Design and Simulation of InGaN p-n Junction Solar Cell

Abstract

The tunability of the InGaN band gap energy over a wide range provides a good spectral match to sunlight, making it a suitable material for photovoltaic solar cells. The main objective of this work is to design and simulate the optimal InGaN single-junction solar cell. For more accurate results and best configuration, the optical properties and the physical models such as the Fermi-Dirac statistics, Auger and Shockley-Read-Hall recombination, and the doping and temperature-dependent mobility model were taken into account in simulations. The single-junction In0.622Ga0.378N (Eg = 1.39 eV) solar cell is the optimal structure found. It exhibits, under normalized conditions (AM1.5G, 0.1 W/cm2, and 300 K), the following electrical parameters: [subscript]Jsc[/subscript] =32.6791 mA/cm2, [subscript]Voc[/subscript] =0.94091 volts, FF = 86.2343%, and η=26.5056%. It was noticed that the minority carrier lifetime and the surface recombination velocity have an important effect on the solar cell performance. Furthermore, the investigation results show that the In0.622Ga0.378N solar cell efficiency was inversely proportional with the temperature.

A. Mesrane 1 and F. Rahmoune 1 and A. Mahrane 2 and A. Oulebsir 3

Academic Editor:Elias Stathatos

1, Laboratoire LIMOSE, Universite M'hamed Bougara de Boumerdès, 35000 Boumerdès, Algeria
2, Unite de Developpement des Equipements Solaires (UDES), Centre de Developpement des Energies Renouvelables (CDER), Route Nle No. 11, BP 386, Bou Ismaïl, 42415 Tipaza, Algeria
3, Laboratoire d'Électronique Quantique, Faculte de Physique, USTHB, BP 32, El Alia, Bab Ezzouar, 16111 Alger, Algeria

Received 21 March 2015; Revised 17 May 2015; Accepted 17 June 2015; 30 July 2015

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Recently, various studies on solar cells using III-nitrides semiconductors in the photovoltaic applications have been done. Among them the InGaN alloy is a promising candidate for the photovoltaic applications because it exhibits attractive photovoltaic properties such as high tolerance to radiation, high mobility, and large absorption coefficient allowing thinner layers of material to absorb most of the solar spectrum [1].

Moreover, the most important advantage of InGaN alloy might be the direct band gap energy which can be adjusted according to the indium composition. Thus, the InGaN's energy band gap can be tuned from 0.7 eV to 3.42 eV, covering approximately the total solar spectrum.

The layers of InGaN solar cell can be deposited using the cost effective techniques, such as Metal Organic Chemical Vapor Deposition (MOCVD), Metal Organic Vapor Phase Epitaxy (MOVPE), and Molecular Beam Epitaxy (MBE) [2]. Whatever the deposition technique used, higher growth rates (~1.0 Angstrom/second) and lower temperature (~550°C) characterize the InGaN growth [3].

In 2007, Zhang et al. have modeled the performance of In_0.65 Ga_0.35 N single-junction solar cell and achieved a conversion efficiency of 20.284% [4]. In 2008, Shen et al. have obtained for the similar In_0.65 Ga_0.35 N solar cell higher efficiency (24.95%) due to the adoption of the density of states (DOS) model, providing much more information about recombination/generation in semiconductors than the lifetime model, and neglecting the defect effects [5]. The InGaN-based solar cell modeled by Bouzid and Ben Machiche [6], for a fraction of composition of indium ( [figure omitted; refer to PDF] ), has reached 24.88% conversion efficiency. The same solar cell was improved by [7] attaining 25.16% efficiency. Benmoussa et al. have simulated In_0.52 Ga_0.48 N using AMPS-1D software and published 22.99% efficiency in 2013 [8]. Recently, in 2014, In_0.64 Ga_0.36 N single-junction solar cell was designed and numerically optimized by Akter, exhibiting a high efficiency of 25.02% [2].

