## Terahertz emission by diffusion of carriers and metal-mask dipole inhibition of radiation |

Optics Express, Vol. 20, Issue 8, pp. 8898-8906 (2012)

http://dx.doi.org/10.1364/OE.20.008898

Acrobat PDF (1250 KB)

### Abstract

Terahertz (THz) radiation can be generated by ultrafast photo-excitation of carriers in a semiconductor partly masked by a gold surface. A simulation of the effect taking into account the diffusion of carriers and the electric field shows that the total net current is approximately zero and cannot account for the THz radiation. Finite element modelling and analytic calculations indicate that the THz emission arises because the metal inhibits the radiation from part of the dipole population, thus creating an asymmetry and therefore a net current. Experimental investigations confirm the simulations and show that metal-mask dipole inhibition can be used to create THz emitters.

© 2012 OSA

## 1. Introduction

1. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. **5**, 124–166 (2011). [CrossRef]

2. M. B. Johnston, D. Whittaker, A. Corchia, A. G. Davies, and E. Linfield, “Simulation of terahertz generation at semiconductor surfaces,” Phys. Rev. B **65**, 165301 (2002). [CrossRef]

4. P. Gu, M. Tani, S. Kono, K. Sakai, and X. C. Zhang, “Study of terahertz radiation from InAs and InSb,” J. Appl. Phys. **91**, 5533–5537 (2002). [CrossRef]

2. M. B. Johnston, D. Whittaker, A. Corchia, A. G. Davies, and E. Linfield, “Simulation of terahertz generation at semiconductor surfaces,” Phys. Rev. B **65**, 165301 (2002). [CrossRef]

5. M. B. Johnston, D. M. Whittaker, A. Dowd, A. G. Davies, E. H. Linfield, X. Li, and D. A. Ritchie, “Generation of high-power terahertz pulses in a prism,” Opt. Lett. **27**, 1935–1937 (2002). [CrossRef]

6. G. Klatt, B. Surrer, D. Stephan, O. Schubert, M. Fischer, J. Faist, A. Leitenstorfer, R. Huber, and T. Dekorsy, “Photo-Dember terahertz emitter excited with an Er:fiber laser,” Appl. Phys. Lett. **98**, 021114 (2011). [CrossRef]

7. G. Klatt, F. Hilser, W. Qiao, M. Beck, R. Gebs, A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B. Johnston, M. Fischer, J. Faist, and T. Dekorsy, “Terahertz emission from lateral photo-Dember currents,” Opt. Express **18**, 4939–4947 (2010). [CrossRef] [PubMed]

7. G. Klatt, F. Hilser, W. Qiao, M. Beck, R. Gebs, A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B. Johnston, M. Fischer, J. Faist, and T. Dekorsy, “Terahertz emission from lateral photo-Dember currents,” Opt. Express **18**, 4939–4947 (2010). [CrossRef] [PubMed]

9. D. McBryde, M. E. Barnes, A. L. Chung, Z. Mihoubi, G. J. Daniell, A. H. Quarterman, K. G. Wilcox, H. E. Beere, D. A. Ritchie, A. C. Tropper, and V. Apostolopoulos, “Simulation of metallic nanostructures for emission of THz radiation using the lateral photo-Dember effect,” in Proceedings of The 36th International Conference on Infrared, Millimeter and Terahertz Waves (IRMMW-THz) , pp.1–2 (2011). [CrossRef]

10. D. McBryde, M. E. Barnes, A. L. Chung, Z. Mihoubi, G. J. Daniell, A. H. Quarterman, K. G. Wilcox, H. E. Beere, D. A. Ritchie, A. C. Tropper, and V. Apostolopoulos, “Simulation of metallic nanostructures for emission of THz radiation using the lateral photo-Dember effect,” arXiv:1202.1459v1, (2012), http://arxiv.org/abs/1202.1459v1.

