## Laser cooling of CdS nanobelts: Thickness matters |

Optics Express, Vol. 21, Issue 16, pp. 19302-19310 (2013)

http://dx.doi.org/10.1364/OE.21.019302

Acrobat PDF (1163 KB)

### Abstract

We report on the thickness dependent laser cooling in CdS nanobelts pumped by a 532 nm green laser. The lowest achievable cooling temperature is found to strongly depend on thickness. No net cooling can be achieved in nanobelts with a thickness below 65 nm due to nearly zero absorption and larger surface nonradiative recombination. While for nanobelts thicker than ~120 nm, the reabsorption effect leads to the reduction of the cooling temperature. Based on the thickness dependent photoconductivity gain, mean emission energy and external quantum efficiency, the modeling of the normalized temperature change suggests a good agreement with the experimental results.

© 2013 OSA

## 1. Introduction

*i.e.*,

3. M. Sheik-Bahae and R. I. Epstein, “Optical Refrigeration,” Nat. Photonics **1**(12), 693–699 (2007). [CrossRef]

4. R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature **377**(6549), 500–503 (1995). [CrossRef]

5. D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics **4**(3), 161–164 (2010). [CrossRef]

7. D. V. Seletskiy, S. D. Melgaard, R. I. Epstein, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Local laser cooling of Yb:YLF to 110 K,” Opt. Express **19**(19), 18229–18236 (2011). [CrossRef] [PubMed]

7. D. V. Seletskiy, S. D. Melgaard, R. I. Epstein, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Local laser cooling of Yb:YLF to 110 K,” Opt. Express **19**(19), 18229–18236 (2011). [CrossRef] [PubMed]

3. M. Sheik-Bahae and R. I. Epstein, “Optical Refrigeration,” Nat. Photonics **1**(12), 693–699 (2007). [CrossRef]

8. M. Sheik-Bahae and R. I. Epstein, “Laser cooling of solids,” Laser Photon. Rev. **3**(1-2), 67–84 (2009). [CrossRef]

9. M. Sheik-Bahae and R. I. Epstein, “Can laser light cool semiconductors?” Phys. Rev. Lett. **92**(24), 247403 (2004). [CrossRef] [PubMed]

14. G. Rupper, N. H. Kwong, and R. Binder, “Optical refrigeration of GaAs: Theoretical study,” Phys. Rev. B **76**(24), 245203 (2007). [CrossRef]

15. E. Finkeißen, M. Potemski, P. Wyder, L. Vina, and G. Weimann, “Cooling of a semiconductor by luminescence up-conversion,” Appl. Phys. Lett. **75**(9), 1258–1260 (1999). [CrossRef]

18. D. A. Bender, J. G. Cederberg, C. Wang, and M. Sheik-Bahae, “Development of high quantum efficiency GaAs/GaInP double heterostructures for laser cooling,” Appl. Phys. Lett. **102**(25), 252102 (2013). [CrossRef]

19. J. Zhang, D. H. Li, R. J. Chen, and Q. H. Xiong, “Laser cooling of a semiconductor by 40 kelvin,” Nature **493**(7433), 504–508 (2013). [CrossRef] [PubMed]

20. D. H. Li, J. Zhang, and Q. H. Xiong, “Surface Depletion Induced Quantum Confinement in CdS Nanobelts,” ACS Nano **6**(6), 5283–5290 (2012). [CrossRef] [PubMed]

21. D. H. Li, J. Zhang, Q. Zhang, and Q. H. Xiong, “Electric-Field-Dependent Photoconductivity in CdS Nanowires and Nanobelts: Exciton Ionization, Franz-Keldysh, and Stark Effects,” Nano Lett. **12**(6), 2993–2999 (2012). [CrossRef] [PubMed]

## 2. Modeling of the cooling power and normalized temperature change

3. M. Sheik-Bahae and R. I. Epstein, “Optical Refrigeration,” Nat. Photonics **1**(12), 693–699 (2007). [CrossRef]

*T*,

*P*is the power of the incident laser,

_{0}*t*is the thickness of the nanobelt,

*A*,

*B*and

*C*are nonradiative recombination coefficient, radiative recombination coefficient and Auger recombination coefficient, respectively;

