## Laser cooling of a semiconductor load to 165 K |

Optics Express, Vol. 18, Issue 17, pp. 18061-18066 (2010)

http://dx.doi.org/10.1364/OE.18.018061

Acrobat PDF (8511 KB)

### Abstract

Abstract: We demonstrate cooling of a 2 micron thick GaAs/InGaP double-heterostructure to 165 K from ambient using an all-solid-state optical refrigerator. Cooler is comprised of Yb^{3+}-doped YLF crystal, utilizing 3.5 Watts of absorbed power near the E4-E5 Stark manifold transition.

© 2010 OSA

## 1. Introduction

1. P. Pringsheim, “Zwei bemerkungen uËber den unterschied von lumineszenz- und Temperaturstrahlung,” Z. Phys. **57**(11-12), 739–746 (1929). [CrossRef]

*λ*) of the transition, the subsequent fluorescence upconversion requires phonon absorption in order to establish quasi equilibrium. The efficient escape of the fluorescence then carries heat and entropy away from the material resulting in net cooling [2

_{f}2. M. Sheik-Bahae and R. I. Epstein, “Optical Refrigeration: Advancing toward an all-solid-state cryocooler,” Nat. Photonics **1**(12), 693–699 (2007). [CrossRef]

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

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

5. A. N. Oraevsky, “Cooling of semiconductors by laser radiation,” J. Russ. Laser Res. **17**(5), 471–479 (1996). [CrossRef]

9. J. B. Khurgin, “Band gap engineering for laser cooling of semiconductors,” J. Appl. Phys. **100**(11), 113116 (2006). [CrossRef]

10. 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]

13. C. Wang, M. P. Hasselbeck, C.-Y. Li, and M. Sheik-Bahae, “Characterization of external quantum efficiency and absorption efficiency in GaAs/ InGaP double heterostructures for laser cooling applications,” Proc. SPIE **7614**, 76140B (2010). [CrossRef]

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

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

_{c}) to the absorbed laser power, has been given as [2

2. M. Sheik-Bahae and R. I. Epstein, “Optical Refrigeration: Advancing toward an all-solid-state cryocooler,” Nat. Photonics **1**(12), 693–699 (2007). [CrossRef]

*η*is the external quantum efficiency (EQE) defined as the fraction of excited ions that lead to a fluorescence photon exiting the host material. The absorption coefficients

_{ext}*α(λ,T)*and

*α*are associated with the cooling transition of the active ion (e.g. Yb

_{b}^{3+}), and the background parasitic absorption. Rare-earth ions in low phonon energy hosts (such as fluorides) have provided high

*η*(> 99%), making them ideal candidates for laser cooling. However, what ultimately limits the minimum achievable temperature is that only a fraction of absorbed photons lead to an excitation of cooling transition. This quantity, also known as the absorption efficiency

_{ext}*η*, is indicated by the bracketed term in Eq. (1), which depends on the ratio

_{abs}*α*As the temperature is lowered, the cooling efficiency decreases due to primarily two factors: decreasing of the resonant absorption and red-shifting of

_{b}/α(λ,T).*λ*as a consequence of Boltzmann distribution of excitations in the ground- and excited states respectively. The background absorption originates from unwanted contamination such as transition metals, and is taken to be temperature independent and broadband within the spectral region of cooling transition [15

_{f}(T),15. M. P. Hehlen, R. I. Epstein, and H. Inoue, “Model of laser cooling in the Yb^{3+}-doped fluorozirconate glass ZBLAN,” Phys. Rev. B **75**(14), 144302 (2007). [CrossRef]

^{2}F

_{7/2}–

^{2}F

_{5/2}transition in Yb

^{3+}-doped YLF crystalline host (5% doped, excitation is polarized along the c-axis). As is evident from the figure, cooling efficiency is enhanced at 1020 nm, corresponding to E4-E5 Stark manifold transition. In a recent set of experiments, by exciting Yb:YLF sample near the E4-E5 transition (1023 nm) with 9 Watts of incident power we demonstrated cooling to 155K [14

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

16. N. Coluccelli, G. Galzerano, L. Bonelli, A. Di Lieto, M. Tonelli, and P. Laporta, “Diode-pumped passively mode-locked Yb:YLF laser,” Opt. Express **16**(5), 2922–2927 (2008). [CrossRef] [PubMed]

