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&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Short description|Photodetector sensitive to infrared radiation}}&lt;br /&gt;
&lt;br /&gt;
{{Quantum methods backlink|Measurement techniques}}&lt;br /&gt;
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&amp;lt;div style=&amp;quot;float:right; border:1px solid #e0d890; background:#fff8cc; padding:6px; margin:0 0 1em 1em; width:520px;&amp;quot;&amp;gt;&lt;br /&gt;
[[File:Quantum cascade detector band alignment.png|500px]]&lt;br /&gt;
&amp;lt;div style=&amp;quot;font-size:90%;&amp;quot;&amp;gt;Typical band structure of one period of a quantum cascade detector. The optical quantum well absorbs the photon, while adjacent wells extract the photoexcited electron and cascade it into the next period.&amp;lt;ref name=&amp;quot;:3&amp;quot;&amp;gt;{{Citation |last=Delga |first=Alexandre |title=Quantum cascade detectors: A review |date=2020 |work=Mid-infrared Optoelectronics |pages=337–377 |publisher=Elsevier |doi=10.1016/b978-0-08-102709-7.00008-5 |isbn=978-0-08-102709-7}}&amp;lt;/ref&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A &amp;#039;&amp;#039;&amp;#039;quantum cascade detector&amp;#039;&amp;#039;&amp;#039; (&amp;#039;&amp;#039;&amp;#039;QCD&amp;#039;&amp;#039;&amp;#039;) is an infrared [[Physics:Photodetector|photodetector]] based on engineered [[Physics:Quantum well|multiple quantum wells]]. It detects incident [[Physics:Infrared|infrared]] radiation through intersubband electronic transitions in a semiconductor heterostructure.&amp;lt;ref name=&amp;quot;:2&amp;quot;&amp;gt;{{Cite journal |last1=Gendron |first1=L. |last2=Carras |first2=M. |last3=Huynh |first3=A. |last4=Ortiz |first4=V. |last5=Koeniguer |first5=C. |last6=Berger |first6=V. |date=2004-10-04 |title=Quantum cascade photodetector |url=https://pubs.aip.org/apl/article/85/14/2824/327142/Quantum-cascade-photodetector |journal=Applied Physics Letters |language=en |volume=85 |issue=14 |pages=2824–2826 |doi=10.1063/1.1781731 |bibcode=2004ApPhL..85.2824G |issn=0003-6951|url-access=subscription }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The word &amp;#039;&amp;#039;cascade&amp;#039;&amp;#039; refers to the path followed by photoexcited electrons through a sequence of coupled quantum wells. After absorbing a photon, an electron is promoted to a higher confined state and then transported through an extraction region into the next period of the structure.&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
QCDs are fabricated by stacking thin semiconductor layers on lattice-matched substrates using epitaxial growth techniques such as [[Physics:Molecular-beam epitaxy|molecular-beam epitaxy]] and metal-organic vapor-phase epitaxy.&amp;lt;ref name=&amp;quot;:3&amp;quot; /&amp;gt; By changing the thickness and composition of the wells and barriers, the detector wavelength can be tuned from short-wave infrared to long-wave infrared and terahertz regimes.&amp;lt;ref&amp;gt;{{Cite journal |last1=Buffaz |first1=A. |last2=Carras |first2=M. |last3=Doyennette |first3=L. |last4=Nedelcu |first4=A. |last5=Marcadet |first5=X. |last6=Berger |first6=V. |date=2010-04-26 |title=Quantum cascade detectors for very long wave infrared detection |url=https://pubs.aip.org/apl/article/96/17/172101/118282/Quantum-cascade-detectors-for-very-long-wave |journal=Applied Physics Letters |language=en |volume=96 |issue=17 |article-number=172101 |doi=10.1063/1.3409139 |bibcode=2010ApPhL..96q2101B |issn=0003-6951|url-access=subscription }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;:4&amp;quot;&amp;gt;{{Cite journal |last1=Giorgetta |first1=F. R. |last2=Baumann |first2=E. |last3=Théron |first3=R. |last4=Pellaton |first4=M. L. |last5=Hofstetter |first5=D. |last6=Fischer |first6=M. |last7=Faist |first7=J. |date=2008-03-24 |title=Short wavelength (4μm) quantum cascade detector based on strain compensated InGaAs∕InAlAs |url=https://pubs.aip.org/apl/article/92/12/121101/334292/Short-wavelength-4-m-quantum-cascade-detector |journal=Applied Physics Letters |language=en |volume=92 |issue=12 |article-number=121101 |doi=10.1063/1.2902301 |bibcode=2008ApPhL..92l1101G |issn=0003-6951|url-access=subscription }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;:0&amp;quot;&amp;gt;{{Cite journal |last=Ravikumar |first=Arvind P. |date=11 August 2014 |title=High detectivity short-wavelength II-VI quantum cascade detector |url=https://pubs.aip.org/aip/apl/article/105/6/061113/385018 |journal=Applied Physics Letters |volume=105 |issue=6|article-number=061113 |doi=10.1063/1.4893359 |bibcode=2014ApPhL.105f1113R |url-access=subscription }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;:1&amp;quot;&amp;gt;{{Cite journal |last1=Quach |first1=P. |last2=Jollivet |first2=A. |last3=Babichev |first3=A. |last4=Isac |first4=N. |last5=Morassi |first5=M. |last6=Lemaitre |first6=A. |last7=Yunin |first7=P. A. |last8=Frayssinet |first8=E. |last9=de Mierry |first9=P. |last10=Jeannin |first10=M. |last11=Bousseksou |first11=A. |last12=Colombelli |first12=R. |last13=Tchernycheva |first13=M. |last14=Cordier |first14=Y. |last15=Julien |first15=F. H. |date=2022-04-25 |title=A 5.7 THz GaN/AlGaN quantum cascade detector based on polar step quantum wells |journal=Applied Physics Letters |volume=120 |issue=17 |article-number=171103 |doi=10.1063/5.0086641 |arxiv=2204.07117 |bibcode=2022ApPhL.120q1103Q |issn=0003-6951}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Unlike many photoconductive detectors, QCDs operate in [[Chemistry:Photovoltaic effect|photovoltaic]] mode and do not require an external bias to generate a photoresponse. In this sense they can be viewed as the photovoltaic counterpart of [[Physics:Quantum well infrared photodetector|quantum well infrared photodetectors]] (QWIPs).&amp;lt;ref name=&amp;quot;link.aps.org&amp;quot;&amp;gt;{{Cite journal |last1=Lagrée |first1=M. |last2=Jeannin |first2=M. |last3=Quinchard |first3=G. |last4=Ouznali |first4=O. |last5=Evirgen |first5=A. |last6=Trinité |first6=V. |last7=Colombelli |first7=R. |last8=Delga |first8=A. |date=2022-04-12 |title=Direct Polariton-To-Electron Tunneling in Quantum Cascade Detectors Operating in the Strong Light-Matter Coupling Regime |url=https://link.aps.org/doi/10.1103/PhysRevApplied.17.044021 |journal=Physical Review Applied |volume=17 |issue=4 |article-number=044021 |doi=10.1103/PhysRevApplied.17.044021|arxiv=2110.08060 |bibcode=2022PhRvP..17d4021L }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Applications ==&lt;br /&gt;
&lt;br /&gt;
Because many molecular vibrational modes lie in the mid-infrared, QCDs are useful for infrared sensing and spectroscopy. They have been investigated for gas sensing, high-resolution spectroscopy, dual-comb systems and free-space optical communication.&amp;lt;ref name=&amp;quot;:3&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{Cite journal |last1=Harrer |first1=Andreas |last2=Szedlak |first2=Rolf |last3=Schwarz |first3=Benedikt |last4=Moser |first4=Harald |last5=Zederbauer |first5=Tobias |last6=MacFarland |first6=Donald |last7=Detz |first7=Hermann |last8=Andrews |first8=Aaron Maxwell |last9=Schrenk |first9=Werner |last10=Lendl |first10=Bernhard |last11=Strasser |first11=Gottfried |date=2016-02-18 |title=Mid-infrared surface transmitting and detecting quantum cascade device for gas-sensing |journal=Scientific Reports |language=en |volume=6 |issue=1 |article-number=21795 |doi=10.1038/srep21795 |issn=2045-2322 |pmc=4757892 |pmid=26887891|bibcode=2016NatSR...621795H }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;:6&amp;quot;&amp;gt;{{Cite journal |last1=Marschick |first1=G. |last2=David |first2=M. |last3=Arigliani |first3=E. |last4=Opačak |first4=N. |last5=Schwarz |first5=B. |last6=Giparakis |first6=M. |last7=Delga |first7=A. |last8=Lagree |first8=M. |last9=Poletti |first9=T. |last10=Trinite |first10=V. |last11=Evirgen |first11=A. |last12=Gerard |first12=B. |last13=Ramer |first13=G. |last14=Maulini |first14=R. |last15=Butet |first15=J. |date=2022-10-24 |title=High-responsivity operation of quantum cascade detectors at 9 µm |url=https://opg.optica.org/abstract.cfm?URI=oe-30-22-40188 |journal=Optics Express |language=en |volume=30 |issue=22 |pages=40188–40195 |doi=10.1364/OE.470615 |pmid=36298955 |bibcode=2022OExpr..3040188M |issn=1094-4087|doi-access=free }}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite journal |last1=Dougakiuchi |first1=Tatsuo |last2=Akikusa |first2=Naota |date=30 July 2021 |title=Application of High-Speed Quantum Cascade Detectors for Mid-Infrared, Broadband, High-Resolution Spectroscopy |journal=Sensors |language=en |volume=21 |issue=17 |page=5706 |doi=10.3390/s21175706 |doi-access=free |issn=1424-8220 |pmc=8433808 |pmid=34502596|bibcode=2021Senso..21.5706D }}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite journal |last1=Villares |first1=Gustavo |last2=Hugi |first2=Andreas |last3=Blaser |first3=Stéphane |last4=Faist |first4=Jérôme |date=2014-10-13 |title=Dual-comb spectroscopy based on quantum-cascade-laser frequency combs |url=https://www.nature.com/articles/ncomms6192 |journal=Nature Communications |language=en |volume=5 |issue=1 |page=5192 |doi=10.1038/ncomms6192 |pmid=25307936 |bibcode=2014NatCo...5.5192V |issn=2041-1723}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite conference |last1=Grillot |first1=Frederic |last2=Didier |first2=Pierre |last3=Dely |first3=Hamza |last4=Bonazzi |first4=Thomas |last5=Spitz |first5=Olivier |last6=Awwad |first6=Elie |last7=Rodriguez |first7=Etienne |last8=Vasanelli |first8=Angela |last9=Sirtori |first9=Carlo |date=November 2022 |title=Free-space laser communications with quantum cascade devices in the thermal-infrared atmospheric window |conference=2022 IEEE Photonics Conference (IPC)|location=Vancouver |publisher=IEEE |pages=1–2 |doi=10.1109/IPC53466.2022.9975702 |isbn=978-1-6654-3487-4}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== History ==&lt;br /&gt;
&lt;br /&gt;
In 2002, Daniel Hofstetter, Mattias Beck and Jérôme Faist reported the use of an [[Chemistry:Indium gallium arsenide|InGaAs]]/[[Chemistry:Aluminium indium arsenide|InAlAs]] [[Engineering:Quantum-cascade laser|quantum-cascade-laser]] structure as a room-temperature photodetector. Its [[Physics:Specific detectivity|specific detectivity]] was comparable to established infrared detectors such as QWIPs and [[Physics:Mercury cadmium telluride|HgCdTe]] detectors.&amp;lt;ref name=&amp;quot;:9&amp;quot;&amp;gt;{{Cite journal |last1=Hofstetter |first1=Daniel |last2=Beck |first2=Mattias |last3=Faist |first3=Jérôme |date=2002-10-07 |title=Quantum-cascade-laser structures as photodetectors |url=https://pubs.aip.org/apl/article/81/15/2683/510656/Quantum-cascade-laser-structures-as-photodetectors |journal=Applied Physics Letters |language=en |volume=81 |issue=15 |pages=2683–2685 |doi=10.1063/1.1512954 |bibcode=2002ApPhL..81.2683H |issn=0003-6951|url-access=subscription }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This result led to research on bi-functional quantum cascade devices combining lasing and detection in a single photonic architecture.