# Simulation of  Nonpolar  p-GaN/i-InxGa1−xN/n-GaN Solar Cells

Authors: Ming-Jer Jeng
Journal: International Journal of Photoenergy
 (2012)

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## Abstract

It is well known that nitride-based devices suffer the polarization effects. A promising way to overcome the polarization effects is growth in a direction perpendicular to thec-axis (nonpolar direction). Nonpolar devices do not suffer polarization charge, and then they have a chance to achieve the high solar efficiency. The understanding of the solar performance of non-polar InGaN-based solar cells will be interesting. For a pin non-polar solar cell with GaN p- and n-cladding layers, the conduction band offset (or barrier height, ΔE) between an intrinsic layer and n-GaN layer is an important issue correlating to the efficiency and fill factor. The efficiency and fill factor will be seriously degraded due to sufficiently high barrier height. To reduce a high barrier height, some graded layers with an energy bandgap between the energy bandgap of n-GaN and InxGa1−xN intrinsic layer can be inserted to the interface of n-GaN and InxGa1-xN layers. From simulation, it indicates that the insertion of graded layer is an effective method to lower energy barrier when there exists a high energy band offset in non-polar nitride devices.


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## Body

## 1. Introduction

Nitride-based materials such as InxGa1−xN have become important in fabricating photovoltaic devices due to their energy band gaps lying between 0.7 and 3.4 eV [1–5]. It can absorb the full solar spectrum by a single material of InxGa1−xN with different indium contents. Many theoretical calculations on the performance evaluation of InGaN-based solar cells have been performed [1, 4, 5]. They demonstrated that a very high solar efficiency could be achieved. The direct bandgap properties and high absorption coefficients make it have great potential in photovoltaic application. Further, the GaN-based materials have a high resistant to high energy irradiation and temperature variations [6, 7]. Thus, it is suitable for space applications or high concentrator solar cell systems. However, a good-quality InGaN film with high indium composition cannot be obtained due to the low miscibility of InN in GaN. It also suffers polarization effects that degrade the device performance seriously [8–11]. Although the current nitride devices suffer the polarization effects, a promising way to overcome the polarization effects is growth in a direction perpendicular to the c-axis (nonpolar direction) [12–14]. In the heterojunction of p-GaN/i-InxGa1−xN/n-GaN structure on r-plane sapphire (nonpolar a-plane GaN), the nitride devices do not suffer polarization charge, and then they have a chance to achieve a high solar efficiency. The understanding of solar performance on non-polar InGaN-based solar cells will be interesting. In this work, the solar performance of non-polar p-GaN/i-InxGa1−xN/n-GaN solar cells with different InxGa1−xN energy bandgaps from 1.1 to 3.2 eV has been simulated. It is observed that the conduction band offset between InxGa1−xN and n-GaN layer will be an important issue for the efficiency of pin solar cells. Although a pn junction device is the most common structure in solar cells, a pin structure will be the best choice for high-defect materials due to drift field assistant properties. It is known that an intrinsic layer with low energy bandgap in pin solar cells has higher solar efficiency than that with high energy bandgap. But, one has to pay attention to the effects of the conduction band offset on the efficiency of solar cells. The photogenerated carriers cannot tunnel through the energy barrier if the ΔE is too high. To reduce the barrier height, some graded layers with an energy bandgap between the energy bandgap of n-GaN and InxGa1−xN intrinsic layer can be inserted to the interface of n-GaN and InxGa1−xN layers. It can assist the photogenerated carriers to tunnel through the energy barrier and result in a higher solar efficiency. Thus, a graded GaN/InxGa1−xN/GaN solar cell grown on a nonpolar epilayer is simulated.