*N*is the

*e-h*population density. Therefore, the cooling power is given by [19

19. J. Zhang, D. H. Li, R. J. Chen, and Q. H. Xiong, “Laser cooling of a semiconductor by 40 kelvin,” Nature **493**(7433), 504–508 (2013). [CrossRef] [PubMed]

21. D. H. Li, J. Zhang, Q. Zhang, and Q. H. Xiong, “Electric-Field-Dependent Photoconductivity in CdS Nanowires and Nanobelts: Exciton Ionization, Franz-Keldysh, and Stark Effects,” Nano Lett. **12**(6), 2993–2999 (2012). [CrossRef] [PubMed]

20. D. H. Li, J. Zhang, and Q. H. Xiong, “Surface Depletion Induced Quantum Confinement in CdS Nanobelts,” ACS Nano **6**(6), 5283–5290 (2012). [CrossRef] [PubMed]

**1**(12), 693–699 (2007). [CrossRef]

19. J. Zhang, D. H. Li, R. J. Chen, and Q. H. Xiong, “Laser cooling of a semiconductor by 40 kelvin,” Nature **493**(7433), 504–508 (2013). [CrossRef] [PubMed]

20. D. H. Li, J. Zhang, and Q. H. Xiong, “Surface Depletion Induced Quantum Confinement in CdS Nanobelts,” ACS Nano **6**(6), 5283–5290 (2012). [CrossRef] [PubMed]

**6**(6), 5283–5290 (2012). [CrossRef] [PubMed]

**493**(7433), 504–508 (2013). [CrossRef] [PubMed]

*e-h*population density

*N*, the optimum

*e-h*population density

*N*for the maximum external quantum efficiency can be determined by [22]By inserting the

_{opt}*N*into the Eq. (2), finally we express the external quantum efficiency at the e-h population density

_{opt}*N*asIn this equation, the nonradiative recombination coefficient

_{opt}*A*and the luminescence extraction efficiency

**6**(6), 5283–5290 (2012). [CrossRef] [PubMed]

*A*dominates the coefficient

_{s}*A*. The surface nonradiavtive combination

*A*relates to the thickness

_{s}*t*via surface recombination velocity

*S*by [24

24. G. W. Hooft and C. van Opdorp, “Determination of bulk minority-carrier lifetime and surface/interface recombination velocity from photoluminescence decay of a semi-infinite semiconductor slab,” J. Appl. Phys. **60**(3), 1065–1070 (1986). [CrossRef]

*S*is assumed to be the same for nanobelts with different thickness since the surface recombination velocity is only dependent on the nature of the surface and independent on the carrier density and layer thickness. The luminescence extraction efficiency

*B*= 10

^{−11}cm

^{3}/s,

*C*= 10

^{−30}cm

^{6}/s [25

25. P. T. Landsberg and M. J. Adams, “Radiative and Auger processes in semiconductors,” J. Lumin. **7**, 3–34 (1973). [CrossRef]

*S*= 250 cm/s [26

26. D. Huppert, M. Evenor, and Y. Shapira, “Measurements of surface recombination velocity on CdS surfaces and Au interfaces,” J. Vac. Sci. Technol. A **2**(2), 532–533 (1984). [CrossRef]

*α*= 4.6 μm

_{eff}^{−1}and

*η*= 0.996, the thickness dependent external quantum efficiency can be obtained as displayed in Fig. 2(b). The calculated optimum e-h population density

_{0}*N*by substituting the above parameters into Eq. (4) is around 10

_{opt}^{18}cm

^{−3}, which is consistent with the photogenerated e-h population density in experiment regarding the carrier lifetime is on the order of 100 ps [27

27. X. Xu, Y. Zhao, E. J. Sie, Y. Lu, B. Liu, S. A. Ekahana, X. Ju, Q. Jiang, J. Wang, H. Sun, T. C. Sum, C. H. A. Huan, Y. P. Feng, and Q. H. Xiong, “Dynamics of Bound Exciton Complexes in CdS Nanobelts,” ACS Nano **5**(5), 3660–3669 (2011). [CrossRef] [PubMed]

*α*= 4.6 μm

_{eff}^{−1}and

*η*= 0.998 is to match the experimental results that the external quantum efficiency for the 110 nm CdS nanobelt is 0.996 and the maximum external quantum efficiency appears around 110 nm (see Fig. 4(e)). Besides,

_{0}*α*= 4.6 μm

_{eff}^{−1}corresponds to the absorption coefficient at around 520 nm, which falls into the band tail range [23].

