Application of broadband terahertz spectroscopy in semiconductor nonlinear dynamics

Abstract

Semiconductor nonlinearity in the range of terahertz (THz) frequency has been attracting considerable attention due to the recent development of high-power semiconductor-based nanodevices. However, the underlying physics concerning carrier dynamics in the presence of high-field THz transients is still obscure. This paper introduces an ultrafast, time-resolved THz pump/THz probe approach to study semiconductor properties in a nonlinear regime. The carrier dynamics regarding two mechanisms, intervalley scattering and impact ionization, was observed for doped InAs on a sub-picosecond time scale. In addition, polaron modulation driven by intense THz pulses was experimentally and theoretically investigated. The observed polaron dynamics verifies the interaction between energetic electrons and a phonon field. In contrast to previous work which reported optical phonon responses, acoustic phonon modulations were addressed in this study. A further understanding of the intense field interacting with solid materials will accelerate the development of semiconductor devices.

This paper can be divided into 4 sections. Section 1 starts with the design and performance of a table-top THz spectrometer, which has the advantages of ultra-broad bandwidth (one order higher bandwidth compared to a conventional ZnTe sensor) and high electric field strength (>100 kV/cm). Unlike the conventional THz timedomain spectroscopy, the spectrometer integrated a novel THz air-biased-coherent-detection (THz-ABCD) technique and utilized gases as THz emitters and sensors. In comparison with commonly used electro-optic (EO) crystals or photoconductive (PC) dipole antennas, the gases have the benefits of no phonon absorption as existing in EO crystals and no carrier life time limitation as observed in PC dipole antennas. In Section 2, the newly development THz-ABCD spectrometer with a strong THz field strength capability provides a platform for various research topics especially on the nonlinear carrier dynamics of semiconductors. Two mechanisms, electron intervalley scattering and impact ionization of InAs crystals, were observed under the excitation of intense THz field on a sub-picosecond time scale. These two competing mechanisms were demonstrated by changing the impurity doping type of the semiconductors and varying the strength of the THz field. p ]Another investigation of nonlinear carrier dynamics in Section 3 was the observation of coherent polaron oscillation in n-doped semiconductors excited by intense THz pulses. Through modulations of surface reflection with a THz pump/THz probe technique, this work experimentally verifies the interaction between energetic electrons and a phonon field, which has been theoretically predicted by previous publications, and shows that this interaction applies for the acoustic phonon modes. Usually, two transverse acoustic (2TA) phonon responses are inactive in infrared measurement, while they are detectable in second-order Raman spectroscopy. The study of polaron dynamics, with nonlinear THz spectroscopy (in the farinfrared range), provides a unique method to diagnose the overtones of 2TA phonon responses of semiconductors, and therefore incorporates the abilities of both infrared and Raman spectroscopy. Finally, some conclusions were presented in Section 4. In a word, this work presents a new milestone in wave-matter interaction and seeks to benefit the industrial applications in high power, small scale devices.

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References

  1. 1.

    Cook D J, Hochstrasser R M. Intense terahertz pulses by four-wave rectification in air. Optics Letters, 2000, 25(16): 1210–1212

    Article  Google Scholar 

  2. 2.

    Xie X, Dai J, Zhang X C. Coherent control of THz wave generation in ambient air. Physical Review Letters, 2006, 96(7): 075005-1–075005-4

    Article  Google Scholar 

  3. 3.

    Kim K Y, Glownia J H, Taylor A J, Rodriguez G. Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields. Optics Express, 2007, 15(8): 4577–4584

    Article  Google Scholar 

  4. 4.

    Karpowicz N, Zhang X C. Coherent terahertz echo of tunnel ionization in gases. Physical Review Letters, 2009, 102(9): 093001-1–093001-4

    Article  Google Scholar 

  5. 5.

    Dai J, Xie X, Zhang X C. Detection of broadband terahertz waves with a laser-induced plasma in gases. Physical Review Letters, 2006, 97(10): 103903-1–103903-4

    Article  Google Scholar 

  6. 6.

    Karpowicz N, Dai J M, Lu X, Chen Y, Yamaguchi M, Zhao H, Zhang X C, Zhang L, Zhang C, Price-Gallagher M, Fletcher C, Mamer O, Lesimple A, Johnson K. Coherent heterodyne timedomain spectrometry covering the entire “terahertz gap”. Applied Physics Letters, 2008, 92(1): 011131-1–011131-3

    Article  Google Scholar 

  7. 7.

