## Specific series resistance evaluation using photoluminescence signal of Si solar cells |

Optics Express, Vol. 20, Issue S6, pp. A822-A827 (2012)

http://dx.doi.org/10.1364/OE.20.00A822

Acrobat PDF (1434 KB)

### Abstract

A new method is introduced to evaluate the specific series resistance distribution of solar cells using photoluminescence images under both short circuit and open circuit conditions. An experiment was perfomed to confirm that method is insensitive to the illumination intensity distribution and valid for different illumination levels.

© 2012 OSA

## 1. Introduction

*i-V*curve of solar cells have been proposed to evaluate the effective series resistance [1

1. D. Pysch, A. Mette, and S. W. Glunz, “A review and comparison of different methods to determine the series resistance of solar cells,” Sol. Energy Mater. Sol. Cells **91**(18), 1698–1706 (2007). [CrossRef]

^{2}of solar cells [3

3. T. Trupke, E. Pink, R. A. Bardos, and M. D. Abbott, “Spatially resolved series resistance of silicon solar cells obtained from luminescence imaging,” Appl. Phys. Lett. **90**(9), 093506 (2007). [CrossRef]

4. H. Kampwerth, T. Trupke, J. W. Weber, and Y. Augarten, “Advanced luminescence based effective series resistance imaging of silicon solar cells,” Appl. Phys. Lett. **93**(20), 202102 (2008). [CrossRef]

5. T. Trupke, R. A. Bardos, M. C. Schubert, and W. Warta, “Photoluminescence imaging of silicon wafers,” Appl. Phys. Lett. **89**(4), 044107 (2006). [CrossRef]

## 2. Theory

*R*is the series resistance,

_{s}*R*is the shunt resistance,

_{sh}*V*is the photovoltage,

_{ph}*V*is the terminal voltage,

_{term}*i*is the photocurrent and

_{ph}*i*is the terminal current.

_{term}*R*is the external resistance load of the solar cell. For an efficient solar cell, the shunt resistance should be large enough to reduce the leakage yet the series resistance should be small to reduce the power consumption inside the solar cell. In the following discussion, the shunt resistance is assumed to be much larger than the series resistance and will be excluded.

_{load}*i-V*relation of the diode part of the solar cell without light illumination can be written as the Shockley ideal diode Eq. orwhere

*i*is the saturation current,

_{s}*q*is the electron charge,

*V*is the voltage across the ideal diode,

_{D}*k*is the Boltzmann constant,

*T*is the temperature and

*η*is the ideality factor of the solar cell. The saturation current can be written as [7]where

_{ideal}*A*is the cross section area,

*p*

_{n}_{0}is the hole number density in the n-type region,

*n*

_{p}_{0}is the electron number density in the p-type region,

*D*is the hole diffusivity in the n-type region,

_{np}*D*is the electron diffusivity in the p-type region, and

_{pn}*τ*is the excess carrier lifetime. The carrier diffusivities can be obtained when the corresponding doping concentrations are given. The excess carrier lifetime spatial distribution can also be obtained using the PL method [5

5. T. Trupke, R. A. Bardos, M. C. Schubert, and W. Warta, “Photoluminescence imaging of silicon wafers,” Appl. Phys. Lett. **89**(4), 044107 (2006). [CrossRef]

8. M. D. Abbott, J. E. Cotter, F. W. Chen, T. Trupke, R. A. Bardos, and K. C. Fisher, “Application of photoluminescence characterization to the development and manufacturing of high-efficiency silicon solar cells,” J. Appl. Phys. **100**(11), 114514 (2006). [CrossRef]

9. S. Herlufsen, J. Schmidt, D. Hinken, K. Bothe, and R. Brendel, “Photoconductance-calibrated photoluminescence lifetime imaging of crystalline silicon,” Phys Status Solidi-R **2**(6), 245–247 (2008). [CrossRef]

3. T. Trupke, E. Pink, R. A. Bardos, and M. D. Abbott, “Spatially resolved series resistance of silicon solar cells obtained from luminescence imaging,” Appl. Phys. Lett. **90**(9), 093506 (2007). [CrossRef]

4. H. Kampwerth, T. Trupke, J. W. Weber, and Y. Augarten, “Advanced luminescence based effective series resistance imaging of silicon solar cells,” Appl. Phys. Lett. **93**(20), 202102 (2008). [CrossRef]

