## Non-exponential photoluminescence decay dynamics of localized carriers in disordered InGaN/GaN quantum wells: the role of localization length

Optics Express, Vol. 14, Issue 26, pp. 13151-13157 (2006)

http://dx.doi.org/10.1364/OE.14.013151

Acrobat PDF (660 KB)

### Abstract

In this article, we report a combined experimental and theoretical study on the luminescence dynamics of localized carriers in disordered InGaN/GaN quantum wells. The luminescence intensity of localized carriers is found to exhibit an unusual non-exponential decay. Adopting a new model taking the radiative recombination and phonon-assisted hopping transition between different localized states into account, which was recently developed by Rubel *et al.*, the non-exponential decay behavior of the carriers can be quantitatively interpreted. Combining with precise structure characterization, the theoretical simulations show that the localization length of localized carriers is a key parameter governing their luminescence decay dynamics.

© 2006 Optical Society of America

## 1. Introduction

2. H. Morkoc, *Nitride Semiconductors and Devices*, Springer Series in Materials Science, Vol. 32, (Springer, Berlin, 1999). [CrossRef]

3. N. M. Johnson, A. V. Nurmikko, and S. P. DenBaars, “Blue diode lasers,” Phys. Today **53**, 31–36 (2000). [CrossRef]

4. S. J. Xu, G. Q. Li, Y. J. Wang, Y. Zhao, G. H. Chen, D. G. Zhao, H. Yang, D. P. Yu, and J. N. Wang, “Quantum dissipation and broadening mechanisms due to electron-phonon interactions in self-formed InGaN quantum dots,” Appl. Phys. Lett. **88**, 083123 (2006). [CrossRef]

5. S. Kalliakos, X. B. Zhang, T. Taliercio, P. Lefebvre, B. Gil, N. Grandjean, B. Damilano, and J. Massies, “Large size dependence of exciton-longitudinal-optical-phonon coupling in nitride-based quantum wells and quantum boxes,” Appl. Phys. Lett. **80**, 428–430 (2002). [CrossRef]

6. A. Morel, P. Lefebvre, S. Kalliakos, T. Taliercio, T. Bretagnon, and B. Gil, “Donor-acceptor-like behavior of electron-hole pair recombinations in low-dimensional (Ga,In)N/GaN systems,” Phys. Rev. B **68**, 045331 (2003). [CrossRef]

7. H. Haratizadeh, B. Monemar, P. P. Paskov, P. O. Holtz, G. Pozina, S. Kamiyama, M. Iwaya, H. Amano, and I. Akasaki, “Time resolved photoluminescence study of Si modulation doped GaN/Al_{0.07}Ga_{0.93}N multiple quantum wells,” Phys. Stat. sol. (b) **241**, 1124–1133 (2004). [CrossRef]

8. D. Alderichi, A. Vinattieri, F. Bogani, M. Colocci, S. Gottardo, N. Grandjean, and J. Massies, “Phonon replica dynamics in high quality GaN epilayers and AlGaN/GaN quantum wells,” Phys. Stat. sol. (a) **183**, 129–134 (2001). [CrossRef]

9. S. J. Xu, M. B. Yu, Rusli, S. F. Yoon, and C. M. Che, “Time-resolved photoluminescence spectra of strong visible light-emitting SiC nanocrystalline films on Si deposited by electron-cyclotron-resonance chemical-vapor deposition,” Appl. Phys. Lett. **76**, 2550–2552 (2000). [CrossRef]

*et al.*[12

12. O. Rubel, S. D. Baranovskii, K. Hantke, J. D. Heber, J. Koch, P. Thomas, J. M. Marshall, W. Stolz, and W. W. Rühle, “Quantitative description of disorder parameters in (GaIn)(NAs) quantum wells from the temperature-dependent photoluminescence spectroscopy,” J. Optoelectronics and Adv. Materials **7**, 115–120 (2005).

