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Energy Express

Energy Express

  • Editor: Christian Seassal
  • Vol. 22, Iss. S5 — Aug. 25, 2014
  • pp: A1222–A1228
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Vertical InGaN-based green-band solar cells operating under high solar concentration up to 300 suns

Jinn-Kong Sheu, Fu-Bang Chen, Shou-Hung Wu, Ming-Lun Lee, Po-Cheng Chen, and Yu-Hsiang Yeh  »View Author Affiliations


Optics Express, Vol. 22, Issue S5, pp. A1222-A1228 (2014)
http://dx.doi.org/10.1364/OE.22.0A1222


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Abstract

InGaN/GaN-based solar cells with vertical-conduction feature on silicon substrates were fabricated by wafer bonding technique. The vertical solar cells with a metal reflector sandwiched between the GaN-based epitaxial layers and the Si substrate could increase the effective thickness of the absorption layer. Given that the thermally resistive sapphire substrates were replaced by the Si substrate with high thermal conductivity, the solar cells did not show degradation in power conversion efficiency (PCE) even when the solar concentrations were increased to 300 suns. The open circuit voltage increased from 1.90 V to 2.15 V and the fill factor increased from 0.55 to 0.58 when the concentrations were increased from 1 sun to 300 suns. With the 300-sun illumination, the PCE was enhanced by approximately 33% compared with the 1-sun illumination.

© 2014 Optical Society of America

1. Introduction

2. Device fabrication and experiment methods

InGaN epitaxial layers were deposited on c-face sapphire substrates by a metalorganic vapor-phase epitaxy reactor. The layer structure consisted of a 30 nm-thick low-temperature GaN nucleation layer, followed by a 2 µm-thick undoped GaN with chamber pressure at 500 Torr. Thereafter, a p–i–n heterostructure consisting of a 3 µm-thick Si-doped n+-GaN (n ~5 × 1018 cm−3), an undoped InGaN/GaN (2.5/14.5 nm for 12 pairs) MQW structure, and a 200 nm-thick Mg-doped p-GaN (p ~5 × 1017 cm−3) were sequentially deposited. The typical peak wavelength of the electroluminescence spectra taken from the InGaN/GaN/Si solar cells was approximately 525 nm, corresponding to the In composition of approximately 28% in the InGaN well layers [13

13. J. Wu, W. Walukiewicz, K. M. Yu, W. J. Ager III, E. E. Haller, H. Lu, and W. J. Schaff, “Small band gap bowing in InxGa1-xN alloys,” Appl. Phys. Lett. 80(25), 4741–4743 (2002). [CrossRef]

, 14

14. P. G. Moses and C. G. Van de Walle, “Band bowing and band alignment in InGaN alloys,” Appl. Phys. Lett. 96(2), 021908 (2010). [CrossRef]

]. After epitaxial growth, a bilayer metal of Ni/Ag (1/200 nm) was deposited onto the p-GaN top layer to serve as reflector/ohmic contact layer [15

15. Y. C. Yang, J. K. Sheu, M. L. Lee, C. K. Hsu, S. J. Tu, S. Y. Liu, C. C. Yang, and F. W. Huang, “Vertical InGaN light-emitting diodes with Ag paste as bonding layer,” Microelectron. Reliab. 52(5), 949–951 (2012). [CrossRef]

]. After the formation of the reflector layer, a barrier layer, which was configured to alleviate the diffusion of Ag from the reflector layer to the bonding layer and consisted of a 200 nm-thick TiW layer and a 50 nm-thick Pt layer, was deposited between the reflector and bonding layers. In the proposed vertical InGaN/GaN/Si solar cells, a 3 µm-thick In layer was used as the bonding layer. The Si substrates were dipped in buffered oxide etch solution for 60 s to remove the native silicon dioxide, then a bilayer Ti/Au (20/1,500 nm) metal was deposited onto the surfaces of Si substrates to serve as ohmic contact and bonding layer. These wafers served as receptors for the wafer bonding process. After the bonding process, the sapphire substrate was removed by laser lift-off technique to expose the n+-GaN layer. Thus, the InxGa1 − xN/GaN-based heteroepitaxial layers were transferred to the Si substrate with the n+-GaN top layer. Then, the samples were treated in potassium hydroxide (concentration of 3 M) solution at an elevated temperature of 60 °C to texture the n+-GaN layer to enhance light trapping. Ti/Al/Ni/Au (20/30/150/2,000 nm) metal layers were then deposited onto the exposed n+-GaN layer to form the n-type ohmic contacts (cathode electrodes) on the wafers. Finally, the Si substrates were thinned to 150 µm and coated with Ti/Au (50/500 nm) metals to serve as the back ohmic contact layer. The entire fabricated device area was 1 × 1 mm2.
Fig. 1 (a) Typical top-view SEM image taken from the proposed vertical InGaN/GaN/Si solar cell. The inset shows the enlarged SEM image taken from the surface. (b) Schematic layer structure of the vertical solar cell.
Figure 1(a) shows a typical top view scanning electron microscopy image taken from the proposed vertical InGaN/GaN/Si solar cells. The dashed line in Fig. 1(a) indicates where the cross section corresponds to a schematic layer structure of the vertical solar cell, as shown in Fig. 1(b).