## 2. Simulation Parameters

The simulation parameters for InxGa1−xN materials at 300 K are listed in Table 1 [1, 15–23]. The In composition dependence of InxGa1−xN energy bandgap at 300 K is calculated by Wu’s fitting equation [15]. The doping level dependence of the carrier mobility in InxGa1−xN materials at 300 K is based on the fitting data [16–18], and the other related calculation parameters are assumed to be the same as GaN [22]. The simulation software of AMPS-1D is used to simulate the characteristics of InxGa1−xN pin solar cells. The parameter of the front contact reflectivity is set to 0.1 in order to reflect general condition, and the back contact reflectivity is set to zero. It is noted that the series and shunt resistance of solar cells will degrade the solar performance. The series resistance mainly consists of contact and film resistance, and the shunt resistance results from the bulk and surface leakage current. It is known that the film quality of the p-type GaN is not good for a very high concentration. In addition, it is difficult to form a good ohmic contact when the concentration of the p-type GaN is lower than 1 × 1017 cm−3. So, a concentration of 5 × 1017 cm−3 is used as the doping concentration of p-type GaN region and a concentration of 1 × 1018 cm−3 is assumed in the n-type GaN region. The concentration of the intrinsic layer is assumed as 5 × 1016 cm−3 due to un-intentionally high background concentration of donors. A quite good ohmic contact to p-GaN with a concentration of 5 × 1017 cm−3 was obtained by semitransparent ohmic contact formation and metal grid deposition [3]. Thus, an ideal contact is assumed in this simulation. No attempt is made to find the optimum condition for the layer thickness and doping concentration. It just wants to demonstrate the needed layer structure of pin solar cells for a small energy bandgap of the intrinsic layer due to a high conduction band energy barrier at the interface of InxGa1−xN and n-GaN layers.Table 1
The simulation parameters for InxGa1−xN materials at 300 K [1].
ParametersExpressionReferencesEnergy bandgap (eV)Eg(InxGa1-xN)=0.7x+3.4(1-x)-1.43x(1-x)[15]Electron mobility (cm2 eV−1 s−1)Linear fitting: 170 atP=4×1018 cm−3 and 100 at P=1×1019 cm−3[16, 17]Hole mobility (cm2 eV−1 s−1)Linear fitting: 22 atn=3×1017 cm−3 and 13 at  n=1×1018 cm−3[16, 18]Relative permittivityεε(InxGa1-xN)=x·εInN+(1-x)·εGaN[19, 20]Electron affinityχ (eV)χGaN+0.7·(3.4-Eg)[19, 21]Effective density of states in the conduction band Nc (cm−3)Nc(InxGa1−xN) = xNcInN+ (1 − x)NcGaN[19]Effective density of states in the valence band Nv (cm−3)Nv(InxGa1−xN) = xNvInN+ (1 − x)NvGaN[19]Absorption coefficientα (cm−1)α(λ)=2.2×105(1.24/λ)-Eg[19]Carrier lifetimeτ (ns)1 ns[22]Surface recombination velocities Sp0, SpL, Sn0, SnL (cms−1)1000[23]