## 2. Experiment and result

^{18}cm

^{-3}. Structure characterization of the samples was performed using cross-sectional transmission electron microscopy (TEM) while the optical measurements of the samples were carried out with time-resolved photoluminescence (TRPL) technique. The details of structure characterization and optical measurements have been previously described elsewhere [4

4. S. J. Xu, G. Q. Li, Y. J. Wang, Y. Zhao, G. H. Chen, D. G. Zhao, H. Yang, D. P. Yu, and J. N. Wang, “Quantum dissipation and broadening mechanisms due to electron-phonon interactions in self-formed InGaN quantum dots,” Appl. Phys. Lett. **88**, 083123 (2006). [CrossRef]

13. Y. J. Wang, S. J. Xu, Q. Li, D. G. Zhao, and H. Yang, “Band gap renormalization and carrier localization effects in InGaN/GaN quantum-wells light emitting diodes with Si doped barriers,” Appl. Phys. Lett. **88**, 041903 (2006). [CrossRef]

12. O. Rubel, S. D. Baranovskii, K. Hantke, J. D. Heber, J. Koch, P. Thomas, J. M. Marshall, W. Stolz, and W. W. Rühle, “Quantitative description of disorder parameters in (GaIn)(NAs) quantum wells from the temperature-dependent photoluminescence spectroscopy,” J. Optoelectronics and Adv. Materials **7**, 115–120 (2005).

## 3. Theoretical interpretation and discussion

_{r}denotes the recombination rate for a localized electron to recombination with a localized hole and Γ

_{j→k}(Γ

_{k→j}) is the rate for a charge carrier to perform a non-radiative hopping transition from an occupied state

*j*(

*k*) to an empty localized state

*k*(

*j*) over a distance

*r*

_{jk}. In general, the rate for hopping transition depends exponentially on the distance involved [12

12. O. Rubel, S. D. Baranovskii, K. Hantke, J. D. Heber, J. Koch, P. Thomas, J. M. Marshall, W. Stolz, and W. W. Rühle, “Quantitative description of disorder parameters in (GaIn)(NAs) quantum wells from the temperature-dependent photoluminescence spectroscopy,” J. Optoelectronics and Adv. Materials **7**, 115–120 (2005).

*ε*

_{j}and

*ε*

_{k}are the energies of states

*j*and

*k*, respectively,

*α*is the localization length and

*ν*

_{0}is the attempt to escape frequency. For the transition from the slice k downward in energy,

*ε*

_{k}>

*ε*

_{j}, only the tunneling term remains and the downwards transition rate can be considered as [12

**7**, 115–120 (2005).

*R*

_{k}is the typical hopping distance, determined by the concentration of unoccupied states with energy below

*ε*

_{k}[12

**7**, 115–120 (2005).

*d*

_{j}is the concentration of localized states in the energy slice. On the other hand, the upward transition from slice

*j*to

*k*can be derived from the downward transition rate [12

**7**, 115–120 (2005).

*R*between them [12

**7**, 115–120 (2005).

*τ*

_{0}is a time constant which depends on the particular recombination mechanism and is of the order of excitonic radiative lifetime. The most efficient recombination is the pairs of localized states in which the state for electrons is as close to the state for holes as the localization length. Correspondingly, the recombination time does not contain the exponential factor and is close to

*τ*

_{0}. The concentration of such pairs is the product of the density of filled electron states n and the probability

*α*

^{2}. The recombination rate [12

**7**, 115–120 (2005).

_{r}(

*R*)=

*n*(

*t*)

*α*

^{2}. The time-resolved luminescence spectrum is calculated as a convolution of carrier densities obtained by solving above equations.

*α*is a key parameter characterizing the disorder degree. It can be viewed as the average spreading length of the wave functions of the localized carriers in the localized states. Such a length essentially determines the dynamic behaviors of localized carriers. Using the model briefly described above, the localization length can be obtained by fitting to the experimental decay curve of the emission intensity. The solid curves in Fig. 4 are the fitting results when the values of parameters

*τ*

_{0}=1 ns,

*ν*

_{0}=10

^{10}s

^{-1},

*kT*=6.64 meV,

*ε*

_{0}=8 meV were adopted. Note that the obtained localization length is 4.3 nm for sample A and 2.6 nm for sample B. The symbols represent the experimental decay curves of the emission intensities of sample A and B in the figure. The initial concentration of electron-hole pairs just after the excitation pulse is 4×10

