Center for Quantum Devices - Most Downloaded Journal Articles

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2.	Energy harvesting from millimetric ZnO single wire piezo-generators Rogers, D. J.; Carroll, C.; Bove, P.; Sandana, V. E.; Goubert, L.; Largeteau, A.; Teherani, F. Hosseini; Demazeau, G.; McClintock, R.; Drouhin, H.-J.; Razeghi, M. Oxide-based Materials and Devices III. Edited by Teherani, Ferechteh H.; Look, David C.; Rogers, David J. Proceedings of the SPIE, Volume 8263, article id. 82631X, 7 pp. (2012).-- February 9, 2013 ...[Visit Journal] This work reports on investigations into the possibility of harvesting energy from the piezoelectric response of millimetric ZnO rods to movement. SEM & PL studies of hydrothermally grown ZnO rods revealed sizes ranging from 1 - 3 mm x 100 - 400 microns and suggested that each was a wurtzite monocrystal. Studies of current & voltage responses as a function of time during bending with a probe arm gave responses coherent with those reported elsewhere in the literature for ZnO nanowires or micro-rod single wire generators. The larger scale of these rods provided some advantages over such nano- and microstructures in terms of contacting ease, signal level & robustness. [reprint (PDF)]
2.	Direct growth of thick AlN layers on nanopatterned Si substrates by cantilever epitaxy Ilkay Demir, Yoann Robin, Ryan McClintock, Sezai Elagoz, Konstantinos Zekentes, and Manijeh Razeghi Phys. Status Solidi A, pp. 1–6-- September 30, 2016 ...[Visit Journal] AlN layers have been grown on 200 nm period of nanopatterned Si (111) substrates by cantilever epitaxy and compared with AlN layers grown by maskless lateral epitaxial overgrowth (LEO) on micropatterned Si (111) substrates. The material quality of 5–10 µm thick AlN grown by LEO is comparable to that of much thinner layers (2 µm) grown by cantilever epitaxy on the nanopatterned substrates. Indeed, the latter exhibited root mean square (RMS) roughness of 0.65 nm and X-ray diffraction full width at half-maximum (FWHM) of 710 arcsec along the (0002) reflection and 930 arcsec along the (10̅15) reflection. The corresponding room temperature photoluminescence spectra was dominated by a sharp band edge peak. Back emission ultra violet light emitting diodes (UV LEDs) were fabricated by flip chip bonding to patterned AlN heat sinks followed by complete Si (111) substrate removal demonstrating a peak pulsed power of ∼0.7 mW at 344 nm peak emission wavelength. The demonstrated UV LEDs were fabricated on a cost effective epitaxial structure grown on the nanopatterned Si substrate with a total thickness of 3.3 µm [reprint (PDF)]
2.	InTlSb alloys for infrared detection E. Bigan, Y.H. Choi, G. Labeyrie, and M. Razeghi Proceedings, SPIE Nonlinear Optics for High-Speed Electronics and Optical Frequency Conversion, Vol. 2145-- January 24, 1994 ...[Visit Journal] InTISb alloys have been grown by low-pressure metalorganic chemical vapor deposition, and characterized. Photoconductors exhibit a cutoff wavelength that can be tailored from 5.5 μm up to 9 μm by varying the thallium content. Experimental observations suggest that this can be further extended by increasing the thallium content. An InTISb photoconductor having a 9 μm cutoff wavelength exhibited a D* of 10⁹ cm·Hz^½·W^-1 at 7 μm operating wavelength. [reprint (PDF)]
2.	Monolithic Integration of GaInAs/InP Quantum Well Infrared Photodetectors on Si Substrate M. Erdtmann and M. Razeghi SPIE Conference, San Jose, CA, -- January 22, 2001 ...[Visit Journal] Using low-pressure metalorganic chemical vapor deposition, we have grown GaInAs/InP QWIP structures on GaAs-coated Si substrate. First, the procedure to optimize the epitaxy of the InP buffer layer on Si substrate is given. Excellent crystallinity and a mirror-like surface morphology were obtained by using both a two-step growth process at the beginning of the InP buffer layer growth and several series of thermal cycle annealing throughout the InP buffer layer growth. Second, results of fabricated GaInAs/InP QWIPs on Si substrate are presented. At a temperature of 80 K, the peak response wavelength occurs at 7.4 μm. The responsivities of QWIPs on both Si and InP substrates with identical structures are equal up to biases of 1.5 V. At a bias of 3 V, the responsivity of the QWIPs on Si substrate is 1.0 A/W. [reprint (PDF)]