The different yields obtained in the works cited above can be principally attributed to the different optical properties, physical parameters, and band gap energy used for each solar cell studied. Thus, the obtained conversion efficiencies for InGaN solar cells with a band gap energy of 1.32 eV [5], 1.34 eV [2], 1.622 eV [7], and 1.64 eV [8] are, respectively, 24.95%, 25.02%, 25.16%, and 22.99%.

Given that the band gap energy of about 1.39 eV permits a single-junction solar cell to achieve theoretically the maximum conversion efficiency of ~31% [9, 10], we have opted in our study for [figure omitted; refer to PDF] -based single-junction solar cell with a fraction composition of indium of [figure omitted; refer to PDF] .

In contrast with the previous work [4-8], we have simulated the [figure omitted; refer to PDF] -based single-junction solar cell with the optimum band gap energy of 1.39 eV, using the optical and physical properties of In_0.622 Ga_0.378 N and taking into account the Auger and SRH recombination. Furthermore, we have adopted an appropriate carrier mobility model which takes into account the doping concentration, the temperature, and the material composition, which was different from previous work where the carrier mobility in [figure omitted; refer to PDF] was considered similar to GaN and depending only on doping concentration.

The aim of this simulation work is to obtain the maximum conversion efficiency of In_0.622 Ga_0.378 N (1.39 eV) single-junction solar cell with the best structure parameters. The effects of the concentration doping and the thickness of each layer on the electrical parameters of the solar cell, such as the short circuit current density ( [figure omitted; refer to PDF] ), the open circuit voltage ( [figure omitted; refer to PDF] ), the fill factor (FF), and the conversion efficiency ( [figure omitted; refer to PDF] ), were investigated. Furthermore, the effects of the minority carrier lifetime and the surface recombination velocity on the conversion efficiency of the single-junction In_0.622 Ga_0.378 N solar cell were also studied.

Finally, the behavior of the electrical characteristics of the solar cell versus the temperature has been studied.

2. Modelling and Simulation

2.1. Structure

As the numerical simulation is an important way to explore the possibility of a new solar cell structure, the In_0.622 Ga_0.378 N [figure omitted; refer to PDF] - [figure omitted; refer to PDF] single-junction solar cells have been studied using two-dimensional numerical computer simulation tool (ATLAS from Silvaco).

Atlas is a physically based two- and three-dimensional device simulator. It predicts the electrical behavior of specified semiconductor structures [11].

All the simulations were performed under normalized conditions that are 1 sun, a temperature of 300 K, and AM1.5 illumination. The antireflecting layer is considered as perfect without reflection losses.

The In_0.622 Ga_0.378 N single-junction solar cell structure studied consists of a P-type emitter and N-type base, as shown in Figure 1.

Figure 1: In_0.622 Ga_0.378 N single-junction solar cell structure.

[figure omitted; refer to PDF]

2.2. Electrical Parameters Calculation

The density of the total photocurrent drawn from the [figure omitted; refer to PDF] - [figure omitted; refer to PDF] junction solar cell at a given wavelength is the sum of the photocurrent densities collected from each layer of the [figure omitted; refer to PDF] - [figure omitted; refer to PDF] junction and is given by [12, 13] as follows: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are the photocurrent densities due to electrons and holes collected, respectively, at the depletion edges [figure omitted; refer to PDF] and [figure omitted; refer to PDF] . [figure omitted; refer to PDF] is the electron charge, [figure omitted; refer to PDF] is the density of the incident photon flux per unit bandwidth, [figure omitted; refer to PDF] is the device reflectance, and [figure omitted; refer to PDF] is the absorption coefficient. [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] are the minority carrier diffusion length, surface recombination velocity, and lifetime, respectively, in [figure omitted; refer to PDF] -layer and [figure omitted; refer to PDF] -layer. [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] are the junction depth, the depletion region width, and the neutral thicknesses of the N-type region, respectively.

