# Fileset

[MIyazaki_APL124_231103_2024.pdf](https://mdr.nims.go.jp/filesets/71f72e60-4fbe-4050-ae09-01adc3f5590a/download)

## Creator

[Hideki T. Miyazaki](https://orcid.org/0000-0003-4152-1171), [Takaaki Mano](https://orcid.org/0000-0002-6955-260X), [Takeshi Noda](https://orcid.org/0000-0002-6705-8552), [Takeshi Kasaya](https://orcid.org/0000-0002-1976-8760), [Yusuf B. Habibullah](https://orcid.org/0000-0002-8129-1545)

## Rights

VC 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://
creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0208399[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Antenna-enhanced high-resistance photovoltaic infrared detectors based on quantum ratchet architecture](https://mdr.nims.go.jp/datasets/967aaf41-543a-4af8-9e69-01535b08b661)

## Fulltext

Antenna-enhanced high-resistance photovoltaic infrared detectors based on quantum ratchet architectureViewOnlineExportCitationRESEARCH ARTICLE |  JUNE 03 2024Antenna-enhanced high-resistance photovoltaic infrareddetectors based on quantum ratchet architecture Hideki T. Miyazaki   ; Takaaki Mano  ; Takeshi Noda  ; Takeshi Kasaya  ; Yusuf B. Habibullah Appl. Phys. Lett. 124, 231103 (2024)https://doi.org/10.1063/5.0208399 03 June 2024 09:58:37https://pubs.aip.org/aip/apl/article/124/23/231103/3295651/Antenna-enhanced-high-resistance-photovoltaichttps://pubs.aip.org/aip/apl/article/124/23/231103/3295651/Antenna-enhanced-high-resistance-photovoltaic?pdfCoverIconEvent=citejavascript:;https://orcid.org/0000-0003-4152-1171javascript:;https://orcid.org/0000-0002-6955-260Xjavascript:;https://orcid.org/0000-0002-6705-8552javascript:;https://orcid.org/0000-0002-1976-8760javascript:;https://orcid.org/0000-0002-8129-1545https://crossmark.crossref.org/dialog/?doi=10.1063/5.0208399&domain=pdf&date_stamp=2024-06-03https://doi.org/10.1063/5.0208399https://servedbyadbutler.com/redirect.spark?MID=176720&plid=2356778&setID=592934&channelID=0&CID=866323&banID=521803772&PID=0&textadID=0&tc=1&scheduleID=2275660&adSize=1640x440&data_keys=%7B%22%22%3A%22%22%7D&matches=%5B%22inurl%3A%5C%2Fapl%22%5D&mt=1717408717731514&spr=1&referrer=http%3A%2F%2Fpubs.aip.org%2Faip%2Fapl%2Farticle-pdf%2Fdoi%2F10.1063%2F5.0208399%2F19973195%2F231103_1_5.0208399.pdf&hc=d5148facf12a28b8b12ac447dec0bb5cfd6c595c&location=Antenna-enhanced high-resistance photovoltaicinfrared detectors based on quantum ratchetarchitectureCite as: Appl. Phys. Lett. 124, 231103 (2024); doi: 10.1063/5.0208399Submitted: 14 March 2024 . Accepted: 23 May 2024 .Published Online: 3 June 2024Hideki T. Miyazaki,a) Takaaki Mano, Takeshi Noda, Takeshi Kasaya, and Yusuf B. Habibullahb)AFFILIATIONSNational Institute for Materials Science, Tsukuba 305-0047, Japana)Author to whom correspondence should be addressed:miyazaki.hideki@nims.go.jpb)Present address: Rakuten Mobile, Inc., Tokyo 158-0094, Japan.ABSTRACTWe demonstrate a quantum ratchet detector, which is a high-resistance photovoltaic mid-infrared detector based on an engineered spatialarrangement of subbands. In photovoltaic quantum-well photodetectors, in which unidirectional photocurrent is generated by asymmetricquantum-well structures, maximization of device resistance by suppressing undesired electron transports is crucial for minimizing noise.A semi-quantitative guideline suggests the significance of spatial separation between wavefunctions for reducing the conductance from theground state. Here, we employ a step quantum well made of a shallow floor and a deep well. Photoexcited electrons are quickly transferred toa separated location from the ground state through fast resonant tunneling and phonon scattering, and then they are allowed to flow in onlyone direction. This architecture is made possible by the use of a GaAs/AlGaAs material system, and it achieves a resistance as high as6.0� 104Xcm2 with a single-period structure. Combined with optical patch antennas for responsivity enhancement, we demonstrate a maxi-mum background-limited specific detectivity of 6.8� 1010 cmHz1/2/W at 6.4lm, 77K for normal incidence, and a background-limited-infrared-photodetector temperature of 98K.VC 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0208399Manipulation of intersubband transitions by engineeredquantum-well (QW) structures is a key technology for mid-infraredregion applications. Quantum cascade lasers have become dominantmid-infrared light sources.1 In quantum-well infrared photodetectors(QWIPs), the necessity of an incident electric field vertical to the QWshas long been a