Center for Quantum Devices - Most Downloaded Journal Articles

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14.	Type-II Antimonide-based Superlattices for the Third Generation Infrared Focal Plane Arrays Manijeh Razeghi, Edward Kwei-wei Huang, Binh-Minh Nguyen, Siamak Abdollahi Pour, and Pierre-Yves Delaunay SPIE Proceedings, Infrared Technology and Applications XXXVI, Vol. 7660, pp. 76601F-- May 10, 2010 ...[Visit Journal] In recent years, the Type-II superlattice (T2SL) material platform has seen incredible growth in the understanding of its material properties which has lead to unprecedented development in the arena of device design. Its versatility in band-structure engineering is perhaps one of the greatest hallmarks of the T2SL that other material platforms are lacking. In this paper, we discuss advantages of the T2SL, specifically the M-structure T2SL, which incorporates AlSb in the traditional InAs/GaSb superlattice. Using the M-structure, we present a new unipolar minority electron detector coined as the p-M-p, the letters which describe the composition of the device. Demonstration of this device structure with a 14 μm cutoff attained a detectivity of 4x10¹⁰ Jones (-50 mV) at 77 K. As device performance improves year after year with novel design contributions from the many researchers in this field, the natural progression in further enabling the ubiquitous use of this technology is to reduce cost and support the fabrication of large infrared imagers. In this paper, we also discuss the use of GaAs substrates as an enabling technology for third generation imaging on T2SLs. Despite the 7.8% lattice mismatch between the native GaSb and alternative GaAs substrates, T2SL photodiodes grown on GaAs at the MWIR and LWIR have been demonstrated at an operating temperature of 77 K [reprint (PDF)]
14.	Conduction‐ and valence‐band offsets in GaAs/Ga0.51In0.49P single quantum wells grown by metalorganic chemical vapor deposition D. Biswas; N. Debbar; P. Bhattacharya; M. Razeghi; M. Defour; F. Omnes Appl. Phys. Lett. 56, 833–835 (1990)-- February 26, 1990 ...[Visit Journal] We have independently estimated the conduction- and valence-band offsets D.Ec and D.Ev in GaAs/Gao . 51 Ino49 P quantum wells by measuring the capacitance transient resulting from thermal emission of carriers from the respective wens. The heterostructure samples were grown by low-pressure metalorganic chemical vapor deposition. The band offsets are extrapolated from the emission activation energies with appropriate corrections. The estimated values of AEc and AEv are 0.198 and 0.285 eV, respectively. [reprint (PDF)]
14.	High Power 3-12 μm Infrared Lasers: Recent Improvements and Future Trends M. Razeghi, S. Slivken, A. Tahraoui, A. Matlis, and Y.S. Park Physica E: Low-Dimensional Systems and Nanostructures 11 (2-3)-- October 1, 2001 ...[Visit Journal] In this paper, we discuss the progress of quantum cascade lasers (QCLs) grown by gas-source molecular beam epitaxy. Room temperature QCL operation has been reported for lasers emitting between 5-11 μm, with 9-11 μm lasers operating up to 425 K. Laser technology for the 3-5 μm range takes advantage of a strain-balanced active layer design. We also demonstrate record room temperature peak output powers at 9 and 11 μm (2.5 and 1 W, respectively) as well as record low 80K threshold current densities (250 A/cm²) for some laser designs. Preliminary distributed feedback (DFB) results are also presented and exhibit single mode operation for 9 μm lasers at room temperature. [reprint (PDF)]
14.	High-power, room-temperature and continuous-wave operation of distributed-feedback quantum-cascade lasers at λ = 4.8 µm J.S. Yu, S. Slivken, S.R. Darvish, A. Evans, B. Gokden and M. Razeghi Virtual Journal of Nanoscale Science and Technology 12 (5)-- August 1, 2005 ...[Visit Journal][reprint (PDF)]
14.	Investigation of the factors influencing nanostructure array growth by PLD towards reproducible wafer-scale growth Vinod E. Sandana; David. J. Rogers; Ferechteh Hosseini Teherani; Philippe Bove; Manijeh Razeghi physica status solidi (a) Applications and Materials Science. Volume 211, Issue 2, pages 449–454, (February 2014)-- January 14, 2014 ...[Visit Journal] The growth of catalyst-free ZnO nanostructure arrays on silicon (111) substrates by pulsed laser deposition was investigated. Without an underlayer, randomly oriented, micron-scale structures were obtained. Introduction of a c-axis oriented ZnO underlayer resulted in denser arrays of vertically oriented nanostructures with either tapering, vertical-walled or broadening forms, depending on background Ar pressure. Nanostructure pitch seemed to be determined by underlayer grain size while nanostructure widths could be narrowed from ∼100–500 to ∼10–50 nm by a 50 °C increase in growth temperature. A dimpled underlayer topography correlated with the moth-eye type arrays while a more granular surface was linked to vertically walled nanocolumns. Between-wafer reproducibility was demonstrated for both moth-eye and vertical nanocolumn arrays. Broadening nanostructures proved difficult to replicate, however. Full 2 inch wafer coverage was obtained by rastering the target with the laser beam. [reprint (PDF)]
