## A transmission-grating-modulated pump-probe absorption spectroscopy and demonstration of diffusion dynamics of photoexcited carriers in bulk intrinsic GaAs film |

Optics Express, Vol. 20, Issue 4, pp. 3580-3585 (2012)

http://dx.doi.org/10.1364/OE.20.003580

Acrobat PDF (1242 KB)

### Abstract

A transmission-grating-modulated time-resolved pump-probe absorption spectroscopy is developed and formularized. The spectroscopy combines normal time-resolved pump-probe absorption spectroscopy with a binary transmission grating, is sensitive to the spatiotemporal evolution of photoinjected carriers, and has extensive applicability in the study of diffusion transport dynamics of photoinjected carriers. This spectroscopy has many advantages over reported optical methods to measure diffusion dynamics, such as simple experimental setup and operation, and high detection sensitivity. The measurement of diffusion dynamics is demonstrated on bulk intrinsic GaAs films. A carrier density dependence of carrier diffusion coefficient is obtained and agrees well with reported results.

© 2012 OSA

## 1. Introduction

1. S. Nargelas, K. Jarašiūnas, K. Bertulis, and V. Pačebutas, “Hole diffusivity in GaAsBi alloys measured by a picosecond transient grating technique,” Appl. Phys. Lett. **98**(8), 082115 (2011). [CrossRef]

2. R. Aleksiejūnas, M. Sūdžius, T. Malinauskas, J. Vaitkus, K. Jarašiūnas, and S. Sakai, “Determination of free carrier bipolar diffusion coefficient and surface recombination velocity of undoped GaN epilayers,” Appl. Phys. Lett. **83**(6), 1157–1159 (2003). [CrossRef]

3. H. W. Yoon, D. R. Wake, J. P. Wolfe, and H. Morkoç, “In-plane transport of photoexcited carriers in GaAs quantum wells,” Phys. Rev. B Condens. Matter **46**(20), 13461–13470 (1992). [CrossRef] [PubMed]

4. B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. **97**(26), 262119 (2010). [CrossRef]

5. F. P. Logue, D. T. Fewer, S. J. Hewlett, J. F. Heffernan, C. Jordan, P. Rees, J. F. Donegan, E. M. McCabe, J. Hegarty, S. Taniguchi, T. Hino, K. Nakano, and A. Ishibashi, “Optical measurement of the ambipolar diffusion length in a ZnCdSe-ZnSe single quantum well,” J. Appl. Phys. **81**(1), 536–538 (1997). [CrossRef]

6. L. Baird, C. P. Ong, R. A. Cole, N. M. Haegel, A. A. Talin, Q. M. Li, and G. T. Wang, “Transport imaging for contact-free measurements of minority carrier diffusion in GaN, GaN/AlGaN, and GaN/InGaN core-shell nanowires,” Appl. Phys. Lett. **98**(13), 132104 (2011). [CrossRef]

7. N. Gedik and J. Orenstein, “Absolute phase measurement in heterodyne detection of transient gratings,” Opt. Lett. **29**(18), 2109–2111 (2004). [CrossRef] [PubMed]

8. A. Miller, R. J. Manning, P. K. Milsom, D. C. Hutchings, D. W. Crust, and K. Woodbridge, “Transient grating studies of excitonic optical nonlinearities in GaAs/AlGaAs multiple quantum well structures,” J. Opt. Soc. Am. B **6**, 567–578 (1989). [CrossRef]

9. K. Jarasiunas and N. Lovergine, “Characterization of bulk crystals and structures by light-induced transient grating technique,” Mater. Sci. Eng. B **91–92**, 100–104 (2002). [CrossRef]

10. B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. **97**(26), 262119 (2010). [CrossRef]

11. J. F. Young and H. M. van Driel, “Ambipolar diffusion of high-density electrons and holes in Ge, Si, and GaAs: Many-body effects,” Phys. Rev. B **26**(4), 2147–2158 (1982). [CrossRef]