problem.2,3 However, recent progress in nanophoton-ics, particularly plasmonic antennas, has essentially solved the couplingissue with normally incident radiation.4–9The majority of QWIPs have belonged to the photoconductivetype. Nevertheless, the dark current due to bias voltage induces signifi-cant generation–recombination noise and limits the device operationto cryogenic temperatures. For imaging devices or uncooled detectors,photovoltaic (PV) QWIPs are advantageous because they do notrequire biasing and thus exhibit no dark current. PV-QWIPs based onasymmetric QW structures have been demonstrated since the earlydays of QWIP research.10–12 The most promising scheme in thisregard would be quantum cascade detectors (QCDs).13–16Performance enhancement of QCDs by incorporating micro/nano-photonics has also been attempted.17–22In QCDs, the electrons are transported by tunneling and longitu-dinal optical (LO) phonon scattering through stairs of subbands. Thedifficulty in QCD design lies in the trade-off between responsivity andresistance.15,16 For suppressing dominant Johnson noise, it is necessaryto raise the resistance (R0) area (A) product. Since the birth of QCDs,there have been various trials for improving R0A, by methods such asthickening the barriers,15,23 changing materials,15,24,25 diagonal transi-tion,26 and using coupled QWs.21 However, these efforts haveremained within the framework of binary energy profiles.In this Letter, we present a high-resistance PV-QWIP architec-ture, which we call a quantum ratchet detector (QRD), where the R0Ais raised by suppressing the overlap of wavefunctions using a stepQW27 to trap electrons at a distant location. With the aid of responsiv-ity enhancement by optical antennas,28–30 a single-period detectordemonstrated a maximum background-limited specific detectivity of6.8� 1010 cmHz1/2/W at 6.4lm, 77K as well as a background-limited-infrared-photodetector (BLIP) temperature of 98K. This performanceis achieved through a high resistance of 6.0� 104Xcm2, 29 timesgreater than conventional QCDs with a similar design.Appl. Phys. Lett. 124, 231103 (2024); doi: 10.1063/5.0208399 124, 231103-1VC Author(s) 2024Applied Physics Letters ARTICLE pubs.aip.org/aip/apl 03 June 2024 09:58:37https://doi.org/10.1063/5.0208399https://doi.org/10.1063/5.0208399https://www.pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0208399http://crossmark.crossref.org/dialog/?doi=10.1063/5.0208399&domain=pdf&date_stamp=2024-06-03https://orcid.org/0000-0003-4152-1171https://orcid.org/0000-0002-6955-260Xhttps://orcid.org/0000-0002-6705-8552https://orcid.org/0000-0002-1976-8760https://orcid.org/0000-0002-8129-1545mailto:miyazaki.hideki@nims.go.jphttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1063/5.0208399pubs.aip.org/aip/aplThe essential property of infrared detectors is expressed by itsspecific detectivity,2,3,15,16 which is essentially the signal-to-noise ratio:D� ¼ RespffiffiffiffiApinsd; (1)where Resp is the responsivity and insd is the current noise spectral den-sity. Here, Resp is given byResp ¼ ekhc� gabspeNw; (2)where e is the electron charge, k the wavelength, h the Planck constant,c the speed of light, gabs the absorption efficiency, pe the escape proba-bility, Nw the number of periods of the unit structure, and gabspe/Nwthe external quantum efficiency (EQE).Dark state and background state are key concepts in infrareddetectors. In the dark state, the detector is covered with a cold shieldand no radiation is incident. In the background state, the detector isexposed to radiation from a 300K environment. The parameters corre-sponding to these two states are indicated by subscripts DK and BG,respectively.Except for a special cryogenic region, the characteristics of adetector are expressed using dark-state properties, even in the back-ground state. Therefore, we must first consider the dark-state proper-ties. Here, insd,DK of a PV-QWIP is dominated by Johnson noise:15,16insd;DK ¼ffiffiffiffiffiffiffiffiffiffi4kBTR0s; (3a)where kB is the Boltzmann constant and T is the temperature of thedetector. Accordingly,D�DK ¼ RespffiffiffiffiffiffiffiffiffiffiR0A4kBTr/ gabs�pe �ffiffiffiffiffiffiffiffiR0Ap� 1NW; (3b)raising gabs, pe, and R0A and decreasing Nw is crucial for improving theD�DK of PV-QWIPs.As T decreases, D�DK exponentially increases, and the detectorfinally enters the BLIP region, where the shot noise by detected back-ground radiation from a 300K environment is dominant.15,16 Here,insd and D� for this region are given