7. G. Klatt, F. Hilser, W. Qiao, M. Beck, R. Gebs, A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B. Johnston, M. Fischer, J. Faist, and T. Dekorsy, “Terahertz emission from lateral photo-Dember currents,” Opt. Express **18**, 4939–4947 (2010). [CrossRef] [PubMed]

**18**, 4939–4947 (2010). [CrossRef] [PubMed]

**18**, 4939–4947 (2010). [CrossRef] [PubMed]

11. K. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Luminol. **1**, 693–701 (1970). [CrossRef]

## 2. Results of the diffusion equation with drift current

3. K. Liu, J. Z. Xu, T. Yuan, and X. C. Zhang, “Terahertz radiation from InAs induced by carrier diffusion and drift,” Phys. Rev. B **73**, 155330 (2006). [CrossRef]

12. T. Dekorsy, T. Pfeifer, W. Kütt, and H. Kurz, “Subpicosecond carrier transport in GaAs surface-space-charge fields,” Phys. Rev. B **47**, 3842–3849 (1993). [CrossRef]

13. J. S. Blakemore, “Semiconducting and other major properties of gallium-arsenide,” J. Appl. Phys. **53**, R123–R181 (1982). [CrossRef]

*n*, the hole densiy is

_{e}*n*and the electric field is

_{h}*E*. The mobility,

*μ*, and the diffusion coefficient,

*D*, follow the Einstein relation and the temperature is assumed to be 3000 K for electrons and 300 K for holes [3

3. K. Liu, J. Z. Xu, T. Yuan, and X. C. Zhang, “Terahertz radiation from InAs induced by carrier diffusion and drift,” Phys. Rev. B **73**, 155330 (2006). [CrossRef]

12. T. Dekorsy, T. Pfeifer, W. Kütt, and H. Kurz, “Subpicosecond carrier transport in GaAs surface-space-charge fields,” Phys. Rev. B **47**, 3842–3849 (1993). [CrossRef]

*τ*

_{1}, is set at 20 ps for LT and SI-GaAs and the electron-defect recombination time constant,

*τ*

_{2}, is set at 200 fs and used only in the case of LT-GaAs [14

14. I. S. Gregory, W. R. Tribe, C. Baker, B. E. Cole, M. J. Evans, L. Spencer, M. Pepper, and M. Missous, “Continuous-wave terahertz system with a 60 dB dynamic range,” Appl. Phys. Lett. **86**, 204104 (2005). [CrossRef]

*μ*m. A mobility of 8500 cm

^{2}

*V*

^{−1}s

^{−1}was used both for SI and LT-GaAs. Here the results for SI-GaAs are shown, in Fig. 3(a) the temporal evolution of the electron concentration over 80 ps is shown in steps of 20 ps. In this graph the metal sheet shadows the left region from 0 to −20

*μ*m. The time evolution shows that electrons are annihilated at every step due to recombination and a large flux of electrons towards the left due to diffusion is caused by the initial large gradient. A kink in the electron distribution forms at the metal edge due to the fact that electrons that diffuse to the left recombine at a much lower rate due to the decreased hole density. The hole concentration profiles are shown in Fig. 3(b), diffusion of the holes in this timescale is negligible on account of the lower mobility and lower temperature. A peak forms in the hole concentration at the metal edge because the maximum concentration of electrons moves to the right as a result of diffusion. The current density that is created by this time evolution can be seen in Fig. 3(c), which shows a large positive current spike at the edge of the metal. However, Fig. 3(c) also reveals a negative current in the area of the unmasked semiconductor which shows that there is also diffusion towards the right. This is not obvious in Fig. 3(a) and 3(b) due to the smooth gradient of the concentration curves. The total current is the integration of these curves of Fig. 3(c) in space and the result is very small, in comparison to the result of the simulation for a classical PD geometry, but not zero. In order to test if this current is due to diffusion or electric field we ran the simulation only with the effects of diffusion and this resulted to a total current which at any time is exactly zero. Therefore, this small current is due to the effect of the electric field, because the electrons travelling towards the left are attracted by the entire hole population. The current density due to the electric field is approximately 4 orders of magnitude smaller in comparison to what our simulation predicts for the diffusion current density of the classical PD case [2

2. M. B. Johnston, D. Whittaker, A. Corchia, A. G. Davies, and E. Linfield, “Simulation of terahertz generation at semiconductor surfaces,” Phys. Rev. B **65**, 165301 (2002). [CrossRef]

4. P. Gu, M. Tani, S. Kono, K. Sakai, and X. C. Zhang, “Study of terahertz radiation from InAs and InSb,” J. Appl. Phys. **91**, 5533–5537 (2002). [CrossRef]

*E*-field and diffusion generated currents can be estimated to be ∼

*r*

^{2}/

*λ*

^{2}, where

*r*is a typical length scale for the diffusion and

*λ*is the Debye length. The importance of the

*E*-field current is dependent on how the Debye length compares with the diffusion distance, in the LPD case

*λ*≫

*r*, and diffusion predominates. By comparing the simulation results of the lateral and classical PD emitters we conclude that the current generated from the E-field is negligible and would not be enough to create measurable THz radiation, this explains why the structures depicted in Fig. 2 do not produce measurable THz radiation.

