## Detailed balance analysis of nanophotonic solar cells |

Optics Express, Vol. 21, Issue 1, pp. 1209-1217 (2013)

http://dx.doi.org/10.1364/OE.21.001209

Acrobat PDF (1421 KB)

### Abstract

We present a detailed balance based approach for performing current density-voltage characteristic modeling of nanophotonic solar cells. This approach takes into account the intrinsic material non-idealities, and is useful for determining the theoretical limit of solar cell efficiency for a given structure. Our approach only requires the cell’s absorption spectra over all angles, which can be readily calculated using available simulation tools. Using this approach, we elucidate the physics of open-circuit voltage enhancement over bulk cells in nanoscale thin film structures, by showing that the enhancement is related to the absorption *suppression* in the immediate spectral region above the bandgap. We also show that with proper design, the use of a grating on a nanoscale thin film can increase its short-circuit current, while preserving its voltage-enhancing capabilities.

© 2013 OSA

## 1. Introduction

1. D. Redfield, “Unified model of fundamental limitations on the performance of silicon solar cells,” IEEE Trans. Electron. Dev. **27**, 766–771 (1980). [CrossRef]

2. T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. **31**, 711–716 (1984). [CrossRef]

3. O. D. Miller, E. Yablonovitch, and S. R. Kurtz, “Strong internal and external luminescence as solar cells approach the shockley-queisser limit,” IEEE J. Photovolt. **2**, 303–311 (2012). [CrossRef]

4. H. A. Atwater, “Paths to high efficiency low-cost photovoltaics,” in “Photovoltaic Specialists Conference (PVSC), 2011 37th IEEE ,” (2011), pp. 000001–000003. [CrossRef]

5. A. Shah, P. Torres, R. Tscharner, N. Wyrsch, and H. Keppner, “Photovoltaic technology: The case for thin-film solar cells,” Science **285**, 692–698 (1999). [CrossRef] [PubMed]

6. S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. **101**, 093105 (2007). [CrossRef]

17. C. O. McPheeters and E. T. Yu, “Computational analysis of thin film ingaas/gaas quantum well solar cells with back side light trapping structures,” Opt. Express **20**, A864–A878 (2012). [CrossRef] [PubMed]

18. M. G. Deceglie, V. E. Ferry, A. P. Alivisatos, and H. A. Atwater, “Design of nanostructured solar cells using coupled optical and electrical modeling,” Nano Lett. **12**, 2894–2900 (2012). [CrossRef] [PubMed]

19. N. Huang, C. Lin, and M. L. Povinelli, “Limiting efficiencies of tandem solar cells consisting of iii–v nanowire arrays on silicon,” J. Appl. Phys. **112**, 064321 (2012). [CrossRef]

20. A. Niv, M. Gharghi, C. Gladden, O. D. Miller, and X. Zhang, “Near-field electromagnetic theory for thin solar cells,” Phys. Rev. Lett. **109**, 138701 (2012). [CrossRef] [PubMed]

20. A. Niv, M. Gharghi, C. Gladden, O. D. Miller, and X. Zhang, “Near-field electromagnetic theory for thin solar cells,” Phys. Rev. Lett. **109**, 138701 (2012). [CrossRef] [PubMed]

21. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. **107**, 17491–17496 (2010). [CrossRef] [PubMed]

20. A. Niv, M. Gharghi, C. Gladden, O. D. Miller, and X. Zhang, “Near-field electromagnetic theory for thin solar cells,” Phys. Rev. Lett. **109**, 138701 (2012). [CrossRef] [PubMed]

23. C. Luo, A. Narayanaswamy, G. Chen, and J. D. Joannopoulos, “Thermal radiation from photonic crystals: A direct calculation,” Phys. Rev. Lett. **93**, 213905 (2004). [CrossRef] [PubMed]

## 2. Computational procedure

24. W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. **32**, 510–519 (1961). [CrossRef]

*V*is the voltage across the cell,

*J*is the current density generated by the cell, and

*q*is the electron charge.