^{12}cm

^{-2}. Clearly, sample B (Si doped) has a shorter localization length, which indicates that the Si doping in the barrier layers of InGaN/GaN QWs can lead to further localization of carriers and can reduce the hopping rate of carriers between different localized states. In fact, the localization length is determined by the density of localized states. The lower the density of localized states, the farther distance the wave function can decay, hence the longer the localization length. This result is supported by the TEM observation (as shown in Fig. 1) which shows that sample B has the higher density of In-clusters than sample A. According to Eq. (6), the recombination time is exponentially dependent on the inverse of the localization length. The longer lifetime for the Si-doped sample, as observed in Fig. 4, is consistent with the theoretical prediction. The decay curve will tend to exhibit an exponential variation if the lifetime is long enough.

## 4. Conclusions

## Acknowledgments

## References and links

1. | S. Nakamura, S. Pearton, and G. Fasol, |

2. | H. Morkoc, |

3. | N. M. Johnson, A. V. Nurmikko, and S. P. DenBaars, “Blue diode lasers,” Phys. Today |

4. | S. J. Xu, G. Q. Li, Y. J. Wang, Y. Zhao, G. H. Chen, D. G. Zhao, H. Yang, D. P. Yu, and J. N. Wang, “Quantum dissipation and broadening mechanisms due to electron-phonon interactions in self-formed InGaN quantum dots,” Appl. Phys. Lett. |

5. | S. Kalliakos, X. B. Zhang, T. Taliercio, P. Lefebvre, B. Gil, N. Grandjean, B. Damilano, and J. Massies, “Large size dependence of exciton-longitudinal-optical-phonon coupling in nitride-based quantum wells and quantum boxes,” Appl. Phys. Lett. |

6. | A. Morel, P. Lefebvre, S. Kalliakos, T. Taliercio, T. Bretagnon, and B. Gil, “Donor-acceptor-like behavior of electron-hole pair recombinations in low-dimensional (Ga,In)N/GaN systems,” Phys. Rev. B |

7. | H. Haratizadeh, B. Monemar, P. P. Paskov, P. O. Holtz, G. Pozina, S. Kamiyama, M. Iwaya, H. Amano, and I. Akasaki, “Time resolved photoluminescence study of Si modulation doped GaN/Al |

8. | D. Alderichi, A. Vinattieri, F. Bogani, M. Colocci, S. Gottardo, N. Grandjean, and J. Massies, “Phonon replica dynamics in high quality GaN epilayers and AlGaN/GaN quantum wells,” Phys. Stat. sol. (a) |

9. | S. J. Xu, M. B. Yu, Rusli, S. F. Yoon, and C. M. Che, “Time-resolved photoluminescence spectra of strong visible light-emitting SiC nanocrystalline films on Si deposited by electron-cyclotron-resonance chemical-vapor deposition,” Appl. Phys. Lett. |

10. | D. G. Thomas, J. J. Hopfield, and W. M. Augustyniak, “Kinetics of Radiative Recombination at Randomly Distributed Donors and Acceptors,” Rhys. Rev. |

11. | P. Y. Yu and M. Cardona, |

12. | O. Rubel, S. D. Baranovskii, K. Hantke, J. D. Heber, J. Koch, P. Thomas, J. M. Marshall, W. Stolz, and W. W. Rühle, “Quantitative description of disorder parameters in (GaIn)(NAs) quantum wells from the temperature-dependent photoluminescence spectroscopy,” J. Optoelectronics and Adv. Materials |

13. | Y. J. Wang, S. J. Xu, Q. Li, D. G. Zhao, and H. Yang, “Band gap renormalization and carrier localization effects in InGaN/GaN quantum-wells light emitting diodes with Si doped barriers,” Appl. Phys. Lett. |

14. | J. M. Marshall, “Analytical procedures for the modeling of hopping transport in disordered semiconductor,” Philos. Mag. Lett. |

**OCIS Codes**

(160.6000) Materials : Semiconductor materials

(300.6500) Spectroscopy : Spectroscopy, time-resolved

(320.7130) Ultrafast optics : Ultrafast processes in condensed matter, including semiconductors