## 3. Results and Discussions

Figures1(a) and 1(b) show the efficiency and short circuit current (Jsc) as well as open circuit voltage (Voc) and fill factor of InxGa1−xN pn junction solar cells, respectively, with an In composition from x=0 (Eg=3.4 eV) to x=0.75 (Eg=1.11 eV) under AM1.5G illumination. The inset of Figures 1(a) and 1(b) shows the structure of InxGa1−xN pn junction solar cells. By doing the simulation, the thickness of n-type region doped with 1 × 1018 cm−3 is fixed at 250 nm and the thickness of p-type region doped with 5 × 1017 cm−3 is optimized to obtain the highest efficiency at each In composition. A small optimum thickness range of 180 to 310 nm in p-type region is observed. It is noted that the efficiency reaches the maximum of 18.4% (Voc=0.9 V, Jsc=26.1 mA/cm2) at an In composition of x=0.6 (Eg=1.44 eV) and then decreases with further increase in In composition. The higher the In composition of InxGa1−xN is, the higher the Jsc, the lower the FF, and the lower the Voc are. With the increase of In composition from x=0 to 0.75, the Voc linearly decreases from 2.64 to 0.59 V, the Jsc monotonously increases from 0.38 to 37.2 mA/cm2, and the fill factor decreases from 0.89 to 0.72.(a) The efficiency and short circuit current (Jsc) as well as (b) open circuit voltage (Voc) and fill factor of InxGa1−xN pn junction solar cells, respectively, with an In composition from x=0 (Eg=3.4 eV) to x=0.75 (Eg=1.11 eV) under AM1.5 illumination. The inset shows the structure of InxGa1−xN pn junction solar cells.
(a)(b)It is noted that a pn junction device has the best performance in solar cells for good-quality material. However, a pin structure will be the best choice for high-defect materials. In this paper, it is assumed that the carrier lifetime is 1 ns that is obtained from a more real quality GaN film [22]. So, the efficiency of the pn junction solar cells is better than that of the pin solar cells. One can demonstrate the clear advantages of the pin solar cells over pn junction if the carrier lifetime is shorter than 0.3 ns. (i.e., high-defect In0.6Ga0.4N film) The carrier lifetime is strongly correlated to the film quality. The longer the carrier lifetime is, the better the film quality is. Figure 2 presents the comparison of the efficiency in In0.6Ga0.4N pn and pin solar cells versus the carrier lifetime. Clearly, the pin solar cells exhibit better efficiency than the pn solar cells when the carrier lifetime is shorter than 0.3 ns.Figure 2
The efficiency of In0.6Ga0.4N solar cells with a pn junction and a pin structure as a function of carrier lifetime.It is difficult to grow good-quality film especially in a thick InxGa1−xN film with high In composition due to InN segregation problems. Presently, the film quality for a thin InxGa1−xN film (several tenth nanometers) is good, but it is not good for a thick InxGa1−xN film (several hundred nanometers). Generally, the acceptable film quality of InxGa1−xN film is less than 100 nm for higher In composition (x>0.3). However, the thickness of an InxGa1−xN solar cell with enough light absorption is larger than 400 nm, which is mainly determined by the carrier lifetime and the material light absorption coefficients. The good solar cell performance of InxGa1−xN(p)/InxGa1−xN(n) or InxGa1−xN(p)/InxGa1−xN(i)/InxGa1−xN(n) structures with high In composition cannot be achieved due to poor InxGa1−xN quality film with high In composition. An alternate structure of GaN(p)/InxGa1−xN(i)/GaN(n) is more easy to be achieved, like the recent published papers with relative high quantum efficiency [2, 3]. Thus, for more practical realization consideration, both of p-GaN and n-cladding layers are used in this simulation although the 17.3% efficiency of the In0.6Ga0.4N(p)/In0.6Ga0.4N(i)/In0.6Ga0.4N(n) solar cells is slightly better than the 16.8% efficiency of the GaN(p)/In0.6Ga0.4N(i)/GaN(n) with three graded-layer insertions at the carrier lifetime of 1 ns. The efficiency of p-GaN (100 nm)/i-InxGa1−xN (200~500 nm)/n-GaN (100 nm) solar cells with an In composition of x=0.05–0.3 is shown in Figure 3(a). Clearly, the higher the thickness of intrinsic layer, the higher the efficiency of the solar cell, but the increment is small due to high absorption in InxGa1−xN layer. It is noted that the efficiency reaches the maximum of 9.2% at an In composition of x=0.26 and then drops dramatically with the further increase of In composition. However, it is well known that an intrinsic layer with low energy bandgap in pin solar cells has higher solar efficiency than that with high energy bandgap under the same illumination. What reason causes the efficiency drop after the increase of In composition to higher than 0.26? It is possibly due to that a large conduction band energy barrier, ΔE, exists between InxGa1−xN intrinsic layer and n-type GaN region. It is noted that high energy barrier in pin solar cells will seriously degrade the solar efficiency and the fill factor.The efficiency (a) and  the fill factor (b) of a p-GaN (100 nm)/i-InxGa1−xN (200~500 nm)/n-GaN (100 nm) solar cells with an In composition of x=0.05–0.3.