3. Results and discussion

Fig. 2 (a) Typical J-V and P-V characteristics of the vertical GaN/InGaN solar cells with green-band absorption layer illuminated by the one-sun AM1.5G condition. (b) Relative external quantum efficiency (EQE) as a function of incident light wavelength and electroluminescence spectrum as the vertical green cells was driven with a forward current of 350 mA.
Figure 2(a) illustrates the typical characteristics of current density and power density versus voltage (JV and PV, respectively) of the vertical InGaN/GaN/Si green band solar cells (vertical green cells) illuminated by the 1-sun condition, which was calibrated by the calibration cell of the National Renewable Energy Laboratory with global air mass of 1.5 (AM1.5G) terrestrial solar spectrum. The typical VOC, short-circuit current density (JSC), and fill factor (FF) of the solar cells were 1.90 V, 2.07 mA/cm2, and 0.55, respectively, corresponding to the PCE of 2.16%. Although the conversion efficiency was significantly higher than that reported for cells with green-band InGaN absorption layers [16

16. J. Bai, C. C. Yang, M. Athanasiou, and T. Wang, “Efficiency enhancement of InGaN/GaN solar cells with nanostructures,” Appl. Phys. Lett. 104(5), 051129 (2014). [CrossRef]

], the PCE was still considerably lower than the theoretical value by single-junction materials with optical band gap at 2.36 eV (525 nm) [17

17. C. H. Henry, “Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells,” J. Appl. Phys. 51(8), 4494–4500 (1980). [CrossRef]

]. The PCE was mainly limited by material quality because of the large lattice mismatch between InGaN and GaN [18

18. R. Singh, D. Doppalapudi, T. D. Moustakas, and L. T. Romano, “Phase separation in InGaN thick films and formation of InGaN/GaN double heterostructures in the entire alloy composition,” Appl. Phys. Lett. 70(9), 1089–1091 (1997). [CrossRef]

]. Figure 2(b) shows the relative external quantum efficiency (EQE) as a function of incident light wavelength. The main response covered a part of visible light in the blue and green regions with a long-wavelength cutoff of approximately 520 nm. This wavelength cutoff was consistent with the emission peak wavelength as the vertical green cells were driven with a forward current of 350 mA, as illustrated in Fig. 2(b). In addition, a steep decrease in EQE in the ultraviolet (UV) region was attributed to the surface absorption of the n+-GaN top layer with a thickness of 3 µm, which would lead to a short-wavelength cutoff at approximately 365 nm. Although the incident photons contributed by the UV light are far less than those of the visible and infrared light in the solar spectrum, the thickness of the n-GaN top layer could be further decreased to collect more photogenerated carriers from UV light and alleviate the heating effect. In principle, the thickness of the n-GaN top layer should be considerably less than 1 µm because the absorption coefficient of GaN is as high as ~1 × 105 cm−1 [10

10. C. J. Neufeld, N. G. Toledo, S. C. Cruz, M. Iza, S. P. DenBaars, and U. K. Mishra, “High quantum efficiency InGaN/GaN solar cells with 2.95 eV band gap,” Appl. Phys. Lett. 93(14), 143502 (2008). [CrossRef]

]. In a p–i–n homojunction or a lattice-matched heterojunction solar cell with a single absorption layer, conversion efficiency increases theoretically with the decrease in the band gap of the absorption layer. However, the lattice mismatch between the GaN and InxGa1 − xN limits the critical thickness of the InxGa1 − xN layer in a p–i–n GaN/InxGa1 − xN heterojunction solar cell, particularly when the In contents are increased to convert more sunlight. In this study, the proposed vertical green-band cells with a metal reflector were combined with silicon substrate by using the wafer bonding technique to increase the effective thickness of the InGaN absorption layer. Moreover, the Si substrate with higher thermal conductivity replaces the sapphire substrate, allowing the vertical green cells to operate under high solar concentration. A solar simulator concentrator (Oriel Instruments) was used to study the concentrated solar response of MQW-type solar cells made from InGaN/GaN-based materials and to produce different irradiance intensities of 50 suns to 300 suns with the AM1.5D solar spectrum (ASTM G-173-03). In this study, flash-mode light source with light pulse width of 500 ms was applied to irradiance the bare cells (not in a packaged form).