_{2}/Si substrate to reduce the thermal loss (see the inset of Fig. 3(b)) [19

**493**(7433), 504–508 (2013). [CrossRef] [PubMed]

**493**(7433), 504–508 (2013). [CrossRef] [PubMed]

**493**(7433), 504–508 (2013). [CrossRef] [PubMed]

*k*is the thermal conductivity of the CdS,

*M*is the cross-section area of the nanobelts,

28. X. Liu, R. Wang, Y. Jiang, Q. Zhang, X. Shan, and X. Qiu, “Thermal conductivity measurement of individual CdS nanowires using microphotoluminescence spectroscopy,” J. Appl. Phys. **108**(5), 054310 (2010). [CrossRef]

## 3. Experiment and results

^{−6}Torr to eliminate the convective coupling to the surrounding air. The CdS nanobelts are synthesized in a home-built chemical vapor deposition system. More detailed information on the PPLT method and nanobelt synthesis can be found elsewhere [19

**493**(7433), 504–508 (2013). [CrossRef] [PubMed]

27. X. Xu, Y. Zhao, E. J. Sie, Y. Lu, B. Liu, S. A. Ekahana, X. Ju, Q. Jiang, J. Wang, H. Sun, T. C. Sum, C. H. A. Huan, Y. P. Feng, and Q. H. Xiong, “Dynamics of Bound Exciton Complexes in CdS Nanobelts,” ACS Nano **5**(5), 3660–3669 (2011). [CrossRef] [PubMed]

## 4. Summary

## Acknowledgments

## References and links

1. | P. Pringsheim, “Zwei Bemerkungen über den Unterschied von Lumineszenz- und Temperaturstrahlung ,” Zeitschrift für Physik A Hadrons and Nuclei |

2. | R. I. Epstein and M. Sheik-Bahae, |

3. | M. Sheik-Bahae and R. I. Epstein, “Optical Refrigeration,” Nat. Photonics |

4. | R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature |

5. | D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics |

6. | D. V. Seletskiy, S. D. Melgaard, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of a semiconductor load to 165 K,” Opt. Express |

7. | D. V. Seletskiy, S. D. Melgaard, R. I. Epstein, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Local laser cooling of Yb:YLF to 110 K,” Opt. Express |

8. | M. Sheik-Bahae and R. I. Epstein, “Laser cooling of solids,” Laser Photon. Rev. |

9. | M. Sheik-Bahae and R. I. Epstein, “Can laser light cool semiconductors?” Phys. Rev. Lett. |

10. | J. B. Khurgin, “Band gap engineering for laser cooling of semiconductors,” J. Appl. Phys. |

11. | J. B. Khurgin, “Surface plasmon-assisted laser cooling of solids,” Phys. Rev. Lett. |

12. | J. B. Khurgin, “Role of bandtail states in laser cooling of semiconductors,” Phys. Rev. B |

13. | G. Rupper, N. H. Kwong, and R. Binder, “Large excitonic enhancement of optical refrigeration in semiconductors,” Phys. Rev. Lett. |

14. | G. Rupper, N. H. Kwong, and R. Binder, “Optical refrigeration of GaAs: Theoretical study,” Phys. Rev. B |

15. | E. Finkeißen, M. Potemski, P. Wyder, L. Vina, and G. Weimann, “Cooling of a semiconductor by luminescence up-conversion,” Appl. Phys. Lett. |

16. | H. Gauck, T. H. Gfroerer, M. J. Renn, E. A. Cornell, and K. A. Bertness, “External radiative quantum efficiency of 96% from a GaAs/GaInP heterostructure,” Appl. Phys., A Mater. Sci. Process. |

17. | B. Imangholi, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, and S. Kurtz, “Effects of epitaxial lift-off on interface recombination and laser cooling in GaInP/GaAs heterostructures,” Appl. Phys. Lett. |