## 2. Experiment and results

17. D. V. Seletskiy, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, S. Bigotta, and M. Tonelli, “Cooling of Yb:YLF using cavity enhanced resonant absorption,” Proc. SPIE **6907**, 69070B (2008). [CrossRef]

18. D. V. Seletskiy, M. P. Hasselbeck, and M. Sheik-Bahae, “Cavity-enhanced absorption for optical refrigeration,” Appl. Phys. Lett. **96**(18), 181106 (2010). [CrossRef]

19. B. C. Edwards, J. E. Anderson, R. I. Epstein, G. L. Mills, and A. J. Mord, “Demonstration of a Solid-State Optical Cooler: An Approach to Cryogenic Refrigeration,” J. Appl. Phys. **86**(11), 6489–6493 (1999). [CrossRef]

20. J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling to 208 K by optical refrigeration,” Appl. Phys. Lett. **86**(15), 154107 (2005). [CrossRef]

21. B. Imangholi, M. P. Hasselbeck, D. A. Bender, C. Wang, M. Sheik-Bahae, R. I. Epstein, and S. Kurtz, “Differential luminescence thermometry in semiconductor laser cooling,” Proc. SPIE **6115**, 61151C (2006). [CrossRef]

**4**(3), 161–164 (2010). [CrossRef]

22. Y. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica **34**(1), 149–154 (1967). [CrossRef]

23. G. L. Mills and A. J. Mord, “Performance modeling of optical refrigerators,” Cryogenics **46**(2-3), 176–182 (2006). [CrossRef]

**4**(3), 161–164 (2010). [CrossRef]

## 3. Analysis of the Temperature Dynamics

^{−4}torr) conditions, the dominant thermal load on the sample is assumed to be radiative or black-body (BB), and from the 6 fiber supports that hold the sample in place within the chamber. Due to high thermal conductivity of the YLF crystal, the sample reaches a uniform temperature within a second or so. We, therefore, ignore the initial dynamics and consider temperature evolution of the whole sample at larger time scales determined by the aforementioned thermal loads as given by:Here

*C(T) = ρc*is the heat capacity of the cooling sample (YLF) in terms of its density (

_{v}(T)V_{s}*ρ*), temperature-dependent specific heat from Debye theory (

*c*), and sample volume

_{v}(T)*V*The first term in the right hand side of Eq. (2) is the driving term which is the total cooling power in terms of cooling efficiency (

_{s}.*η*

_{c}_{,}Eq. (1)) and the absorbed laser power (

*P*), both varying with wavelength and temperature. The second term is the black-body radiation load with

_{abs}*σ*denoting Stefan-Boltzmann constant ( = 5.67 × 10

^{−8}W/m

^{2}/K

^{4}). In our case, this radiative load is lowered by using the low thermal emissivity coating on the chamber walls by a factor of 1 + χ where χ = (1-ε

_{c})ε

_{s}A

_{s}/ε

_{c}A

_{c}, with ε

_{j}and A

_{j}(j = s,c) denoting the thermal emissivity and the surface areas of the sample and chamber respectively [24

24. C. W. Hoyt, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, S. Greenfield, J. Thiede, J. Distel, and J. Valencia, “Advances in laser cooling of thulium-doped glass,” J. Opt. Soc. Am. B **20**(5), 1066–1074 (2003). [CrossRef]

*N*fiber support links each having area

*A*, length

_{L}*d*, and thermal conductivity

_{L}*κ*. Once the Debye temperature of the Yb:YLF is fixed [25

_{L}25. R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y_{3}Al_{5}O_{12}, Lu_{3}Al_{5}O_{12}, YAIO_{3}, LiYF_{4}, LiLuF_{4}, BaY_{2}F_{8}, KGd(WO_{4})_{2}, and KY(WO_{4})_{2} laser crystals in the 80–300 K temperature range,” J. Appl. Phys. **98**, 103514 (2005). [CrossRef]

_{L}= Cd

_{L}/(Nκ

_{L}A

_{L}) and factor χ. Due to non-trivial temperature dependent coefficients, we fit Eq. (2) numerically to obtain cooling (with the driving term) and warm-up (no driving term) dynamics. By fitting the temperature evolution in the warm-up regime, parasitic loads can be estimated without having to include the cooling power dynamics itself. This fit yields τ

_{L}~800 min and χ = 2.1, for A

_{s}~1.5 cm

^{2}, ε

_{s}~0.8,

*ρc*(YLF)~3 J/K/cm

_{v}^{3}(at 300 K) and V

_{s}= 0.3x0.3x1~0.1 cm

^{3}. The fact that τ

_{L}is much longer than the time scale of the experiment suggests the black-body is the dominant load on the sample (Fig. 3(a) ), consistent with the earlier findings [14