Fig. 3 Typical J-V characteristics under different irradiance intensities up to 300 suns.
Figure 3 shows the typical JV characteristics under different irradiance intensities. Evidently, the short-circuit current density (JSC) increases linearly with irradiance intensity. In an equivalent circuit of a solar cell modeled by an ideal current source (JSC) in parallel with a diode, the JV characteristic is expressed in Eq. (1) as follows:
J=J0{exp(qVnkT)1}JSC
(1)
where n, k, q, and T are the ideality factor, Boltzmann constant, elementary charge, and absolute temperature, respectively. J0 is the diode saturation current density. From Eq. (1), VOC at a given concentration ratio (M) can be expressed in Eq. (2) as follows:
VOC(M)=nkTqln(Jsc(M)J0+1)VOC(1)+nkTqln(M)
(2)
From Eq. (2), VOC increases logarithmically with M (i.e., irradiance intensity). In a worst case scenario, the measured value of VOC may decrease with an increase in irradiance intensity when the irradiance intensity is too high. This finding can be attributed to the significant increase in cell temperature by increasing the irradiance intensity up to a certain high M. As a result, J0 increases significantly, causing VOC to decrease with the increase in cell temperature. The increase in J0 with the increase in temperature occurs mainly from changes in intrinsic carrier concentration (ni). Thus, the conversion efficiency is decreased by the decrease in VOC at a high M. In this study, the cell temperature was maintained at 25 °C by placing the devices on a temperature-controlled stage.
Fig. 4 (a) VOC and FF as functions of solar concentration. (b) PCE as functions of solar concentration.
As shown in Fig. 4(a), VOC increased with irradiance intensity when the concentration ratios increased up to 300 suns. The VOC increased from 1.90 V to 2.15 V and the FF increased from 0.55 to 0.58 when the concentration ratios were increased from 1 sun to 300 suns, as illustrated in Fig. 4(a). Compared with the 1-sun irradiance, the measured VOC and FF increased by 13.15% and 3.6%, respectively, when the solar cells were tested under the 300-sun conditions. At the 300-sun (M = 300) test condition, the corresponding PCE was 2.93%. This result corresponded to an enhancement of PCE by approximately 33% compared with the 1-sun irradiance. An empirical expression for the FF as a function of VOC is expressed as follows [19

19. M. A. Green, Solar Cells: Operating Principles, Technology, and System Applications (Prentice-Hall, 1982).

]
FF=vocln(voc+0.72)voc+1andvoc=qVOCnkT
(3)
when the VOC is significantly greater than the nkT/q.

Because the VOC was approximately 2.0 V for the proposed vertical green cells, Eq. (3) can be estimated roughly as follows:
FF11vocln(voc)
(4)
As shown in Fig. 4(a), the FF increases with the increase in VOC. This trend is consistent with that described in Eq. (4). However, the measured FF was considerably lower than the calculated FF in Eq. (4). This discrepancy could be attributed to the considerable series resistance (Rs) and limited shunt resistance (Rsh) of devices. In other words, the empirical equations, Eqs. (1)(4), were deduced from a diode with Rs and Rsh close to zero and infinity, respectively.

4. Conclusions

We demonstrated that vertical InGaN/GaN/Si solar cells operated under high solar concentration of up to 300 suns. The green band InGaN/GaN-based solar cells showed typical characteristics of HCPV cells. The VOC increased from 1.90 V to 2.15 V, and the FF increased from 0.55 to 0.58 when the concentrated level was increased from 1 sun to 300 suns. At the 300-sun irradiance intensity, the PCE was enhanced by approximately 33% compared with the 1-sun irradiance intensity.

Acknowledgments

This work was supported from National Science Council for the financial support under contract Nos. NSC-101-2221-E-218-012-MY3, NSC-101-2221-E-006-171-MY3, NSC-100-2112-M-006-011-MY3 and NSC-100-3113-E-006-015.