*F*is the radiative generation rate per unit area of hole-electron pairs by the incident sunlight, while

_{s}*F*

_{c}(

*V*) is the corresponding radiative recombination rate per unit area.

*R*(0) and

*R*(

*V*) are the rates of non-radiative recombination and generation, respectively, of hole-electron pairs per unit area [24

24. W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. **32**, 510–519 (1961). [CrossRef]

*V*= 0.

*S*(

*ω*) per unit bandwidth per unit area at a frequency

*ω*. For all our calculations, we used the AM 1.5 global spectrum standard [25

25. National Renewable Energy Lab (NREL), http://rredc.nrel.gov/solar/spectra/am1.5/, Air Mass 1.5 (AM1.5) Global Spectrum (ASTM173-03G) (2008).

*S*(

*ω*). We also assume the cell has an absorption spectra of

*A*(

*ω*,

*θ*,

*ϕ*) where

*θ*and

*ϕ*are the incident polar and azimuthal angles, respectively [Fig. 1(a)].

*A*(

*ω*,

*θ*,

*ϕ*) here is the sum of the absorbing spectras for both the transverse electric and transverse magnetic incident polarizations. The radiative generation rate

*F*in Eq. (1) can be calculated as follows [24

_{s}24. W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. **32**, 510–519 (1961). [CrossRef]

*ω*starting from the cell’s material bandgap frequency

*ω*

_{g}.

*F*(

_{c}*V*) in Eq. (1) relates to the voltage

*V*across the cell as follows [24

**32**, 510–519 (1961). [CrossRef]

*F*

_{co}is the radiative recombination rate when the cell is in thermal equilibrium with a surrounding blackbody,

*k*is the Boltzman constant, and

*T*

_{c}is the temperature of the cell. Assuming that our cell has a perfectly reflecting back surface as in the case of the nanostructures in Figs. 1(a)–1(b),

*F*

_{co}is then just the thermal emission through the 2

*π*solid angle of the front surface of the cell [26]: where

*Planck’s law*[26] for the incident spectral photon flux density from a surrounding blackbody at a temperature

*T*

_{c},

*c*is the speed of light in vacuum, and

*ħ*is the reduced Planck constant. In Eq. (4), we have used

*Kirchoff’s law*[26] to relate the thermal emission rate of the cell to its absorption spectra

*A*(

*ω*,

*θ*,

*ϕ*).

*J*

_{sc}of the cell can be obtained by setting

*V*= 0 in Eq. (1) [24

**32**, 510–519 (1961). [CrossRef]

*J*= 0 in Eq. (1) we get the following equation from which we can solve for the open-circuit voltage

*V*

_{oc}across the cell [24

**32**, 510–519 (1961). [CrossRef]

*V*

_{oc}in Eq. (6) can be approximated as follows:

*A*(

*ω*,

*θ*,

*ϕ*) over all angles is sufficient for the detailed balance analysis of nanophotonic solar cells. Such spectra controls both the absorption and the emission properties of the cell that enters into

*Shockley-Queisser’s analysis*[24

**32**, 510–519 (1961). [CrossRef]

## 3. Results on a GaAs thin film with and without the grating

19. N. Huang, C. Lin, and M. L. Povinelli, “Limiting efficiencies of tandem solar cells consisting of iii–v nanowire arrays on silicon,” J. Appl. Phys. **112**, 064321 (2012). [CrossRef]

29. D. Hill and P. T. Landsberg, “A formalism for the indirect auger effect. i,” Proc. R. Soc. Lond. A Math. Phys. Sci. **347**, 547–564 (1976). [CrossRef]

35. N. Tajik, Z. Peng, P. Kuyanov, and R. R. LaPierre, “Sulfur passivation and contact methods for gaas nanowire solar cells,” Nanotechnology **22**, 225402 (2011). [CrossRef] [PubMed]

36. U. Strauss, W. W. Ruhle, and K. Kohler, “Auger recombination in intrinsic gaas,” Appl. Phys. Lett. **62**, 55–57 (1993). [CrossRef]

37. M. Green, “Limits on the open-circuit voltage and efficiency of silicon solar cells imposed by intrinsic auger processes,” IEEE Trans. Electron. Dev. **31**, 671–678 (1984). [CrossRef]

*n*(

*p*) is the electron (hole) concentration,

*C*

_{n}(

*C*

_{p}) is the conduction-band (valance-band) Auger coefficient, and

*L*is the thickness of the cell. In addition, we also assume that the GaAs cell is approximately intrinsic under illumination (i.e.