**4**(3), 161–164 (2010). [CrossRef]

20. J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling to 208 K by optical refrigeration,” Appl. Phys. Lett. **86**(15), 154107 (2005). [CrossRef]

**4**(3), 161–164 (2010). [CrossRef]

_{cool}= 140 mW, in good agreement with the fitting results. At low temperature however we obtain agreement with the temperature dynamics only if we increase the background absorption by factor of 4 (Eq. (1)). We attribute such increase due to the parasitic absorption in the material of the load as well as the adhesive used for attachment. Finally, we note that GaAs absorption spectrally overlaps with the upconverted emission due to other rare-earth species in the Yb:YLF crystal which can also be responsible for the deduced increase in the background absorption.

## 4. Summary

## Acknowledgements

## References and links

1. | P. Pringsheim, “Zwei bemerkungen uËber den unterschied von lumineszenz- und Temperaturstrahlung,” Z. Phys. |

2. | M. Sheik-Bahae and R. I. Epstein, “Optical Refrigeration: Advancing toward an all-solid-state cryocooler,” Nat. Photonics |

3. | M. Sheik-Bahae and R. I. Epstein, “Laser Cooling of Solids,” Laser Photonics Rev. |

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

5. | A. N. Oraevsky, “Cooling of semiconductors by laser radiation,” J. Russ. Laser Res. |

6. | L. A. Rivlin and A. A. Zadernovsky, “Laser cooling of semiconductors,” Opt. Commun. |

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

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

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

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

11. | 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. |

12. | M. Sheik-Bahae, B. Imangholi, M. P. Hasselbeck, R. I. Epstein, and S. Kurtz, “Advances in Laser Cooling of Semiconductors,” Proc. SPIE |

13. | C. Wang, M. P. Hasselbeck, C.-Y. Li, and M. Sheik-Bahae, “Characterization of external quantum efficiency and absorption efficiency in GaAs/ InGaP double heterostructures for laser cooling applications,” Proc. SPIE |

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

15. | M. P. Hehlen, R. I. Epstein, and H. Inoue, “Model of laser cooling in the Yb |

16. | N. Coluccelli, G. Galzerano, L. Bonelli, A. Di Lieto, M. Tonelli, and P. Laporta, “Diode-pumped passively mode-locked Yb:YLF laser,” Opt. Express |

17. | D. V. Seletskiy, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, S. Bigotta, and M. Tonelli, “Cooling of Yb:YLF using cavity enhanced resonant absorption,” Proc. SPIE |

18. | D. V. Seletskiy, M. P. Hasselbeck, and M. Sheik-Bahae, “Cavity-enhanced absorption for optical refrigeration,” Appl. Phys. Lett. |

19. | B. C. Edwards, J. E. Anderson, R. I. Epstein, G. L. Mills, and A. J. Mord, “Demonstration of a Solid-State Optical Cooler: An Approach to Cryogenic Refrigeration,” J. Appl. Phys. |

20. | J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling to 208 K by optical refrigeration,” Appl. Phys. Lett. |

21. | B. Imangholi, M. P. Hasselbeck, D. A. Bender, C. Wang, M. Sheik-Bahae, R. I. Epstein, and S. Kurtz, “Differential luminescence thermometry in semiconductor laser cooling,” Proc. SPIE |

22. | Y. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica |

23. | G. L. Mills and A. J. Mord, “Performance modeling of optical refrigerators,” Cryogenics |

24. | C. W. Hoyt, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, S. Greenfield, J. Thiede, J. Distel, and J. Valencia, “Advances in laser cooling of thulium-doped glass,” J. Opt. Soc. Am. B |

25. | R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y |

**OCIS Codes**

(140.3320) Lasers and laser optics : Laser cooling

(160.5690) Materials : Rare-earth-doped materials

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: June 28, 2010

Revised Manuscript: August 2, 2010

Manuscript Accepted: August 2, 2010

Published: August 6, 2010

**Citation**

Denis V. Seletskiy, Seth D. Melgaard, Alberto Di Lieto, Mauro Tonelli, and Mansoor Sheik-Bahae, "Laser cooling of a semiconductor load to 165 K," Opt. Express **18**, 18061-18066 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-18061