2.	Fabrication and characterization of novel hybrid green light emitting didoes based on substituting n-type ZnO for n-type GaN in an inverted p-n junction C. Bayram, D. Rogers, F. H. Teherani, and M. Razeghi Journal of Vacuum Science and Technology B, Vol. 27, No. 3, May/June, p. 1784-1788-- May 29, 2009 ...[Visit Journal] Details of the fabrication and characterization of hybrid green light emitting diodes, composed of n-ZnO/(InGaN/GaN) multi-quantum-wells/p-GaN on AlN/sapphire, are reported. Scanning electron microscope, atomic force microscopy, high resolution x-ray diffraction, and photoluminescence were used to study the hybrid device. The effects of solvents, annealing, and etching on n-ZnO are discussed. Successful hybridization of ZnO and (In)GaN into a green light emitting diode was realized. [reprint (PDF)]
2.	Self-assembled semiconductor quantum dot infrared photodetector operating at room temperature and focal plane array Ho-Chul Lim; Stanley Tsao; Wei Zhang; Manijen Razeghi Proc. SPIE 6542, Infrared Technology and Applications XXXIII, 65420R (May 14, 2007)-- May 14, 2007 ...[Visit Journal] Self-assembled semiconductor quantum dots have attracted much attention because of their novel properties and thus possible practical applications including the lasers, detectors and modulators. Especially the photodetectors which have quantum dots in their active region have been developed and show promising performances such as high operation temperature due to three dimensional confinement of the carriers and normal incidence in contrast to the case of quantum well detectors which require special optical coupling schemes. Here we report our recent results for mid-wavelength infrared quantum dot infrared photodetector grown by low-pressure metalorganic chemical vapor deposition. The material system we have investigated consists of 25 period self-assembled InAs quantum dot layers on InAlAs barriers, which are lattice-matched to InP substrates, covered with InGaAs quantum well layers and InAlAs barriers. This active region was sandwiched by highly doped InP contact layers. The device operates at 4.1 μm with a peak detectivity of 2.8×10¹¹ cm·Hz^1/2/W at 120 K and a quantum efficiency of 35 %. The photoresponse can be observed even at room temperature resulting in a peak detectivity of 6×10⁷ cm·Hz^1/2/W. A 320×256 focal plane array has been fabricated in this kind of device. Its performance will also be discussed here. [reprint (PDF)]
2.	High Performance InAs/GaSb Superlattice Photodiodes for the Very Long Wavelength Infrared Range H. Mohseni, M. Razeghi, G.J. Brown, Y.S. Park Applied Physics Letters 78 (15)-- April 9, 2001 ...[Visit Journal] We report on the demonstration of high-performance p-i-n photodiodes based on type-II InAs/GaSb superlattices with 50% cut-off wavelength λ_c = 16 μm operating at 80 K. Material is grown by molecular beam epitaxy on GaSb substrates with excellent crystal quality as evidenced by x-ray diffraction and atomic force microscopy. The processed devices show a current responsivity of 3.5 A/W at 80 K leading to a detectivity of ∼ 1.51×10¹⁰ cm·Hz^½/W. The quantum efficiency of these devices is about 35% which is comparable to HgCdTe detectors with a similar active layer thickness. [reprint (PDF)]
2.	Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers Q.Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai and M. Razeghi Applied Physics Letters, Vol. 99, Issue 13, p. 131106-1-- September 26, 2011 ...[Visit Journal] We demonstrate room temperature single-mode THz emission at 4 THz based on intracavity difference-frequency generation from mid-infrared dual-wavelength quantum cascade lasers. An integrated dual-period distributed feedback grating is defined on the cap layer to purify both mid-infrared pumping wavelengths and in turn the THz spectra. Single mode operation of the pumping wavelengths results in a single-mode THz operation with a narrow linewidth of 6.6 GHz. A maximum THz power of 8.5 μW with a power conversion efficiency of 10 μW/W² is obtained at room temperature. [reprint (PDF)]
