.e., open circuit voltage, short circuit current and efficiency are justified with the variation of band gap difference and donor and acceptor doping concentration. The maximum efficiency is found when the baseline cell is designed at 1.424eV and the maximum efficiency is 30.17% and 31.94% for a band gap difference of 0.3eV and donor doping concentration of 5*1018 cm-3 respectively.

\end{abstract}


\keywords{PV Technology, MQW, baseline cell, donor concentration, acceptor concentration.}

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\let\tabcellsep& 	 	 		 
\section[{I. INTRODUCTION}]{I. INTRODUCTION}\par
olar energy represents a clean, renewable energy. As solar light is at our disposal, it represents a primary source of abundant clean energy. The internal quantum efficiency close to 100\% in bulk hetero junction Solar Cells (SCs) makes SCs promising candidates among renewable energy sources \hyperref[b0]{[1]}. But the cost per KWH is high due to low efficiency of the conventional solar cell. In conventional solar cell (Si p-n solar cell) maximum 18\%-20\% energy conversion can be possible \hyperref[b1]{[2]}. To be competitive with the conventional energy source the efficiency of solar cell must be improved. There are many approaches to increase the efficiency, such as MJ solar cells, multiple spectrum solar cells; multiple absorption path solar cells, multiple energy level solar cells, multiple temperature solar cells, p-i-n and Multi quantum well solar cell. Among these approaches MJ solar cell is being studied widely all over the world during last few decades. But this approach has some limitations. Practically, there is a very little range of materials that could be used to make these cells. The primary requirements for the materials used for MJ solar cells are band gap matching with the solar spectrum, highmotilities and lifetimes of charge carriers, thermal and lattice matching etc. The currently used conventional materials for MJ solar cells are not suitable according to the requirements. Formation of series resistance is another problem when several cells are placed in tandem. The fabrication of MJ solar cell requires highly sophisticated technology which results in higher fabrication cost. But in case of p-i-n and quantum well solar cell there are no such problems. So, the fabrication cost may be lower in these approaches.\par
A multiple-energy gap structure, similar to tandem solar cells, can also be achieved using the Quantum-Well Solar Cell (QWSC) structure was proposed by Keith Barnham's group in 1991 \hyperref[b1]{[2]} \hyperref[b2]{[3]}.The Multi-Quantum Well solar cell tries to overcome the single band gap limitations by combining more than one band gap, into an intrinsic region between the p and n regions, one or normally more quantum wells are added \hyperref[b3]{[4]}. Carriers can be absorbed at energies below the band gap of most of the cell, giving more current that of a wide band gap cell alone. Well depth of the quantum well should be carefully considered to get a reasonable open circuit voltage. The AlGaAs MQW solar cell developed by Joanna Prazmowska \&, Ryszard Korburowicz was able to provide maximum efficiency of 27.4\% on air mass AM1.5 \hyperref[b1]{[2]}. Although the efficiency is greater than convention one, it can be increased more by other approaches. R. Dahal B. Pantha, worked on In x Ga 1-x N MQW solar cell's wave length dependence and found that a maximum efficiency can be obtained at 420nm wavelength \hyperref[b4]{[5]}. J. Li. K. Aryal developed a model of In x Ga 1-x N MQW solar cell for x=0.3 and discussed about the effect of the concentrator \hyperref[b5]{[6]}. Omkar Jani in his research developed p-i-n solar cell and showed that a maximum efficiency is found to be 27\% \hyperref[b6]{[7]}, which can also be increased by other approaches.\par