&amp;lt;ref&amp;gt;{{Cite journal |last1=Schwarz |first1=Benedikt |last2=Reininger |first2=Peter |last3=Detz |first3=Hermann |last4=Zederbauer |first4=Tobias |last5=Maxwell Andrews |first5=Aaron |last6=Kalchmair |first6=Stefan |last7=Schrenk |first7=Werner |last8=Baumgartner |first8=Oskar |last9=Kosina |first9=Hans |last10=Strasser |first10=Gottfried |date=2012-11-05 |title=A bi-functional quantum cascade device for same-frequency lasing and detection |url=https://pubs.aip.org/aip/apl/article/127548 |journal=Applied Physics Letters |language=en |volume=101 |issue=19 |page=191109 |doi=10.1063/1.4767128 |bibcode=2012ApPhL.101s1109S |issn=0003-6951|url-access=subscription }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;:12&amp;quot;&amp;gt;{{Cite journal |last1=Schwarz |first1=Benedikt |last2=Wang |first2=Christine A. |last3=Missaggia |first3=Leo |last4=Mansuripur |first4=Tobias S. |last5=Chevalier |first5=Paul |last6=Connors |first6=Michael K. |last7=McNulty |first7=Daniel |last8=Cederberg |first8=Jeffrey |last9=Strasser |first9=Gottfried |last10=Capasso |first10=Federico |date=2017-05-17 |title=Watt-Level Continuous-Wave Emission from a Bifunctional Quantum Cascade Laser/Detector |journal=ACS Photonics |language=en |volume=4 |issue=5 |pages=1225–1231 |doi=10.1021/acsphotonics.7b00133 |issn=2330-4022 |pmc=5437807 |pmid=28540324 |bibcode=2017ACSP....4.1225S }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;:13&amp;quot;&amp;gt;{{Cite journal |last1=Schwarz |first1=Benedikt |last2=Ristanic |first2=Daniela |last3=Reininger |first3=Peter |last4=Zederbauer |first4=Tobias |last5=MacFarland |first5=Donald |last6=Detz |first6=Hermann |last7=Andrews |first7=Aaron Maxwell |last8=Schrenk |first8=Werner |last9=Strasser |first9=Gottfried |date=2015-08-17 |title=High performance bi-functional quantum cascade laser and detector |journal=Applied Physics Letters |volume=107 |issue=7 |article-number=071104 |doi=10.1063/1.4927851 |bibcode=2015ApPhL.107g1104S |issn=0003-6951|doi-access=free }}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite journal |last1=Schwarz |first1=Benedikt |last2=Reininger |first2=Peter |last3=Detz |first3=Hermann |last4=Zederbauer |first4=Tobias |last5=Andrews |first5=Aaron Maxwell |last6=Schrenk |first6=Werner |last7=Strasser |first7=Gottfried |date=4 January 2013 |title=Monolithically Integrated Mid-Infrared Quantum Cascade Laser and Detector |journal=Sensors |language=en |volume=13 |issue=2 |pages=2196–2205 |doi=10.3390/s130202196 |doi-access=free |pmid=23389348 |pmc=3649417 |bibcode=2013Senso..13.2196S |issn=1424-8220}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The term &amp;#039;&amp;#039;quantum cascade detector&amp;#039;&amp;#039; was introduced in 2004 when L. Gendron and V. Berger demonstrated a cascade device dedicated to photodetection using a GaAs/AlGaAs heterostructure.&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt; Later work extended QCDs to material systems such as II-VI ZnCdSe/ZnCdMgSe, GaN/AlGaN and ZnO/MgZnO, enabling broader wavelength coverage and room-temperature operation.&amp;lt;ref name=&amp;quot;:0&amp;quot; /&amp;gt;&amp;lt;ref name=&amp;quot;:1&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{Cite journal |last1=Sakr |first1=S. |last2=Giraud |first2=E. |last3=Dussaigne |first3=A. |last4=Tchernycheva |first4=M. |last5=Grandjean |first5=N. |last6=Julien |first6=F. H. |date=2012-04-30 |title=Two-color GaN/AlGaN quantum cascade detector at short infrared wavelengths of 1 and 1.7 &amp;#039;&amp;#039;μ&amp;#039;&amp;#039;m |journal=Applied Physics Letters |volume=100 |issue=18 |article-number=181103 |doi=10.1063/1.4707904 |bibcode=2012ApPhL.100r1103S |issn=0003-6951}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{Cite journal |last1=Ravikumar |first1=Arvind P. |last2=De Jesus |first2=Joel |last3=Tamargo |first3=Maria C. |last4=Gmachl |first4=Claire F. |date=2015-10-05 |title=High performance, room temperature, broadband II-VI quantum cascade detector |journal=Applied Physics Letters |volume=107 |issue=14 |article-number=141105 |doi=10.1063/1.4932538 |bibcode=2015ApPhL.107n1105R |issn=0003-6951}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Working principle ==&lt;br /&gt;