12. P. Borowik and J. L. Thobel, “Monte Carlo calculation of diffusion coefficients in degenerate bulk GaAs,” Semicond. Sci. Technol. **14**(5), 450–453 (1999). [CrossRef]

## 2. Principle and model

13. K. Katayama, M. Yamaguchi, and T. Sawada, “Lens-free heterodyne detection of transient grating experiments,” Appl. Phys. Lett. **82**(17), 2775 (2003). [CrossRef]

1. S. Nargelas, K. Jarašiūnas, K. Bertulis, and V. Pačebutas, “Hole diffusivity in GaAsBi alloys measured by a picosecond transient grating technique,” Appl. Phys. Lett. **98**(8), 082115 (2011). [CrossRef]

2. R. Aleksiejūnas, M. Sūdžius, T. Malinauskas, J. Vaitkus, K. Jarašiūnas, and S. Sakai, “Determination of free carrier bipolar diffusion coefficient and surface recombination velocity of undoped GaN epilayers,” Appl. Phys. Lett. **83**(6), 1157–1159 (2003). [CrossRef]

9. K. Jarasiunas and N. Lovergine, “Characterization of bulk crystals and structures by light-induced transient grating technique,” Mater. Sci. Eng. B **91–92**, 100–104 (2002). [CrossRef]

*N*(

*r*,

*t*), will evolve in space and time due to carrier diffusion and recombination, respectively. The evolution is controlled by common diffusion transport equation [3

3. H. W. Yoon, D. R. Wake, J. P. Wolfe, and H. Morkoç, “In-plane transport of photoexcited carriers in GaAs quantum wells,” Phys. Rev. B Condens. Matter **46**(20), 13461–13470 (1992). [CrossRef] [PubMed]

*D*

_{a}is an ambipolar diffusion coefficient.

*τ*

_{r}denotes an electron-hole recombination lifetime. For the initial carrier density distribution shown in Fig. 1(b), Eq. (1) has no analytical solution so that it must be numerically solved for

*N*(

*r*,

*t*) under a preset

*D*

_{a}and the known

*τ*

_{r}which may be measured independently by normal time-resolved pump-probe absorption spectroscopy with no grating added. Maybe no analytical solution may be thought of a drawback of our spectroscopy.

*N*(

*r*,

*t*), corresponding transient absorption may be expressed by [14

14. D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. **20**(3), 265–275 (1984). [CrossRef]

15. T. Lai, L. Liu, Q. Shou, L. Lei, and W. Lin, “Elliptically polarized pump-probe spectroscopy and its application to observation of electron-spin relaxation in GaAs quantum wells,” Appl. Phys. Lett. **85**(18), 4040–4042 (2004). [CrossRef]

*α*

_{0}is a linear absorption coefficient of the sample with no pump excitation.

*N*

_{s}denotes the density of state of the sample, and is usually much larger than

*N*(

*r*,

*t*).

*I*

_{0}(

*r*) is the incident intensity profile of the probe.

*T*

_{G}(

*r*) denotes transmittance of the transmission grating and the

*L*the thickness of the sample.

*C*=

*α*

_{0}

*L exp*(-

*α*

_{0}

*L*)/

*N*

_{s}is a scaling constant.

*D*

_{a}and a scaling constant

*C*. Both

*D*

_{a}and

*C*can be obtained by best fitting transient experiment dynamic data obtained by our spectroscopy with Eq. (5) plus Eq. (1). A numerical optimization program based on Eqs. (1) and (5) has been developed to execute the best fitting.