*j*is the contributed current density on each solar cell node and

_{term}*R*is known as the specific series resistance, which is in units of Ω⋅cm

_{s-s}^{2}. Equation (1) and Eq. (2) can be rewritten as where

*j*is the saturation current of each node and is a function of position. Equation (4) can then be rewritten asIn the PL experiment, the total terminal current and terminal voltage can both be measured. However, each node of the solar cell offers individual voltage and current. The light absorbed by the solar cell generates excess carriers which eventually recombine. The recombination mechanism can be categorized into non-radiative recombination, radiative recombination and outflow current. Since silicon is well-known for its disappointingly low efficiency of band-to-band PL signal, we define the efficiency of excess as the PL signal from each node on the solar cell which is contributed by a small portion of the excess carriers generated. Under the assumption of the carrier diffusion length is much larger than the thickness of the solar cell, the PL quantum efficiency can be defined as

_{s}*I*indicates the light intensity or exitance,

*ν*indicates the frequency of the photon,

*R*indicates the effective reflectivity of the light at the surface of the solar cell and

*h*indicates the Plank’s constant. The subscripts

*and*

_{PL}*represent the PL signal and illumination, respectively; the subscripts*

_{illu}*and*

_{_int}*indicate the quantity is inside and outside the solar cell, correspondingly. The illumination and PL intensities can be obtained experimentally. The observed PL signal by the CCD can be written aswhere*

_{_ext}*η*indicates the collecting efficiency of the entire optical system.

_{opt}*or*

_{sc}*respectively in the following discussion. The total excess carrier density generation rate can be written aswhere*

_{oc}*W*is the thickness of the solar cell. Since silicon is known for its poor band-to-band emission efficiency, the PL signal is only contributed by a small fraction of the excess carrier recombination. The PL signal can be derived and is proportional to the product of the local electron and hole number density for silicon [10

10. T. Trupke, R. A. Bardos, and M. D. Abbott, “Self-consistent calibration of photoluminescence and photoconductance lifetime measurements,” Appl. Phys. Lett. **87**(18), 184102 (2005). [CrossRef]

11. R. A. Bardos, T. Trupke, M. C. Schubert, and T. Roth, “Trapping artifacts in quasi-steady-state photoluminescence and photoconductance lifetime measurements on silicon wafers,” Appl. Phys. Lett. **88**(5), 053504 (2006). [CrossRef]

*i*is the total short circuit current of the entire solar cell and

_{sc}*A*is the total illuminated area of the solar cell sample. Under the short circuit condition, the current provided by each node is the contributed terminal current. Meanwhile,

_{tot}*V*is 0, the saturation current density, excess carrier lifetime and the specific series resistance corresponding to each node can then be solved simultaneously using Eq. (7) and 2D Newton’s method to find the roots. Although the current provided by each node is different. Equation (13) does not contain

_{term}## 3. Experimental setup

^{2}and 10 cm in length. The lightpipe is labeled as LP. A convex lens L1 with a focal length of 2.54 cm is placed near the exit facet of the lightpipe and is used to project the laser light onto the solar cell sample which is about 14.5 cm away from the lens. The normal direction of the solar cell sample has a 26.6° angle with respect to the optical axis of the incident laser light. The sample is in thermal contact with a temperature controlled aluminum plate which is labeled TC. The aluminum plate temperature is set to be 27°C. The sample electrodes are connected to a digital multimeter to measure the short circuit current of the sample. A CCD camera (Electrophysics Micron Viewer 7290A) is placed 42 cm away from the normal of the solar cell sample. A band pass filter, Filter 2, is placed on the CCD camera to ensure the observed signal is from the bandgap transition of the silicon which is 1.1 μm. The transmission spectrum of the filter is shown in Fig. 3 .

## 4. Results and discussion

^{2}using the method proposed here. The darker regions correspond to lower specific series resistance. The dark pattern along the vertical direction indicates the regions near the electrode grid lines where the specific series resistance is noticeably smaller. On the other hand, the specific series resistance is larger right in between the two neighboring grid lines since the current path is expected to be longer. The average specific series resistance is 1.42 Ω⋅cm

^{2}and the error is about 5.0 × 10

^{−3}Ω⋅cm

^{2}. Figure 6(b) shows the calculated spatial distribution of the specific series resistance under the average illumination intensity of 0.67 W/cm

^{2}. The average specific series resistance is 1.45 Ω⋅cm

^{2}. The average error is about 0.01 Ω⋅cm

^{2}. Figure 6(c) shows the pixel-to-pixel fraction between Fig. 6(a) and 6(b). The average value of Fig. 6(c) is about 1.02 which indicates that the proposed method obtains well-agreed results under different levels of illumination.