&lt;br /&gt;
[[File:Diagonal-transition quantum cascade detector.png|thumb|upright=1.5|Diagonal-transition QCD band structure. The electron moves from the optical well directly into the adjacent extraction region.&amp;lt;ref name=&amp;quot;:7&amp;quot;&amp;gt;{{Cite journal |last1=Reininger |first1=Peter |last2=Schwarz |first2=Benedikt |last3=Detz |first3=Hermann |last4=MacFarland |first4=Don |last5=Zederbauer |first5=Tobias |last6=Andrews |first6=Aaron Maxwell |last7=Schrenk |first7=Werner |last8=Baumgartner |first8=Oskar |last9=Gottfried |first9=Strasser |date=1 September 2014 |title=Diagonal-transition quantum cascade detector |journal=Applied Physics Letters |volume=105 |issue=9 |article-number=091108 |doi=10.1063/1.4894767|bibcode=2014ApPhL.105i1108R |doi-access=free }}&amp;lt;/ref&amp;gt;]]&lt;br /&gt;
&lt;br /&gt;
A QCD is a unipolar device: only one type of [[Physics:Charge carrier|charge carrier]], usually electrons, contributes to the [[Physics:Photocurrent|photocurrent]]. Each period contains an optical quantum well and an extraction region. The optical well absorbs radiation by promoting an electron between confined subbands. The extraction region then transfers the electron through a cascade of states until it reaches the next period.&amp;lt;ref name=&amp;quot;:3&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The electronic levels are controlled by [[Physics:Band-gap engineering|band-gap engineering]]. In a simplified infinite-well model, the confined-state energy is&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;E_{n}(\bold{k})=\frac{\hbar^{2}(k_{x}^{2}+k_{y}^{2})}{2m^{*}_{e}}+\frac{\pi^{2}\hbar^{2}}{2m^{*}_{e}W^{2}}n^{2},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\hbar&amp;lt;/math&amp;gt; is the reduced Planck constant, &amp;lt;math&amp;gt;\bold{k}&amp;lt;/math&amp;gt; is the in-plane wave vector, &amp;lt;math&amp;gt;m_{e}^{*}&amp;lt;/math&amp;gt; is the electron effective mass, &amp;lt;math&amp;gt;W&amp;lt;/math&amp;gt; is the well thickness and &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; labels the confined state.&amp;lt;ref&amp;gt;{{Citation |last1=Fox |first1=Mark |title=Quantum Wells, Superlattices, and Band-Gap Engineering |date=2007 |work=Springer Handbook of Electronic and Photonic Materials |pages=1021–1040 |editor-last=Kasap |editor-first=Safa |place=Boston, MA |publisher=Springer US |language=en |doi=10.1007/978-0-387-29185-7_42 |isbn=978-0-387-29185-7 |last2=Ispasoiu |first2=Radu |bibcode=2007shep.book.1021F |editor2-last=Capper |editor2-first=Peter}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
After photoexcitation, [[Physics:Quantum tunnelling|quantum tunnelling]] and scattering with longitudinal optical phonons transfer the electron through adjacent wells. Efficient extraction occurs when the energy spacing between states matches the optical phonon energy.&amp;lt;ref name=&amp;quot;:8&amp;quot;&amp;gt;{{Cite journal |last1=Hofstetter |first1=D. |last2=Giorgetta |first2=F. R. |last3=Baumann |first3=E. |last4=Yang |first4=Q. |last5=Manz |first5=C. |last6=Köhler |first6=K. |date=17 March 2010 |title=Mid-infrared quantum cascade detectors for applications in spectroscopy and pyrometry |url=http://link.springer.com/10.1007/s00340-010-3965-2 |journal=Applied Physics B |language=en |volume=100 |issue=2 |pages=313–320 |doi=10.1007/s00340-010-3965-2 |bibcode=2010ApPhB.100..313H |issn=0946-2171|url-access=subscription }}&amp;lt;/ref&amp;gt; Because longitudinal optical phonon scattering occurs on picosecond time scales, QCDs can have cut-off frequencies in the 100 GHz range.&amp;lt;ref name=&amp;quot;:3&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Figures of merit ==&lt;br /&gt;