## 3. Discussion and simulations of dipole radiation

*∂n*, therefore the total current due to diffusion will be the definite integral ∫ (

_{e}/∂x*∂n*)

_{e}/∂x*dx*from a large negative to positive value. As long as the initial concentration starts from zero and ends to zero this integral will be equal to zero. Furthermore, in diffusion an electron has an equal probability of diffusing in any direction, so the net current due to diffusion must be equal to zero for a large number of electrons.

*y*where the THz emission is measured experimentally. In Fig. 4(b) there is a metallic layer (gold) with a refractive index estimated from [17]. It can be seen that the radiation from the dipole under the metal is completely suppressed; only the dipole in the free area is radiating and of course this gives THz emission in the

*y*-direction of the receiver and the mechanism is depicted in Fig. 4(c). The suppression of radiation happens due to the long wavelength of the THz radiation in relation to the distance between the dipole and metal. The radiation that is reflected by the surface of the metal acquires a

*π*-phase shift in relation to the non-reflected radiation [18

18. T. Doi, K. Toyoda, and Y. Tanimura, “Effects of phase changes on reflection and their wavelength dependence in optical profilometry,” Appl. Opt. **36**, 7157–7161 (1997). [CrossRef]

19. H. Yasuda and I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. **47**, 1632–1634 (2008). [CrossRef]

*y*direction [11

11. K. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Luminol. **1**, 693–701 (1970). [CrossRef]

*x*-direction and the THz wave is generated in the

*y*-direction, as shown in Fig. 1(a). An expression for the radiated electric field from an oscillating dipole under the surface is:

*r*

_{0}is the distance of the dipole from the edge of the metal sheet and

*y*

_{0}is the distance in the vertical direction and

*k*is the wavenumber. Φ is the Fresnel integral defined by

*x*is positive and the positive sign when

*x*is negative. The derivation is done in free space which underestimates the amount of suppression and a perfect metal has been assumed.

*y*direction as a function of the position of the dipole. As expected, when under the metal there is suppression, whereas when the dipole is out of the metallic region it emits. The amount of suppression depends on how close the dipole is to the metal and the oscillation frequency. Here the dipole separation from the metal is set at 1

*μ*m as an approximation of the absorption length of GaAs at a wavelength of 800 nm [3

3. K. Liu, J. Z. Xu, T. Yuan, and X. C. Zhang, “Terahertz radiation from InAs induced by carrier diffusion and drift,” Phys. Rev. B **73**, 155330 (2006). [CrossRef]

**65**, 165301 (2002). [CrossRef]

4. P. Gu, M. Tani, S. Kono, K. Sakai, and X. C. Zhang, “Study of terahertz radiation from InAs and InSb,” J. Appl. Phys. **91**, 5533–5537 (2002). [CrossRef]

**18**, 4939–4947 (2010). [CrossRef] [PubMed]

**18**, 4939–4947 (2010). [CrossRef] [PubMed]

## 4. Experimental verification

**18**, 4939–4947 (2010). [CrossRef] [PubMed]

*μ*m-gap bowtie PC antenna was used, as shown in Fig. 5(a) with the laser focused on top of position A. The polarity of the THz emission was mapped with the direction of current by biasing the PC antenna in opposite polarities and one of the measurements is shown in Fig. 5(c). The same PC antenna (LT-GaAs) was then disconnected from the bias, and translated across to the area B, shown in Fig. 5(a), where a metallic edge was used as a LPD emitter. The polarity of the THz waveform indicated that the current was flowing as expected in our argument where the radiating dipole is in the non-masked region of the antenna and the THz waveform is also shown in Fig. 5(c). The LT-GaAs PC emitter was then replaced with a dedicated LT-GaAs-LPD emitter and we measured the LPD effect on two opposite edges of metal strips, areas C and D in Fig. 5(b); the beam waist at the focus was approximately 60

*μ*m. The results are shown in Fig. 5(d), where we note the expected polarity change between opposite edges. In Fig. 5(e) the spectra of PC and LPD antennae are illustrated, showing similar bandwidths produced from the LPD and PC emitter. The spectra were obtained in ambient atmosphere and show water absorption features.