byinsd;BG ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2eAResp;pPBG;pDkNws; (4a)andD�BG ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikpgabs;ppe2hcPBG;pDks/ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigabs;p�pep; (4b)where Resp,p is the peak responsivity, PBG,p the background Planckradiation intensity at the peak wavelength kp, Dk the effective band-width, and gabs,p the absorption efficiency at kp. See supplementarymaterial S1 for details. In the BLIP region, D� is solely determined bythe responsivity (gabs,p and pe), and R0A no longer appears. However, adetector with a higher R0A exhibits a higher D�DK and reaches the BLIPregion at a higher temperature (BLIP temperature, TBLIP). TBLIP is afundamental index of a photodetector that specifies its operationtemperature; cooling a detector below TBLIP will not lead to a D� aboveD�BG, so long as it is used in a 300K environment. Consequently, thehigher the R0A, the higher the TBLIP, and the lower the burden of cool-ing the detector in practical use. TBLIP values for conventionalPV-QWIPs at similar wavelengths have been 70–83K.18,21Let us start with a discussion on the fundamental strategy forengineering R0A. In a PV-QWIP (Fig. 1, inset), the electrons suppliedfrom the left side are photoexcited at the active QW and then trans-ferred to the right side through a series of subbands. The resistance canbe expressed as the sum of the transition rates from the ground state ofthe active well S1 to the other states:31R0A ¼ kBTe2Pj G1j; (5)where Gij is the global transition rate between states i (Si) and j (Sj) foremission and absorption of LO phonons. Here, Gij is essentially givenby two factors: the overlap of wavefunctions of the two states (formfactor)32 and the Fermi–Dirac occupation factor, which express theeffects of spatial and energetic distances between the states, respec-tively. Gij can be viewed as the conductance between states due to itsinverse relationship with resistance. The resistance of a PV-QWIP isdominated by the transport between S1 and a few limited states Sj’swith high conductance.Figure 1 quantitatively displays the significance of the spatial andenergetic distances between S1 and Sj on R0A for a model PV-QWIP(see supplementary material S2). The colors indicate the G1j betweenFIG. 1. Relationship of state-to-state conductance G1j with spatial and energeticdistances at 77 K assuming a 5-nm-wide QW. Each color step denotes one orderdifference. Inset: schematic of a generalized PV-QWIP. States 1 and j are separatedby (Dz, DE). Superimposed curves represent actual (Dz, DE) positions in thispaper (red: QRD and blue: QCD).Applied Physics Letters ARTICLE pubs.aip.org/aip/aplAppl. Phys. Lett. 124, 231103 (2024); doi: 10.1063/5.0208399 124, 231103-2VC Author(s) 2024 03 June 2024 09:58:37https://doi.org/10.60893/figshare.apl.c.7250137https://doi.org/10.60893/figshare.apl.c.7250137https://doi.org/10.60893/figshare.apl.c.7250137pubs.aip.org/aip/aplthe ground state S1 at the origin and a state Sj with an identical wave-function shape virtually placed at (Dz, DE). As Sj moves away spatially(rightward) or energetically (upward), the conductance of the pathexponentially decays. The horizontal singular peak at DE¼ �hxLO¼ 36meV indicates the LO phonon scattering of GaAs.For the energy DE of each state, the design freedom is limited,since this is determined by the target wavelength and energy step closeto �hxLO. However, we have sufficient freedom in the spatial location ofthe wavefunctions Dz, which should be maximized so long as faster for-ward transition than backward is achieved. Quantitatively,G1j decreasesby one order of magnitude for a spatial distance of Dz0¼ 2.1 nm andan energetic distance of DE0¼ 14.5meV. Considering the slopeDz0/DE0, a spatial distance sufficiently exceeding Dz�5.2 nm for a typi-cal energy step of DE� �hxLO is necessary for a significant reduction inthe conductance. A structure keeping the wavefunction as far away aspossible, preferably about 10nm, would be necessary.A band diagram of the proposed QRD made from GaAs/AlxGa1-xAs is shown in Fig. 2(a). The thickness of each layer (in nm)of the device region is as follows: 9.05/5.09/5.65/11.31(0.32)/5.65(0.25)/5.65/1.70/3.96/1.98/3.96/2.54/3.96/3.11/3.96, where AlGaAsbarriers with x¼ 0.40 are shown in bold, the doped layer (Si,1� 1018 cm�3) is underlined, and () denotes the x value of AlxGa1-xAsfor some well regions.Because Resp is inversely proportional to Nw, Nw¼ 1 gives thehighest Resp.7,9,22 In addition, for