&lt;br /&gt;
[[File:Responsivity of a QCD.png|thumb|upright=1.5|Experimental responsivity spectra of InGaAs/InAlAs QCDs at room temperature.&amp;lt;ref name=&amp;quot;:6&amp;quot; /&amp;gt;]]&lt;br /&gt;
&lt;br /&gt;
The responsivity of a quantum photodetector is&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;R(\lambda)=\frac{\eta\lambda e}{hc},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\eta&amp;lt;/math&amp;gt; is the external quantum efficiency, &amp;lt;math&amp;gt;\lambda&amp;lt;/math&amp;gt; is the wavelength, &amp;lt;math&amp;gt;e&amp;lt;/math&amp;gt; is the elementary charge, &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; is Planck&amp;#039;s constant and &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; is the speed of light.&amp;lt;ref&amp;gt;{{Cite book |last1=Rosencher |first1=Emmanuel |url=https://www.cambridge.org/core/books/optoelectronics/86B6621671230A798D5BFBE24266EE3F |title=Optoelectronics |last2=Vinter |first2=Borge |date=2002 |publisher=Cambridge University Press |isbn=978-0-521-77129-0 |location=Cambridge |translator-last=Piva |translator-first=P. G. |doi=10.1017/cbo9780511754647}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
For a QCD,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;R(\lambda)=\eta_{abs}\frac{p_{e}}{N}\frac{\lambda e}{hc},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\eta_{abs}&amp;lt;/math&amp;gt; is the absorption efficiency, &amp;lt;math&amp;gt;p_{e}&amp;lt;/math&amp;gt; is the extraction probability and &amp;lt;math&amp;gt;N&amp;lt;/math&amp;gt; is the number of active periods.&amp;lt;ref name=&amp;quot;:5&amp;quot;&amp;gt;{{Cite journal |last1=Giorgetta |first1=Fabrizio R. |last2=Baumann |first2=Esther |last3=Graf |first3=Marcel |last4=Yang |first4=Quankui |last5=Manz |first5=Christian |last6=Kohler |first6=Klaus |last7=Beere |first7=Harvey E. |last8=Ritchie |first8=David A. |last9=Linfield |first9=Edmund |last10=Davies |first10=Alexander G. |last11=Fedoryshyn |first11=Yuriy |last12=Jackel |first12=Heinz |last13=Fischer |first13=Milan |last14=Faist |first14=Jérome |last15=Hofstetter |first15=Daniel |date=14 July 2009 |title=Quantum Cascade Detectors |journal=IEEE Journal of Quantum Electronics |volume=45 |issue=8 |pages=1039–1052 |doi=10.1109/JQE.2009.2017929 |bibcode=2009IJQE...45.1039G |issn=0018-9197}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The specific detectivity &amp;lt;math&amp;gt;D^{*}&amp;lt;/math&amp;gt; is used to compare detectors with different area and bandwidth. When Johnson noise dominates, it can be estimated as&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;D^{*}=R_{p}\sqrt{\frac{R_{0}A}{4K_{b}T}},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;R_{p}&amp;lt;/math&amp;gt; is peak responsivity, &amp;lt;math&amp;gt;R_{0}&amp;lt;/math&amp;gt; is the zero-bias resistance, &amp;lt;math&amp;gt;A&amp;lt;/math&amp;gt; is detector area, &amp;lt;math&amp;gt;K_{b}&amp;lt;/math&amp;gt; is Boltzmann&amp;#039;s constant and &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; is temperature.&amp;lt;ref name=&amp;quot;:2&amp;quot; /&amp;gt;&amp;lt;ref name=&amp;quot;:8&amp;quot; /&amp;gt;&amp;lt;ref name=&amp;quot;:5&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Optical coupling ==&lt;br /&gt;
&lt;br /&gt;