    Ho I C, Guo X, Zhang X C. Design and performance of reflective terahertz air-biased-coherent-detection for time-domain spectroscopy. Optics Express, 2010, 18(3): 2872–2883

    Article  Google Scholar 

  8. 8.

    Hu B B, Nuss M C. Imaging with terahertz waves. Optics Letters, 1995, 20(16): 1716–1718

    Article  Google Scholar 

  9. 9.

    Mittleman D M, Jacobsen R H, Nuss M C. T-ray imaging. IEEE Journal on Selected Topics in Quantum Electronics, 1996, 2(3): 679–692

    Article  Google Scholar 

  10. 10.

    Ferguson B, Zhang X C. Materials for terahertz science and technology. Nature Materials, 2002, 1(1): 26–33

    Article  Google Scholar 

  11. 11.

    Grischkowsky D, Keiding S, Exter M V, Fattinger Ch. Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors. Journal of the Optical Society of America B, Optical Physics, 1990, 7(10): 2006–2015

    Article  Google Scholar 

  12. 12.

    Nuss M C, Auston D H, Capasso F. Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide. Physical Review Letters, 1987, 58(22): 2355–2358

    Article  Google Scholar 

  13. 13.

    Stepanov A G, Hebling J, Kuhl J. Efficient generation of subpicosecond terahertz radiation by phase-matched optical rectification using ultrashort laser pulses with tilted pulse fronts. Applied Physics Letters, 2003, 83(15): 3000–3002

    Article  Google Scholar 

  14. 14.

    Yeh K L, Hoffmann M C, Hebling J, Nelson K A. Generation of 10 μJ ultrashort terahertz pulses by optical rectification. Applied Physics Letters, 2007, 90(17): 171121

    Article  Google Scholar 

  15. 15.

    McLaughlin C V, Hayden L M, Polishak B, Huang S, Luo J, Kim T D, Jen A K Y. Wideband 15 THz response using organic electrooptic polymer emitter-sensor pairs at telecommunication wavelengths. Applied Physics Letters, 2008, 92(15): 151107-1–151107-3

    Article  Google Scholar 

  16. 16.

    Hamster H, Sullivan A, Gordon S, White W, Falcone R W. Subpicosecond, electromagnetic pulses from intense laser-plasma interaction. Physical Review Letters, 1993, 71(17): 2725–2728

    Article  Google Scholar 

  17. 17.

    Bartel T, Gaal P, Reimann K, Woerner M, Elsaesser T. Generation of single-cycle THz transients with high electric-field amplitudes. Optics Letters, 2005, 30(20): 2805–2807

    Article  Google Scholar 

  18. 18.

    Lu X, Karpowicz N, Zhang X C. Broadband terahertz detection with selected gases. Journal of the Optical Society of America B, Optical Physics, 2009, 26(9): A66–A73

    Article  Google Scholar 

  19. 19.

    Rønne C, Thrane L, Åstrand P O, Wallqvist A, Mikkelsen K V, Keiding S R. Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation. Journal of Chemical Physics, 1997, 107(14): 5319–5351

    Article  Google Scholar 

  20. 20.

    Hashimshony D, Geltner I, Cohen G, Avitzour Y, Zigler A, Smith C. Characterization of the electrical properties and thickness of thin epitaxial semiconductor layers by THz reflection spectroscopy. Journal of Applied Physics, 2001, 90(11): 5778–5781

    Article  Google Scholar 

  21. 21.

    Shon C H, Chong W Y, Jeon S G, Kim G J, Kim J I, Jin Y S. High speed terahertz pulse imaging in the reflection geometry and image quality enhancement by digital image processing. International Journal of Infrared and Millimeter Waves, 2008, 29(1): 79–88

    Article  Google Scholar 

  22. 22.

    Khazan M, Meissner R, Wilke I. Convertible transmission-reflection time-domain terahertz spectrometer. Review of Scientific Instruments, 2001, 72(8): 3427–3430

    Article  Google Scholar 

  23. 23.

    Pashkin A, Kempa M, Němec H, Kadlec F, Kužel P. Phase-sensitive time-domain terahertz reflection spectroscopy. Review of Scientific Instruments, 2003, 74(11): 4711–4717

    Article  Google Scholar 

  24. 24.