a single-period structure, the influ-ence of the energy profile at individual parts can be straightforwardlyobserved and compared. Therefore, we employ Nw¼ 1. Both sides ofthe device region in Fig. 2 are Ohmically connected to electrodesthrough highly doped contact layers. The structure was designed aim-ing at a responsivity peak at k¼ 6.3lm.For rapid transport of electrons from the active well W1 to a dis-tant location, we employed a step QW made of a shallow floor and adeep well as the second well, W2 (Ref. 27) [represented by a red framein Fig. 2(a)]. This structure is made possible by the use of a GaAs/AlGaAs material system, which permits an arbitrary conduction bandoffset by composition x. S7 and S8 are formed by tunnel couplingbetween the second states of W1 and W2, and the fundamental state S6of W2 is located at ��hxLO below those levels. Electrons excited fromS1 to S7 or S8 by infrared absorption relax to S6 at a rate ofCfor¼ 8.7� 1011 s�1 by LO phonon scattering (see supplementarymaterial S3). This process is faster than the backward transition(Cback¼ 3.9� 1011 s�1) downward (to S1) or leftward (to the left con-tact). Thus, the electrons preferentially flow in the right direction witha probability of pe¼Cfor/(CbackþCfor)¼ 0.69.The structure from W3 was designed so that each subbanddescends by ��hxLO based on an earlier work.23 The barriers here areslightly thicker than in the original study but are unified to the samethickness for easy interpretation of the results.In this study, a conventional QCD with similar design parametersshown below is also discussed for a straightforward comparison[Fig. 2(b)]: 9.05/5.37/5.65/1.13/3.96/1.41/3.39/1.70/3.96/1.98/3.96/2.54/3.96/3.11/3.96.The conduction band forms a binary profile made of only twolevels. The extraction region from W4 is identical to that from W3 inFig. 2(a). Electrons excited from S1 to S7 or S8 relax to S6, which is��hxLO below S7/S8, at a rate of Cfor¼ 1.22� 1012 s�1, faster than thebackward rate of Cback¼ 4.7� 1011 s�1; pe¼ 0.72 is expected.The locations of the gravity centers of the squared wavefunctionswith respect to the ground state of the structures in Fig. 2 are plottedin Fig. 1. Note that the G1j values for j¼ 8 and 7 are overestimated by1–2 orders of magnitude in Fig. 1, since the actual wavefunctions forS8 and S7 have a very different form than the assumed shape. In thereference QCD, the G1j values for j¼ 6 and 5 exhibit a substantial con-tribution toPj G1j. Therefore, these states short-circuit the electronflow to the ground state S1 and limit R0A to a low level. A more quanti-tative discussion is provided in supplementary material S2.In contrast, in the proposed QRD, the location of S6 is more dis-tant by 9 nm than the reference QCD by the employment of the stepQW, which suppresses the conductance by several orders of magni-tude. Once the electrons are moved to such a far location, the back-ward transition from S6 to the ground state S1 then becomes negligible;S6 functions as a ratchet to restrict the flow of electrons to one direc-tion. Having no short-circuit path, QRDs can achieve drasticallyenhanced R0A.We fabricated both structures in Fig. 2 and compared their prop-erties. The QWIP layer grown by molecular beam epitaxy on a GaAsFIG. 2. Conduction band diagrams with squared wavefunction profiles for (a) theproposed QRD and (b) reference QCD. Black arrows indicate electron flow. Redframe in (a) shows the step QW.Applied Physics Letters ARTICLE pubs.aip.org/aip/aplAppl. Phys. Lett. 124, 231103 (2024); doi: 10.1063/5.0208399 124, 231103-3VC Author(s) 2024 03 June 2024 09:58:37https://doi.org/10.60893/figshare.apl.c.7250137https://doi.org/10.60893/figshare.apl.c.7250137https://doi.org/10.60893/figshare.apl.c.7250137pubs.aip.org/aip/aplsubstrate was transferred to a Au substrate by wafer bonding andremoval of the original substrate. The transferred QWIP layer includesthe device region and contact layers consisting of a 20-nm-thickn-GaAs layer (Si, 2� 1018 cm�3) and a 28-nm-thick heavily dopedlayer (Si, 5� 1018 cm�3, and seven periodic d-doped layers of3� 1012 cm�2) for nonalloyed Ohmic contact with the electrodes.33The actual QW structures suffered from fabrication errors, which aretaken into consideration in the band diagrams in Fig. 2.On a 160-lm-square QWIP layer, square Au patch antennas(side length: L) were periodically arranged (period: P) by electronbeam drawing and liftoff in a 100-lm-square detector area. The fabri-cated antenna-enhanced QRD is shown