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: September 11, 2006

Revised Manuscript: November 5, 2006

Manuscript Accepted: November 9, 2006

Published: December 22, 2006

**Citation**

Y. J. Wang, S. J. Xu, D. G. Zhao, J. J Zhu, H. Yang, X. D. Shan, and D. P. Yu, "Non-exponential photoluminescence decay
dynamics of localized carriers in disordered
InGaN/GaN quantum wells: the role of
localization length," Opt. Express **14**, 13151-13157 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-26-13151

Sort: Year | Journal | Reset

### References

- S. Nakamura, S. Pearton, and G. Fasol, The Blue Laser Diode (Springer, Berlin, 2000).
- H. Morkoc, Nitride Semiconductors and Devices, Springer Series in Materials Science, Vol. 32, (Springer, Berlin, 1999). [CrossRef]
- N. M. Johnson, A. V. Nurmikko, and S. P. DenBaars, "Blue diode lasers," Phys. Today 53, 31-36 (2000). [CrossRef]
- S. J. Xu, G. Q. Li, Y. J. Wang, Y. Zhao, G. H. Chen, D. G. Zhao, H. Yang, D. P. Yu, and J. N. Wang, "Quantum dissipation and broadening mechanisms due to electron-phonon interactions in self-formed InGaN quantum dots," Appl. Phys. Lett. 88, 083123 (2006). [CrossRef]
- S. Kalliakos, X. B. Zhang, T. Taliercio, P. Lefebvre, B. Gil, N. Grandjean, B. Damilano, and J. Massies, "Large size dependence of exciton-longitudinal-optical-phonon coupling in nitride-based quantum wells and quantum boxes," Appl. Phys. Lett. 80, 428-430 (2002). [CrossRef]
- A. Morel, P. Lefebvre, S. Kalliakos, T. Taliercio, T. Bretagnon, and B. Gil, "Donor-acceptor-like behavior of electron-hole pair recombinations in low-dimensional (Ga,In)N/GaN systems," Phys. Rev. B 68, 045331 (2003). [CrossRef]
- H. Haratizadeh, B. Monemar, P. P. Paskov, P. O. Holtz, G. Pozina, S. Kamiyama, M. Iwaya, H. Amano, and I. Akasaki, "Time resolved photoluminescence study of Si modulation doped GaN/Al0.07Ga0.93N multiple quantum wells," Phys. Stat. sol.(b) 241, 1124-1133 (2004). [CrossRef]
- D. Alderichi, A. Vinattieri, F. Bogani, M. Colocci, S. Gottardo, N. Grandjean, and J. Massies, "Phonon replica dynamics in high quality GaN epilayers and AlGaN/GaN quantum wells," Phys. Stat. sol.(a) 183, 129-134 (2001). [CrossRef]
- S. J. Xu, M. B. Yu, Rusli, S. F. Yoon, and C. M. Che, "Time-resolved photoluminescence spectra of strong visible light-emitting SiC nanocrystalline films on Si deposited by electron-cyclotron-resonance chemical-vapor deposition," Appl. Phys. Lett. 76, 2550-2552 (2000). [CrossRef]
- D. G. Thomas, J. J. Hopfield, and W. M. Augustyniak, "Kinetics of Radiative Recombination at Randomly Distributed Donors and Acceptors," Rhys. Rev. 140, A202-A220 (1965).
- P. Y. Yu and M. Cardona, Fundamentals of Semiconductors-Physics and Materials Properties, 3rd Ed., (Springer-Verlag, 2001), pp. 356.
- O. Rubel, S. D. Baranovskii, K. Hantke, J. D. Heber, J. Koch, P. Thomas, J. M. Marshall, W. Stolz and W. W. Rühle, "Quantitative description of disorder parameters in (GaIn)(NAs) quantum wells from the temperature-dependent photoluminescence spectroscopy," J. Optoelectronics and Adv. Materials 7, 115-120 (2005).
- Y. J. Wang, S. J. Xu, Q. Li, D. G. Zhao, and H. Yang, "Band gap renormalization and carrier localization effects in InGaN/GaN quantum-wells light emitting diodes with Si doped barriers, " Appl. Phys. Lett. 88, 041903 (2006). [CrossRef]
- J. M. Marshall, "Analytical procedures for the modeling of hopping transport in disordered semiconductor," Philos. Mag. Lett. 80, 691-701 (2000). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.