References and links

1.

R. R. King, A. Boca, W. Hong, X. Q. Liu, D. Bhusari, D. Larrabee, K. M. Edmondson, D. C. Law, C. M. Fetzer, S. Mesropian, and N. H. Karam, “Band-gap-engineered architectures for high-efficiency multijunction concentrator solar cells,” in Proc. 24th Eur. PVSEC (2009), pp. 55–61.

2.

A. D. Vos, Thermodynamics of Solar Energy Conversion (Wiley, 2008).

3.

J. Wu, W. Walukiewicz, K. M. Yu, W. Shan, J. W. Ager III, E. E. Haller, H. Lu, W. J. Schaff, W. K. Metzger, and S. Kurtz, “Superior radiation resistance of In1-xGaxN alloys: full-solar-spectrum photovoltaic material system,” J. Appl. Phys. 94(10), 6477–6482 (2003). [CrossRef]

4.

H. Hamzaoui, A. S. Bouazzi, and B. Rezig, “Theoretical possibilities of InxGa1-xN tandem PV structures,” Sol. Energy Mater. Sol. Cells 87(1–4), 595–603 (2005). [CrossRef]

5.

C. C. Yang, C. H. Jang, J. K. Sheu, M. L. Lee, S. J. Tu, F. W. Huang, Y. H. Yeh, and W. C. Lai, “Characteristics of InGaN-based concentrator solar cells operating under 150X solar concentration,” Opt. Express 19(S4), A695–A700 (2011). [CrossRef] [PubMed]

6.

J. K. Sheu, C. C. Yang, S. J. Tu, K. H. Chang, M. L. Lee, W. C. Lai, and L. C. Peng, “Demonstration of GaN-based solar cells with GaN/InGaN superlattice absorption layers,” IEEE Electron Device Lett. 30(3), 225–227 (2009). [CrossRef]

7.

R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well solar cells with long operating wavelengths,” Appl. Phys. Lett. 94(6), 063505 (2009). [CrossRef]

8.

isR. Dahal, J. Li, K. Aryal, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well concentrator solar cells,” Appl. Phys. Lett. 97(7), 073115 (2010). [CrossRef]

9.

C. C. Yang, J. K. Sheu, X. W. Liang, M. S. Huang, M. L. Lee, K. H. Chang, S. J. Tu, F. W. Huang, and W. C. Lai, “Enhancement of the conversion efficiency of GaN-based photovoltaic devices with AlGaN/InGaN absorption layers,” Appl. Phys. Lett. 97(2), 021113 (2010). [CrossRef]

10.

C. J. Neufeld, N. G. Toledo, S. C. Cruz, M. Iza, S. P. DenBaars, and U. K. Mishra, “High quantum efficiency InGaN/GaN solar cells with 2.95 eV band gap,” Appl. Phys. Lett. 93(14), 143502 (2008). [CrossRef]

11.

D. Holec, P. M. F. J. Costa, M. J. Kappers, and C. J. Humphreys, “Critical thickness calculations for InGaN/GaN,” J. Cryst. Growth 303(1), 314–317 (2007). [CrossRef]

12.

R. H. Horng, S. T. Lin, Y. L. Tsai, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “Improved conversion efficiency of GaN/InGaN thin-film solar cells,” IEEE Electron Device Lett. 30(7), 724–726 (2009). [CrossRef]

13.

J. Wu, W. Walukiewicz, K. M. Yu, W. J. Ager III, E. E. Haller, H. Lu, and W. J. Schaff, “Small band gap bowing in InxGa1-xN alloys,” Appl. Phys. Lett. 80(25), 4741–4743 (2002). [CrossRef]

14.

P. G. Moses and C. G. Van de Walle, “Band bowing and band alignment in InGaN alloys,” Appl. Phys. Lett. 96(2), 021908 (2010). [CrossRef]

15.

Y. C. Yang, J. K. Sheu, M. L. Lee, C. K. Hsu, S. J. Tu, S. Y. Liu, C. C. Yang, and F. W. Huang, “Vertical InGaN light-emitting diodes with Ag paste as bonding layer,” Microelectron. Reliab. 52(5), 949–951 (2012). [CrossRef]

16.

J. Bai, C. C. Yang, M. Athanasiou, and T. Wang, “Efficiency enhancement of InGaN/GaN solar cells with nanostructures,” Appl. Phys. Lett. 104(5), 051129 (2014). [CrossRef]

17.

