Center for Quantum Devices - Most Downloaded Journal Articles

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20.	InSb Infrared Photodetectors on Si Substrates Grown by Molecular Beam Epitaxy E. Michel, J. Xu, J.D. Kim, I. Ferguson, and M. Razeghi IEEE Photonics Technology Letters 8 (5) pp. 673-- May 1, 1996 ...[Visit Journal] The InSb infrared photodetectors grown heteroepitaxially on Si substrates by molecular beam epitaxy (MBE) are reported. Excellent InSb material quality is obtained on 3-in Si substrates (with a GaAs predeposition) as confirmed by structural, optical, and electrical analysis. InSb infrared photodetectors on Si substrates that can operate from 77 K to room temperature have been demonstrated. The peak voltage-responsitivity at 4 μm is about 1.0×10³ V/W and the corresponding Johnson-noise-limited detectivity is calculated to be 2.8×10¹⁰ cm·Hz^½/W. This is the first important stage in developing InSb detector arrays or monolithic focal plane arrays (FPAs) on silicon. The development of this technology could provide a challenge to traditional hybrid FPA's in the future. [reprint (PDF)]
20.	Materials characterization of n-ZnO/p-GaN:Mg/c-Al(2)O(3) UV LEDs grown by pulsed laser deposition and metal-organic chemical vapor deposition D. Rogers, F.H. Teherani, P. Kung, K. Minder, and M. Razeghi Superlattices and Microstructures-- April 1, 2007 ...[Visit Journal] n-ZnO/p-GaN:Mg hybrid heterojunctions grown on c-Al₂O₃ substrates showed 375 nm room temperature electroluminescence. It was suggested that the high materials and interface quality obtained using pulsed laser deposition for the n-ZnO growth and metal–organic chemical vapor deposition for the p-GaN:Mg were key factors enabling the injection of holes and the radiative near band edge recombination in the ZnO. In this paper we present the materials characterization of this structure using x-ray diffraction, scanning electron microscopy and atomic force microscopy. [reprint (PDF)]
20.	Modeling Type-II InAs/GaSb Superlattices Using Empirical Tight-Binding Method: New Aspects Y. Wei, M. Razeghi, G.J. Brown, and M.Z. Tidrow SPIE Conference, Jose, CA, Vol. 5359, pp. 301-- January 25, 2004 ...[Visit Journal] The recent advances in the experimental work on the Type-II InAs/GaSb superlattices necessitate a modeling that can handle arbitrary layer thickness as well as different types of interfaces in order to guide the superlattice design. The empirical tight-binding method (ETBM) is a very good candidate since it builds up the Hamiltonian atom by atom. There has been a lot of research work on the modeling of Type-II InAs/GaSb superlattices using the ETBM. However, different groups generate very different accuracy comparing with experimental results. We have recently identified two major aspects in the modeling: the antimony segregation and the interface effects. These two aspects turned out to be of crucial importance governing the superlattice properties, especially the bandgap. We build the superlattice Hamiltonian using antimony segregated atomic profile taking into account the interface. Our calculations agree with our experimental results within growth uncertainties. In addition we introduced the concept of Ga_xIn_1-x type interface engineering, which will add another design freedom especially in the mid-wavelength infrared range (3~7 µm) in orderto reduce the lattice mismatch. [reprint (PDF)]
20.	High Performance Quantum Cascade Lasers at λ ~ 6 μm M. Razeghi, S. Slivken, J. Yu, A. Evans, and J. David Microelectronics Journal, 34 (5-8)-- May 1, 2003 ...[Visit Journal] This talk will focus on the recent efforts at the Center for Quantum Devices to deliver a high average power quantum cascade laser source at λ ~6 μm. Strain-balancing is used to reduce leakage for these shorter wavelength quantum cascade lasers. Further, the effect of reducing the doping in the injector is explored relative to the threshold current density and maximum average output power. Lastly, to demonstrate more of the potential of these devices, epilayer down bonding is explored as a technique to significantly enhance device performance. [reprint (PDF)]
