View source for Terahertz spectroscopy and technology

'''Terahertz spectroscopy''' detects and controls properties of matter with [[electromagnetic fields]] that are in the frequency range between a few hundred [[gigahertz]] and several [[Terahertz (unit)|terahertz]] (abbreviated as THz). In [[many-body]] systems, several of the relevant states have an energy difference that matches with the energy of a THz [[photon]]. Therefore, THz spectroscopy provides a particularly powerful method in resolving and controlling individual transitions between different many-body states. By doing this, one gains new insights about many-body [[quantum kinetics]] and how that can be utilized in developing new technologies that are optimized up to the elementary quantum level.

Different electronic excitations within semiconductors are already widely used in [[lasers]], electronic components and [[computer]]s. At the same time, they constitute an interesting many-body system whose quantum properties can be modified, e.g., via a [[nanostructure]] design. Consequently, THz spectroscopy on semiconductors is relevant in revealing both new technological potentials of nanostructures as well as in exploring the fundamental properties of many-body systems in a controlled fashion.

==Background==

There are a great variety of techniques to generate [[THz radiation]] and to detect THz fields. One can, e.g., use an [[antenna (radio)|antenna]], a [[quantum cascade laser|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 ''E''<sub>THz</sub>(''t''). Present-day experiments can already output ''E''<sub>THz</sub>(''t'') that has a peak value in the range of MV/cm (megavolts per centimeter).<ref name="JungingerSell2010">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]]</ref> 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&nbsp;nm. One simply multiplies the peak ''E''<sub>THz</sub>(''t'') with [[elementary charge]] ''e'' and ''L'' to obtain ''e'' ''E''<sub>THz</sub>(''t'') ''L'' = 100 meV. In other words, such fields have a major effect on electronic systems because the mere field strength of ''E''<sub>THz</sub>(''t'') can induce electronic transitions over [[microscopic scale]]s. One possibility is to use such THz fields to study [[Bloch oscillations]]<ref name="FeldmannLeo1992">Feldmann, 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.46.7252]]</ref><ref name="Ben DahanPeik1996">Ben 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]]</ref> 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,<ref name="JepsenCooke2011">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]]</ref> 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 ''E''<sub>THz</sub>(''t'') provides vast new possibilities to systematic studies in semiconductors. 

Besides the strength and duration of ''E''<sub>THz</sub>(''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 [[electron hole|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 [[exciton]]s 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 detected<ref name="TimuskNavarro1978">Timusk, 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)90216-8]]</ref><ref name="KiraHoyer2001">Kira, 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]]</ref> based on the absorption spectrum of a weak THz field.<ref name="KaindlCarnahan2003">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/nature01676]]</ref><ref name="KiraHoyer2004">Kira, 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]]</ref> Also simple states, such as [[plasma (physics)|plasma]] and correlated electron–hole plasma<ref name="KiraKoch2006"/> can be monitored or modified by THz fields.

==Terahertz time-domain spectroscopy==

{{Main|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  [[Terahertz time-domain spectroscopy#Electro-optical sampling|electro-optical sampling]], that can be applied to measure the time evolution of ''E''<sub>THz</sub>(''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]].
[[File:Using Terahertz for developing transmission images of packaged items.gif|thumb|Using Terahertz for developing transmission images of packaged items.<ref>{{Cite patent|title=Method and system for enhancing resolution of terahertz imaging|country=US|number=10783612|pubdate=2020-09-22|inventor1-last=Ahi|inventor1-first=Kiarash}}</ref>]]
By using short THz pulses,<ref name="JepsenCooke2011" />  a great variety of physical phenomena have already been studied. For unexcited, [[intrinsic semiconductor]]s one can determine the [[Permittivity#Complex permittivity|complex permittivity]] or THz-absorption coefficient and refractive index, respectively.<ref name="GrischkowskyKeiding1990">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]]</ref> The frequency of transversal-optical [[phonon]]s, to which THz photons can couple, lies for most semiconductors at several THz.<ref name="HanZhang1998">Han, P. Y.; Zhang, X.-C. (1998). "Coherent, broadband midinfrared terahertz beam sensors". ''Applied Physics Letters'' '''73''' (21): 3049. [[doi:10.1063/1.122668]]</ref> Free carriers in [[Doping (semiconductor)|doped semiconductors]] or optically excited semiconductors lead to a considerable absorption of THz photons.<ref name="ZhangAzad2003">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]]</ref> Since THz pulses passes through non-metallic materials, they can be used for inspection and transmission of packaged items.   