*n*≈

*p*). In this intrinsic approximation, the Auger recombination rate [Eq. (8)] is minimized and given by [2

2. T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. **31**, 711–716 (1984). [CrossRef]

3. O. D. Miller, E. Yablonovitch, and S. R. Kurtz, “Strong internal and external luminescence as solar cells approach the shockley-queisser limit,” IEEE J. Photovolt. **2**, 303–311 (2012). [CrossRef]

*n*

_{i}is the intrinsic carrier concentration. In all our calculations, we consider GaAs cells operating at a temperature of

*T*

_{c}= 300K, where

*C*

_{n}+

*C*

_{p}= 7 × 10

^{−30}cm

^{6}· s

^{−1}[36

36. U. Strauss, W. W. Ruhle, and K. Kohler, “Auger recombination in intrinsic gaas,” Appl. Phys. Lett. **62**, 55–57 (1993). [CrossRef]

*n*

_{i}= 2 × 10

^{6}cm

^{−3}[38].

39. B. Kayes, H. Nie, R. Twist, S. Spruytte, F. Reinhardt, I. Kizilyalli, and G. Higashi, “27.6% conversion efficiency, a new record for single-junction solar cells under 1 sun illumination,” in “Photovoltaic Specialists Conference (PVSC), 2011 37th IEEE ,” (2011), pp. 000004–000008. [CrossRef]

2. T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. **31**, 711–716 (1984). [CrossRef]

*L*= 43.8 nm. The use of the thin film results in a

*V*

_{oc}of 1.21V, which is significantly higher than the

*V*

_{oc}of 1.12V for bulk GaAs cells [20

**109**, 138701 (2012). [CrossRef] [PubMed]

*J*

_{sc}of the thin film suffers significantly as compared to that of GaAs bulk cells [3

3. O. D. Miller, E. Yablonovitch, and S. R. Kurtz, “Strong internal and external luminescence as solar cells approach the shockley-queisser limit,” IEEE J. Photovolt. **2**, 303–311 (2012). [CrossRef]

*J*

_{sc}of the thin film is by introducing light trapping [21

21. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. **107**, 17491–17496 (2010). [CrossRef] [PubMed]

*L*′ = 50 nm is the actual grating structure thickness,

*a*= 456 nm is the grating periodicity, and (

*w*= 0.24

*a*,

*h*= 0.52

*L*′) are the (width, height) of the grating’s air groove [Fig. 1(a)]. [The definiton of the effective thickness here is such that different structures with the same effective thickness have the same amount of absorbing material.] Figure 1(c) shows a large enhancement in the

*J*

_{sc}of the grating structure relative to that of the thin film. Moreover, the

*V*

_{oc}of the grating structure is maintained at approximately the same enhanced value as that of the thin film.

*J*

_{sc},

*V*

_{oc}and efficiency (

*η*) of the thin film and the grating structure for a wide range of thicknesses

*L*. The efficiency here is defined as

*P*

_{inc}is the total incident sun radiation power per unit cell area, and FF is the cell’s fill-factor [24

**32**, 510–519 (1961). [CrossRef]

*a*= 456 nm, and air groove dimensions (

*w*= 0.24

*a*,

*h*= 0.52

*L*′) [Fig. 1(a)]. We see that, in general, the grating structures maintain the same

*V*

_{oc}enhancement as in the thin films while still drastically improving the

*J*

_{sc}and, hence, the efficiency of such thin solar cell structures.