As the quantum efficiency in the space charge region is close to 100%, all the absorbed photons contribute to the photocurrent [13]. Thus, the photocurrent density collected from the depletion region is given by [12, 13] as follows: [figure omitted; refer to PDF]

The surface recombination, the open circuit voltage, and the reverse saturation current density are given by the following expressions [14, 15]: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the open circuit voltage, [figure omitted; refer to PDF] is the short circuit current density, and [figure omitted; refer to PDF] is the reverse saturation current density. [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are Boltzmann's constant and the lattice temperature, respectively. [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are the initial acceptor and donor doping concentrations, respectively. [figure omitted; refer to PDF] is the intrinsic carrier concentration, which is expressed as [figure omitted; refer to PDF] where [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are the effective densities of states in the conduction and valence band, respectively. [figure omitted; refer to PDF] is the band gap energy.

The conversion efficiency of the solar cell is given by the following equation [15]: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the incident power of the solar spectrum, [figure omitted; refer to PDF] is the short circuit current, and FF is the fill factor of the solar cell.

2.3. Physical and Optical Parameters

The single-junction solar cell used in our study is based on In_0.622 Ga_0.378 N alloy with a band gap energy of 1.39 eV, which is related to the indium composition fraction [figure omitted; refer to PDF] at a temperature of 300 K by [7, 16]: [figure omitted; refer to PDF] where the band gap energy of InN ( [figure omitted; refer to PDF] ) and GaN ( [figure omitted; refer to PDF] ) is 0.7 eV and 3.42 eV, respectively. [figure omitted; refer to PDF] is the indium content and [figure omitted; refer to PDF] is the bowing parameter ( [figure omitted; refer to PDF] ) [7, 16].

The dependence of the energy band gap to the temperature is modeled in the Atlas software as follows [11]: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is given by (1). [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are the parameters related to the materials used in the single junction. They are set, respectively, at 9.09 × 10^-4 eV·K^-1 and 650 K [11] and are valid for the whole composition range of [figure omitted; refer to PDF] .

The other modeling parameters of the [figure omitted; refer to PDF] alloy were calculated using the following equations.

: Electron Affinity ( [figure omitted; refer to PDF] ) [4, 8, 17]: [figure omitted; refer to PDF]

: Relative permittivity ( [figure omitted; refer to PDF] ) [16]: [figure omitted; refer to PDF]

: Effective density of states in the conduction band ( [figure omitted; refer to PDF] ) [8, 17]: [figure omitted; refer to PDF]

: Effective density of states in the valence band ( [figure omitted; refer to PDF] ) [8, 17]: [figure omitted; refer to PDF]

: Effective masses ( [figure omitted; refer to PDF] ) [11]: [figure omitted; refer to PDF]

The low field mobility model developed by Farahmand et al. [18] has also been used in order to study the hole and the electron mobility behavior in the [figure omitted; refer to PDF] alloy depending on the material composition and the temperature. The electron or hole mobility is given by the following expression [18]: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the total doping of the layer and [figure omitted; refer to PDF] is the doping of the substrate which is fixed at 10¹⁷ cm^-3 . [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] are the specific parameters for a given material.

[figure omitted; refer to PDF] and [figure omitted; refer to PDF] , the values for the carrier mobility, are given in Table 1.

Table 1: Nitride low field mobility model parameter values [18].

Material	[figure omitted; refer to PDF] (cm2 /V[sm middot]s)	[figure omitted; refer to PDF] (cm2 /V[sm middot]s)
InN	3138.4	774
In0.8 Ga0.2 N	1252.7	644.3
In0.5 Ga0.5 N	758.1	459.4
In0.2 Ga0.8 N	684.2	389.4
GaN	1460.7	295

For other composition fractions not listed in Table 1, [figure omitted; refer to PDF] electron mobility was got by a linear interpolation from the nearest composition fractions. As the experimental data for the hole mobility in the InGaN alloys are not available, we have assumed that the hole mobility in [figure omitted; refer to PDF] is the same as in GaN [6, 7].

The InGaN alloys absorption coefficient [figure omitted; refer to PDF] is given by [16, 19]: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the photon energy and [figure omitted; refer to PDF] and [figure omitted; refer to PDF] , given in Table 2, are parameters dependent on the alloy composition.

Table 2: Fitting parameters used to calculate the absorption coefficient of the [figure omitted; refer to PDF] alloys [19].