In this research we intend to develop a model for In x Ga 1-x N MQW solar cell where x=.4. Different parameters such as quantum well width, depth, doping concentration, intrinsic layer length, no. of well will be varied to get the optimized model, so that an efficiency S Global Journal of Researches in Engineering ( ) F Volume XIV Issue IV Version I more than the existing can be found. In this model we intend to use air mass AM 1.5 \hyperref[b7]{[8]}. In order to design the solar cell Sim windows software is to use. Collecting the data from the software MATLAB coding is to use to analysis the performance of the designed MQW solar cell and consequently determine the optimized condition.\par
II. MODELING OF IN X GA 1-X N MQW SOLAR CELL MQW's are made by inserting quantum wells, which are very thin layers of lower band gap material, within the intrinsic region of a p-i-n solar cell. In this proposed model InGaN is used as high band gap material (barrier) and GaN as low band gap material (channel).\par
The band gap energy Eg of solar cell material is the minimum for which an electron in the valance band can be excited into conduction band in order to produce electricity. Here approximate calculations were performed in order to identify the band gap energy, Eg, of In x Ga 1?x N alloys that are used for MQW solar cell.E g InGaN (x) = (1 ? x) E g GaN + x E g InN ? bx(1 ? x)\textbf{(2)}\par
Where energy gap E g GaN and E g InN are equal to 3.4eV and 0.7eV, respectively and bowing parameter b=2.5eV (In x Ga 1?x N ). The compositional dependence of the band gap energy in In x Ga 1?x N material is shown Fig. For this model some simplifying assumptions e.g. Depletion Approximation, Radiative Limit, Quasi-Equilibrium, Infinite Mobility Limit, Symmetry have been considered \hyperref[b1]{[2]}.
\begin{quote}
1\end{quote}
\par
The band gap difference (?E) at which quantum well recombination becomes important can be found by calculating the point at which r G ? = 1 for ?E , which yields:-?E = kT q ln ? 1??(1? f W ) ?f W ? B ? DOS 2 ?\textbf{(2)}\par
The J-V equations for the multy quantum well solar cells areJ MQW (V) = J 0 (1 + r R ?) ?exp ? qV kT ? ? 1? + (J 1 r NR + J s ) × ?exp ? qV 2kT ? ? 1? ? qW?\textbf{(3)} 
\section[{III. PROPOSED MODEL}]{III. PROPOSED MODEL}\par
The schematic arrangement of a InGaN/GaN MQW consists of a InGaN/GaN MQW with p-GaN and n-GaN on both side respectively \hyperref[b4]{[5]} Figure  {\ref 2}     The fig. \hyperref[fig_2]{3} (a) implies that at every baseline band gap as the ?E increases, the V oc decreases. For example, in case of baseline cell of 1.424eV band gap as the ?E increases from 0.1eV to 0.2eV the ?? oc decreases from 1.82V to 1.73V. When there is an increase of ?E, it puts an impact on the ?? ?? which is exponentially depends on the ?E and is the parameter giving rise to the reduced open circuit voltage in the quantum well cell. As the ?E increases the recombination of carriers at the well increases which results in the reduced open circuit voltage. Fig \hyperref[fig_2]{3(c)} shows the variation of efficiency at various ?E for baseline cell band gap of 1.424eV and 2eV. The maximum efficiency is found when the baseline cell is designed at 1.424eV with ?E =0.3eV and the maximum efficiency is 30.17\%.  The doping density plays an important role on efficiency. It is well known that radioactive lifetime decreases with increasing doping level. Consequently, radioactive recombination becomes dominant compared to non radioactive recombination. The variation of efficiency with donor doping concentrations is shown in Fig. 4(c   The acceptor concentration is varied keeping Nd=5*10 17 cm -3 constant. The variation of efficiency is shown in figure 5(c), where the efficiency increases with the increase of acceptor concentration .This is because, the open circuit voltage also increases shown in fig. 5 (a). 