## 4. Physics of voltage enhancement

*V*

_{oc}enhancement in nanophotonic structures, we first examine the thermal emission properties of an

*L*= 10 μm thick bulk structure with multi-layer anti-reflection coating on its front surface. Figure 2(a) shows its absorptivity spectra as a function of incident polar angle

*θ*. We see that the absorptivity of the bulk structure is ∼ 100% for almost all polar angles and wavelengths up to the GaAs band edge at ∼ 870 nm [38]. This strong absorptivity results in a strong radiative generation rate

*F*

_{s}[Eq. (2)] and, consequently, a

*J*

_{sc}of 31.6mA, which is close to the maximum possible

*J*

_{sc}for a GaAs solar cell [3

**2**, 303–311 (2012). [CrossRef]

*F*

_{co}[Eq. (4)] that is close to the maximum value for GaAs. Therefore, the contrast between

*F*

_{s}and

*F*

_{co}is low [Eq. (7)], resulting in a

*V*

_{oc}of 1.16V, which is significantly lower than the enhanced

*V*

_{oc}of the nanostructures associated with the J-V curves in Fig. 1(c).

*θ*. Such absorption suppression in the immediate frequency range above the bandgap in Fig. 2(b) results in a large reduction of the thin film’s thermal equilibrium recombination rate

*F*

_{co}. This can be seen by examining the spectral integration above the bandgap frequency

*ω*

_{g}in Eq. (4). Since the cell is operating at a temperature

*T*

_{c}that satisfies

*kT*

_{c}≪

*ħω*

_{g}, the thermal emission photon flux spectrum Θ(

*ω*) in Eq. (4) can be approximated as: where

*H*(·) is the Heaviside step function. Therefore, the thermal emission spectrum of the cell is located immediately above the bandgap and has a relatively narrow width of

*kT*

_{c}. Accordingly, reducing the absorption of the cell in this frequency range will have a very strong influence on the cell’s thermal emission and, hence, strongly influences

*F*

_{co}. On the other hand, the thermal emission spectral width corresponds only to a very small fraction of the total absorption bandwidth of the cell. Moreover, since the solar radiation has a much wider bandwidth, reducing the absorption in the immediate frequency range above the bandgap has far less influence on the radiative generation rate

*F*

_{s}. Therefore, it follows that reducing the absorption in the immediate frequency range above the bandgap increases the contrast between

*F*

_{s}and

*F*

_{co}[Eq. (7)] and, consequently, leads to the enhancement of the structure’s

*V*

_{oc}.

*θ*= 0 over the entire frequency range above the bandgap as compared to the bulk structure’s spectra in Fig. 2(a). This leads to a significant reduction of the

*J*

_{sc}in the thin film case. However, as illustrated above, the

*V*

_{oc}and

*J*

_{sc}are really controlled by different parts of the absorptivity spectra. This observation motivates incorporating light trapping [21

21. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. **107**, 17491–17496 (2010). [CrossRef] [PubMed]

*J*

_{sc}, and (ii) still preserve the absorption suppression in the

*kT*

_{c}region immediately above the bandgap in order to maintain the

*V*

_{oc}enhancement over the bulk structure. The optimized grating structure associated with the solid J-V curve in Fig. 1(c) indeed has such characteristics in its absorptivity spectra [Fig. 2(c)]. In particular, the spectra in Fig. 2(c) preserves the absorption suppression in the spectral region immediately above the GaAs bandgap. Consequently, the grating structure has a

*V*

_{oc}of 1.2V, which is a large enhancement over the bulk structure, and similar to the

*V*

_{oc}of the thin film with equivalent thickness

*L*[Fig. 1(c)]. In addition, the grating’s enhanced absorption, away from the GaAs bandgap region, at the normal incidence angle

*θ*= 0 [Fig. 2(c)] results in a large

*J*

_{sc}enhancement over the thin film as shown in Fig. 1(c).