## 5. Conclusion

## Acknowledgment

## References and links

1. | D. Pysch, A. Mette, and S. W. Glunz, “A review and comparison of different methods to determine the series resistance of solar cells,” Sol. Energy Mater. Sol. Cells |

2. | L. Raniero, N. Martins, P. Canhola, S. Zhang, S. Pereira, I. Ferreira, E. Fortunato, and R. Martins, “Influence of the layer thickness and hydrogen dilution on electrical properties of large area amorphous silicon p-i-n solar cell,” Sol. Energy Mater. Sol. Cells |

3. | T. Trupke, E. Pink, R. A. Bardos, and M. D. Abbott, “Spatially resolved series resistance of silicon solar cells obtained from luminescence imaging,” Appl. Phys. Lett. |

4. | H. Kampwerth, T. Trupke, J. W. Weber, and Y. Augarten, “Advanced luminescence based effective series resistance imaging of silicon solar cells,” Appl. Phys. Lett. |

5. | T. Trupke, R. A. Bardos, M. C. Schubert, and W. Warta, “Photoluminescence imaging of silicon wafers,” Appl. Phys. Lett. |

6. | S. O. Kasap, |

7. | B. G. Streetman and S. Banerjee, |

8. | M. D. Abbott, J. E. Cotter, F. W. Chen, T. Trupke, R. A. Bardos, and K. C. Fisher, “Application of photoluminescence characterization to the development and manufacturing of high-efficiency silicon solar cells,” J. Appl. Phys. |

9. | S. Herlufsen, J. Schmidt, D. Hinken, K. Bothe, and R. Brendel, “Photoconductance-calibrated photoluminescence lifetime imaging of crystalline silicon,” Phys Status Solidi-R |

10. | T. Trupke, R. A. Bardos, and M. D. Abbott, “Self-consistent calibration of photoluminescence and photoconductance lifetime measurements,” Appl. Phys. Lett. |

11. | R. A. Bardos, T. Trupke, M. C. Schubert, and T. Roth, “Trapping artifacts in quasi-steady-state photoluminescence and photoconductance lifetime measurements on silicon wafers,” Appl. Phys. Lett. |

**OCIS Codes**

(040.5350) Detectors : Photovoltaic

(250.5230) Optoelectronics : Photoluminescence

**ToC Category:**

Photovoltaics

**History**

Original Manuscript: August 14, 2012

Revised Manuscript: September 11, 2012

Manuscript Accepted: September 13, 2012

Published: September 19, 2012

**Citation**

Te-yuan Chung, Ying-Chang Chung, and Sheng-Hui Chen, "Specific series resistance evaluation using photoluminescence signal of Si solar cells," Opt. Express **20**, A822-A827 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-S6-A822

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### References

- D. Pysch, A. Mette, and S. W. Glunz, “A review and comparison of different methods to determine the series resistance of solar cells,” Sol. Energy Mater. Sol. Cells91(18), 1698–1706 (2007). [CrossRef]
- L. Raniero, N. Martins, P. Canhola, S. Zhang, S. Pereira, I. Ferreira, E. Fortunato, and R. Martins, “Influence of the layer thickness and hydrogen dilution on electrical properties of large area amorphous silicon p-i-n solar cell,” Sol. Energy Mater. Sol. Cells87(1-4), 349–355 (2005). [CrossRef]
- T. Trupke, E. Pink, R. A. Bardos, and M. D. Abbott, “Spatially resolved series resistance of silicon solar cells obtained from luminescence imaging,” Appl. Phys. Lett.90(9), 093506 (2007). [CrossRef]
- H. Kampwerth, T. Trupke, J. W. Weber, and Y. Augarten, “Advanced luminescence based effective series resistance imaging of silicon solar cells,” Appl. Phys. Lett.93(20), 202102 (2008). [CrossRef]
- T. Trupke, R. A. Bardos, M. C. Schubert, and W. Warta, “Photoluminescence imaging of silicon wafers,” Appl. Phys. Lett.89(4), 044107 (2006). [CrossRef]
- S. O. Kasap, Optoelectronics and photonics: principles and practices (Prentice Hall, 2001).
- B. G. Streetman and S. Banerjee, Solid state electronic devices (Prentice Hall, 2000).
- M. D. Abbott, J. E. Cotter, F. W. Chen, T. Trupke, R. A. Bardos, and K. C. Fisher, “Application of photoluminescence characterization to the development and manufacturing of high-efficiency silicon solar cells,” J. Appl. Phys.100(11), 114514 (2006). [CrossRef]
- S. Herlufsen, J. Schmidt, D. Hinken, K. Bothe, and R. Brendel, “Photoconductance-calibrated photoluminescence lifetime imaging of crystalline silicon,” Phys Status Solidi-R2(6), 245–247 (2008). [CrossRef]
- T. Trupke, R. A. Bardos, and M. D. Abbott, “Self-consistent calibration of photoluminescence and photoconductance lifetime measurements,” Appl. Phys. Lett.87(18), 184102 (2005). [CrossRef]
- R. A. Bardos, T. Trupke, M. C. Schubert, and T. Roth, “Trapping artifacts in quasi-steady-state photoluminescence and photoconductance lifetime measurements on silicon wafers,” Appl. Phys. Lett.88(5), 053504 (2006). [CrossRef]

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