2.	High performance InGaAs/InGaP quantum dot infrared photodetector achieved through doping level optimization S. Tsao, K. Mi, J. Szafraniec, W. Zhang, H. Lim, B. Movaghar, and M. Razeghi SPIE Conference, Jose, CA, Vol. 5732, pp. 334-- January 22, 2005 ...[Visit Journal] We report an InGaAs/InGaP/GaAs quantum dot infrared photodetector grown by metalorganic chemical vapor deposition with detectivity of 1.3x10¹¹ cm·Hz^½/W at 77K and 1.2x10¹⁰ ccm·Hz^½/W at 120K. Modeling of the Quantum dot energy levels showed us that increased photoresponse could be obtained by doping the quantum dots to 4 electrons per dot instead of the usual 2 electrons per dot. This happens because the primary photocurrent transition is from the first excited state to a higher excited state. Increasing the quantum doping in our device yielded significant responsivity improvement and much higher detectivity as a result. This paper discusses the performance of this higher doping device and compares it to our previously reported device with lower doping. [reprint (PDF)]
2.	Band gap tunability of Type-II Antimonide-based superlattices M. Razeghi and B.M. Nguyen Physics Procedia, Vol. 3, Issue 2, p. 1207-1212 (14th International Conference on Narrow Gap Semiconductors and Systems NGSS-14, Sendai, Japan, July 13-17, 2009)-- January 31, 2010 ...[Visit Journal] Current state-of-the art infrared photon detectors based on bulk semiconductors such as InSb or HgCdTe are now relatively mature and have almost attained the theoretical limit of performance. It means, however, that the technology can not be expected to demonstrate revolutionary improvements, in terms of device performances. In contrasts, low dimensional quantum systems such as superlattices, quantum wells, quantum dots, are still the development stage, yet have shown comparable performance to the bulk detector family. Especially for the Type-II Antimony-based superlattices, recent years have seen significant improvements in material quality, structural design as well as fabrication techniques which lift the performance of Type-II superlattice photodetectors to a new level. In this talk, we will discuss the advantages of Type-II-superlattices, from the physical nature of the material to the practical realisms. We will demonstrate the flexibility in controlling the energy gap and their overall band alignment for the suppression of Auger recombination, as well as to create sophisticated hetero-designs. [reprint (PDF)]
2.	Electroluminescence of InAs/GaSb heterodiodes D. Hoffman, A. Hood, E. Michel, F. Fuchs, and M. Razeghi IEEE Journal of Quantum Electronics, 42 (2)-- February 1, 2006 ...[Visit Journal] The electroluminescence of a Type-II InAs-GaSb superlattice heterodiode has been studied as a function of injection current and temperature in the spectral range between 3 and 13 μm. The heterodiode comprises a Be-doped midwavelength infrared (MWIR) superlattice with an effective bandgap around 270 meV and an undoped long wavelength infrared (LWIR) superlattice with an effective bandgap of 115 meV. [reprint (PDF)]
2.	Use of PLD-grown moth-eye ZnO nanostructures as templates for MOVPE growth of InGaN-based photovoltaics Dave Rogers, V. E. Sandana, F. Hosseini Teherani, S. Gautier, G. Orsal, T. Moudakir, M. Molinari, M. Troyon, M. Peres, M. J. Soares, A. J. Neves, T. Monteiro, D. McGrouther, J. N. Chapman, H. J. Drouhin, M. Razeghi, and A. Ougazzaden Renewable Energy and the Environment, OSA Technical Digest paper PWB3, Optical Society of America, (2011)-- November 2, 2011 ...[Visit Journal] At this time, no abstract is available. Scopus has content delivery agreements in place with each publisher and currently contains 30 million records with an abstract. An abstract may not be present due to incomplete data, as supplied by the publisher, or is still in the process of being indexed. [reprint (PDF)]