(a)(b)Figure3(b) shows the fill factor of pin solar cells with various intrinsic layer thicknesses and In compositions. The fill factor begins to reduce dramatically when the In composition of InxGa1−xN intrinsic layer is higher than 0.26, which is corresponding to an energy barrier of 0.68 eV. The photogenerated carriers cannot tunnel through the energy barrier if the  ΔE  is higher than 0.68 eV or if an existing electric field is small. It will seriously reduce the electric current and then result in a very low fill factor. It is noted that the diffusion current is dominated in the pn junction solar cells. However, the drift current is dominated in pin solar cells especially for high-defect materials. In the InxGa1−xN pn junction structures, the diffusion current is dominated.  In the InxGa1−xN(p)/InxGa1−xN(i)/InxGa1−xN(n) structures, the diffusion current is still dominated when the carrier lifetime is longer than 0.3 ns and the drift current will be dominated when the carrier lifetime is shorter than 0.3 ns (a lot of diffusion currents will be recombined by defects and cannot be effectively collected by the contact). In the GaN(p)/InxGa1−xN/GaN(n) structures, the drift current is dominated due to less current contribution in GaN, which generates less photocurrent by its high bandgap. More photogenerated currents will be contributed in GaN by the InxGa1−xN intrinsic layer.The current-voltage (I-V) curve of pin solar cells with various InxGa1−xN energy bandgaps (corresponding to an In composition of 0.25–0.3 in Figure 3) is shown in Figure 4. Clearly, the I-V curve begins to deform with increase of voltage bias when the InxGa1−xN energy bandgap is lower than 2.42 eV (x=0.26). The deformation of I-V curve will gradually worsen with the decrease of InxGa1−xN energy bandgap (increasing In composition). It means that the fill factor will become smaller. A completely deformed curve is observed in the InxGa1−xN energy bandgap of 2.29 eV (x=0.3), which has a very low fill factor of 0.13. The inset of Figure 4 shows the conduction band energy barrier in pin solar cells with an In composition of 0.25–0.3. The InxGa1−xN intrinsic layer with an In composition of 0.3 exhibits the highest energy barrier at the interface. Therefore, it has the lowest fill factor. Figure 5 shows the conduction band energy diagram of In0.3Ga0.7N pin solar cells at the voltage bias of 0, 0.54 and 1.67 V, respectively. It can clearly explain why a large reduction of fill factor is in a high energy barrier of pin solar cells. At lower voltage bias (around 0V), there exists a high electric field in intrinsic layer. Most of the photogenerated carriers can tunnel through the energy barrier due to high field-assisted tunneling and then be collected by electrode contact; hence, a high Jsc is observed. However, the electric field will gradually reduce with the increase of voltage bias. At a higher voltage bias, most of the photogenerated carriers cannot tunnel through the energy barrier due to low field-assisted tunneling or high energy barriers, existing at the interface between InxGa1−xN intrinsic layer and n-GaN region. Few photogenerated carriers are collected in the electrode contact and result in a small electric current. It is noted that a reduction of the electric current will begin to occur at moderate voltage bias if the energy barrier at the interface is too high, for example, in the case of In composition with 0.27–0.3 it will seriously degrade the fill factor of solar cells due to poor current shape gradually changing from a seemingly rectangular shape to a triangular shape with an increasing energy barrier, which is consistent with the I-V observations in Figure 4. Recently, both In0.2Ga0.8N/GaN and In0.28Ga0.72N/GaN multiple quantum well solar cells (MQWSCs) are experimentally fabricated and compared. The I-V curve behavior of In0.2Ga0.8N/GaN and In0.28Ga0.72N/GaN MQWSCs is similar to the simulation observation in Figure 4 [24]. The higher the energy barrier height is, the lower the fill factor is. The In0.28Ga0.72N/GaN MQWSCs with the higher energy barrier between well and barrier materials exhibit more deformed I-V curve and lower fill factor than the In0.2Ga0.8N/GaN MQWSCs. It is believed that this behavior is possibly related to the energy barrier height (or conduction band offset).Figure 4
The current-voltage (I-V) curve of pin solar cells with various InxGa1−xN energy bandgaps (corresponding to an In composition of 0.25–0.3 in Figure 2).Figure 5
The conduction band energy diagram of In0.3Ga0.7N pin solar cells at the voltage bias of 0, 0.54 and 1.67 V.To reduce the high energy barrier height, one can insert a graded layer of 10 nm with an energy bandgap between the energy bandgap of GaN and InxGa1−xN intrinsic layer to the interface of GaN and InxGa1−xN. Figure 6(a) presents the efficiency of one graded-layer In0.3Ga0.7N pin solar cells with four different graded energy bandgaps of 3.01, 2.81, 2.63, and 2.46 eV as a function of the graded layer thickness. The pin solar cells with a graded layer having an energy bandgap of 2.81 eV exhibit the highest efficiency, when the energy barrier is closely to a half of bandgap difference between GaN (3.4 eV) and In0.3Ga0.7N (2.29 eV). A graded layer with an energy bandgap of 2.46 eV has the worst efficiency due to poor fill factor (large energy barrier). To achieve high efficiency, the optimized thickness of the graded layer is observed at 6 nm and the efficiency drops dramatically at 2 nm. The energy band diagram of one graded-layer In0.3Ga0.7N pin solar cells with four different graded energy bandgap of 3.01, 2.81, 2.63, and 2.46 eV is shown in Figure 6(b). Clearly, an In0.3Ga0.7N pin solar cell with a graded-layer insertion exhibits an energy barrier lower than that without a graded layer insertion. Especially for a graded layer with an energy bandgap of 2.81 eV, it has the lowest energy barrier. This indicates that the barrier height (ΔE) between an intrinsic layer and n-GaN is an important issue correlating to the efficiency and fill factor. The higher the barrier height is, the poorer the efficiency and fill factor are, as shown in Figure 4.(a) The efficiency of one graded-layer In0.3Ga0.7N pin solar cells with four different graded energy bandgap of 3.01, 2.81, 2.63, and 2.46 eV as a function of the graded layer thickness. (b) The energy band diagram of one graded-layer In0.3Ga0.7N pin solar cells with four different graded energy bandgap of 3.01, 2.81, 2.63, and 2.46 eV.