C. H. Henry, “Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells,” J. Appl. Phys. 51(8), 4494–4500 (1980). [CrossRef]

18.

R. Singh, D. Doppalapudi, T. D. Moustakas, and L. T. Romano, “Phase separation in InGaN thick films and formation of InGaN/GaN double heterostructures in the entire alloy composition,” Appl. Phys. Lett. 70(9), 1089–1091 (1997). [CrossRef]

19.

M. A. Green, Solar Cells: Operating Principles, Technology, and System Applications (Prentice-Hall, 1982).

20.

K. Nishioka, T. Takamoto, T. Agui, M. Kaneiwa, Y. Uraoka, and T. Fuyuki, “Evaluation of InGaP/InGaAs/Ge triple-junction solar cell and optimization of solar cell’s structure focusing on series resistance for high-efficiency concentrator photovoltaic systems,” Sol. Energy Mater. Sol. Cells 90(9), 1308–1321 (2006). [CrossRef]

21.

R. R. King, D. Bhusari, D. Larrabee, X. Q. Liu, E. Rehder, K. Edmondson, H. Cotal, R. K. Jones, J. H. Ermer, C. M. Fetzer, D. C. Law, and N. H. Karam, “Solar cell generations over 40% efficiency,” Prog. Photovolt. Res. Appl. 20(6), 801–815 (2012). [CrossRef]

22.

K. Araki, M. Yamaguchi, T. Takamoto, E. Ikeda, T. Agui, H. Kurita, K. Takahashi, and T. Unno, “Characteristics of GaAs-based concentrator cells,” Sol. Energy Mater. Sol. Cells 66(1–4), 559–565 (2001). [CrossRef]

23.

G. S. Kinsey, P. Hebert, K. E. Barbour, D. D. Krut, H. L. Cotal, and R. A. Sherif, “Concentrator multi-junction solar cell characteristics under variable intensity and temperature,” Prog. Photovolt. Res. Appl. 16(6), 503–508 (2008). [CrossRef]

OCIS Codes
(040.5350) Detectors : Photovoltaic
(230.0250) Optical devices : Optoelectronics
(230.5590) Optical devices : Quantum-well, -wire and -dot devices

ToC Category:
Photovoltaics

History
Original Manuscript: June 3, 2014
Revised Manuscript: June 23, 2014
Manuscript Accepted: June 27, 2014
Published: July 9, 2014

Citation
Jinn-Kong Sheu, Fu-Bang Chen, Shou-Hung Wu, Ming-Lun Lee, Po-Cheng Chen, and Yu-Hsiang Yeh, "Vertical InGaN-based green-band solar cells operating under high solar concentration up to 300 suns," Opt. Express 22, A1222-A1228 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-S5-A1222