20.	High operability 1024 x 1024 long wavelength infrared focal plane array base on Type-II InAs/GaSb superlattice A. Haddadi, S.R. Darvish, G. Chen, A.M. Hoang, B.M. Nguyen and M. Razeghi AIP Conference Proceedings, Vol. 1416, p. 56-58_NGS15 Conf_Blacksburg, VA_Aug 1-5, 2011-- December 31, 2011 ...[Visit Journal] Fabrication and characterization of a high performance 1024×1024 long wavelength infrared type‐II superlattice focal plane array are described. The FPA performs imaging at a continous rate of 15.00 frames/sec. Each pixel has pitch of 18μm with a fill factor of 71.31%. It demonstrates excellent operability of 95.8% and 97.4% at 81 and 68K operation temperature. The external quantum efficiency is ∼81% without any antireflective coating. Using F∕2 optics and an integration time of 0.13ms, the FPA exhibits an NEDT as low as 27 and 19mK at operating temperatures of 81 and 68K respectively. [reprint (PDF)]
20.	Novel Method for Reclaim/Reuse of Bulk GaN Substrates using Sacrifical ZnO Release Layers A. Rajan, S. Sundaram, Y. El Gmili, P. L. Voss, K. Pantzas, T. Moudakir, A. Ougazzaden, D. J. Rogers, F. Hosseini Teherani, V. E. Sandana, P. Bove, K. Prior, R. McClintock & M. Razeghi Proc. SPIE 8987, Oxide-based Materials and Devices V, 898719-- April 2, 2014 ...[Visit Journal] Free-standing (0002)-oriented GaN substrates (f = 2”) were coated with 200 nm of ZnO and used as templates for the growth of GaN thin films. SEM and AFM revealed that such GaN layers had a relatively homogenous surface morphology with an RMS roughness (5 μm x 5 μm) of less than 4nm. XRD studies revealed strained ZnO growth on the GaN substrate and the reproduction of the substrate rocking curve for the GaN overlayers after only a hundred nm of growth, thus indicating that the GaN films had superior crystallographic quality compared to those grown on sapphire or ZnO/sapphire substrates. Quarter-wafer areas of GaN were removed from the GaN substrate (by selective chemical etching away of the ZnO interlayer). The expensive GaN substrates were then reclaimed/reused (without the need for polishing) for a second cycle of ZnO and GaN growth, which gave similar XRD, SEM, CL and AFM results to the first cycle. [reprint (PDF)]
20.	Modeling of Type-II InAs/GaSb Superlattices Using Empirical Tight-Binding Method and Interface Engineering Y. Wei and M. Razeghi Physical Review B, 69 (8)-- February 15, 2004 ...[Visit Journal] We report the most recent work on the modeling of type-II InAs/GaSb superlattices using the empirical tight binding method in an sp3s* basis. After taking into account the antimony segregation in the InAs layers, the modeling accuracy of the band gap has been improved. Our calculations agree with our experimental results within a certain growth uncertainty. In addition, we introduce the concept of Ga_xIn_1-x type interface engineering in order to reduce the lattice mismatch between the superlattice and the GaSb (001) substrate to improve the overall superlattice material quality. [reprint (PDF)]
20.	High-performance bias-selectable dual-band mid-/long-wavelength infrared photodetectors and focal plane arrays based on InAs/GaSb Type-II superlattices M. Razeghi; A. Haddadi; A.M. Hoang; G. Chen; S. Ramezani-Darvish; P. Bijjam Proc. SPIE 8704, Infrared Technology and Applications XXXIX, 87040S (June 11, 2013)-- June 11, 2013 ...[Visit Journal] We report a bias selectable dual-band mid-wave infrared (MWIR) and long-wave infrared (LWIR) co-located detector with 3 μm active region thickness per channel that is highly selective and can perform under high operating temperatures for the MWIR band. Under back-side illumination, a temperature evolution study of the MWIR detector's electro-optical performance found the 300 K background-limit with 2π field-of-view to be achieved below operating temperatures of 160 K, at which the temperature's 50% cutoff wavelength was 5.2 μm. The measured current reached the system limit of 0.1 pA at 110 K for 30 μm pixel-sized diodes. At 77 K, where the LWIR channel operated with a 50% cutoff wavelength at 11.2 μm, an LWIR selectivity of ∼17% was achieved in the MWIR wave band between 3 and 4.7 μm, making the detector highly selective. [reprint (PDF)]