==Terahertz-induced plasma and exciton transitions==

The THz fields can be applied to accelerate electrons out of their equilibrium. If this is done fast enough, one can measure the elementary processes, such as how fast the [[Electric-field screening|screening]] of the Coulomb interaction is built up. This was experimentally explored in Ref.<ref name="HuberTauser2001">Huber, R.; Tauser, F.; Brodschelm, A.; Bichler, M.; Abstreiter, G.; Leitenstorfer, A. (2001). ''Nature'' '''414''' (6861): 286–289. [[doi:10.1038/35104522]]</ref> where it was shown that screening is complete within tens of femtoseconds in semiconductors. These insights are very important to understand how electronic plasma behaves in [[solid]]s.

The Coulomb interaction can also pair electrons and holes into excitons, as discussed above. Due to their analog to the [[hydrogen atom]], excitons have  [[bound state]]s that can be uniquely identified by the usual [[quantum number]]s 1''s'', 2''s'', 2''p'', and so on. In particular, 1''s''-to-2''p'' transition is dipole allowed and can be directly generated by ''E''<sub>THz</sub>(''t'') if the photon energy matches the transition energy. In [[gallium arsenide]]-type systems, this transition energy is roughly 4 meV that corresponds to 1 THz photons. At resonance, the dipole ''d''<sub>1''s'',2''p''</sub> defines the Rabi energy Ω<sub>Rabi</sub> = ''d''<sub>1''s'',2''p''</sub> ''E''<sub>THz</sub>(''t'') that determines the time scale at which the 1''s''-to-2''p'' transition proceeds.

For example, one can excite the excitonic transition with an additional optical pulse which is synchronized with the THz pulse. This technique is called transient THz spectroscopy.<ref name="JepsenCooke2011" /> Using this technique one can follow the formation dynamics of excitons<ref name="KaindlCarnahan2003" /><ref name="KiraHoyer2004" /> or observe THz gain arising from intraexcitonic transitions.<ref name="KiraKoch2004">Kira, M.; Koch, S. (2004). "Exciton-Population Inversion and Terahertz Gain in Semiconductors Excited to Resonance". ''Physical Review Letters'' '''93''' (7). [[doi:10.1103/PhysRevLett.93.076402]]</ref><ref name="HuberSchmid2006">Huber, Rupert; Schmid, Ben; Shen, Y.; Chemla, Daniel; Kaindl, Robert (2006). "Stimulated Terahertz Emission from Intraexcitonic Transitions in Cu2O". ''Physical Review Letters'' '''96''' (1). [[doi:10.1103/PhysRevLett.96.017402]]</ref>

Since a THz pulse can be intense and short, e.g., single-cycle, it is experimentally possible to realize situations where duration of the pulse, time scale related to Rabi- as well as the THz photon energy ħω are degenerate. In this situation, one enters the realm of [[extreme nonlinear optics]]<ref name="Wegener2005">Wegener, M. (2005). M. ''Extreme Nonlinear Optics: An Introduction''. Springer. {{ISBN|978-3642060908}}</ref> where the usual approximations, such as the [[Rotating wave approximation|rotating-wave approximation]] (abbreviated as RWA) or the conditions for complete state transfer, break down. As a result, the [[Rabi oscillation]]s become strongly distorted by the non-RWA contributions, the [[multiphoton absorption]] or emission processes, and the dynamic [[Franz–Keldysh effect]], as measured in Refs.<ref name="DanielsonLee2007">Danielson, J.; Lee, Yun-Shik; Prineas, J.; Steiner, J.; Kira, M.; Koch, S. (2007). "Interaction of Strong Single-Cycle Terahertz Pulses with Semiconductor Quantum Wells". ''Physical Review Letters'' '''99''' (23). [[doi:10.1103/PhysRevLett.99.237401]]</ref><ref name="LeinßKampfrath2008">Leinß, S.; Kampfrath, T.; v.Volkmann, K.; Wolf, M.; Steiner, J.; Kira, M.; Koch, S.; Leitenstorfer, A. et al. (2008). "Terahertz Coherent Control of Optically Dark Paraexcitons in Cu2O". ''Physical Review Letters'' '''101''' (24). [[doi:10.1103/PhysRevLett.101.246401]]</ref>