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References

  1. R. R. King, A. Boca, W. Hong, X. Q. Liu, D. Bhusari, D. Larrabee, K. M. Edmondson, D. C. Law, C. M. Fetzer, S. Mesropian, and N. H. Karam, “Band-gap-engineered architectures for high-efficiency multijunction concentrator solar cells,” in Proc. 24th Eur. PVSEC (2009), pp. 55–61.
  2. A. D. Vos, Thermodynamics of Solar Energy Conversion (Wiley, 2008).
  3. J. Wu, W. Walukiewicz, K. M. Yu, W. Shan, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, W. K. Metzger, and S. Kurtz, “Superior radiation resistance of In1-xGaxN alloys: full-solar-spectrum photovoltaic material system,” J. Appl. Phys.94(10), 6477–6482 (2003). [CrossRef]
  4. H. Hamzaoui, A. S. Bouazzi, and B. Rezig, “Theoretical possibilities of InxGa1-xN tandem PV structures,” Sol. Energy Mater. Sol. Cells87(1–4), 595–603 (2005). [CrossRef]
  5. C. C. Yang, C. H. Jang, J. K. Sheu, M. L. Lee, S. J. Tu, F. W. Huang, Y. H. Yeh, and W. C. Lai, “Characteristics of InGaN-based concentrator solar cells operating under 150X solar concentration,” Opt. Express19(S4), A695–A700 (2011). [CrossRef] [PubMed]
  6. J. K. Sheu, C. C. Yang, S. J. Tu, K. H. Chang, M. L. Lee, W. C. Lai, and L. C. Peng, “Demonstration of GaN-based solar cells with GaN/InGaN superlattice absorption layers,” IEEE Electron Device Lett.30(3), 225–227 (2009). [CrossRef]
  7. R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well solar cells with long operating wavelengths,” Appl. Phys. Lett.94(6), 063505 (2009). [CrossRef]
  8. isR. Dahal, J. Li, K. Aryal, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well concentrator solar cells,” Appl. Phys. Lett.97(7), 073115 (2010). [CrossRef]
  9. C. C. Yang, J. K. Sheu, X. W. Liang, M. S. Huang, M. L. Lee, K. H. Chang, S. J. Tu, F. W. Huang, and W. C. Lai, “Enhancement of the conversion efficiency of GaN-based photovoltaic devices with AlGaN/InGaN absorption layers,” Appl. Phys. Lett.97(2), 021113 (2010). [CrossRef]
  10. C. J. Neufeld, N. G. Toledo, S. C. Cruz, M. Iza, S. P. DenBaars, and U. K. Mishra, “High quantum efficiency InGaN/GaN solar cells with 2.95 eV band gap,” Appl. Phys. Lett.93(14), 143502 (2008). [CrossRef]
  11. D. Holec, P. M. F. J. Costa, M. J. Kappers, and C. J. Humphreys, “Critical thickness calculations for InGaN/GaN,” J. Cryst. Growth303(1), 314–317 (2007). [CrossRef]
  12. R. H. Horng, S. T. Lin, Y. L. Tsai, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “Improved conversion efficiency of GaN/InGaN thin-film solar cells,” IEEE Electron Device Lett.30(7), 724–726 (2009). [CrossRef]
  13. J. Wu, W. Walukiewicz, K. M. Yu, W. J. Ager, E. E. Haller, H. Lu, and W. J. Schaff, “Small band gap bowing in InxGa1-xN alloys,” Appl. Phys. Lett.80(25), 4741–4743 (2002). [CrossRef]
  14. P. G. Moses and C. G. Van de Walle, “Band bowing and band alignment in InGaN alloys,” Appl. Phys. Lett.96(2), 021908 (2010). [CrossRef]
  15. Y. C. Yang, J. K. Sheu, M. L. Lee, C. K. Hsu, S. J. Tu, S. Y. Liu, C. C. Yang, and F. W. Huang, “Vertical InGaN light-emitting diodes with Ag paste as bonding layer,” Microelectron. Reliab.52(5), 949–951 (2012). [CrossRef]
  16. J. Bai, C. C. Yang, M. Athanasiou, and T. Wang, “Efficiency enhancement of InGaN/GaN solar cells with nanostructures,” Appl. Phys. Lett.104(5), 051129 (2014). [CrossRef]
  17. C. H. Henry, “Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells,” J. Appl. Phys.51(8), 4494–4500 (1980). [CrossRef]
  18. R. Singh, D. Doppalapudi, T. D. Moustakas, and L. T. Romano, “Phase separation in InGaN thick films and formation of InGaN/GaN double heterostructures in the entire alloy composition,” Appl. Phys. Lett.70(9), 1089–1091 (1997). [CrossRef]
  19. M. A. Green, Solar Cells: Operating Principles, Technology, and System Applications (Prentice-Hall, 1982).
  20. K. Nishioka, T. Takamoto, T. Agui, M. Kaneiwa, Y. Uraoka, and T. Fuyuki, “Evaluation of InGaP/InGaAs/Ge triple-junction solar cell and optimization of solar cell’s structure focusing on series resistance for high-efficiency concentrator photovoltaic systems,” Sol. Energy Mater. Sol. Cells90(9), 1308–1321 (2006). [CrossRef]
  21. R. R. King, D. Bhusari, D. Larrabee, X. Q. Liu, E. Rehder, K. Edmondson, H. Cotal, R. K. Jones, J. H. Ermer, C. M. Fetzer, D. C. Law, and N. H. Karam, “Solar cell generations over 40% efficiency,” Prog. Photovolt. Res. Appl.20(6), 801–815 (2012). [CrossRef]
  22. K. Araki, M. Yamaguchi, T. Takamoto, E. Ikeda, T. Agui, H. Kurita, K. Takahashi, and T. Unno, “Characteristics of GaAs-based concentrator cells,” Sol. Energy Mater. Sol. Cells66(1–4), 559–565 (2001). [CrossRef]
  23. G. S. Kinsey, P. Hebert, K. E. Barbour, D. D. Krut, H. L. Cotal, and R. A. Sherif, “Concentrator multi-junction solar cell characteristics under variable intensity and temperature,” Prog. Photovolt. Res. Appl.16(6), 503–508 (2008). [CrossRef]

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