## 3. Sample and experiment

## 4. Measurements of diffusion dynamics and its photoexcited carrier concentration dependence

^{17}cm

^{−3}, and plotted in Fig. 2(a) by red open squares. As well known, it reflects the dynamics of carrier recombination. Then, a transmission grating with transparent slit width of 2 μm and a period of 6 μm is added in front of the sample. A transient differential transmission trace is taken again under the same excited carrier concentration as afore, and also plotted in Fig. 2(a) by green open circles. Obviously, it decays faster than red trace with no grating added. That is just the effect of carrier diffusion. To further demonstrate the role of the grating in visual enhancement of diffusion effect, another grating with a narrower slit of 1 μm is used. The transient trace is recorded again under a same excited carrier concentration and also plotted in Fig. 2(a) by blue open triangles. Evidently, it decays faster than green trace, again revealing the key role of the grating in the enhancement of diffusion effect.

^{17}to 8.6x10

^{17}cm

^{−3}. One set of transient traces with no gratings are plotted in Fig. 2(b), while the other ones with the grating added in Fig. 2(c) for the same carrier concentrations as ones used in Fig. 2(b). It is obvious that each transient trace in Fig. 2(c) decays faster than the corresponding one in Fig. 2(b), showing the enhancement of carrier diffusion after the grating added. Furthermore, it looks that the decay rate of transient traces increases with carrier concentration regardless of the grating added.

## 5. Results and discussions

*τ*

_{r}of carriers. A best fitting to the red square trace in Fig. 2(a) gives out a recombination lifetime of

*τ*

_{r}= 3.06 ± 0.06 ns, and is also plotted by a solid line in Fig. 2(a). Similarly, a best fitting to the green circle and blue triangle traces in Fig. 2(a) with Eq. (5) plus Eq. (1) with a given

*τ*

_{r}= 3.06 ns gives out a similar diffusion coefficient of

*D*

_{a}= 13.0 ± 0.3 cm

^{2}/s. The best fittings are also plotted in Fig. 2(a) by solid lines. The obtained diffusion coefficient of

*D*

_{a}= 13.0 cm

^{2}/s agrees well with previous reports. Jarasiunas and Lovergine measured the

*D*

_{a}of bulk GaAs with the diffraction of transient gratings, and found

*D*

_{a}= 11.0 cm

^{2}/s at a low excited carrier concentration and

*D*

_{a}= 18.0 cm

^{2}/s at high excitations [9

9. K. Jarasiunas and N. Lovergine, “Characterization of bulk crystals and structures by light-induced transient grating technique,” Mater. Sci. Eng. B **91–92**, 100–104 (2002). [CrossRef]

^{17}cm

^{3}, and in a moderate concentration range. Therefore, our measured value of

*D*

_{a}= 13.0 cm

^{2}/s locating between 11.0 cm

^{2}/s and 18.0 cm

^{2}/s should be reasonable. Ruzicka et al also measured the

*D*

_{a}of bulk GaAs with the spatiotemporal scanning of tightly focused pump and probe spots, and found

*D*

_{a}= ~20.0 cm

^{2}/s at room temperature [10

10. B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. **97**(26), 262119 (2010). [CrossRef]

*D*

_{a}should be expected.

*τ*

_{r}and diffusion coefficient

*D*

_{a}of carriers, which are plotted in Fig. 3(a) . It is interesting to note the non-monotonous variation of

*D*

_{a}with the increase of N. In the range of low excitations with N < ~1.2 × 10

^{17}cm

^{3},

*D*

_{a}decreases slowly with increasing N. Contrarily, in the range of high excitations with N > ~1.2 × 10

^{17}cm

^{3},

*D*

_{a}increases slowly with N. Such a variation tendency has been well predicted theoretically by Young and van Driel [11

11. J. F. Young and H. M. van Driel, “Ambipolar diffusion of high-density electrons and holes in Ge, Si, and GaAs: Many-body effects,” Phys. Rev. B **26**(4), 2147–2158 (1982). [CrossRef]

*D*

_{a}agrees very well with the theoretical prediction of Young and van Driel [11

11. J. F. Young and H. M. van Driel, “Ambipolar diffusion of high-density electrons and holes in Ge, Si, and GaAs: Many-body effects,” Phys. Rev. B **26**(4), 2147–2158 (1982). [CrossRef]