in Fig. 3(a). On the Au patchside, the current laterally flows through the contact layer and reachesthe surrounding electrode.34 The QW structure in Fig. 2 rotated to theleft by 90� is sandwiched between the Au patch and Au substrate. Theelectrode potential of the extractor side with respect to the W1 side isdefined as the bias voltage Vb. The Au patches were optimized to max-imize the responsivity: (L, P)¼ (0.87, 2.00) for QRD and (0.88, 1.90)for reference QCD in micrometers.Electric field distribution of the QRD at the responsivity peakobtained by finite element analysis is displayed in Fig. 3(b). At theactive QW (white dotted line), vertical electric field intensity is magni-fied 178 times at maximum.The fabricated devices were installed in a cryostat with ZnSe win-dows, and their responsivity spectra were measured with a Fouriertransform infrared spectrometer by feeding the amplified currentsignal to the external port. When required, lock-in measurement witha step-scan mode was used. The spectral responsivity was quantifiedbased on a calibrated HgCdTe detector.The current–voltage relationship was measured with a sourcemeter. The insd was measured with a fast Fourier transform analyzerconnected to a current amplifier in two environments: dark state andbackground state. The cryostat is equipped with a rotatable cold shieldat 29K with a blackbody coating. For the dark state, the detector wascovered with the cold shield, while for the background state it wasexposed to a 300K environment with a field of view of 162�. See sup-plementary material S4 for details on fabrication, calculation, andcharacterization.Figure 4(a) shows the current–voltage relationship for dark andbackground states. At zero bias, a photovoltaic signal higher than thedark current by several orders of magnitude is observed by backgroundillumination. The dark current of the QRD is much lower than that ofthe QCD.Figure 4(b) shows the responsivity spectra at 77K. The value ofResp,p at zero bias for QRD was 0.207A/W (EQE¼ 0.040,k¼ 6.40lm), which was 36% of Resp,p¼ 0.570A/W for the referenceQCD (0.106, 6.67lm). However, by increasing the value of Vb, Respincreased, and eventually both detectors exhibited similar maximumResp,p values (QRD: Resp,p¼ 0.949A/W, EQE¼ 0.183; QCD:0.931A/W, 0.174). As shown in Fig. 4(c), two or three peaks emerge inResp,p as Vb increases.Compared with QCDs, in QRDs, more precise band alignmentseems to be required for electron transport at zero bias. In addition,despite the design efforts aiming at an identical peak wavelength, theobserved responsivity peak positions of the fabricated QRD and QCDshowed a discrepancy. We attribute the incompleteness to inappropri-ate material parameters, particularly the conduction band offset, in theQW design. We also observed a change in the properties due to waferbonding. Further refinement of the QW design and fabrication processis necessary.Because gabs is determined by the doping to the active QW, itshould be identical in both detectors. Therefore, the maximum EQE of�0.18 for the peak bias would represent gabs. In this situation, the elec-trons are forcibly extracted to the right side; thus, pe� 1 could beassumed (see supplementary material S5).We can evaluate pe at zero bias from the ratio of Resp,p at zerobias to that at peak bias from Eq. (2), since gabs is almost the same atpeak bias and zero bias, and pe at peak bias is almost 1. At zero bias,pe¼ 0.61 is estimated for the reference QCD, fairly consistent with thepredicted value. In contrast, pe¼ 0.22 for the QRD. With future opti-mization, improvement by a factor of�3 is expected.Figure 4(b) also presents the maximum Resp based on calculation,which is 40% higher than the observed maximum Resp. This could bedue to excess absorption loss in the fabricated detectors or an overesti-mation of the imaginary part of the dielectric constant of W1 used inthe calculation. However, this discrepancy would be within a reason-able range.Figure 5(a) shows the temperature dependence of insd for boththe dark and background states. Lower noise for the QRD is con-firmed. The inset shows the Arrhenius plot displaying the temperaturedependence of R0A for dark current. At 77K, QRD and QCD exhibitR0A¼ 6.0� 104 and 2.1� 103Xcm2, respectively. Resistance improve-ment by 29 times was achieved using the ratchet architecture.FIG. 3. (a) Scanning electron micrograph of a fabricated antenna-enhanced QRD.Inset: magnification of arrayed patch antennas. (b) Distribution of jEzj2 (Ez: verticalelectric