20.	High-power, continuous-wave, phase-locked quantum cascade laser arrays emitting at 8 μm WENJIA ZHOU,QUAN-YONG LU,DONG-HAI WU, STEVEN SLIVKEN, AND MANIJEH RAZEGHI OPTICS EXPRESS 27, 15776-15785-- May 20, 2019 ...[Visit Journal] We report a room-temperature eight-element phase-locked quantum cascade laser array emitting at 8 μm with a high continuous-wave power of 8.2 W and wall plug efficiency of 9.5%. The laser array operates primarily via the in-phase supermode and has single-mode emission with a side-mode suppression ratio of ~20 dB. The quantum cascade laser active region is based on a high differential gain (8.7 cm/kA) and low voltage defect (90 meV) design. A record high wall plug efficiency of 20.4% is achieved from a low loss buried ridge type single-element Fabry-Perot laser operating in pulsed mode at 20 °C. [reprint (PDF)]
20.	High-performance short-wavelength infrared photodetectors based on type-II InAs/InAs_1-xSb_x/AlAs_1-xSb_x superlattices M. Razeghi, A. Haddadi, X. V. Suo, S. Adhikary, P. Dianat, R. Chevallier, A. M. Hoang, A. Dehzangi Proc. SPIE 9819, Infrared Technology and Applications XLII, 98190A -- May 20, 2016 ...[Visit Journal] We present a high-performance short-wavelength infrared n-i-p photodiode, whose structure is based on type-II superlattices with InAs/InAs_1-xSb_x/AlAs_1-xSb_x on GaSb substrate. At room temperature (300K) with front-side illumination, the device shows the peak responsivity of 0.47 A/W at 1.6mm, corresponding to 37% quantum efficiency at zero bias. At 300K, the device has a 50% cut-off wavelength of ~1.8mm. For −50mV applied bias at 300 K the photodetector has dark current density of 9.6x10^-5 A/cm² and RxA of 285 Ω•cm², and it revealed a detectivity of 6.45x10¹⁰ cm•Hz^½/W. Dark current density reached to 1.3x10^-8 A/cm² at 200 K, with 36% quantum efficiency which leads to the detectivity value of 5.66x10¹² cm•Hz^½/W. [reprint (PDF)]
20.	Polarization-free GaN emitters in the ultraviolet and visible spectra via heterointegration on CMOS-compatible Si (100) C. Bayram, J. Ott, K. T. Shiu, C. W. Cheng, Y. Zhu, J. Kim, D. K. Sadana, M. Razeghi Proc. SPIE 9370, Quantum Sensing and Nanophotonic Devices XII, 93702F -- February 8, 2015 ...[Visit Journal] This work presents a new type of polarization-free GaN emitter. The unique aspect of this work is that the ultraviolet and visible emission originates from the cubic phase GaN and the cubic phase InGaN/GaN multi-quantum-wells, respectively. Conventionally, GaN emitters (e.g. light emitting diodes, laser diodes) are wurtzite phase thus strong polarization fields exist across the structure contributing to the “droop” behavior – a phenomenon defined as “the reduction in emitter efficiency as injection current increases”. The elimination of piezoelectric fields in GaN-based emitters as proposed in this work provide the potential for achieving a 100% internal efficiency and might lead to droopfree light emitting diodes. In addition, this work demonstrates co-integration of GaN emitters on cheap and scalable CMOS-compatible Si (100) substrate, which yields possibility of realizing a GaN laser diode uniquely – via forming mirrors along the naturally occurring cubic phase GaN-Si(100) cleavage planes. [reprint (PDF)]
20.	Room temperature terahertz semiconductor frequency comb Quanyong Lu, Feihu Wang, Donghai Wu, Steven Slivken & Manijeh Razeghi Nature Communications 10, 2403-- June 3, 2019 ...[Visit Journal] A terahertz (THz) frequency comb capable of high-resolution measurement will significantly advance THz technology application in spectroscopy, metrology and sensing. The recently developed cryogenic-cooled THz quantum cascade laser (QCL) comb has exhibited great potentials with high power and broadband spectrum. Here, we report a room temperature THz harmonic frequency comb in 2.2 to 3.3 THz based on difference-frequency generation from a mid-IR QCL. The THz comb is intracavity generated via down-converting a mid-IR comb with an integrated mid-IR single mode based on distributed-feedback grating without using external optical elements. The grating Bragg wavelength is largely detuned from the gain peak to suppress the grating dispersion and support the comb operation in the high gain spectral range. Multiheterodyne spectroscopy with multiple equally spaced lines by beating it with a reference Fabry-Pérot comb confirms the THz comb operation. This type of THz comb will find applications to room temperature chip-based THz spectroscopy. [reprint (PDF)]