*D*

_{a}agree well with both previous experimental reports [9

**91–92**, 100–104 (2002). [CrossRef]

10. B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. **97**(26), 262119 (2010). [CrossRef]

**26**(4), 2147–2158 (1982). [CrossRef]

*L*

_{d}= (

*D*

_{a}

*τ*

_{r})

^{1/2}with the data in Fig. 3(a), and is plotted in Fig. 3(b). It decreases slowly with the increase of N. The diffusion length is less than 2.5 μm. Therefore, the diffusion effect is not apparent and can be ignored in normal pump-probe absorption spectroscopy where pump and probe spots are in order of several tens of micrometers at least, whereas in our spectroscopy it is the transmission grating added that makes diffusion effect visible.

## 5. Conclusion

## Acknowledgments

## References and links

1. | S. Nargelas, K. Jarašiūnas, K. Bertulis, and V. Pačebutas, “Hole diffusivity in GaAsBi alloys measured by a picosecond transient grating technique,” Appl. Phys. Lett. |

2. | R. Aleksiejūnas, M. Sūdžius, T. Malinauskas, J. Vaitkus, K. Jarašiūnas, and S. Sakai, “Determination of free carrier bipolar diffusion coefficient and surface recombination velocity of undoped GaN epilayers,” Appl. Phys. Lett. |

3. | H. W. Yoon, D. R. Wake, J. P. Wolfe, and H. Morkoç, “In-plane transport of photoexcited carriers in GaAs quantum wells,” Phys. Rev. B Condens. Matter |

4. | B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. |

5. | F. P. Logue, D. T. Fewer, S. J. Hewlett, J. F. Heffernan, C. Jordan, P. Rees, J. F. Donegan, E. M. McCabe, J. Hegarty, S. Taniguchi, T. Hino, K. Nakano, and A. Ishibashi, “Optical measurement of the ambipolar diffusion length in a ZnCdSe-ZnSe single quantum well,” J. Appl. Phys. |

6. | L. Baird, C. P. Ong, R. A. Cole, N. M. Haegel, A. A. Talin, Q. M. Li, and G. T. Wang, “Transport imaging for contact-free measurements of minority carrier diffusion in GaN, GaN/AlGaN, and GaN/InGaN core-shell nanowires,” Appl. Phys. Lett. |

7. | N. Gedik and J. Orenstein, “Absolute phase measurement in heterodyne detection of transient gratings,” Opt. Lett. |

8. | A. Miller, R. J. Manning, P. K. Milsom, D. C. Hutchings, D. W. Crust, and K. Woodbridge, “Transient grating studies of excitonic optical nonlinearities in GaAs/AlGaAs multiple quantum well structures,” J. Opt. Soc. Am. B |

9. | K. Jarasiunas and N. Lovergine, “Characterization of bulk crystals and structures by light-induced transient grating technique,” Mater. Sci. Eng. B |

10. | B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. |

11. | J. F. Young and H. M. van Driel, “Ambipolar diffusion of high-density electrons and holes in Ge, Si, and GaAs: Many-body effects,” Phys. Rev. B |

12. | P. Borowik and J. L. Thobel, “Monte Carlo calculation of diffusion coefficients in degenerate bulk GaAs,” Semicond. Sci. Technol. |

13. | K. Katayama, M. Yamaguchi, and T. Sawada, “Lens-free heterodyne detection of transient grating experiments,” Appl. Phys. Lett. |

14. | D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. |

15. | T. Lai, L. Liu, Q. Shou, L. Lei, and W. Lin, “Elliptically polarized pump-probe spectroscopy and its application to observation of electron-spin relaxation in GaAs quantum wells,” Appl. Phys. Lett. |

