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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Cook D J, Hochstrasser R M. Intense terahertz pulses by four-wave rectification in air. Optics Letters, 2000, 25(16): 1210–1212
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
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
Karpowicz N, Zhang X C. Coherent terahertz echo of tunnel ionization in gases. Physical Review Letters, 2009, 102(9): 093001-1–093001-4
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
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
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
Hu B B, Nuss M C. Imaging with terahertz waves. Optics Letters, 1995, 20(16): 1716–1718
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
Ferguson B, Zhang X C. Materials for terahertz science and technology. Nature Materials, 2002, 1(1): 26–33
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
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
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
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
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
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
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
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
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
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
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
Khazan M, Meissner R, Wilke I. Convertible transmission-reflection time-domain terahertz spectrometer. Review of Scientific Instruments, 2001, 72(8): 3427–3430
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
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
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
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
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
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
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
Cheville R A, Grischkowsky D. Far-infrared terahertz time-domain spectroscopy of flames. Optics Letters, 1995, 20(15): 1646–1648
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
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
Akturk S, Couairon A, Franco M, Mysyrowicz A. Spectrogram representation of pulse self compression by filamentation. Optics Express, 2008, 16(22): 17626–17636
Bignell L J, Lewis R A. Reflectance studies of candidate THz emitters. Journal of Materials Science Materials in Electronics, 2009, 20(1): 326–331
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
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
Sze S M, Ng K K. Physics of Semiconductor Devices. New Jersey: John Wiley & Sons, 2006
Dumke W P. Theory of avalanche breakdown in InSb and InAs. Physical Review, 1968, 167(3): 783–789
Rode D L. Electron transport in InSb, InAs, and InP. Physical Review B: Condensed Matter and Materials Physics, 1971, 3(10): 3287–3299
Brennan K, Hess K. High field transport in GaAs, InP and InAs. Solid-State Electronics, 1984, 27(4): 347–357
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
Ganichev S D, Diener J, Yassievich I N, Prettl W. Poole-Frenkel effect in terahertz electromagnetic fields. Europhysics Letters, 1995, 29(4): 315–320
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
Devreese J T, van Welzenis R G. Impact ionisation probability in InSb. Applied Physics A, Solids and Surfaces, 1982, 29(3): 125–132
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
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
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
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
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
Fröhlich H. Electrons in lattice fields. Advances in Physics, 1954, 3 (11): 325–361
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
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
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
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
Bányai L. Motion of a classical polaron in a dc electric field. Physical Review Letters, 1993, 70(11): 1674–1677
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
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
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
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
Borcherds P H, Kunc K. The lattice dynamics of indium pnictides. Journal of Physical Chemistry, 1978, 11(20): 4145–4155
Smith E, Dent G. Modern Raman Spectroscopy. West Sussex: John Wiley & Sons, 2005
Hecht E. Optics. San Francisco: Addison Wesley, 2002
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
- terahertz (THz)