[[File:45°-facet double-pass geometry.png|thumb|45°-facet double-pass geometry.&amp;lt;ref name=&amp;quot;:11&amp;quot;&amp;gt;{{Cite journal |last1=Giparakis |first1=Miriam |last2=Windischhofer |first2=Andreas |last3=Isceri |first3=Stefania |last4=Schrenk |first4=Werner |last5=Schwarz |first5=Benedikt |last6=Strasser |first6=Gottfried |last7=Andrews |first7=Aaron Maxwell |date=2024-04-03 |title=Design and performance of GaSb-based quantum cascade detectors |journal=Nanophotonics |language=en |volume=13 |issue=10 |pages=1773–1780 |doi=10.1515/nanoph-2023-0702 |issn=2192-8614 |pmc=11052536 |pmid=38681680|bibcode=2024Nanop..13.1773G }}&amp;lt;/ref&amp;gt;]]&lt;br /&gt;
&lt;br /&gt;
As intersubband devices, QCDs absorb only [[Physics:Polarization (waves)|TM-polarized]] light. This follows from intersubband [[Physics:Selection rule|selection rules]], which require an electric-field component perpendicular to the quantum-well planes.&amp;lt;ref&amp;gt;{{Cite book |last1=Schneider |first1=Harald |title=Quantum Well Infrared Photodetectors Physics and Applications |last2=Liu |first2=Hui Chun |publisher=Berlin : Springer |year=2007 |isbn=978-3-540-36323-1}}&amp;lt;/ref&amp;gt; Several coupling geometries are therefore used to direct suitable optical modes into the active region.&amp;lt;ref name=&amp;quot;:3&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=== 45° wedge configuration ===&lt;br /&gt;
&lt;br /&gt;
In the 45° wedge configuration, incident light is reflected from a polished facet so that part of the radiation becomes TM-polarized inside the active region. It is simple to fabricate and is widely used for characterization, although only part of the input optical power is efficiently coupled.&amp;lt;ref name=&amp;quot;:3&amp;quot; /&amp;gt;&amp;lt;ref name=&amp;quot;:9&amp;quot; /&amp;gt;&amp;lt;ref name=&amp;quot;:8&amp;quot; /&amp;gt;&amp;lt;ref name=&amp;quot;:5&amp;quot; /&amp;gt;&amp;lt;ref name=&amp;quot;:11&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=== Brewster-angle configuration ===&lt;br /&gt;
&lt;br /&gt;
At the [[Brewster&amp;#039;s angle|Brewster angle]], p-polarized light is transmitted through an interface with minimal reflection. For a semiconductor of refractive index &amp;lt;math&amp;gt;n_{s}&amp;lt;/math&amp;gt;, the angle is&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\theta_{B}=arctan({\frac{1}{n_{s}}}).&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This method avoids tilted facets but generally couples only a small fraction of the total incident power into the detector.&amp;lt;ref&amp;gt;{{Cite journal |date=1815-12-31 |title=IX. On the laws which regulate the polarisation of light by reflexion from transparent bodies. By David Brewster, LL. D. F. R. S. Edin. and F. S. A. Edin. In a letter addressed to Right Hon. Sir Joseph Banks, Bart. K. B. P. R. S |url=https://royalsocietypublishing.org/doi/10.1098/rstl.1815.0010 |journal=Philosophical Transactions of the Royal Society of London |language=en |volume=105 |pages=125–159 |doi=10.1098/rstl.1815.0010 |issn=0261-0523|url-access=subscription }}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;:3&amp;quot; /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=== Diffraction grating couplers ===&lt;br /&gt;
&lt;br /&gt;