20.	Widely tuned room temperature terahertz quantum cascade laser sources based on difference-frequency generation Q.Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai and M. Razeghi Applied Physics Letters, Vol. 101, No. 25, p. 251121-1-- December 17, 2012 ...[Visit Journal] We demonstrate room temperature THz quantum cascade laser sources with a broad spectral coverage based on intracavity difference-frequency generation. Two mid-infrared active cores based on the single-phonon resonance scheme are designed with a THz nonlinearity specially optimized at the high operating fields that correspond to the highest mid-infrared output powers. A Čerenkov phase-matching scheme along with integrated dual-period distributed feedback gratings are used for efficient THz extraction and spectral purification. Single mode emissions from 1.0 to 4.6 THz with a side-mode suppression ratio and output power up to 40 dB and 32 μW are obtained, respectively. [reprint (PDF)]
20.	4.5 mW Operation of AlGaN-based 267 nm Deep-Ultraviolet Light-Emitting Diodes A. Yasan, R. McClintock, K. Mayes, D. Shiell, L. Gautero, S.R. Darvish, P. Kung and M. Razeghi Applied Physics Letters, 83 (23)-- December 8, 2003 ...[Visit Journal] We demonstrate 4.5 mW output power from AlGaN-based single quantum well ultraviolet light-emitting diodes at a very short wavelength of 267 nm in pulsed operation mode. The output power in continuous-wave mode reaches a value of 165 µW at an injected current of 435 mA. The measurements were done on arrays of four devices flip chip bonded to AlN submounts for thermal management. [reprint (PDF)]
20.	Fabrication of 12 µm pixel-pitch 1280 × 1024 extended short wavelength infrared focal plane array using heterojunction type-II superlattice-based photodetector Arash Dehzangi , Abbas Haddadi, Romain Chevallier, Yiyun Zhang and Manijeh Razegh Semicond. Sci. Technol. 34, 03LT01-- February 4, 2019 ...[Visit Journal] We present an initial demonstration of a 1280 × 1024 extended short-wavelength infrared focal plane array (FPA) imager with 12μm pixel-pitch based on type–II InAs/AlSb/GaSb superlattice heterojunction photodetectors, with a novel bandstructure-engineered photo-generated carrier extractor as the window layer in the hetero structure to efﬁciently extract the photo-generated carriers. This heterostructure with a larger bandgap top window/contact layer leads to the device having lower dark current density compared to conventional pn junction devices. The large format FPA was fabricated with 12 μm pixel-pitch using a developed fabrication process. Test pixels fabricated separately exhibit 100% cut–off wavelengths of ∼2.22, ∼2.34μm, and ∼2.45μm at 150, 200K, and 300K. The test devices achieve saturated quantum efﬁciency values under zero bias of 54.3% and 68.4% at 150 and 300K, under back-side illumination and without any anti-reﬂection coating. At 150K, these photodetectors exhibit dark current density of 1.63 × 10⁻⁷ A·cm⁻² under −20mV applied bias providing a speciﬁc detectivity of 1.01 × 10¹¹ cm ·Hz^½/W at 1.9μm. [reprint (PDF)]
20.	Kinetics of Quantum States in Quantum Cascade Lasers: Device Design Principles and fabrication M. Razeghi special issue of Microelectronics Journal 30 (10)-- October 1, 1999[reprint (PDF)]
20.	High Performance Solar-Blind Ultraviolet Focal Plane Arrays Based on AlGaN Erdem Cicek, Ryan McClintock, Abbas Haddadi, William A. Gaviria Rojas, and Manijeh Razeghi IEEE Journal of Quantum Electronics, Vol. 50, Issue 8, p 591-595-- August 1, 2014 ...[Visit Journal] We report on solar-blind ultraviolet, AlxGa1-x N- based,p-i-n,focal plane array (FPA) with 92% operability. At the peak detection wavelength of 278 nm, 320×256-FP A-pixel showed unbiased peak external quantum efficiency (EQE) and responsivity of 49% and 109 mA/W, respectively, increasing to 66% under 5 volts of reverse bias. Electrical measurements yielded a low-dark current density: <7×10^-9A/cm², at FPA operating voltage of 2 volts of reverse bias. [reprint (PDF)]