2.	High performance LWIR Type-II InAs/GaSb superlattice photodetectors and infrared focal plane array Y. Wei, A. Hood, A. Gin, V. Yazdanpanah, M. Razeghi and M. Tidrow SPIE Conference, Jose, CA, Vol. 5732, pp. 309-- January 22, 2005 ...[Visit Journal] We report on the demonstration of a focal plane array based on Type-II InAs-GaSb superlattices grown on n-type GaSb substrate with a 50% cutoff wavelength at 10 μm. The surface leakage occurring after flip-chip bonding and underfill in the Type-II devices was suppressed using a double heterostructure design. The R₀A of diodes passivated with SiO₂ was 23 Ω·cm² after underfill. A focal plane array hybridized to an Indigo readout integrated circuit demonstrated a noise equivalent temperature difference of 33 mK at 81 K, with an integration time of 0.23 ms. [reprint (PDF)]
2.	High brightness ultraviolet light-emitting diodes grown on patterned silicon substrate Yoann Robin, Kai Ding, Ilkay Demir, Ryan McClintock, Sezai Elagoz, Manijeh Razeghi Materials Science in Semiconductor Processing 90, pp. 87–91-- November 5, 2018 ...[Visit Journal] We report on the fabrication of high brightness AlGaN-based ultraviolet light emitting diodes (UV-LED) on patterned silicon. Using the lateral epitaxial overgrowth approach, we demonstrate the growth of a 6 μm thick AlN layer of high crystalline quality. X-ray diffraction characterization showed a rocking curve with a full width at half maximum of 553 and 768″ for the (00.2) and (10.2) planes, respectively. The low dislocation density of the AlN template enabled the growth of bright AlGaN/ GaN quantum wells emitting at 336 nm. By appropriate flip-chip bonding and silicon substrate removal processing steps, the patterned AlN surface was exposed and efficient bottom-emission UV-LEDs were realized. Improvement of the AlN quality and the structure design allowed the optical output power to reach the milliwatt range under pulsed current, exceeding the previously reported maximum efficiency. Further investigations of the optical power at different pulsed currents and duty cycles show that thermal management in this device structure is still challenging, especially in continuous wave mode operation. The strategy presented here is of interest, since AlN crystalline quality improvement and optimization of the light extraction are the main issues inhibiting efficient UV emitter on silicon fabrication. [reprint (PDF)]
2.	High operating temperature MWIR photon detectors based on Type-II InAs/GaSb superlattice M. Razeghi, B.M. Nguyen, P.Y. Delaunay, S. Abdollahi Pour, E.K.W. Huang, P. Manukar, S. Bogdanov, and G. Chen SPIE Proceedings, San Francisco, CA (January 22-28, 2010), Vol. 7608, p. 76081Q-1-- January 22, 2010 ...[Visit Journal] Recent efforts have been paid to elevate the operating temperature of Type-II InAs/GaSb superlattice Mid Infrared photon detectors. Optimized growth parameters and interface engineering technique enable high quality material with a quantum efficiency above 50%. Intensive study on device architecture and doping profile has resulted in almost one order of magnitude of improvement to the electrical performance and lifted up the 300 K-background BLIP operation temperature to 166 K. At 77 K, the ~4.2 µm cut-off devices exhibit a differential resistance area product in excess of the measurement system limit (10⁶ Ω·cm²) and a detectivity of 3x10¹³ cm·Hz^½·W⁻¹. High quality focal plane arrays were demonstrated with a noise equivalent temperature of 10 mK at 77 K. Uncooled camera is capable to capture hot objects such as soldering iron. [reprint (PDF)]
2.	Passivation of Type-II InAs/GaSb superlattice photodetectors A. Hood, Y. Wei, A. Gin, M. Razeghi, M. Tidrow, and V. Nathan SPIE Conference, Jose, CA, Vol. 5732, pp. 316-- January 22, 2005 ...[Visit Journal] Leakage currents limit the operation of high performance Type-II InAs/GaSb superlattice photodiode technology. Surface leakage current becomes a dominant limiting factor, especially at the scale of a focal plane array pixel (< 25 µm) and must be addressed. A reduction of the surface state density, unpinning the Fermi level at the surface, and appropriate termination of the semiconductor crystal are all aims of effective passivation. Recent work in the passivation of Type-II InAs\GaSb superlattice photodetectors with aqueous sulfur-based solutions has resulted in increased R₀A products and reduced dark current densities by reducing the surface trap density. Additionally, photoluminescence of similarly passivated Type-II InAs/GaSb superlattice and InAs GaSb bulk material will be discussed. [reprint (PDF)]