**OCIS Codes**

(050.2770) Diffraction and gratings : Gratings

(300.1030) Spectroscopy : Absorption

(300.6500) Spectroscopy : Spectroscopy, time-resolved

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

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: December 9, 2011

Revised Manuscript: January 20, 2012

Manuscript Accepted: January 22, 2012

Published: January 30, 2012

**Citation**

Ke Chen, Wenfang Wang, Jianming Chen, Jinhui Wen, and Tianshu Lai, "A transmission-grating-modulated pump-probe absorption spectroscopy and demonstration of diffusion dynamics of photoexcited carriers in bulk intrinsic GaAs film," Opt. Express **20**, 3580-3585 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3580

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### References

- S. Nargelas, K. Jarašiūnas, K. Bertulis, and V. Pačebutas, “Hole diffusivity in GaAsBi alloys measured by a picosecond transient grating technique,” Appl. Phys. Lett.98(8), 082115 (2011). [CrossRef]
- R. Aleksiejūnas, M. Sūdžius, T. Malinauskas, J. Vaitkus, K. Jarašiūnas, and S. Sakai, “Determination of free carrier bipolar diffusion coefficient and surface recombination velocity of undoped GaN epilayers,” Appl. Phys. Lett.83(6), 1157–1159 (2003). [CrossRef]
- H. W. Yoon, D. R. Wake, J. P. Wolfe, and H. Morkoç, “In-plane transport of photoexcited carriers in GaAs quantum wells,” Phys. Rev. B Condens. Matter46(20), 13461–13470 (1992). [CrossRef] [PubMed]
- B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett.97(26), 262119 (2010). [CrossRef]
- F. P. Logue, D. T. Fewer, S. J. Hewlett, J. F. Heffernan, C. Jordan, P. Rees, J. F. Donegan, E. M. McCabe, J. Hegarty, S. Taniguchi, T. Hino, K. Nakano, and A. Ishibashi, “Optical measurement of the ambipolar diffusion length in a ZnCdSe-ZnSe single quantum well,” J. Appl. Phys.81(1), 536–538 (1997). [CrossRef]
- L. Baird, C. P. Ong, R. A. Cole, N. M. Haegel, A. A. Talin, Q. M. Li, and G. T. Wang, “Transport imaging for contact-free measurements of minority carrier diffusion in GaN, GaN/AlGaN, and GaN/InGaN core-shell nanowires,” Appl. Phys. Lett.98(13), 132104 (2011). [CrossRef]
- N. Gedik and J. Orenstein, “Absolute phase measurement in heterodyne detection of transient gratings,” Opt. Lett.29(18), 2109–2111 (2004). [CrossRef] [PubMed]
- A. Miller, R. J. Manning, P. K. Milsom, D. C. Hutchings, D. W. Crust, and K. Woodbridge, “Transient grating studies of excitonic optical nonlinearities in GaAs/AlGaAs multiple quantum well structures,” J. Opt. Soc. Am. B6, 567–578 (1989). [CrossRef]
- K. Jarasiunas and N. Lovergine, “Characterization of bulk crystals and structures by light-induced transient grating technique,” Mater. Sci. Eng. B91–92, 100–104 (2002). [CrossRef]
- B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett.97(26), 262119 (2010). [CrossRef]
- J. F. Young and H. M. van Driel, “Ambipolar diffusion of high-density electrons and holes in Ge, Si, and GaAs: Many-body effects,” Phys. Rev. B26(4), 2147–2158 (1982). [CrossRef]
- P. Borowik and J. L. Thobel, “Monte Carlo calculation of diffusion coefficients in degenerate bulk GaAs,” Semicond. Sci. Technol.14(5), 450–453 (1999). [CrossRef]
- K. Katayama, M. Yamaguchi, and T. Sawada, “Lens-free heterodyne detection of transient grating experiments,” Appl. Phys. Lett.82(17), 2775 (2003). [CrossRef]
- D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron.20(3), 265–275 (1984). [CrossRef]
- T. Lai, L. Liu, Q. Shou, L. Lei, and W. Lin, “Elliptically polarized pump-probe spectroscopy and its application to observation of electron-spin relaxation in GaAs quantum wells,” Appl. Phys. Lett.85(18), 4040–4042 (2004). [CrossRef]

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