\section[{b) Effect of doping concentration}]{b) Effect of doping concentration} 
\section[{V. CONCLUSION}]{V. CONCLUSION}\par
In the proposed model InGaN is used because, InGaN has low effective mass of electron. As a result it has greater mobility, high peak and saturation velocities, high absorption coefficients and radiation tolerance \hyperref[b10]{[11]}.\par
InGaN also has an apparent insensitivity to high dislocation densities as the polarization and piezoelectric properties \hyperref[b8]{[9]}[10] of the material introduce electric fields and surface diploes that may counter the effect of dislocations. With the incorporation of MQW structure in the i-region, the conversion efficiency exceed the efficiency limit of a conventional homojunction single-gap solar cell. The overall result is that, InGaN solar cell attains greater short circuit current density consequently the efficiency of InGaN MQW solar cell is higher than the AlGaAs MQW solar cell. 
\section[{VI.}]{VI.} 
\section[{FUTURE WORK}]{FUTURE WORK}\par
In future the optimization of the geometry and composition of all layers of the structure should be more improver in order to achieve the enhancement of the quantum well solar cell structure performance. The lattice mismatch could be minimized by selecting materials of appropriate band gap. \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Figure 3 :}\end{figure}
     \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.17155963302752295\textwidth}P{0.22224770642201833\textwidth}P{0.28073394495412846\textwidth}P{0.17545871559633028\textwidth}}
Band gap\tabcellsep Open circuit\tabcellsep Short circuit\tabcellsep Efficiency\\
difference\tabcellsep voltage V oc\tabcellsep current\tabcellsep ?(\%)\\
Î?"E(eV)\tabcellsep (V)\tabcellsep density J sc\tabcellsep \\
\tabcellsep \tabcellsep (mA/cm 2 )\tabcellsep \\
0.0\tabcellsep 1.345\tabcellsep 22.56\tabcellsep 26.76\\
0.1\tabcellsep 1.245\tabcellsep 25.79\tabcellsep 28.32\\
0.2\tabcellsep 1.145\tabcellsep 29.46\tabcellsep 29.75\\
0.3\tabcellsep 1.045\tabcellsep 32.73\tabcellsep 30.17\\
0.4\tabcellsep 0.9449\tabcellsep 35.63\tabcellsep 29.69\\
0.5\tabcellsep 0.85\tabcellsep 38.57\tabcellsep 28.74\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.1798076923076923\textwidth}P{0.20841346153846152\textwidth}P{0.29423076923076924\textwidth}P{0.1675480769230769\textwidth}}
Band gap\tabcellsep Open circuit\tabcellsep Short circuit\tabcellsep Efficiency\\
difference\tabcellsep voltage V oc\tabcellsep current density\tabcellsep ?(\%)\\
Î?"E(eV)\tabcellsep (V)\tabcellsep J sc (mA/cm 2 )\tabcellsep \\
0.0\tabcellsep 1.92\tabcellsep 12.05\tabcellsep 20.4\\
0.1\tabcellsep 1.82\tabcellsep 13.4\tabcellsep 21.5\\
0.2\tabcellsep 1.73\tabcellsep 14.94\tabcellsep 22.8\\
0.3\tabcellsep 1.62\tabcellsep 16.39\tabcellsep 23.42\\
0.4\tabcellsep 1.52\tabcellsep 18.16\tabcellsep 24.35\\
0.5\tabcellsep 1.42\tabcellsep 20.46\tabcellsep 25.6\end{longtable} \par
  {\small\itshape [Note: © 2014 Global Journals Inc. (US)]} 
\caption{\label{tab_2}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.23124999999999998\textwidth}P{0.33749999999999997\textwidth}P{0.03125\textwidth}P{0.1875\textwidth}P{0.03125\textwidth}P{0.03125\textwidth}}
\tabcellsep 32.8\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 32.7\tabcellsep \tabcellsep \tabcellsep \\
short circuit current density(mA/cm2)\tabcellsep 32 32.1 32.2 32.3 32.4 32.5 32.6\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 31.9\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 10 15 31.8\tabcellsep 10 16\tabcellsep 10 17\tabcellsep 10 18\tabcellsep 10 19\\
\tabcellsep \tabcellsep \tabcellsep donor concentration(cm-3)\tabcellsep \end{longtable} \par
 
\caption{\label{tab_3}Table 4 :}\end{figure}
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