Indium composition	[figure omitted; refer to PDF]	[figure omitted; refer to PDF]
1	0.69642	0.46055
0.83	0.66796	0.68886
0.69	0.58108	0.66902
0.57	0.60946	0.62182
0.5	0.51672	0.46836
0	3.52517	-0.65710

For the [figure omitted; refer to PDF] alloys, Adachi's wavelength-dependent refractive index model is given by the following equation [16, 20]: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] and [figure omitted; refer to PDF] depend on the material composition. In the case of the [figure omitted; refer to PDF] alloy, [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are given by the following equation [16]: [figure omitted; refer to PDF]

In order to take into account the action of several physical phenomena that take place in the structure, the following physical models have also been implemented:

(i) the doping and temperature-dependent mobility models;

(ii) the Auger recombination models;

(iii): the Shockley-Read-Hall recombination models;

(iv) the Fermi-Dirac statistics.

Some assumptions have been made to simplify the simulations. Thus, the Auger recombination coefficients for both electrons and holes, for the [figure omitted; refer to PDF] alloys, are set at 1.5 × 10^-30 cm⁶ ·s^-1 [16]. As the hole lifetimes of GaN and InN are, respectively, 6.5 ns and 5.4 ns [7, 19], the [figure omitted; refer to PDF] alloys have probably lower minority carrier lifetimes, and hence the electrons and holes lifetimes were assumed to be 1 ns [16, 19].

The surface recombination velocities of the minorities (electrons or holes) were taken to be 10³ cm·s^-1 [4, 5, 7].

3. Results and Discussion

For the case studied, the initial physical and geometrical parameter values used for the single-junction In_0.622 Ga_0.378 N solar cell are presented in Table 3.

Table 3: Initial physical and geometrical parameters.

Parameters	Values
[figure omitted; refer to PDF] (eV)	1.39
[figure omitted; refer to PDF] (cm-3 )	5[sm middot]1017
[figure omitted; refer to PDF] (cm-3 )	5[sm middot]1017
[figure omitted; refer to PDF] (ns)	1.00
[figure omitted; refer to PDF] (cm[sm middot]s-1 )	103
[figure omitted; refer to PDF] (µ m)	4.00

[figure omitted; refer to PDF] is approximately the proper total thickness of the In_0.622 Ga_0.378 N single-junction solar cell (~3.918 µ m).

The dependence of the In_0.622 Ga_0.378 N single-junction solar cell conversion efficiency on the minority carrier lifetimes and the surface recombination velocities was investigated.

3.1. Effect of Minority Carrier Lifetimes on In_0.622 Ga_0.378 N Conversion Efficiency

Assuming that the surface recombination velocity was set at 10³ cm/s, the conversion efficiency of In_0.622 Ga_0.378 N single-junction solar cell was determined for different values of minority carrier lifetimes as shown in Figure 2.

Figure 2: In_0.622 Ga_0.378 N efficiency versus minority carrier lifetimes.

[figure omitted; refer to PDF]

The results of simulations show that the conversion efficiency increases with the minority carrier (electrons/holes) lifetimes. According to (1)-(6) and (8), this is due to the low defect density that leads to the increase of the photocurrent density and the decrease of the reverse saturation current density inducing the enhancement of the open circuit voltage and so the conversion efficiency.

3.2. Effect of Surface Recombination Velocities on In_0.622 Ga_0.378 N Conversion Efficiency

Given that the minority carrier lifetimes were set at 1 ns, the influence of the surface recombination velocity on the In_0.622 Ga_0.378 N single-junction solar cell efficiency was presented in Figure 3.

Figure 3: In_0.622 Ga_0.378 N efficiency versus surface recombination velocities.

[figure omitted; refer to PDF]

We notice that when the surface recombination velocities exceed 10³ cm·s^-1 , the single-junction In_0.622 Ga_0.378 N solar cell efficiency decreases heavily due to the high dropping in photogenerated carrier collection by the electrodes. In fact, according to (1)-(6) and (8), the increase of the surface recombination velocity, due to the high surface defect density, conducts to the decrease of the photocurrent density and the open circuit voltage, via the increasing reverse saturation current which is directly proportional to the defect density, and this results in the decrease of the conversion efficiency.