    Nashima S, Morikawa O, Takata K, Hangyo M. Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy. Applied Physics Letters, 2001, 79(24): 3923–3925

    Article  Google Scholar 

  25. 25.

    Jeon T I, Grischkowsky D. Characterization of optically dense, doped semiconductors by reflection THz time domain spectroscopy. Applied Physics Letters, 1998, 72(23): 3032–3034

    Article  Google Scholar 

  26. 26.

    Watanabe S, Kondo R, Kagoshima S, Shimano R. Spin-densitywave gap in (TMTSF)2PF6 probed by reflection-type terahertz timedomain spectroscopy. Physica Status Solidi. B, Basic Research, 2008, 245(12): 2688–2691

    Google Scholar 

  27. 27.

    Palik E D, ed. Silicon (Si), Calcium Carbonate, Calcite (CaCO3), Indium Arsenide (InAs), and Indium Antimonide (InSb) in Handbook of Optical Constants of Solids. New York: Elsevier, 1998

    Google Scholar 

  28. 28.

    Naftaly M, Dudley R. Methodologies for determining the dynamic ranges and signal-to-noise ratios of terahertz time-domain spectrometers. Optics Letters, 2009, 34(8): 1213–1215

    Article  Google Scholar 

  29. 29.

    Hase M, Kitajima M, Constantinescu A M, Petek H. The birth of a quasiparticle in silicon observed in time-frequency space. Nature, 2003, 426(6962): 51–54

    Article  Google Scholar 

  30. 30.

    Cheville R A, Grischkowsky D. Far-infrared terahertz time-domain spectroscopy of flames. Optics Letters, 1995, 20(15): 1646–1648

    Article  Google Scholar 

  31. 31.

    Podobedov V B, Plusquellic D F, Siegrist K E, Fraser G T, Ma Q, Tipping R H. New measurements of the water vapor continuum in the region from 0.3 to 2.7 THz. Journal of Quantitative Spectroscopy & Radiative Transfer, 2008, 109(3): 458–467

    Article  Google Scholar 

  32. 32.

    Liu J, Zhang X C. Birefringence and absorption coefficients of alpha barium borate in terahertz range. Journal of Applied Physics, 2009, 106(2): 023107-1–023107-5

    Google Scholar 

  33. 33.

    Akturk S, Couairon A, Franco M, Mysyrowicz A. Spectrogram representation of pulse self compression by filamentation. Optics Express, 2008, 16(22): 17626–17636

    Article  Google Scholar 

  34. 34.

    Bignell L J, Lewis R A. Reflectance studies of candidate THz emitters. Journal of Materials Science Materials in Electronics, 2009, 20(1): 326–331

    Google Scholar 

  35. 35.

    Wu Q, Sun F G, Campbell P, Zhang X C. Dynamic range of an electro-optic field sensor and its imaging applications. Applied Physics Letters, 1996, 68(23): 3224–3326

    Article  Google Scholar 

  36. 36.

    Han P Y, Tani M, Usami M, Kono S, Kersting R, Zhang X C. A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy. Journal of Applied Physics, 2001, 89(4): 2357–2359

    Article  Google Scholar 

  37. 37.

    Sze S M, Ng K K. Physics of Semiconductor Devices. New Jersey: John Wiley & Sons, 2006

    Book  Google Scholar 

  38. 38.

    Dumke W P. Theory of avalanche breakdown in InSb and InAs. Physical Review, 1968, 167(3): 783–789

    Article  Google Scholar 

  39. 39.

    Rode D L. Electron transport in InSb, InAs, and InP. Physical Review B: Condensed Matter and Materials Physics, 1971, 3(10): 3287–3299

    Article  Google Scholar 

  40. 40.

    Brennan K, Hess K. High field transport in GaAs, InP and InAs. Solid-State Electronics, 1984, 27(4): 347–357

    Article  Google Scholar 

  41. 41.

    Brennan K F, Mansour N S. Monte Carlo calculation of electron impact ionization in bulk InAs and HgCdTe. Journal of Applied Physics, 1991, 69(11): 7844–7847

    Article  Google Scholar 

  42. 42.

    Ganichev S D, Diener J, Yassievich I N, Prettl W. Poole-Frenkel effect in terahertz electromagnetic fields. Europhysics Letters, 1995, 29(4): 315–320

    Article  Google Scholar 

  43. 43.