By using a free-electron laser, one can generate longer THz pulses that are more suitable for detecting the Rabi oscillations directly.  This technique could indeed demonstrate the Rabi oscillations, or actually the related [[Autler–Townes splitting]], in experiments.<ref name="WagnerSchneider2010">Wagner, Martin; Schneider, Harald; Stehr, Dominik; Winnerl, Stephan; Andrews, Aaron M.; Schartner, Stephan; Strasser, Gottfried; Helm, Manfred (2010). "Observation of the Intra-exciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells". ''Physical Review Letters'' '''105''' (16). [[doi:10.1103/PhysRevLett.105.167401]]</ref> The Rabi splitting has also been measured with a short THz pulse<ref name="SteinerKira2008">Steiner, J.; Kira, M.; Koch, S. (2008). "Optical nonlinearities and Rabi flopping of an exciton population in a semiconductor interacting with strong terahertz fields". ''Physical Review B'' '''77''' (16). [[doi:10.1103/PhysRevB.77.165308]]</ref> and also the onset to multi-THz-photon ionization has been detected,<ref name="EwersKöster2012">Ewers, B.; Köster, N. S.; Woscholski, R.; Koch, M.; Chatterjee, S.; [[Galina Khitrova|Khitrova, G.]]; Gibbs, H. M.; Klettke, A. C.; Kira, M.; Koch, S. W. (2012). "Ionization of coherent excitons by strong terahertz fields". ''Physical Review B'' '''85''' (7). [[doi:10.1103/PhysRevB.85.075307]]</ref> as the THz fields are made stronger. Recently, it has also been shown that the Coulomb interaction causes nominally dipole-forbidden intra-excitonic transitions to become partially allowed.<ref name="RiceKono2013">Rice, W. D.; Kono, J.; Zybell, S.; Winnerl, S.; Bhattacharyya, J.; Schneider, H.; Helm, M.; Ewers, B.; Chernikov, A.; Koch, M.; Chatterjee, S.; [[Galina Khitrova|Khitrova, G.]]; Gibbs, H. M.; Schneebeli, L.; Breddermann, B.; Kira, M.; Koch, S. W. (2013). "Observation of Forbidden Exciton Transitions Mediated by Coulomb Interactions in Photoexcited Semiconductor Quantum Wells". ''Physical Review Letters'' '''110''' (13). [[doi:10.1103/PhysRevLett.110.137404]]</ref>

==Theory of terahertz transitions==

Terahertz transitions in solids can be systematically approached by generalizing the [[semiconductor Bloch equations]]<ref name="KiraKoch2006">{{cite journal|last1=Kira|first1=M.|last2=Koch|first2=S.W.|title=Many-body correlations and excitonic effects in semiconductor spectroscopy|journal=Progress in Quantum Electronics|volume=30|issue=5|date=2006|pages=155–296|issn=0079-6727|doi=10.1016/j.pquantelec.2006.12.002|bibcode = 2006PQE....30..155K |doi-access=free}}</ref> and the related many-body correlation dynamics. At this level, one realizes the THz field are directly absorbed by [[cluster-expansion approach|two-particle correlations]] that modify the quantum kinetics of electron and hole distributions. Therefore, a systematic THz analysis must include the quantum kinetics of many-body correlations, that can be treated systematically, e.g., with the [[cluster-expansion approach]]. At this level, one can explain and predict a wide range of effects with the same theory, ranging from [[Drude model|Drude]]-like response<ref name="ZhangAzad2003" /> of plasma to extreme nonlinear effects of excitons.

==See also==
* [[Terahertz nondestructive evaluation]]
* [[Terahertz time-domain spectroscopy]]
* [[Terahertz radiation]]
* [[Ultrafast laser spectroscopy]]
* [[Semiconductor Bloch equations]]
* [[Cluster-expansion approach]]
* [[Elliott formula]]

==References==
{{Reflist}}

{{Branches of Spectroscopy}}

[[Category:Spectroscopy]]
[[Category:Terahertz technology]]