2.	The effect of doping the M-barrier in very long-wave type-II InAs/GaSb heterodiodes D. Hoffman, B.M. Nguyen, E.K. Huang, P.Y. Delaunay, M. Razeghi, M.Z. Tidrow and J. Pellegrino Applied Physics Letters, Vol. 93, No. 3, p. 031107-1-- July 21, 2008 ...[Visit Journal] A variation on the standard homo-diode Type-II superlattice with an M-barrier between the pi-region and the n-region is shown to suppress the dark currents. By determining the optimal doping level of the M-superlattice, dark current densities of 4.95 mA·cm^-2 and quantum efficiencies in excess of 20% have been demonstrated at the moderate reverse bias of 50 mV; allowing for near background-limited performance with a Johnson-noise detectivity of 3.11×10¹⁰ Jones at 77 K for a 14.58 µm cutoff wavelength for large area diodes without passivation. This is comparable to values for the state-of-the-art HgCdTe photodiodes. [reprint (PDF)]
2.	Development of material quality and structural design for high performance type-II InAs/GaSb superlattice photodiodes and focal plane arrays M. Razeghi, B.M. Nguyen, D. Hoffman, P.Y. Delaunay, E.K. Huang, M.Z. Tidrow and V. Nathan SPIE Porceedings, Vol. 7082, San Diego, CA 2008, p. 708204-- August 11, 2008 ...[Visit Journal] Recent progress made in the structure design, growth and processing of Type-II InAs/GaSb superlattice photo-detectors lifted both the quantum efficiency and the R0A product of the detectors. Type-II superlattice demonstrated its ability to perform imaging in the Mid-Wave Infrared (MWIR)and Long-Wave Infrared (LWIR) ranges, becoming a potential competitor for technologies such as Quantum Well Infrared Photo-detectors (QWIP) and Mercury Cadmium Telluride (MCT). Using an empirical tight-binding model, we developed superlattices designs that were nearly lattice-matched to the GaSb substrates and presented cutoff wavelengths of 5 and 11 μm. We demonstrated high quality material growth with X-ray FWHM below 30 arcsec and an AFM rms roughness of 1.5 Å over an area of 20x20 μm2. The detectors with a 5 μm cutoff, capable of operating at room temperature, showed a R0A of 1.25 106 Ω.cm2 at 77K, and a quantum efficiency of 32%. In the long wavelength infrared, we demonstrated high quantum efficiencies above 50% with high R0A products of 12 Ω.cm2 by increasing the thickness of the active region. Using the novel M-structure superlattice design, more than one order of magnitude improvement has been observed for electrical performance of the devices. Focal plane arrays in the middle and long infrared range, hybridized to an Indigo read out integrated circuit, exhibited high quality imaging. [reprint (PDF)]
2.	Type-II InAs/GaSb superlattice photovoltaic detectors with cutoff wavelength approaching 32 μm Y. Wei, A. Gin, M. Razeghi and G.J. Brown Applied Physics Letters, 81 (19)-- November 4, 2002 ...[Visit Journal] We report the most recent advance in the area of type-II InAs/GaSb superlattice photovoltaic detectors that have cutoff wavelengths beyond 25 μm, with some at nearly 32 μm. The photodiodes with a heterosuperlattice junction showed Johnson noise limited peak detectivity of 1.05 x 10¹⁰ cm Hz^½/W at 15 μm under zero bias, and peak responsivity of 3 A/W under -40 mV reverse bias at 34 K illuminated by ~300 K background with a 2π field-of-view. The maximum operating temperature of these detectors ranges from 50 to 65 K. No detectable change in the blackbody response has been observed after 5-6 thermal cyclings, with temperature varying between 15 and 296 K in vacuum. [reprint (PDF)]
2.	Long-term reliability of Al-free InGaAsP/GaAs λ = 808 nm) lasers at high-power high-temperature operation J. Diaz, H. Yi, M. Razeghi and G.T. Burnham Applied Physics Letters 71 (21)-- November 24, 1997 ...[Visit Journal] We report the long-term reliability measurement on uncoated Al-free InGaAsP/GaAs (λ = 808 nm) lasers at high-power and high-temperature operation. No degradation in laser performance has been observed for over 30 ,000 h of lifetime testing in any of randomly selected several 100 μm-wide uncoated lasers operated at 60 °C with 1 W continuous wave output power. This is the first and the most conclusive evidence ever reported that directly shows the high long-term reliability of uncoated Al-free lasers. [reprint (PDF)]