To get the best In_0.622 Ga_0.378 N single-junction solar cell configuration, a great number of simulations were done to select the optimal device parameters as the optimal doping concentration and the optimal thickness of each layer of the solar cell.

3.3. Optimal Doping Concentration of the Front Layer

The doping concentration of the front layer has an effect on the number of the photogenerated carriers which has a consequence on the short circuit current density, the open circuit voltage, the maximal power, and the conversion efficiency. To study this effect, we have varied the acceptor doping concentration [figure omitted; refer to PDF] from 10¹⁷ cm^-3 to 10¹⁹ cm^-3 .

As shown by Figure 4, when the acceptor doping concentration [figure omitted; refer to PDF] decreases, the carrier mobility and the minority carrier lifetime increase, inducing an enhancement in the minority carrier diffusion length and better collection efficiency, resulting in the improvement of the current density. According to (5) and (6), the reverse saturation current density decreases with the increasing of the doping concentration, inducing the increase of the open circuit current.

Figure 4: The short circuit current density and the open circuit voltage versus the acceptor doping concentration [figure omitted; refer to PDF] .

[figure omitted; refer to PDF]

As shown in Figure 5, while the doping concentration [figure omitted; refer to PDF] increases, the maximal power produced by the solar cell and its conversion efficiency increase first and then decrease. The optimum efficiency of In_0.622 Ga_0.378 N single-junction solar cell was reached when the acceptor doping concentration was 1.5 × 10¹⁸ cm^-3 .

Figure 5: The maximal power and the solar cell efficiency versus the acceptor doping concentration [figure omitted; refer to PDF] .

[figure omitted; refer to PDF]

3.4. Optimal Thickness of the Front Layer

Since the optimal acceptor doping concentration was found, the main electrical parameters ( [figure omitted; refer to PDF] , [figure omitted; refer to PDF] ) of the solar cell were calculated for a range of [figure omitted; refer to PDF] -layer thickness comprised between 0.01 and 1 μ m.

As shown in Figures 6 and 7, with the increasing of the front layer thickness of the single-junction In_0.622 Ga_0.378 N solar cell, the short circuit current density ( [figure omitted; refer to PDF] ) and the conversion efficiency ( [figure omitted; refer to PDF] ) increase, first, and then decrease.

Figure 6: Short circuit current density versus the front layer thickness.

[figure omitted; refer to PDF]

Figure 7: Calculated efficiency versus the front layer thickness.

[figure omitted; refer to PDF]

When the front layer thickness decreases, the distance between the space charge region and the surface decreases, which improves the effective collection efficiency inducing the enhancement of the short circuit current density. At the same time, if the surface recombination was taken into account, the collection efficiency of the depletion region will be weakened as this last is too close to the surface. The reduction of the collection efficiency leads to the decrease of the short circuit current density and the conversion efficiency.

Figure 6 shows that the peak of the short circuit current density was reached for a front layer thickness of 0.03 μ m.

As shown in Figure 7, for a front layer thickness of 0.25 μ m, the In_0.622 Ga_0.378 N single-junction solar cell reaches the best conversion efficiency.

3.5. Optimal Thickness of the Back Layer

In this part, we have determined the conversion efficiency of the In_0.622 Ga_0.378 N single-junction solar cell when varying the N-layer thickness as illustrated in Figure 8.

Figure 8: Calculated efficiency versus the back layer thickness.

[figure omitted; refer to PDF]

We notice that the conversion efficiency is enhanced with the increase of the back layer thickness until 1 μ m, but beyond 1 μ m it remains almost constant at 26.50%. Therefore, the electrical parameters of the In_0.622 Ga_0.378 N solar cell are less affected by the back layer thickness than the front layer thickness.