## 5. Conclusion

## References and links

1. | P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. |

2. | M. B. Johnston, D. Whittaker, A. Corchia, A. G. Davies, and E. Linfield, “Simulation of terahertz generation at semiconductor surfaces,” Phys. Rev. B |

3. | K. Liu, J. Z. Xu, T. Yuan, and X. C. Zhang, “Terahertz radiation from InAs induced by carrier diffusion and drift,” Phys. Rev. B |

4. | P. Gu, M. Tani, S. Kono, K. Sakai, and X. C. Zhang, “Study of terahertz radiation from InAs and InSb,” J. Appl. Phys. |

5. | M. B. Johnston, D. M. Whittaker, A. Dowd, A. G. Davies, E. H. Linfield, X. Li, and D. A. Ritchie, “Generation of high-power terahertz pulses in a prism,” Opt. Lett. |

6. | G. Klatt, B. Surrer, D. Stephan, O. Schubert, M. Fischer, J. Faist, A. Leitenstorfer, R. Huber, and T. Dekorsy, “Photo-Dember terahertz emitter excited with an Er:fiber laser,” Appl. Phys. Lett. |

7. | G. Klatt, F. Hilser, W. Qiao, M. Beck, R. Gebs, A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B. Johnston, M. Fischer, J. Faist, and T. Dekorsy, “Terahertz emission from lateral photo-Dember currents,” Opt. Express |

8. | G. Klatt, F. Hilser, W. Chao, R. Gebs, A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B. Johnston, M. Fischer, J. Faist, and T. Dekorsy, “Intense terahertz generation based on the photo-Dember effect,” in Proceedings of OSA/CLEO/QELS 2010 Paper CMJJ2 (2010). |

9. | D. McBryde, M. E. Barnes, A. L. Chung, Z. Mihoubi, G. J. Daniell, A. H. Quarterman, K. G. Wilcox, H. E. Beere, D. A. Ritchie, A. C. Tropper, and V. Apostolopoulos, “Simulation of metallic nanostructures for emission of THz radiation using the lateral photo-Dember effect,” in Proceedings of The 36th International Conference on Infrared, Millimeter and Terahertz Waves (IRMMW-THz) , pp.1–2 (2011). [CrossRef] |

10. | D. McBryde, M. E. Barnes, A. L. Chung, Z. Mihoubi, G. J. Daniell, A. H. Quarterman, K. G. Wilcox, H. E. Beere, D. A. Ritchie, A. C. Tropper, and V. Apostolopoulos, “Simulation of metallic nanostructures for emission of THz radiation using the lateral photo-Dember effect,” arXiv:1202.1459v1, (2012), http://arxiv.org/abs/1202.1459v1. |

11. | K. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Luminol. |

12. | T. Dekorsy, T. Pfeifer, W. Kütt, and H. Kurz, “Subpicosecond carrier transport in GaAs surface-space-charge fields,” Phys. Rev. B |

13. | J. S. Blakemore, “Semiconducting and other major properties of gallium-arsenide,” J. Appl. Phys. |

14. | I. S. Gregory, W. R. Tribe, C. Baker, B. E. Cole, M. J. Evans, L. Spencer, M. Pepper, and M. Missous, “Continuous-wave terahertz system with a 60 dB dynamic range,” Appl. Phys. Lett. |

15. | I. S. Gregory, “The development of a continuous-wave terahertz imaging system,” Ph.D. thesis, University of Cambridge (2004). |

16. | C. Baker, “Development of semiconductor materials for terahertz photoconductive antennas,” Ph.D. thesis, University of Cambridge (2004). |

17. | E. D. Palik, |

18. | T. Doi, K. Toyoda, and Y. Tanimura, “Effects of phase changes on reflection and their wavelength dependence in optical profilometry,” Appl. Opt. |

19. | H. Yasuda and I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. |

20. | P. M. Morse and H. Feshbach, |

21. | M. Abramowitz and I. A. Stegun, |

**OCIS Codes**

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

(300.6495) Spectroscopy : Spectroscopy, teraherz

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: February 14, 2012

Revised Manuscript: March 27, 2012

Manuscript Accepted: March 27, 2012

Published: April 2, 2012

**Citation**

M. E. Barnes, D. McBryde, G. J. Daniell, G. Whitworth, A. L. Chung, A. H. Quarterman, K. G. Wilcox, A. Brewer, H. E. Beere, D. A. Ritchie, and V. Apostolopoulos, "Terahertz emission by diffusion of carriers and metal-mask dipole inhibition of radiation," Opt. Express **20**, 8898-8906 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-8-8898