    Markelz A G, Asmar N G, Brar B, Gwinn E G. Interband impact ionization by terahertz illumination of InAs heterostructures. Applied Physics Letters, 1996, 69(26): 3975–3977

    Article  Google Scholar 

  44. 44.

    Devreese J T, van Welzenis R G. Impact ionisation probability in InSb. Applied Physics A, Solids and Surfaces, 1982, 29(3): 125–132

    Article  Google Scholar 

  45. 45.

    Su F H, Blanchard F, Sharma G, Razzari L, Ayesheshim A, Cocker T L, Titova L V, Ozaki T, Kieffer J C, Morandotti R, Reid M, Hegmann F A. Terahertz pulse induced intervalley scattering in photoexcited GaAs. Optics Express, 2009, 17(12): 9620–9629

    Article  Google Scholar 

  46. 46.

    Hoffmann M C, Hebling J, Hwang H Y, Yeh K L, Nelson K A. Impact ionization in InSb probed by terahertz pump-terahertz probe spectroscopy. Physical Review B: Condensed Matter and Materials Physics, 2009, 79(16): 161201-1–161201-4

    Article  Google Scholar 

  47. 47.

    Razzari L, Su F H, Sharma G, Blanchard F, Ayesheshim A, Bandulet H C, Morandotti R, Kieffer J C, Ozaki T, Reid M, Hegmann F A. Nonlinear ultrafast modulation of the optical absorption of intense few-cycle terahertz pulses in n-doped semiconductors. Physical Review B: Condensed Matter and Materials Physics, 2009, 79(19): 193204-1–193204-4

    Article  Google Scholar 

  48. 48.

    Wen H, Wiczer M, Lindenberg A M. Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses. Physical Review B: Condensed Matter and Materials Physics, 2008, 78(12): 125203

    Article  Google Scholar 

  49. 49.

    Arabshahi H, Golafrooz S. Monte Carlo based calculation of electron transport properties in bulk InAs, AlAs and InAlAs. Bulgarian Journal of Physics, 2010, 37(4): 215–222

    Google Scholar 

  50. 50.

    Fröhlich H. Electrons in lattice fields. Advances in Physics, 1954, 3 (11): 325–361

    Article  Google Scholar 

  51. 51.

    Kuehn W, Gaal P, Reimann K, Woerner M, Elsaesser T, Hey R. Coherent ballistic motion of electrons in a periodic potential. Physical Review Letters, 2010, 104(14): 146602

    Article  Google Scholar 

  52. 52.

    Kuehn W, Gaal P, Reimann K, Woerner M, Elsaesser T, Hey R. Terahertz-induced interband tunneling of electrons in GaAs. Physical Review B: Condensed Matter and Materials Physics, 2010, 82(7): 075204-1–075204-8

    Article  Google Scholar 

  53. 53.

    Gaal P, Kuehn W, Reimann K, Woerner M, Elsaesser T, Hey R. Internal motions of a quasiparticle governing its ultrafast nonlinear response. Nature, 2007, 450(7173): 1210–1213

    Article  Google Scholar 

  54. 54.

    Meinert G, Bányai L, Gartner P. Classical polarons in a constant electric field. Physical Review B: Condensed Matter and Materials Physics, 2001, 63(24): 245203-1–245203-8

    Article  Google Scholar 

  55. 55.

    Bányai L. Motion of a classical polaron in a dc electric field. Physical Review Letters, 1993, 70(11): 1674–1677

    Article  Google Scholar 

  56. 56.

    Ho I C, Zhang X C. Driving intervalley scattering and impact ionization in InAs with intense terahertz pulses. Applied Physics Letters, 2011, 98(24): 241908-1–241908-3

    Article  Google Scholar 

  57. 57.

    Koteles E S, Datars WR, Dolling G. Far-infrared phonon absorption in InSb. Physical Review B: Condensed Matter and Materials Physics, 1974, 9(2): 572–582

    Article  Google Scholar 

  58. 58.

    Kiefer W, Richter W, Cardona M. Second-order Raman scattering in InSb. Physical Review B: Condensed Matter and Materials Physics, 1975, 12(6): 2346–2354

    Article  Google Scholar 

  59. 59.