18. | D. A. Bender, J. G. Cederberg, C. Wang, and M. Sheik-Bahae, “Development of high quantum efficiency GaAs/GaInP double heterostructures for laser cooling,” Appl. Phys. Lett. |

19. | J. Zhang, D. H. Li, R. J. Chen, and Q. H. Xiong, “Laser cooling of a semiconductor by 40 kelvin,” Nature |

20. | D. H. Li, J. Zhang, and Q. H. Xiong, “Surface Depletion Induced Quantum Confinement in CdS Nanobelts,” ACS Nano |

21. | D. H. Li, J. Zhang, Q. Zhang, and Q. H. Xiong, “Electric-Field-Dependent Photoconductivity in CdS Nanowires and Nanobelts: Exciton Ionization, Franz-Keldysh, and Stark Effects,” Nano Lett. |

22. | B. Imangholi, “Investigation of laser cooling in semiconductors,” (The University of New Mexico, United States - New Mexico., 2006). |

23. | U. Rossler, |

24. | G. W. Hooft and C. van Opdorp, “Determination of bulk minority-carrier lifetime and surface/interface recombination velocity from photoluminescence decay of a semi-infinite semiconductor slab,” J. Appl. Phys. |

25. | P. T. Landsberg and M. J. Adams, “Radiative and Auger processes in semiconductors,” J. Lumin. |

26. | D. Huppert, M. Evenor, and Y. Shapira, “Measurements of surface recombination velocity on CdS surfaces and Au interfaces,” J. Vac. Sci. Technol. A |

27. | X. Xu, Y. Zhao, E. J. Sie, Y. Lu, B. Liu, S. A. Ekahana, X. Ju, Q. Jiang, J. Wang, H. Sun, T. C. Sum, C. H. A. Huan, Y. P. Feng, and Q. H. Xiong, “Dynamics of Bound Exciton Complexes in CdS Nanobelts,” ACS Nano |

28. | X. Liu, R. Wang, Y. Jiang, Q. Zhang, X. Shan, and X. Qiu, “Thermal conductivity measurement of individual CdS nanowires using microphotoluminescence spectroscopy,” J. Appl. Phys. |

**OCIS Codes**

(140.3320) Lasers and laser optics : Laser cooling

(160.6000) Materials : Semiconductor materials

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: June 6, 2013

Revised Manuscript: July 27, 2013

Manuscript Accepted: July 28, 2013

Published: August 7, 2013

**Citation**

Dehui Li, Jun Zhang, and Qihua Xiong, "Laser cooling of CdS nanobelts: Thickness matters," Opt. Express **21**, 19302-19310 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-19302