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### References

- P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev.5, 124–166 (2011). [CrossRef]
- M. B. Johnston, D. Whittaker, A. Corchia, A. G. Davies, and E. Linfield, “Simulation of terahertz generation at semiconductor surfaces,” Phys. Rev. B65, 165301 (2002). [CrossRef]
- K. Liu, J. Z. Xu, T. Yuan, and X. C. Zhang, “Terahertz radiation from InAs induced by carrier diffusion and drift,” Phys. Rev. B73, 155330 (2006). [CrossRef]
- P. Gu, M. Tani, S. Kono, K. Sakai, and X. C. Zhang, “Study of terahertz radiation from InAs and InSb,” J. Appl. Phys.91, 5533–5537 (2002). [CrossRef]
- M. B. Johnston, D. M. Whittaker, A. Dowd, A. G. Davies, E. H. Linfield, X. Li, and D. A. Ritchie, “Generation of high-power terahertz pulses in a prism,” Opt. Lett.27, 1935–1937 (2002). [CrossRef]
- G. Klatt, B. Surrer, D. Stephan, O. Schubert, M. Fischer, J. Faist, A. Leitenstorfer, R. Huber, and T. Dekorsy, “Photo-Dember terahertz emitter excited with an Er:fiber laser,” Appl. Phys. Lett.98, 021114 (2011). [CrossRef]
- G. Klatt, F. Hilser, W. Qiao, M. Beck, R. Gebs, A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B. Johnston, M. Fischer, J. Faist, and T. Dekorsy, “Terahertz emission from lateral photo-Dember currents,” Opt. Express18, 4939–4947 (2010). [CrossRef] [PubMed]
- G. Klatt, F. Hilser, W. Chao, R. Gebs, A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B. Johnston, M. Fischer, J. Faist, and T. Dekorsy, “Intense terahertz generation based on the photo-Dember effect,” in Proceedings of OSA/CLEO/QELS 2010 Paper CMJJ2 (2010).
- D. McBryde, M. E. Barnes, A. L. Chung, Z. Mihoubi, G. J. Daniell, A. H. Quarterman, K. G. Wilcox, H. E. Beere, D. A. Ritchie, A. C. Tropper, and V. Apostolopoulos, “Simulation of metallic nanostructures for emission of THz radiation using the lateral photo-Dember effect,” in Proceedings of The 36th International Conference on Infrared, Millimeter and Terahertz Waves (IRMMW-THz), pp.1–2 (2011). [CrossRef]
- D. McBryde, M. E. Barnes, A. L. Chung, Z. Mihoubi, G. J. Daniell, A. H. Quarterman, K. G. Wilcox, H. E. Beere, D. A. Ritchie, A. C. Tropper, and V. Apostolopoulos, “Simulation of metallic nanostructures for emission of THz radiation using the lateral photo-Dember effect,” arXiv:1202.1459v1, (2012), http://arxiv.org/abs/1202.1459v1 .
- K. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Luminol.1, 693–701 (1970). [CrossRef]
- T. Dekorsy, T. Pfeifer, W. Kütt, and H. Kurz, “Subpicosecond carrier transport in GaAs surface-space-charge fields,” Phys. Rev. B47, 3842–3849 (1993). [CrossRef]
- J. S. Blakemore, “Semiconducting and other major properties of gallium-arsenide,” J. Appl. Phys.53, R123–R181 (1982). [CrossRef]
- I. S. Gregory, W. R. Tribe, C. Baker, B. E. Cole, M. J. Evans, L. Spencer, M. Pepper, and M. Missous, “Continuous-wave terahertz system with a 60 dB dynamic range,” Appl. Phys. Lett.86, 204104 (2005). [CrossRef]
- I. S. Gregory, “The development of a continuous-wave terahertz imaging system,” Ph.D. thesis, University of Cambridge (2004).
- C. Baker, “Development of semiconductor materials for terahertz photoconductive antennas,” Ph.D. thesis, University of Cambridge (2004).
- E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).
- T. Doi, K. Toyoda, and Y. Tanimura, “Effects of phase changes on reflection and their wavelength dependence in optical profilometry,” Appl. Opt.36, 7157–7161 (1997). [CrossRef]
- H. Yasuda and I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys.47, 1632–1634 (2008). [CrossRef]
- P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, Inc., New York, 1953).
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, with formulas, graphs, and mathematical tables (Dover Publications, New York, 1972).

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