Terahertz spectroscopy refers to spectroscopic techniques that probe materials using electromagnetic radiation in the terahertz (THz) region, typically from ~0.1 to 10 THz (3 mm–30 μm). THz spectroscopy accesses low-energy excitations such as rotational and vibrational transitions in molecules, phonons and collective modes in solids, charge transport in semiconductors and superconductors, and intermolecular interactions in liquids and biomaterials.Siegel, P. H. (2004). "Terahertz technology". IEEE Transactions on Microwave Theory and Techniques. 52 (10): 2438–2447.Tonouchi, M. (2007). "Cutting-edge terahertz technology". Nature Photonics. 1 (2): 97–105.
Two major approaches are used: time-domain terahertz spectroscopy (THz-TDS), which employs pulsed THz radiation and waveform sampling, and frequency-domain terahertz spectroscopy (THz-FDS), which uses continuous-wave radiation and sweeps frequency.Lee, Y.-S. (2009). Principles of Terahertz Science and Technology. Springer.Coutaz, J.-L.; Garet, F. (2017). Principles of Terahertz Time-Domain Spectroscopy. Stanford University Press. THz-TDS provides broadband access to amplitude and phase information and is widely used for materials characterization, imaging, and non-destructive evaluation.Tonouchi, M. (2007). "Cutting-edge terahertz technology". Nature Photonics. 1 (2): 97–105. THz-FDS offers extremely high spectral resolution, often below 1 MHz, enabling Doppler-limited gas-phase spectroscopy, rotational spectroscopy, and precision metrology.Hindle, F.; Cuisset, A.; Bocquet, R.; Mouret, G. (2008). "Continuous-wave terahertz by photomixing: applications to gas-phase pollutant detection and quantification". Comptes Rendus Physique. 9 (2): 262–275.Roggenbuck, A. et al. (2010). "Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples". New Journal of Physics. 12 (4): 043017.
THz spectroscopy has applications in condensed-matter physics, chemistry, atmospheric and environmental sensing, security screening, pharmaceuticals, telecommunications, cultural-heritage analysis, biomedical imaging, and industrial quality control.Zhang, X.-C.; Xu, J. (2010). Introduction to THz Wave Photonics. Springer.Siegel, P. H. (2002). "Terahertz technology in biology and medicine". IEEE Transactions on Microwave Theory and Techniques. 50 (3): 910–928. THz systems can operate in free-space or waveguide geometries and may employ photoconductive emitters and detectors, nonlinear optical generation, photomixing, electronic sources, or quantum cascade lasers.Koenig, S.; Lopez-Dominguez, M. (2018). Terahertz Technology: Fundamentals and Applications. Wiley.
Background There are a great variety of techniques to generate THz radiation and to detect THz fields. One can, e.g., use an antenna, a quantum-cascade laser, a free-electron laser, or optical rectification to produce well-defined THz sources. The resulting THz field can be characterized via its electric field ETHz(t). Present-day experiments can already output ETHz(t) that has a peak value in the range of MV/cm (megavolts per centimeter).Junginger, F.; Sell, A.; Schubert, O.; Mayer, B.; Brida, D.; Marangoni, M.; Cerullo, G.; Leitenstorfer, A. et al. (2010). "Single-cycle multiterahertz transients with peak fields above 10 MV/cm". Optics Letters 35 (15): 2645. doi:10.1364/OL.35.002645 To estimate how strong such fields are, one can compute the level of energy change such fields induce to an electron over microscopic distance of one nanometer (nm), i.e., L = 1 nm. One simply multiplies the peak ETHz(t) with elementary charge e and L to obtain e ETHz(t) L = 100 meV. In other words, such fields have a major effect on electronic systems because the mere field strength of ETHz(t) can induce electronic transitions over microscopic scales. One possibility is to use such THz fields to study Bloch oscillationsFeldmann, J.; Leo, K.; Shah, J.; Miller, D.; Cunningham, J.; Meier, T.; von Plessen, G.; Schulze, A.; Thomas, P.; Schmitt-Rink, S. (1992). "Optical investigation of Bloch oscillations in a semiconductor superlattice". Physical Review B 46 (11): 7252–7255. doi:10.1103/PhysRevB.46.7252Ben Dahan, Maxime; Peik, Ekkehard; Reichel, Jakob; Castin, Yvan; Salomon, Christophe (1996). "Bloch Oscillations of Atoms in an Optical Potential". Physical Review Letters 76 (24): 4508–4511. doi:10.1103/PhysRevLett.76.4508 where semiconductor electrons move through the Brillouin zone, just to return to where they started, giving rise to the Bloch oscillations.
The THz sources can be also extremely short,Jepsen, P.U.; Cooke, D.G.; Koch, M. (2011). "Terahertz spectroscopy and imaging - Modern techniques and applications". Laser & Photonics Reviews 5 (1): 124–166. doi:10.1002/lpor.201000011 down to single cycle of THz field's oscillation. For one THz, that means duration in the range of one picosecond (ps). Consequently, one can use THz fields to monitor and control ultrafast processes in semiconductors or to produce ultrafast switching in semiconductor components. Obviously, the combination of ultrafast duration and strong peak ETHz(t) provides vast new possibilities to systematic studies in semiconductors.