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### References

- P. Pringsheim, “Zwei Bemerkungen über den Unterschied von Lumineszenz- und Temperaturstrahlung,” Zeitschrift für Physik A Hadrons and Nuclei 57, 739–746 (1929).
- R. I. Epstein and M. Sheik-Bahae, Optical Refrigeration (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2009).
- M. Sheik-Bahae and R. I. Epstein, “Optical Refrigeration,” Nat. Photonics1(12), 693–699 (2007). [CrossRef]
- R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature377(6549), 500–503 (1995). [CrossRef]
- D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics4(3), 161–164 (2010). [CrossRef]
- D. V. Seletskiy, S. D. Melgaard, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of a semiconductor load to 165 K,” Opt. Express18(17), 18061–18066 (2010). [CrossRef] [PubMed]
- D. V. Seletskiy, S. D. Melgaard, R. I. Epstein, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Local laser cooling of Yb:YLF to 110 K,” Opt. Express19(19), 18229–18236 (2011). [CrossRef] [PubMed]
- M. Sheik-Bahae and R. I. Epstein, “Laser cooling of solids,” Laser Photon. Rev.3(1-2), 67–84 (2009). [CrossRef]
- M. Sheik-Bahae and R. I. Epstein, “Can laser light cool semiconductors?” Phys. Rev. Lett.92(24), 247403 (2004). [CrossRef] [PubMed]
- J. B. Khurgin, “Band gap engineering for laser cooling of semiconductors,” J. Appl. Phys.100(11), 113116 (2006). [CrossRef]
- J. B. Khurgin, “Surface plasmon-assisted laser cooling of solids,” Phys. Rev. Lett.98(17), 177401 (2007). [CrossRef]
- J. B. Khurgin, “Role of bandtail states in laser cooling of semiconductors,” Phys. Rev. B77(23), 235206 (2008). [CrossRef]
- G. Rupper, N. H. Kwong, and R. Binder, “Large excitonic enhancement of optical refrigeration in semiconductors,” Phys. Rev. Lett.97(11), 117401 (2006). [CrossRef] [PubMed]
- G. Rupper, N. H. Kwong, and R. Binder, “Optical refrigeration of GaAs: Theoretical study,” Phys. Rev. B76(24), 245203 (2007). [CrossRef]
- E. Finkeißen, M. Potemski, P. Wyder, L. Vina, and G. Weimann, “Cooling of a semiconductor by luminescence up-conversion,” Appl. Phys. Lett.75(9), 1258–1260 (1999). [CrossRef]
- H. Gauck, T. H. Gfroerer, M. J. Renn, E. A. Cornell, and K. A. Bertness, “External radiative quantum efficiency of 96% from a GaAs/GaInP heterostructure,” Appl. Phys., A Mater. Sci. Process.64(2), 143–147 (1997). [CrossRef]
- B. Imangholi, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, and S. Kurtz, “Effects of epitaxial lift-off on interface recombination and laser cooling in GaInP/GaAs heterostructures,” Appl. Phys. Lett.86(8), 081104 (2005). [CrossRef]
- D. A. Bender, J. G. Cederberg, C. Wang, and M. Sheik-Bahae, “Development of high quantum efficiency GaAs/GaInP double heterostructures for laser cooling,” Appl. Phys. Lett.102(25), 252102 (2013). [CrossRef]
- J. Zhang, D. H. Li, R. J. Chen, and Q. H. Xiong, “Laser cooling of a semiconductor by 40 kelvin,” Nature493(7433), 504–508 (2013). [CrossRef] [PubMed]
- D. H. Li, J. Zhang, and Q. H. Xiong, “Surface Depletion Induced Quantum Confinement in CdS Nanobelts,” ACS Nano6(6), 5283–5290 (2012). [CrossRef] [PubMed]
- D. H. Li, J. Zhang, Q. Zhang, and Q. H. Xiong, “Electric-Field-Dependent Photoconductivity in CdS Nanowires and Nanobelts: Exciton Ionization, Franz-Keldysh, and Stark Effects,” Nano Lett.12(6), 2993–2999 (2012). [CrossRef] [PubMed]
- B. Imangholi, “Investigation of laser cooling in semiconductors,” (The University of New Mexico, United States - New Mexico., 2006).
- U. Rossler, Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology, Group III: Condensed Matter. Semiconductors: II–VI and I–VII compounds, Vol. 41B (Springer: Berlin Heidelberg, 1999).
- G. W. Hooft and C. van Opdorp, “Determination of bulk minority-carrier lifetime and surface/interface recombination velocity from photoluminescence decay of a semi-infinite semiconductor slab,” J. Appl. Phys.60(3), 1065–1070 (1986). [CrossRef]
- P. T. Landsberg and M. J. Adams, “Radiative and Auger processes in semiconductors,” J. Lumin.7, 3–34 (1973). [CrossRef]
- D. Huppert, M. Evenor, and Y. Shapira, “Measurements of surface recombination velocity on CdS surfaces and Au interfaces,” J. Vac. Sci. Technol. A2(2), 532–533 (1984). [CrossRef]
- X. Xu, Y. Zhao, E. J. Sie, Y. Lu, B. Liu, S. A. Ekahana, X. Ju, Q. Jiang, J. Wang, H. Sun, T. C. Sum, C. H. A. Huan, Y. P. Feng, and Q. H. Xiong, “Dynamics of Bound Exciton Complexes in CdS Nanobelts,” ACS Nano5(5), 3660–3669 (2011). [CrossRef] [PubMed]
- X. Liu, R. Wang, Y. Jiang, Q. Zhang, X. Shan, and X. Qiu, “Thermal conductivity measurement of individual CdS nanowires using microphotoluminescence spectroscopy,” J. Appl. Phys.108(5), 054310 (2010). [CrossRef]

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