20.	Growth and characterization of InGaAs/InGaP quantum dots for mid-infrared photoconductive detector S. Kim, H. Mohseni, M. Erdtmann, E. Michel, C. Jelen and M. Razeghi Applied Physics Letters 73 (7)-- August 17, 1998 ...[Visit Journal] We report InGaAs quantum dot intersubband infrared photodetectors grown by low-pressure metalorganic chemical vapor deposition on semi-insulating GaAs substrates. The optimum growth conditions were studied to obtain uniform InGaAs quantum dots constructed in an InGaP matrix. Normal incidence photoconductivity was observed at a peak wavelength of 5.5 μm with a high responsivity of 130 mA/W and a detectivity of 4.74×10⁷ cm· Hz^½/W at 77 K. [reprint (PDF)]
19.	High Power, Room Temperature InP-Based Quantum Cascade Laser Grown on Si Steven Slivken and Manijeh Razeghi Journal of Quantum Electronics, Vol. 58, No. 6, 2300206 ...[Visit Journal] We report on the realization of an InP-based long wavelength quantum cascade laser grown on top of a silicon substrate. This demonstration first required the development of an epitaxial template with a smooth surface, which combines two methods of dislocation filtering. Once wafer growth was complete, a lateral injection buried heterostructure laser geometry was employed for efficient current injection and low loss. The laser emits at a wavelength of 10.8 μm and is capable of operation above 373 K, with a high peak power (>4 W) at room temperature. Laser threshold behavior with temperature is characterized by a T0 of 178 K. The far field beam shape is single lobed, showing fundamental transverse mode operation. [reprint (PDF)]
19.	Continuous operation of a monolithic semiconductor terahertz source at room temperature Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi Appl. Phys. Lett. 104, 221105 (2014)-- June 3, 2014 ...[Visit Journal] We demonstrate room temperature continuous wave THz sources based on intracavity difference-frequency generation from mid-infrared quantum cascade lasers. Buried ridge, buried composite distributed-feedback waveguide with Čerenkov phase-matching scheme is used to reduce the waveguide loss and enhance the heat dissipation for continuous wave operation. Continuous emission at 3.6 THz with a side-mode suppression ratio of 20 dB and output power up to 3 μW are achieved, respectively. THz peak power is further scaled up to 1.4 mW in pulsed mode by increasing the mid-infrared power through increasing the active region doping and device area. [reprint (PDF)]
19.	Growth and characterization of long wavelength infrared Type-II superlattice Photodiodes on a 3 B.M. Nguyen, G. Chen, M.A. Hoang, and M. Razeghi SPIE Proceedings, San Francisco, CA (January 22-27, 2011), Vol. 7945, p. 79451O-- January 23, 2011 ...[Visit Journal] One of the great advantages of Type-II InAs/GaSb superlattice over other competing technologies for the third generation infrared imagers is the potential to have excellent uniformity across a large area as the electronic structure of the material is controlled by the layer thicknesses, not by the composition of the materials. This can economize the material growth, reduce the fabrication cost, and especially allow the realization of large format imagers. In this talk, we report the molecular beam epitaxial growth of Type-II superlattices on a 3-inch GaSb substrate for long wavelength infrared detection. The material exhibits excellent structural, optical and electrical uniformity via AFM, Xray, quantum efficiency and I-V measurements. At 77K, 11μm cutoff photodiodes exhibit more than 45% quantum efficiency, and a dark current density of 1.0x10^-4 A/cm² at 50 mV, resulting in a specific detectivity of 6 x 10¹¹ cm·Hz^1/2/W. [reprint (PDF)]
19.	Avalanche multiplication in AlGaN based solar-blind photodetectors R. McClintock, A. Yasan, K. Minder, P. Kung, and M. Razeghi Applied Physics Letters, 87 (24)-- December 12, 2005 ...[Visit Journal] Avalanche multiplication has been observed in solar-blind AlGaN-based p-i-n photodiodes. Upon ultraviolet illumination, the optical gain shows a soft breakdown starting at relatively low electric fields, eventually saturating without showing a Geiger mode breakdown. The devices achieve a maximum optical gain of 700 at a reverse bias of 60 V. By modeling the device, it is found that this corresponds to an electric-field strength of 1.7 MV/cm. [reprint (PDF)]