3.6. Optimal Performance of In_0.622 Ga_0.378 N SJ Solar Cell

The optimal structure obtained from our investigations for the In_0.622 Ga_0.378 N single-junction solar cell was 0.25 μ m P-layer thickness and 1.0 μ m N-layer thickness, with acceptor and donor doping concentrations of 1.5 × 10¹⁸ cm^-3 and 5 × 10¹⁷ cm^-3 , respectively.

The calculated electrical parameters, the [figure omitted; refer to PDF] - [figure omitted; refer to PDF] and [figure omitted; refer to PDF] - [figure omitted; refer to PDF] characteristics of the final In_0.622 Ga_0.378 N single-junction solar cell structure, under normalized conditions, were presented, respectively, in Table 4 and Figure 9.

Table 4: Calculated parameters of the In_0.622 Ga_0.378 N SJ solar cell under AM1.5G, 0.1 W/cm² , and 300 K.

PV parameters	Values
[figure omitted; refer to PDF] (mA/cm2 )	32.6791
[figure omitted; refer to PDF] (volts)	0.94091
[figure omitted; refer to PDF] (mW/cm2 )	26.5154
FF (%)	86.2334
[figure omitted; refer to PDF] (%)	26.5056

Figure 9: [figure omitted; refer to PDF] and [figure omitted; refer to PDF] characteristic for the optimal In_0.622 Ga_0.378 N SJ solar cell configuration.

[figure omitted; refer to PDF]

3.7. The Temperature Dependence of In_0.622 Ga_0.378 N SJ Solar Cell

As the temperature has a great impact on the solar cell operation, we have studied its behavior through the variation of its electrical parameters versus the temperature.

The temperature was varied from 280 K to 400 K as presented in Figure 10.

Figure 10: Current-voltage characteristics of In_0.622 Ga_0.378 N solar cell versus temperature.

[figure omitted; refer to PDF]

As shown in Figure 10, the electrical characteristic [figure omitted; refer to PDF] - [figure omitted; refer to PDF] of the In_0.622 Ga_0.378 N solar cell varies with the temperature. Indeed, while the short circuit current density ( [figure omitted; refer to PDF] ) increases slightly with the temperature, the open circuit voltage ( [figure omitted; refer to PDF] ) decreases strongly, inducing the degradation of the conversion efficiency as illustrated in Figure 11.

Figure 11: In_0.622 Ga_0.378 N solar cell efficiency versus temperature.

[figure omitted; refer to PDF]

The high reduction of the open circuit voltage with the increased temperature was caused by the reduction of the band gap energy and the extreme increase of the reverse saturation current density, which is very sensitive with temperature, as illustrated in Figure 12.

Figure 12: In_0.622 Ga_0.378 N solar cell band gap and reverse saturation current density versus temperature.

[figure omitted; refer to PDF]

According to (6) and (7), the reverse saturation current density increases exponentially with increasing temperature, via the exponential dependence of the intrinsic carrier concentration with the temperature.

4. Conclusion

The calculation of the photovoltaic parameters of the In_0.622 Ga_0.378 N [figure omitted; refer to PDF] - [figure omitted; refer to PDF] single-junction solar cell, for the cases of different doping concentrations and different thicknesses of each layer, has allowed achieving the best solar cell structure with optimum performance. It was found that the solar cell performance was more affected by the front layer than back layer. The optimum efficiency found, under normalized conditions (AM1.5G, 0.1 W/cm² , and 300 K), is 26.50%.

In this paper, we have also studied the effect of the minority carrier lifetime and the surface recombination velocity on the conversion efficiency of the In_0.622 Ga_0.378 N solar cell and it was found that, to minimize the power losses, the carrier lifetime should be improved by reducing the defects density, and the surface recombination velocity should not exceed 10³ cm·s^-1 .

At last, we have studied the electrical characteristics fluctuation of the single-junction In_0.622 Ga_0.378 N solar cell with the temperature variation, and we have noticed a strong performance degradation with the increasing of the temperature; this is due to the temperature dependency of the physical parameters of the solar cell.

Acknowledgment

The authors would like to thank Mr. S. Elmetnani (UDES) for his valuable advice on the writing of this paper.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

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