## 5. Conclusion

*V*

_{oc}) and the short-circuit current (

*J*

_{sc}) are controlled by different parts of the cell’s absorption spectrum, and that the

*V*

_{oc}can be enhanced by suppressing the absorption in the immediate vicinity of the material’s bandgap. Our analysis here, moreover, indicates other opportunities for creating a cell with high

*V*

_{oc}and

*J*

_{sc}. For example, in the angular integral within Eq. (4), the cell’s absorption strength is modulated by a sin(2

*θ*) factor. Therefore, the absorption strength in the immediate vicinity of

*θ*= 0 and

*F*

_{co}. However, strengthening the absorption at the normal incidence angle

*θ*= 0 does enhance the cell’s radiative generation rate

*F*

_{s}[Eq. (2)]. These observations together with Eq. (5) and Eq. (7) indicate that: (i) significant

*V*

_{oc}enhancement due to absorption suppression comes only from the angular region away from

*θ*= 0 and

*kT*

_{c}immediately above the bangap, and (ii) strengthening the absorption at

*θ*= 0 leads to both

*V*

_{oc}and

*J*

_{sc}enhancement. We anticipate that our analysis tool will prove useful to understand the ultimate performance of nanophotonic solar cells in general.

## Acknowledgments

## References and links

1. | D. Redfield, “Unified model of fundamental limitations on the performance of silicon solar cells,” IEEE Trans. Electron. Dev. |

2. | T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. |

3. | O. D. Miller, E. Yablonovitch, and S. R. Kurtz, “Strong internal and external luminescence as solar cells approach the shockley-queisser limit,” IEEE J. Photovolt. |

4. | H. A. Atwater, “Paths to high efficiency low-cost photovoltaics,” in “Photovoltaic Specialists Conference (PVSC), 2011 37th IEEE ,” (2011), pp. 000001–000003. [CrossRef] |

5. | A. Shah, P. Torres, R. Tscharner, N. Wyrsch, and H. Keppner, “Photovoltaic technology: The case for thin-film solar cells,” Science |

6. | S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. |

7. | L. Hu and G. Chen, “Analysis of optical absorption in silicon nanowire arrays for photovoltaic applications,” Nano Lett. |

8. | A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A |

9. | L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. |

10. | C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express |

11. | P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express |

12. | R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. |

13. | S. B. Mallick, M. Agrawal, and P. Peumans, “Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells,” Opt. Express |

14. | X. Sheng, S. G. Johnson, J. Michel, and L. C. Kimerling, “Optimization-based design of surface textures for thin-film si solar cells,” Opt. Express |

15. | A. Raman, Z. Yu, and S. Fan, “Dielectric nanostructures for broadband light trapping in organic solar cells,” Opt. Express |

16. | E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: The supercell concept,” Phys. Rev. B |

17. | C. O. McPheeters and E. T. Yu, “Computational analysis of thin film ingaas/gaas quantum well solar cells with back side light trapping structures,” Opt. Express |

18. | M. G. Deceglie, V. E. Ferry, A. P. Alivisatos, and H. A. Atwater, “Design of nanostructured solar cells using coupled optical and electrical modeling,” Nano Lett. |

19. | N. Huang, C. Lin, and M. L. Povinelli, “Limiting efficiencies of tandem solar cells consisting of iii–v nanowire arrays on silicon,” J. Appl. Phys. |

20. | A. Niv, M. Gharghi, C. Gladden, O. D. Miller, and X. Zhang, “Near-field electromagnetic theory for thin solar cells,” Phys. Rev. Lett. |

21. | Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. |

22. | S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, |

23. | C. Luo, A. Narayanaswamy, G. Chen, and J. D. Joannopoulos, “Thermal radiation from photonic crystals: A direct calculation,” Phys. Rev. Lett. |

24. | W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. |

25. | National Renewable Energy Lab (NREL), http://rredc.nrel.gov/solar/spectra/am1.5/, Air Mass 1.5 (AM1.5) Global Spectrum (ASTM173-03G) (2008). |

26. | L. D. Landau and E. M. Lifshitz, |

27. | V. Liu and S. Fan, “S4 : A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. |

28. | E. D. Palik, |

29. | D. Hill and P. T. Landsberg, “A formalism for the indirect auger effect. i,” Proc. R. Soc. Lond. A Math. Phys. Sci. |