19.	Low Noise Short Wavelength Infrared Avalanche Photodetector Using SB-Based Strained Layer Superlattice Arash Dehzangi, Jiakai Li, Manijeh Razeghi Photonics 2021, 8(5), 148; https://doi.org/10.3390/photonics8050148 Received: 8 March 2021 / Revised: 12 April 2021 / Accepted: 25 April 2021 / Published: 30 April 2021 ...[Visit Journal] We demonstrate low noise short wavelength infrared (SWIR) Sb-based type II superlattice (T2SL) avalanche photodiodes (APDs). The SWIR GaSb/(AlAsSb/GaSb) APD structure was designed based on impact ionization engineering and grown by molecular beam epitaxy on a GaSb substrate. At room temperature, the device exhibits a 50% cut-off wavelength of 1.74 µm. The device was revealed to have an electron-dominated avalanching mechanism with a gain value of 48 at room temperature. The electron and hole impact ionization coefficients were calculated and compared to give a better prospect of the performance of the device. Low excess noise, as characterized by a carrier ionization ratio of ~0.07, has been achieved. [reprint (PDF)]
19.	Bias–selectable nBn dual–band long–/very long–wavelength infrared photodetectors based on InAs/InAsSb/AlAsSb type–II superlattices Abbas Haddadi, Arash Dehzangi, Romain Chevallier, Sourav Adhikary, & Manijeh Razeghi Nature Scientific Reports 7, Article number: 3379-- June 13, 2017 ...[Visit Journal] Type–II superlattices (T2SLs) are a class of artificial semiconductors that have demonstrated themselves as a viable candidate to compete with the state–of–the–art mercury–cadmium–telluride material system in the field of infrared detection and imaging. Within type–II superlattices, InAs/InAs_1−xSb_x T2SLs have been shown to have a significantly longer minority carrier lifetime. However, demonstration of high–performance dual–band photodetectors based on InAs/InAs_1−xSb_x T2SLs in the long and very long wavelength infrared (LWIR & VLWIR) regimes remains challenging. We report the demonstration of high–performance bias–selectable dual–band long–wavelength infrared photodetectors based on new InAs/InAsSb/AlAsSb type–II superlattice design. Our design uses two different bandgap absorption regions separated by an electron barrier that blocks the transport of majority carriers to reduce the dark current density of the device. As the applied bias is varied, the device exhibits well–defined cut–off wavelengths of either ∼8.7 or ∼12.5 μm at 77 K. This bias–selectable dual–band photodetector is compact, with no moving parts, and will open new opportunities for multi–spectral LWIR and VLWIR imaging and detection. [reprint (PDF)]
19.	Sb-based infrared materials and photodetectors for the near room temperature applications J.D. Kim, E. Michel, H. Mohseni, J. Wojkowski, J.J. Lee and M. Razeghi SPIE Conference, San Jose, CA, Vol. 2999, pp. 55-- February 12, 1997 ...[Visit Journal] We report on the growth of InSb, InAsSb, and InTlSb alloys for infrared photodetector applications. The fabrication and characterization of photodetectors based on these materials are also reported. Both photoconductive and photovoltaic devices are investigated. The materials and detector structures were grown on (100) and (111)B semi-insulating GaAs and GaAs coated Si substrates by low pressure metalorganic chemical vapor deposition and solid source molecular beam epitaxy. Photoconductive detectors fabricated from InAsSb and InTlSb have been operated in the temperature range from 77 K to 300 K. The material parameters for photovoltaic device structures have been optimized through theoretical calculations based on fundamental mechanisms. InSb p-i-n photodiodes with 77 K peak responsivities approximately 103 V/W were grown on Si and (111) GaAs substrates. An InAsSb photovoltaic detector with a composition of x equals 0.85 showed photoresponse up to 13 micrometers at 300 K with a peak responsivity of 9.13 X 10-2 V/W at 8 micrometers . The RoA product of InAsSb detectors has been theoretically and experimentally analyzed. [reprint (PDF)]

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