(a)(b)As mentioned above, it is known that the efficiency and fill factor will seriously degrade when an In composition of InxGa1−xN intrinsic layer is larger than 0.26. In order to improve the solar efficiency, a graded layer is needed to lower the energy barrier height. Figure 7 shows the efficiency of one graded-layer pin solar cells as a function of In composition from 0.3 to 0.5. The efficiency of In0.3Ga0.7N pin solar cells can be improved from 1.4% (as shown in Figure 3(a)) to 10.5% with a graded-layer insertion due to a great improvement of the fill factor from 0.15 to 0.87 (due to a lower barrier height  ΔE). It is interesting to note that one graded-layer insertion has an effective improvement of efficiency only in the In composition range of 0.3–0.45. The efficiency begins to drop when an In composition of InxGa1−xN intrinsic layer is larger than 0.45. The graded layer with an In composition of 0.2 has better efficiency than those with the In composition of 0.15 or 0.25 in higher In composition of InxGa1−xN intrinsic layer (x=0.4 or 0.45). One simple rule that can be used to determine the In composition of a graded layer is a half value of In composition of InxGa1−xN intrinsic layer. For example, a pin solar cell with an In composition of 0.3 in InxGa1−xN intrinsic layer optimally needs a graded layer with an In composition of 0.15, while that with an In composition of 0.4 or 0.45 needs a graded layer with an In composition of 0.2. In addition, the energy barrier height of InxGa1−xN pin solar cells with an In composition of 0.5 is still too high and results in a poor efficiency although a graded layer has been inserted. That is to say, more graded layers are needed for high In composition InxGa1−xN intrinsic layer (x>0.45).Figure 7
The efficiency of one graded-layer pin solar cells as a function of In composition from 0.3 to 0.5.The efficiency of two graded-layer pin solar cells as a function of In composition from 0.4 to 0.75 is shown in Figure8. Clearly, an In0.6Ga0.4N pin solar cell with two graded-layer insertion exhibits the highest efficiency of 15.3%. The efficiency of InxGa1−xN pin solar cells dramatically drops when an In composition of pin solar cell is at 0.75. It means that three graded-layer insertions are needed to lower the energy barrier height in such high In composition. Table 2 lists the optimum In composite combination of two graded layers for each In composition of InxGa1−xN pin solar cells. An equally spacing interval of In composition is observed to achieve high efficiency. It is reasonable due to that it can equally minimize the energy barrier height.Table 2
The optimum In-composited combination of two graded layers for each In composition of InxGa1−xN pin solar cells.
The In composition of InxGa1−xN intrinsic layer (corresponding energy bandgap eV)0.4 (1.98)0.45 (1.83)0.5 (1.69)0.55 (1.56)0.6 (1.44)0.65 (1.32)0.7 (1.21)0.75 (1.11)The In composition of the 1st graded layer0.15 (2.81)0.15 (2.81)0.15 (2.81)0.15 (2.81)0.2 (2.63)0.2 (2.63)0.2 (2.63)0.25 (2.46)The In composition of the 2nd graded layer0.3 (2.29)0.3 (2.29)0.3 (2.29)0.35 (2.13)0.4 (1.98)0.4 (1.98)0.45 (1.83)0.5 (1.69)Figure 8
The efficiency of two graded-layer pin solar cells as a function of In composition from 0.4 to 0.75.Figure9 shows the efficiency of three graded-layer pin solar cells as a function of the In composition from 0.6 to 0.75. The efficiency of two graded-layer pin solar cells is also shown for comparison. A great improvement of efficiency from 0.23% to 13.1% can be seen at an In composition of 0.75 by three graded-layer insertion. The three graded-layer pin solar cells exhibits a little increase of efficiency at an In composition lower than 0.7 in comparison with two graded-layer pin solar cells.  The In0.6Ga0.4N pin solar cells with three graded-layer insertions exhibit the highest efficiency of 16.8% (Voc=0.83 V and Jsc=26.2 mA/cm2). The optimum In composite combination of three graded layers for each In composition of InxGa1−xN pin solar cells is listed in Table 3. For the In composition range of 0.6 to 0.75, the first graded layer with an In composition of 0.15 and the second graded layer with an In composition of 0.3 or 0.35 are the best choices. The selection rule of In composition of the third graded layer is that the In composition differences are no more than 0.2 between InxGa1−xN intrinsic layer and the second graded layer.Table 3
The optimum In-composited combination of three graded layers for each In composition of InxGa1−xN pin solar cells.
The In composition of InxGa1−xN intrinsic layer (corresponding energy bandgap eV)0.6 (1.44)0.65 (1.32)0.7 (1.21)0.75 (1.11)The In composition of the 1st graded layer0.15 (2.81)0.15 (2.81)0.15 (2.81)0.15 (2.81)The In composition of the 2nd graded layer0.3 (2.29)0.3 (2.29)0.3 (2.29)0.35 (2.13)The In composition of the 3rd graded layer0.45 (1.83)0.5 (1.69)0.5 (1.69)0.55 (1.56)Figure 9
The efficiency of three graded-layer pin solar cells as a function of the In composition from 0.6 to 0.75.