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### References

- P. Pringsheim, “Zwei bemerkungen uËber den unterschied von lumineszenz- und Temperaturstrahlung,” Z. Phys. 57(11-12), 739–746 (1929). [CrossRef]
- M. Sheik-Bahae and R. I. Epstein, “Optical Refrigeration: Advancing toward an all-solid-state cryocooler,” Nat. Photonics 1(12), 693–699 (2007). [CrossRef]
- M. Sheik-Bahae and R. I. Epstein, “Laser Cooling of Solids,” Laser Photonics Rev. 3(1-2), 67–84 (2009). [CrossRef]
- R. I. Epstein, M. Buchwald, B. Edwards, T. Gosnell, and C. Mungan, “Observation of laser induced fluorescent cooling of a solid,” Nature 377(6549), 500–503 (1995). [CrossRef]
- A. N. Oraevsky, “Cooling of semiconductors by laser radiation,” J. Russ. Laser Res. 17(5), 471–479 (1996). [CrossRef]
- L. A. Rivlin and A. A. Zadernovsky, “Laser cooling of semiconductors,” Opt. Commun. 139(4-6), 219–222 (1997). [CrossRef]
- M. Sheik-Bahae and R. I. Epstein, “Can laser light cool semiconductors?” Phys. Rev. Lett. 92(24), 247403 (2004). [CrossRef] [PubMed]
- 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]
- J. B. Khurgin, “Band gap engineering for laser cooling of semiconductors,” J. Appl. Phys. 100(11), 113116 (2006). [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]
- M. Sheik-Bahae, B. Imangholi, M. P. Hasselbeck, R. I. Epstein, and S. Kurtz, “Advances in Laser Cooling of Semiconductors,” Proc. SPIE 6115, 611518 (2006). [CrossRef]
- C. Wang, M. P. Hasselbeck, C.-Y. Li, and M. Sheik-Bahae, “Characterization of external quantum efficiency and absorption efficiency in GaAs/ InGaP double heterostructures for laser cooling applications,” Proc. SPIE 7614, 76140B (2010). [CrossRef]
- D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4(3), 161–164 (2010). [CrossRef]
- M. P. Hehlen, R. I. Epstein, and H. Inoue, “Model of laser cooling in the Yb3+-doped fluorozirconate glass ZBLAN,” Phys. Rev. B 75(14), 144302 (2007). [CrossRef]
- N. Coluccelli, G. Galzerano, L. Bonelli, A. Di Lieto, M. Tonelli, and P. Laporta, “Diode-pumped passively mode-locked Yb:YLF laser,” Opt. Express 16(5), 2922–2927 (2008). [CrossRef] [PubMed]
- D. V. Seletskiy, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, S. Bigotta, and M. Tonelli, “Cooling of Yb:YLF using cavity enhanced resonant absorption,” Proc. SPIE 6907, 69070B (2008). [CrossRef]
- D. V. Seletskiy, M. P. Hasselbeck, and M. Sheik-Bahae, “Cavity-enhanced absorption for optical refrigeration,” Appl. Phys. Lett. 96(18), 181106 (2010). [CrossRef]
- B. C. Edwards, J. E. Anderson, R. I. Epstein, G. L. Mills, and A. J. Mord, “Demonstration of a Solid-State Optical Cooler: An Approach to Cryogenic Refrigeration,” J. Appl. Phys. 86(11), 6489–6493 (1999). [CrossRef]
- J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling to 208 K by optical refrigeration,” Appl. Phys. Lett. 86(15), 154107 (2005). [CrossRef]
- B. Imangholi, M. P. Hasselbeck, D. A. Bender, C. Wang, M. Sheik-Bahae, R. I. Epstein, and S. Kurtz, “Differential luminescence thermometry in semiconductor laser cooling,” Proc. SPIE 6115, 61151C (2006). [CrossRef]
- Y. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica 34(1), 149–154 (1967). [CrossRef]
- G. L. Mills and A. J. Mord, “Performance modeling of optical refrigerators,” Cryogenics 46(2-3), 176–182 (2006). [CrossRef]
- C. W. Hoyt, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, S. Greenfield, J. Thiede, J. Distel, and J. Valencia, “Advances in laser cooling of thulium-doped glass,” J. Opt. Soc. Am. B 20(5), 1066–1074 (2003). [CrossRef]
- R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAIO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80–300 K temperature range,” J. Appl. Phys. 98, 103514 (2005). [CrossRef]

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