field) normalized by incident field for QRD at responsivity peak. Incidentlight: x-polarized, k¼ 6.4lm, vertical incidence. Structure: T¼ 164 nm,P¼ 2.00lm, L¼ 0.87 lm, and Tm¼ 100 nm.Applied Physics Letters ARTICLE pubs.aip.org/aip/aplAppl. Phys. Lett. 124, 231103 (2024); doi: 10.1063/5.0208399 124, 231103-4VC Author(s) 2024 03 June 2024 09:58:37https://doi.org/10.60893/figshare.apl.c.7250137https://doi.org/10.60893/figshare.apl.c.7250137https://doi.org/10.60893/figshare.apl.c.7250137pubs.aip.org/aip/aplBoth detectors present linear behavior throughout the temperaturerange studied and demonstrate fair agreement with the calculated val-ues. The experimental activation energies derived from the slopes are158 and 131meV for QRD and QCD, respectively. In the banddiagrams in Fig. 2, these activation energies with respect to Fermienergy are located between S7 and S6 for QRD and between S6 and S5for QCD. This means that even S5 influences the R0A in the referenceQCD. In contrast, S6 of the QRD exerts a minor influence on R0A,directly showing the advantage of the ratchet architecture.Moreover, the observed insd,DK’s are well described as�(4kBT/R0)1/2 and thus surely limited by the Johnson noise. On theother hand, insd,BG’s are constant below �100K for both detectors; i.e.,both detectors are in the BLIP region. TBLIP, defined as the temperaturegiving identical dark- and background-origin noise components(2� insd,DK2¼ insd,BG2), is 98 and 94K for QRD and QCD, respectively.All of these noise properties indicate the excellent performance of QRD.Figure 5(b) shows the D�BG spectra at 77K. At zero bias, D�BG val-ues are 3.5� 1010 and 5.5� 1010 cmHz1/2/W for QRD and QCD,respectively. As Eq. (4b) predicts, the QRD could not surpass the QCDwith a higher Resp. Nevertheless, a high R0A makes possible a higherD�BG in a wider Vb range. Therefore, the maximum D�BG at a finite Vbagain showed the higher performance of QRD: 6.8� 1010 and6.4� 1010 cmHz1/2/W for QRD (Vb¼þ0.18V) and QCDFIG. 4. (a) Current density–voltage relationship for QRD (red) and QCD (blue) fordark (solid) and background states (dotted) at 77 K. Filled circle: zero bias signal for300-K background. (b) Responsivity spectra at 77 K for QRD and QCD. Solid lines:zero bias; dotted lines: peak bias (QRD: þ0.32 V; QCD: þ0.20 V); circles: calcula-tion. Equiefficiency lines are also plotted. (c) Bias dependence of peak responsivityat 77 K. Filled circles: zero bias; open circles: peak bias.FIG. 5. (a) Temperature dependence of insd for QRD (red) and QCD (blue). Filledcircles: dark state; open circles: background state. Inset: temperature dependenceof R0A (line: experiment, circle: calculation). (b) D�BG spectra at 77 K for QRD (red)and QCD (blue). Solid lines: zero bias; dotted lines: peak bias. Black curves: theo-retical limits. Solid line: interband detectors; dotted line: narrow-band detectors.Applied Physics Letters ARTICLE pubs.aip.org/aip/aplAppl. Phys. Lett. 124, 231103 (2024); doi: 10.1063/5.0208399 124, 231103-5VC Author(s) 2024 03 June 2024 09:58:37pubs.aip.org/aip/apl(Vb¼þ0.04V), respectively. If the Resp of the QRD was raised by afactor of �3 by improving the band alignment, zero bias D�BG equiva-lent to that of the QCD and a much higher D�BG at an optimum Vbcould be achieved. In addition, TBLIP as high as 110K would beexpected (see supplementary material S1 and S5).Figure 5(b) also displays the theoretical limit of D�BG by blackcurves. The solid line corresponds to interband detectors; our detectorsnearly meet this criterion. However, for narrow-band detectors likeQWIPs, this limit does not apply.15,35 The theoretical limit for a detec-tor with a similar bandwidth (Gaussian profile with a full width at halfmaximum of 6%) is also plotted by the dotted line, showing that thereis still room for improvement.Finally, we comment on the temperature dependence of theresponsivity. Many QCDs have demonstrated room-temperatureresponsivity, including the same material system as ours.18Nevertheless, both detectors in this study exhibited a quick respon-sivity drop at around T¼ 140K, and we could not observe a signifi-cant signal at room temperature (see supplementary material S2 andS5). Because gabs has no remarkable temperature dependence, theproblem clearly lies elsewhere. Moreover, because this feature is com-mon for both detectors, the problem is not due to the ratchet config-uration. Our preliminary electron transport calculation suggests thatthe electron supply through our thick first barriers are