## 4. Conclusions

The non-polar InxGa1−xN pn and pin junction solar cells with different In compositions have been simulated. It is observed that an In0.6Ga0.4N (Eg=1.44 eV) pn junction solar cell exhibits the highest efficiency of 18.4% (Voc=0.9 V and Jsc=26.1 mA/cm2). For the pin solar cells with a GaN/InxGa1−xN/GaN structure, a graded layer is needed at the interface of InxGa1−xN intrinsic layer and n-GaN region when the energy barrier height is too high. In order to obtain higher efficiency, one graded layer is necessary  when  the In composition of InxGa1−xN intrinsic layer is larger than 0.26, while two graded layers are necessary when the In composition of InxGa1−xN intrinsic layer is larger than 0.45. Finally, three graded layers are needed when the In composition of InxGa1−xN intrinsic layer is larger than 0.7. It is interesting to note that one graded-layer insertion has an effective improvement of efficiency only in the In composition range of 0.3–0.45. Two and three graded-layer insertions are needed to improve the efficiency and fill factor when the In composition of the intrinsic layer is larger than 0.45 and 0.7, respectively. The GaN/In0.6Ga0.4N/GaN pin solar cells with two and three graded-layer insertions exhibit the highest efficiency of 15.3% and 16.8%, respectively (Voc=0.82 V and Jsc=26.2 mA/cm2). This simulation work indicates that the insertion of graded layer is an effective method to lower energy barrier when there exists a high energy band offset in non-polar nitride devices.



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