    Carles R, Saint-Cricq N, Renucci J B, Renucci M A, Zwick A. Second-order Raman scattering in InAs. Physical Review B: Condensed Matter and Materials Physics, 1980, 22(10): 4804–4815

    Article  Google Scholar 

  60. 60.

    Borcherds P H, Kunc K. The lattice dynamics of indium pnictides. Journal of Physical Chemistry, 1978, 11(20): 4145–4155

    Google Scholar 

  61. 61.

    Smith E, Dent G. Modern Raman Spectroscopy. West Sussex: John Wiley & Sons, 2005

    Google Scholar 

  62. 62.

    Hecht E. Optics. San Francisco: Addison Wesley, 2002

    Google Scholar 

Download references

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Correspondence to I-Chen Ho or Xi-Cheng Zhang.

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I-Chen Ho received the B.S. degree in physics from Taiwan Normal University, Taipei, Taiwan, in 2004, and the M.S. degree in photonics from Chiao Tung University, Hsinchu, Taiwan, in 2007. She received the Ph.D. degree in physics from Rensselaer Polytechnic Institute, Troy, NY, in 2011. She was engaged in design of ultra-broadband terahertz spectroscopy and dedicated her research to high-field, transient carrier dynamics in semiconductors.

She currently is an Engineer in Intel Corporation, Hillsboro, Oregon. She is the author or coauthor of more than 10 refereed journal papers as well as contribution to book chapters and has delivered over 10 conference presentations.

Dr. Ho was awarded the Coherent Graduate Student Award from Coherent Inc. in 2010, the Founders Award of Excellence at Rensselaer in 2008, the President Award at Chiao Tung University in 2006, the President Award at Taiwan Normal University in 2004, and the Excellent Student Award at Taiwan Normal University in 2003.

Xi-Cheng Zhang-Parker Givens Chair of Optics, assumes Directorship of The Institute of Optics, University of Rochester (UR), NY, a foremost institution in optics and optical physics research and education, on 1/1/2012. Prior to joining UR, he pioneered worldleading research in the field of ultrafast laserbased terahertz technology and optical physics at Rensselaer Polytechnic Institute (RPI), Troy NY (1992–2012). At RPI, he is the Eric Jonsson Professor of Science; Acting Head at the Department of Physics, Applied Physics & Astronomy; Professor of Electrical, Computer & System; and Founding Director of the Center for THz Research. He is co-founder of Zomega Terahertz Corp. With a B.S. (1982) from Peking University, he earned the M.S. (1983) and Ph.D. degree (1985) in Physics from Brown University, RI.

Previous positions included Visiting Scientist at MIT (1985), Physical Tech. Division of Amoco Research Center (1987), EE Dept. at Columbia University (1987–1991); Distinguished Visiting Scientist at Jet Propulsion Lab, Caltech (2006). He holds 27 U.S. patents, and is a prolific author and speaker. He is a Fellow of AAAS, APS (lifetime), IEEE, OSA (lifetime), and SPIE (lifetime). Dr. Zhang is serving as Editor-in-Chief of Optics Letters (2014–2016).

His honors and awards include: IRMMW-THz Kenneth Button Prize (2014); OSA William F. Meggers Award (2012); IEEE Photonics Society William Streifer Scientific Achievement Award (2011); Rensselaer William H. Wiley 1866 Award (2009); Japan Society for the Promotion of Science Fellowship & NRC-CIAR Distinguished Visiting Scientist, Ottawa, Canada (2004); and First Heinrich Rudolf Hertz Lecturer, RWTH, Aachen, Germany (2003). He also served two years as a Distinguished Lecturer of IEEE/LEOS. He received Rensselaer Early Career Award (1996), Research Corporation Cottrell Scholar Award (1995), NSF Early Career Award (1995), K.C. Wong Prize, K.C. Wong Foundation, Hong Kong (1995), NSF Research Initiation Award (1992). In 1993–1994, he was an AFOSR-SRPF Fellow at Hanscom Air Force Base.

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Ho, IC., Zhang, XC. Application of broadband terahertz spectroscopy in semiconductor nonlinear dynamics. Front. Optoelectron. 7, 220–242 (2014). https://doi.org/10.1007/s12200-014-0398-2

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Keywords

  • terahertz (THz)
  • nonlinear
  • spectroscopy
  • broadband
  • semiconductor