bottlenecks athigh temperatures. However, we would like to leave this for futurework.In summary, we proposed a PV-QWIP architecture with a dras-tically improved resistance by a step QW ratchetting the flow of elec-trons. Combined with optical antennas, a single-period detectordemonstrated a maximum D�BG of 6.8� 1010 cmHz1/2/W at 6.4lm,77K, and TBLIP of 98K for normal incidence. While severe require-ment for band alignment was also revealed, these achievementswould be sufficient for proving the significance of QRDs.Improvement of zero bias pe by refining the design and fabrication isexpected.A step QW is a versatile structure with a large amount of designfreedom, and it has demonstrated interesting opto-electronic func-tions. If a step QW were used as the active well, kp could be tuned byVb,36 although the spectral change in our QRD was not so substantial(see supplementary material S5). In particular, optical nonlinearity instep QWs has been extensively studied.37 While a GaAs/AlGaAs mate-rial system is suitable for a wide mid-infrared range, this range can befurther extended by antenna enhancement of nonlinearity, such as sec-ond harmonics. The QRD proposed here could serve as a startingpoint for fabricating diversified functional devices.See the supplementary material for further details on theoreticalcalculations, fabrication, and characterization.The authors are thankful for helpful discussions with a companychoosing to remain anonymous, nextnano GmbH, M. F. Hainey, Jr.,T. Ochiai, N. Ishida, Y. Sakuma, Y. Jimba, H. Miyazaki, K. Watanabe,H. Osato, A. Shigetou, Y. Arai, T. Kawazu, Y. Sugimoto, andA. Ohtake. This work was supported by JSPS KAKENHI Grant Nos.JP22K18990, JP23H01883, and JP24K01367 and by AdvancedResearch Infrastructure for Materials and Nanotechnology in Japan(ARIM) of the Ministry of Education, Culture, Sports, Science andTechnology (MEXT), Proposal No. JPMXP1223NM5062.AUTHOR DECLARATIONSConflict of InterestYes, HTM has a Japanese patent (No. 2024–031328) pending.Author ContributionsHideki T. Miyazaki: Conceptualization (lead); Data curation (lead);Funding acquisition (lead); Investigation (equal); Methodology (lead);Software (lead); Validation (equal); Visualization (lead); Writing –original draft (lead). Takaaki Mano: Conceptualization (supporting);Data curation (supporting); Investigation (equal); Writing – review &editing (supporting). Takeshi Noda: Validation (equal); Writing –review & editing (lead). Takeshi Kasaya: Investigation (equal);Methodology (supporting); Software (supporting). Yusuf B.Habibullah: Investigation (equal).DATA AVAILABILITYThe data that support the findings of this study are available fromthe corresponding author upon reasonable request.REFERENCES1Y. Yao, A. J. Hoffman, and C. F. Gmachl, Nat. Photonics 6, 432–439 (2012).2B. F. Levine, J. Appl. Phys. 74, R1–R81 (1993).3H. Schneider and H. C. Liu, Quantum Well Infrared Photodetectors: Physicsand Applications (Springer, Berlin, 2007).4W. A. Beck and M. S. Mirotznik, Infrared Phys. Technol. 42, 189–198 (2001).5W. Wu, A. Bonakdar, and H. Mohseni, Appl. Phys. Lett. 96, 161107 (2010).6Y. N. Chen, Y. Todorov, B. Askenazi, A. Vasanelli, G. Biasiol, R. Colombelli,and C. Sirtori, Appl. Phys. Lett. 104, 031113 (2014).7Q. Li, Z.-F. Li, N. Li, X.-S. Chen, P.-P. Chen, X.-C. Shen, and W. Lu, Sci. Rep.4, 6332 (2014).8D. Palaferri, Y. Todorov, A. Bigioli, A. Mottaghizadeh, D. Gacemi, A.Calabrese, A. Vasanelli, L. Li, A. G. Davies, E. H. Linfield, F. Kapsalidis, M.Beck, J. Faist, and C. Sirtori, Nature 556, 85–88 (2018).9H. T. Miyazaki, T. Mano, T. Kasaya, H. Osato, K. Watanabe, Y. Sugimoto, T.Kawazu, Y. Arai, A. Shigetou, T. Ochiai, Y. Jimba, and H. Miyazaki, Nat.Commun. 11, 565 (2020).10C. Sch€onbein, H. Schneider, G. Bihlmann, K. Schwarz, and P. Koidl, Appl.Phys. Lett. 68, 973–975 (1996).11H. Schneider, C. Sch€onbein, M. Walther, K. Schwarz, J. Fleissner, and P. Koidl,Appl. Phys. Lett. 71, 246–248 (1997).12G. M. Penello, P. H. Pereira, M. P. Pires, D. Sivco, C. Gmachl, and P. L. Souza,Appl. Phys. Lett. 112, 033503 (2018).13D. Hofstetter, M. Beck, and J. Faist, Appl. Phys. Lett. 81, 2683–2685 (2002).14L. Gendron, M. Carras, A. Huynh, V. Ortiz, C. Koeniguer, and V. Berger, Appl.Phys. Lett. 85, 2824–2826 (2004).15F. R. Giorgetta, E. Baumann, M. Graf, Q. Yang, C. Manz, K. Kohler, H. E.Beere, D. A. Ritchie, E. Linfield, A. G. Davies, Y. Fedoryshyn, H. Jackel, M.Fischer, J. Faist, and D. Hofstetter, IEEE J. Quantum Electron. 