2.	High Power, Continuous-Wave, Quantum Cascade Lasers for MWIR and LWIR Applications S. Slivken, A. Evans, J.S. Yu, S.R. Darvish and M. Razeghi SPIE Conference, San Jose, CA, Vol. 6127, pp. 612703-- January 23, 2006 ...[Visit Journal] Over the past several years, our group has endeavored to develop high power quantum cascade lasers for a variety of remote and high sensitivity infrared applications. The systematic optimization of laser performance has allowed for demonstration of high power, continuous-wave quantum cascade lasers operating above room temperature. Since 2002, the power levels for individual devices have jumped from 20 mW to 600 mW. Expanding on this development, we have able to demonstrate continuous wave operation at many wavelengths throughout the mid- and far-infrared spectral range, and have now achieved >100 mW output in the 4.0 to 9.5 µm range. [reprint (PDF)]
2.	p-doped GaAs/Ga_0.51In_0.49P quantum well intersub-band photodetectors J. Hoff, X. He, M. Erdtmann, E. Bigan, M. Razeghi, and G.J. Brown Journal of Applied Physics 78 (3)-- August 1, 1995 ...[Visit Journal] Lattice‐matched p-doped GaAs–Ga_0.51In_0.49P quantum well intersub‐band photodetectors with three different well widths have been grown on GaAs substrates by metal‐organic chemical‐vapor deposition and fabricated into mesa structures. The photoresponse cutoff wavelength varies between 3.5 and 5.5 μm by decreasing the well width from 50 down to 25 Å. Dark current measurements as a function of temperature reveal activation energies for thermionic emission that closely correspond to measured cutoff wavelengths. Experimental results are in reasonable agreement with Kronig–Penney calculations. [reprint (PDF)]
2.	InAs/InAs_1-xSb_x type-II superlattices for high performance long wavelength infrared detection A. Haddadi , G. Chen , R. Chevallier , A. M. Hoang , and M. Razeghi Appl. Phys. Lett. 105, 121104 (2014)-- September 22, 2014 ...[Visit Journal] High performance long-wavelength infrared nBn photodetectors based on InAs/InAs_1−xSb_x type-II superlattices on GaSb substrate have been demonstrated. The photodetector's 50% cut-off wavelength was ∼10 μm at 77 K. The photodetector with a 6 μm-thick absorption region exhibited a peak responsivity of 4.47 A/W at 7.9 μm, corresponding to a quantum efficiency of 54% at −90 mV bias voltage under front-side illumination and without any anti-reflection coating. With an R × A of 119 Ω·cm² and a dark current density of 4.4 × 10⁻⁴ A/cm² under −90 mV applied bias at 77 K, the photodetector exhibited a specific detectivity of 2.8 × 10¹¹ cm·Hz^1/2·W^-1. [reprint (PDF)]
2.	Al_xGa_1-xN (0 ≤ x ≤ 1) Ultraviolet Photodetectors Grown on Sapphire by Metal-organic Chemical-vapor Deposition D. Walker, X. Zhang, A. Saxler, P. Kung, J. Xu, and M. Razeghi Applied Physics Letters 70 (8)-- February 24, 1997 ...[Visit Journal] Al_xGa_1–xN (0 ≤ x ≤ 1) ultraviolet photoconductors with cutoff wavelengths from 365 to 200 nm have been fabricated and characterized. The maximum detectivity reached 5.5 × 10⁸ cm·Hz^1/2/W at a modulating frequency of 14 Hz. The effective majority carrier lifetime in Al_xGa_1–xN materials, derived from frequency-dependent photoconductivity measurements, has been estimated to be from 6 to 35 ms. The frequency-dependent noise spectrum shows that it is dominated by Johnson noise at high frequencies for low-Al-composition samples. [reprint (PDF)]
2.	Gain-length scaling in quantum dot/quantum well infrared photodetectors T. Yamanaka, B. Movaghar, S. Tsao, S. Kuboya, A. Myzaferi and M. Razeghi Applied Physics Letters, Vol. 95, No. 9-- August 31, 2009 ...[Visit Journal] The gain in quantum dot/quantum well infrared photodetectors is investigated. The scaling of the gain with device length has been analyzed, and the behavior agrees with the previously proposed model. We conclude that we understand the gain in the low bias region, but in the high field region, discrepancies remain. An extension of the gain model is presented to cover the very high electric field region. The high field data are compared to the extended model and discussed. [reprint (PDF)]

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