Metallic diffraction gratings can couple incident light to [[Physics:Surface plasmon polariton|surface plasmon polaritons]] at the metal-semiconductor interface. These modes are TM-polarized and therefore compatible with intersubband absorption.&amp;lt;ref&amp;gt;{{Cite book |last1=Cottam |first1=Michael G. |url=https://www.taylorfrancis.com/books/9781420056914 |title=Introduction to Surface and Superlattice Excitations |last2=Tilley |first2=David R. |date=2019-05-07 |publisher=CRC Press |isbn=978-0-429-18704-9 |edition=2 |language=en |doi=10.1201/9780429187049}}&amp;lt;/ref&amp;gt;&amp;lt;ref name=&amp;quot;:10&amp;quot;&amp;gt;{{Cite journal |title=First demonstration of plasmonic GaN quantum cascade detectors with enhanced efficiency at normal incidence |url=https://opg.optica.org/oe/viewmedia.cfm?uri=oe-22-17-21069&amp;amp;html=true |access-date=2024-07-12 |journal=Optics Express |doi=10.1364/oe.22.021069 |date=2014 |last1=Pesach |first1=Asaf |last2=Sakr |first2=Salam |last3=Giraud |first3=Etienne |last4=Sorias |first4=Ofir |last5=Gal |first5=Lior |last6=Tchernycheva |first6=Maria |last7=Orenstein |first7=Meir |last8=Grandjean |first8=Nicolas |last9=Julien |first9=Francois H. |last10=Bahir |first10=Gad |volume=22 |issue=17 |pages=21069–21078 |pmid=25321307 |bibcode=2014OExpr..2221069P |doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=== Waveguide coupling ===&lt;br /&gt;
&lt;br /&gt;
Planar or ridge [[Physics:Waveguide|waveguides]] can confine the optical mode in the active region of a QCD. This approach is especially useful in integrated photonic devices and bi-functional quantum cascade laser/detector systems.&amp;lt;ref name=&amp;quot;:3&amp;quot; /&amp;gt;&amp;lt;ref name=&amp;quot;:12&amp;quot; /&amp;gt;&amp;lt;ref name=&amp;quot;:13&amp;quot; /&amp;gt;&amp;lt;ref&amp;gt;{{Cite journal |last1=Schwarz |first1=Benedikt |last2=Reininger |first2=Peter |last3=Harrer |first3=Andreas |last4=MacFarland |first4=Donald |last5=Detz |first5=Hermann |last6=Andrews |first6=Aaron M. |last7=Schrenk |first7=Werner |last8=Strasser |first8=Gottfried |date=2017-08-07 |title=The limit of quantum cascade detectors: A single period device |journal=Applied Physics Letters |volume=111 |issue=6 |article-number=061107 |doi=10.1063/1.4985711 |bibcode=2017ApPhL.111f1107S |issn=0003-6951|doi-access=free }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=See also=&lt;br /&gt;
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}&lt;br /&gt;
&lt;br /&gt;
== References ==&lt;br /&gt;
{{reflist|3}}&lt;br /&gt;
&lt;br /&gt;
== Further reading ==&lt;br /&gt;
* {{Cite journal |last1=Faist |first1=Jerome |last2=Capasso |first2=Federico |last3=Sivco |first3=Deborah L. |last4=Sirtori |first4=Carlo |last5=Hutchinson |first5=Albert L. |last6=Cho |first6=Alfred Y. |date=1994-04-22 |title=Quantum Cascade Laser |url=https://www.science.org/doi/10.1126/science.264.5158.553 |journal=Science |language=en |volume=264 |issue=5158 |pages=553–556 |doi=10.1126/science.264.5158.553 |pmid=17732739 |bibcode=1994Sci...264..553F |issn=0036-8075|url-access=subscription }}&lt;br /&gt;
* {{Citation |last=Helm |first=Manfred |title=Chapter 1 The Basic Physics of Intersubband Transitions |date=1999-01-01 |series=Semiconductors and Semimetals |volume=62 |pages=1–99 |editor-last=Liu |editor-first=H. C. |url=https://www.sciencedirect.com/science/article/pii/S008087840860304X |access-date=2024-07-10 |publisher=Elsevier |doi=10.1016/s0080-8784(08)60304-x |isbn=978-0-12-752171-8 |editor2-last=Capasso |editor2-first=Federico|url-access=subscription }}&lt;br /&gt;
* {{Cite journal |last=Levine |first=B. F. |date=1993-10-15 |title=Quantum-well infrared photodetectors |journal=Journal of Applied Physics |volume=74 |issue=8 |pages=R1–R81 |doi=10.1063/1.354252 |issn=0021-8979}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Photodetectors]]&lt;br /&gt;
[[Category:Optoelectronics]]&lt;br /&gt;
[[Category:Photonics]]&lt;br /&gt;
[[Category:Optical devices]]&lt;br /&gt;
&lt;br /&gt;
{{Author|Harold Foppele}}&lt;br /&gt;
&lt;br /&gt;
{{Sourceattribution|Quantum Cascade Detector|1}}&lt;/div&gt;</summary>
		<author><name>imported&gt;WikiHarold</name></author>
	</entry>
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