45, 1039–1052(2009).16A. Delga, “Quantum cascade detectors: A review,” in Mid-InfraredOptoelectronics (Elsevier, 2020), pp. 337–377.17S.-Q. Zhai, J.-Q. Liu, F.-Q. Liu, and Z.-G. Wang, Appl. Phys. Lett. 100, 181104(2012).18A. Bigioli, G. Armaroli, A. Vasanelli, D. Gacemi, Y. Todorov, D. Palaferri, L. Li,A. G. Davies, E. H. Linfield, and C. Sirtori, Appl. Phys. Lett. 116, 161101(2020).19Y. Zhu, S. Zhai, J. Liu, K. Li, K. Yang, S. Liu, J. Zhang, N. Zhuo, L. Wang, and F.Liu, Opt. Express 29, 37327–37335 (2021).20G. Quinchard, C. Mismer, M. Hakl, J. Pereira, Q. Lin, S. Lepillet, V. Trinit�e, A.Evirgen, E. Peytavit, J. L. Reverchon, J. F. Lampin, S. Barbieri, and A. Delga,Appl. Phys. Lett. 120, 091108 (2022).Applied Physics Letters ARTICLE pubs.aip.org/aip/aplAppl. Phys. Lett. 124, 231103 (2024); doi: 10.1063/5.0208399 124, 231103-6VC Author(s) 2024 03 June 2024 09:58:37https://doi.org/10.60893/figshare.apl.c.7250137https://doi.org/10.60893/figshare.apl.c.7250137https://doi.org/10.60893/figshare.apl.c.7250137https://doi.org/10.60893/figshare.apl.c.7250137https://doi.org/10.1038/nphoton.2012.143https://doi.org/10.1063/1.354252https://doi.org/10.1016/S1350-4495(01)00076-7https://doi.org/10.1063/1.3419885https://doi.org/10.1063/1.4862750https://doi.org/10.1038/srep06332https://doi.org/10.1038/nature25790https://doi.org/10.1038/s41467-020-14426-6https://doi.org/10.1038/s41467-020-14426-6https://doi.org/10.1063/1.116116https://doi.org/10.1063/1.116116https://doi.org/10.1063/1.119510https://doi.org/10.1063/1.5006464https://doi.org/10.1063/1.1512954https://doi.org/10.1063/1.1781731https://doi.org/10.1063/1.1781731https://doi.org/10.1109/JQE.2009.2017929https://doi.org/10.1063/1.4710523https://doi.org/10.1063/5.0004591https://doi.org/10.1364/OE.438919https://doi.org/10.1063/5.0078861pubs.aip.org/aip/apl21T. Dougakiuchi, K. Fujita, T. Hirohata, A. Ito, M. Hitaka, and T. Edamura,Appl. Phys. Lett. 109, 261107 (2016).22B. Schwarz, P. Reininger, A. Harrer, D. MacFarland, H. Detz, A. M. Andrews,W. Schrenk, and G. Strasser, Appl. Phys. Lett. 111, 061107 (2017).23L. Gendron, C. Koeniguer, V. Berger, and X. Marcadet, Appl. Phys. Lett. 86,121116 (2005).24A. Vardi, G. Bahir, F. Guillot, C. Bougerol, E. Monroy, S. E. Schacham, M.Tchernycheva, and F. H. Julien, Appl. Phys. Lett. 92, 011112 (2008).25P. Reininger, T. Zederbauer, B. Schwarz, H. Detz, D. MacFarland, A. M.Andrews, W. Schrenk, and G. Strasser, Appl. Phys. Lett. 107, 081107 (2015).26P. Reininger, B. Schwarz, H. Detz, D. MacFarland, T. Zederbauer, A. M.Andrews, W. Schrenk, O. Baumgartner, H. Kosina, and G. Strasser, Appl. Phys.Lett. 105, 091108 (2014).27E. Rosencher, P. Bois, J. Nagle, E. Costard, and S. Delaitre, Appl. Phys. Lett. 55,1597–1599 (1989).28G. Leveque and O. J. F. Martin, Opt. Lett. 31, 2750–2752 (2006).29H. T. Miyazaki and Y. Kurokawa, Phys. Rev. Lett. 96, 097401 (2006).30J. L. Perchec, Y. Desieres, and R. Espiau de Lamaestre, Appl. Phys. Lett. 94,181104 (2009).31C. Koeniguer, G. Dubois, A. Gomez, and V. Berger, Phys. Rev. B 74, 235325(2006).32R. Ferreira and G. Bastard, Phys. Rev. B 40, 1074–1086 (1989).33T. Mano, H. T. Miyazaki, T. Kasaya, T. Noda, and Y. Sakuma, ACS Omega 4,7300–7307 (2019).34M. F. Hainey, Jr., T. Mano, T. Kasaya, Y. Jimba, H. Miyazaki, T. Ochiai, H.Osato, K. Watanabe, Y. Sugimoto, T. Kawazu, Y. Arai, A. Shigetou, and H. T.Miyazaki, Opt. Express 29, 59–69 (2021).35M. F. Hainey, Jr., T. Mano, T. Kasaya, Y. Jimba, H. Miyazaki, T. Ochiai, H.Osato, Y. Sugimoto, T. Kawazu, A. Shigetou, and H. T. Miyazaki, Opt. Express29, 43598–43611 (2021).36E. Martinet, F. Luc, E. Rosencher, P. Bois, and S. Delaitre, Appl. Phys. Lett. 60,895–897 (1992).37E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, Science 271,168–173 (1996).Applied Physics Letters ARTICLE pubs.aip.org/aip/aplAppl. Phys. Lett. 124, 231103 (2024); doi: 10.1063/5.0208399 124, 231103-7VC Author(s) 2024 03 June 2024 09:58:37https://doi.org/10.1063/1.4973582https://doi.org/10.1063/1.4985711https://doi.org/10.1063/1.1884257https://doi.org/10.1063/1.2830704https://doi.org/10.1063/1.4929501https://doi.org/10.1063/1.4894767https://doi.org/10.1063/1.4894767https://doi.org/10.1063/1.102248https://doi.org/10.1364/OL.31.002750https://doi.org/10.1103/PhysRevLett.96.097401https://doi.org/10.1063/1.3132063https://doi.org/10.1103/PhysRevB.74.235325https://doi.org/10.1103/PhysRevB.40.1074https://doi.org/10.1021/acsomega.8b03260https://doi.org/10.1364/OE.408515https://doi.org/10.1364/OE.444223https://doi.org/10.1063/1.106497https://doi.org/10.1126/science.271.5246.168pubs.aip.org/aip/apl