30. | W. Shockley and W. T. Read, “Statistics of the recombinations of holes and electrons,” Phys. Rev. |

31. | R. N. Hall, “Electron-hole recombination in germanium,” Phys. Rev. |

32. | S. M. Sze and M.-K. Lee, |

33. | C.-C. Chang, C.-Y. Chi, M. Yao, N. Huang, C.-C. Chen, J. Theiss, A. W. Bushmaker, S. LaLumondiere, T.-W. Yeh, M. L. Povinelli, C. Zhou, P. D. Dapkus, and S. B. Cronin, “Electrical and optical characterization of surface passivation in gaas nanowires,” Nano Lett. |

34. | G. Mariani, A. Scofield, and D. Huffaker, “High-perfomance patterned arrays of core-shell gaas nanopillar solar cells with in-situ ingap passivation layer,” in “Photovoltaic Specialists Conference (PVSC), 2012 38th IEEE ,” (2012), pp. 003080–003082. [CrossRef] |

35. | N. Tajik, Z. Peng, P. Kuyanov, and R. R. LaPierre, “Sulfur passivation and contact methods for gaas nanowire solar cells,” Nanotechnology |

36. | U. Strauss, W. W. Ruhle, and K. Kohler, “Auger recombination in intrinsic gaas,” Appl. Phys. Lett. |

37. | M. Green, “Limits on the open-circuit voltage and efficiency of silicon solar cells imposed by intrinsic auger processes,” IEEE Trans. Electron. Dev. |

38. | R. F. Pierret, |

39. | B. Kayes, H. Nie, R. Twist, S. Spruytte, F. Reinhardt, I. Kizilyalli, and G. Higashi, “27.6% conversion efficiency, a new record for single-junction solar cells under 1 sun illumination,” in “Photovoltaic Specialists Conference (PVSC), 2011 37th IEEE ,” (2011), pp. 000004–000008. [CrossRef] |

**OCIS Codes**

(050.0050) Diffraction and gratings : Diffraction and gratings

(350.6050) Other areas of optics : Solar energy

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

(310.6628) Thin films : Subwavelength structures, nanostructures

**ToC Category:**

Solar Energy

**History**

Original Manuscript: December 4, 2012

Revised Manuscript: December 23, 2012

Manuscript Accepted: January 1, 2013

Published: January 10, 2013

**Citation**

Sunil Sandhu, Zongfu Yu, and Shanhui Fan, "Detailed balance analysis of nanophotonic solar cells," Opt. Express **21**, 1209-1217 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-1209

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### References

- D. Redfield, “Unified model of fundamental limitations on the performance of silicon solar cells,” IEEE Trans. Electron. Dev.27, 766–771 (1980). [CrossRef]
- T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev.31, 711–716 (1984). [CrossRef]
- O. D. Miller, E. Yablonovitch, and S. R. Kurtz, “Strong internal and external luminescence as solar cells approach the shockley-queisser limit,” IEEE J. Photovolt.2, 303–311 (2012). [CrossRef]
- H. A. Atwater, “Paths to high efficiency low-cost photovoltaics,” in “Photovoltaic Specialists Conference (PVSC), 2011 37th IEEE,” (2011), pp. 000001–000003. [CrossRef]
- A. Shah, P. Torres, R. Tscharner, N. Wyrsch, and H. Keppner, “Photovoltaic technology: The case for thin-film solar cells,” Science285, 692–698 (1999). [CrossRef] [PubMed]
- S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys.101, 093105 (2007). [CrossRef]
- L. Hu and G. Chen, “Analysis of optical absorption in silicon nanowire arrays for photovoltaic applications,” Nano Lett.7, 3249–3252 (2007). [CrossRef] [PubMed]
- A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A78, 023825 (2008). [CrossRef]
- L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett.93, 221105 (2008). [CrossRef]
- C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express17, 19371–19381 (2009). [CrossRef] [PubMed]
- P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express17, 20975–20990 (2009). [CrossRef] [PubMed]
- R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater.21, 3504–3509 (2009). [CrossRef]
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