Besides the strength and duration of ETHz(t), the THz field's photon energy plays a vital role in semiconductor investigations because it can be made resonant with several intriguing many-body transitions. For example, electrons in conduction band and holes, i.e., electronic vacancies, in valence band attract each other via the Coulomb interaction. Under suitable conditions, electrons and holes can be bound to excitons that are hydrogen-like states of matter. At the same time, the exciton binding energy is few to hundreds of meV that can be matched energetically with a THz photon. Therefore, the presence of excitons can be uniquely detectedTimusk, T.; Navarro, H.; Lipari, N.O.; Altarelli, M. (1978). "Far-infrared absorption by excitons in silicon". Solid State Communications 25 (4): 217–219. doi:10.1016/0038-1098(78)90216-8Kira, M.; Hoyer, W.; Stroucken, T.; Koch, S. (2001). "Exciton Formation in Semiconductors and the Influence of a Photonic Environment". Physical Review Letters 87 (17). doi:10.1103/PhysRevLett.87.176401 based on the absorption spectrum of a weak THz field.Kaindl, R. A.; Carnahan, M. A.; Hägele, D.; Lövenich, R.; Chemla, D. S. (2003). "Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas". Nature 423 (6941): 734–738. doi:10.1038/nature01676Kira, M.; Hoyer, W.; Koch, S.W. (2004). "Terahertz signatures of the exciton formation dynamics in non-resonantly excited semiconductors". Solid State Communications 129 (11): 733–736. doi:10.1016/j.ssc.2003.12.015 Also simple states, such as plasma and correlated electron–hole plasma can be monitored or modified by THz fields.
Terahertz time-domain spectroscopy
In optical spectroscopy, the detectors typically measure the intensity of the light field rather than the electric field because there are no detectors that can directly measure electromagnetic fields in the optical range. However, there are multiple techniques, such as antennas and electro-optical sampling, that can be applied to measure the time evolution of ETHz(t) directly. For example, one can propagate a THz pulse through a semiconductor sample and measure the transmitted and reflected fields as function of time. Therefore, one collects information of semiconductor excitation dynamics completely in time domain, which is the general principle of the terahertz time-domain spectroscopy.
By using short THz pulses, a great variety of physical phenomena have already been studied. For unexcited, intrinsic semiconductors one can determine the complex permittivity or THz-absorption coefficient and refractive index, respectively.Grischkowsky, D.; Keiding, Søren; Exter, Martin van; Fattinger, Ch. (1990). "Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors". Journal of the Optical Society of America B 7 (10): 2006. doi:10.1364/JOSAB.7.002006 The frequency of transversal-optical phonons, to which THz photons can couple, lies for most semiconductors at several THz.Han, P. Y.; Zhang, X.-C. (1998). "Coherent, broadband midinfrared terahertz beam sensors". Applied Physics Letters 73 (21): 3049. doi:10.1063/1.122668 Free carriers in doped semiconductors or optically excited semiconductors lead to a considerable absorption of THz photons.Zhang, W.; Azad, Abul K.; Grischkowsky, D. (2003). "Terahertz studies of carrier dynamics and dielectric response of n-type, freestanding epitaxial GaN". Applied Physics Letters 82 (17): 2841. doi:10.1063/1.1569988 Since THz pulses passes through non-metallic materials, they can be used for inspection and transmission of packaged items.
Frequency-domain spectroscopy Frequency-domain terahertz spectroscopy (THz-FDS) uses continuous-wave terahertz radiation whose frequency is swept across a selected range to measure a material’s amplitude and phase response. In contrast to time-domain terahertz spectroscopy (THz-TDS), which measures broadband pulses and analyzes their temporal waveform, THz-FDS operates directly in the frequency domain.Coutaz, J.-L., & Garet, F. (2017). Principles of THz Time-Domain Spectroscopy. Stanford Publishing.Lee, Y.-S. (2009). Principles of Terahertz Science and Technology. Springer.
THz-FDS systems typically rely on photomixing, where two narrow-linewidth near-infrared lasers with a very small frequency offset illuminate an ultrafast photoconductive device (commonly low-temperature-grown GaAs or InGaAs structures). The optical beat frequency generates a continuous-wave terahertz signal. A second photomixer illuminated by the same lasers performs coherent detection, preserving both amplitude and phase of the terahertz field.Brown, E. R.; McIntosh, K. A.; Nicholas, G. M.; DiNatale, W.F.; Dennis, K. L. (1995). "Photomixing up to 3.8 THz in low-temperature-grown GaAs". Applied Physics Letters. 66: 285.Peytavit, E.; Ducournau, G.; Lampin, J.-F. (2021). Fundamentals of THz Devices and Applications. Wiley.
A key advantage of THz-FDS is its extremely high spectral resolution, often better than 1 MHz, enabling it to resolve Doppler-limited gas-phase transitions and other very narrow spectral features.Hindle, F.; Cuisset, A.; Bocquet, R.; Mouret, G. (2008). "Continuous-wave terahertz by photomixing: applications to gas-phase pollutant detection and quantification". Comptes Rendus Physique. 9(2): 262-275.Demers, J.R.; Kasper, B.; Daughton, D.R. (2014). "Simultaneous measurement of the 1st and 2nd harmonics of a phase-modulated coherent frequency-domain THz spectrometer". IRMMW-THz 2014. IEEE. This makes THz-FDS particularly powerful for high-precision rotational spectroscopy, phonon studies in solids, and measurement of sharp resonances in semiconductors, superconductors, metamaterials, and thin-film structures. THz-FDS systems also achieve high dynamic range and provide quantitative measurements of absorption and refractive-index spectra.Roggenbuck, A.; Schmitz, H.; Deninger, A.; Mayorga, I. C.; Hemberger, J.; Güsten, R.; Grüninger, M. (2010). "Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples". New Journal of Physics. 12: 043017.