14.	Optical Investigations of GaAs-GaInP Quantum Wells and Superlattices Grown by Metalorganic Chemical Vapor Deposition Omnes F., and Razeghi M. Applied Physics Letters 59 (9), p. 1034-- May 28, 1991 ...[Visit Journal] Recent experimental results on the photoluminescence and photoluminescence excitation of GaAs‐Ga_0.51In_0.49P lattice‐matched quantum wells and superlattices are discussed. The full width at half maximum of a 10‐period GaAs‐GaInP superlattice with Lz=90 Å and LB=100 Å is 4 meV at 4 K. The photoluminescence excitation exhibits very sharp peaks attributed to the electron to light‐hole and electron to heavy‐hole transitions. The GaInP‐GaAs interface suffers from memory effect of In, rather than P or As elements. [reprint (PDF)]
14.	III-Nitride Optoelectronic Devices: From ultraviolet detectors and visible emitters towards terahertz intersubband devices M. Razeghi, C. Bayram, Z. Vashaei, E. Cicek and R. McClintock IEEE Photonics Society 23rd Annual Meeting, November 7-10, 2010, Denver, CO, Proceedings, p. 351-352-- January 20, 2011 ...[Visit Journal] III-nitride optoelectronic devices are discussed. Ultraviolet detectors and visible emitters towards terahertz intersubband devices are reported. Demonstration of single photon detection efficiencies of 33% in the ultraviolet regime, intersubband energy level as low as in the mid-infrared regime, and GaN-based resonant tunneling diodes with negative resistance of 67 Ω are demonstrated. [reprint (PDF)]
14.	High operating temperature MWIR photon detectors based on Type II InAs/GaSb superlattice M. Razeghi, S. Abdollahi Pour, E.K. Huang, G. Chen, A. Haddadi and B.M. Nguyen SPIE Proceedings, Infrared Technology and Applications XXXVII, Orlando, FL, Vol. 8012, p. 80122Q-1-- April 26, 2011 ...[Visit Journal] Recent efforts have been paid to elevate the operating temperature of Type II superlattice Mid Infrared photon detectors. Using M-structure superlattice, novel device architectures have been developed, resulting in significant improvement of the device performances. In this paper, we will compare different photodetector architectures and discuss the optimization scheme which leads to almost one order of magnitude of improvement to the electrical performance. At 150K, single element detectors exhibit a quantum efficiency above 50%, and a specific detectivity of 1.05x10(12) cm.Hz(1/2)/W. BLIP operation with a 300K background and 2π FOV can be reached with an operating temperature up to 180K. High quality focal plane arrays were demonstrated with a noise equivalent temperature difference (NEDT) of 11mK up to 120K. Human body imaging is achieved at 150K with NEDT of 150mK. [reprint (PDF)]
14.	Recent Advances in LWIR Type-II InAs/GaSb Superlattice Photodetectors and Focal Plane Arrays at the Center for Quantum Devices M. Razeghi, D. Hoffman, B.M. Nguyen, P.Y. Delaunay, E.K. Huang, M.Z. Tidrow, and V. Nathan IEEE Proceedings, Vol. 97, No. 6, p. 1056-1066-- June 1, 2009 ...[Visit Journal] In recent years, Type-II InAs/GaSb superlattice photo-detectors have experienced significant improvements in material quality, structural designs, and imaging applications. They now appear to be a possible alternative to the state-of-the-art HgCdTe (MCT) technology in the long and very long wavelength infrared regimes. At the Center for Quantum Devices, we have successfully realized very high quantum efficiency, very high dynamic differential resistance R₀A - product LWIR Type – II InAs/GaSb superlattice photodiodes with efficient surface passivation techniques. The demonstration of high quality LWIR Focal Plane Arrays that were 100 % fabricated in - house reaffirms the pioneer position of this university-based laboratory. [reprint (PDF)]
14.	Efficiency of photoluminescence and excess carrier confinement in InGaAsP/GaAs structures prepared by metal-organic chemical vapor deposition J. Diaz, H.J. Yi, M. Erdtmann, X. He, E. Kolev, D. Garbuzov, E. Bigan, and M. Razeghi Journal of Applied Physics 76 (2)-- July 15, 1994 ...[Visit Journal] Special double‐ and separate‐confinement InGaAsP/GaAs heterostructures intended for photoluminescence measurements have been grown by low‐pressure metal‐organic chemical‐vapor deposition. The band gap of the active region quaternary material was close to 1.5 eV, and the waveguide of the separate‐confinement structures was near 1.8 eV. Measurement of the integrated luminescence efficiency at 300 K has shown that over a wide range of excitation level (10–10³ W/cm²) radiative transitions are the dominant mechanism for excess carrier recombination in the active region of the structures studied. As determined by spectral measurements, the excess carrier concentration in the waveguide of the separate‐confinement heterostructures and the intensity of the waveguide emission band correspond to a condition of thermal equilibrium of the excess carrier populations in the active region and the waveguide. The ratio of the intensity of the waveguide emission to the active region emission fits a model which assumes that the barrier height for minority carriers (holes) is equal to the difference in band gaps between the active region and the waveguide region. [reprint (PDF)]
14.	Combined resonant tunneling and rate equation modeling of terahertz quantum cascade lasers Zhichao Chen , Andong Liu, Dong Chang , Sukhdeep Dhillon , Manijeh Razeghi , Feihu Wang Journal of Applied Physics, 135, 115703 ...[Visit Journal] Terahertz (THz) quantum cascade lasers (QCLs) are technologically important laser sources for the THz range but are complex to model. An efficient extended rate equation model is developed here by incorporating the resonant tunneling mechanism from the density matrix formalism, which permits to simulate THz QCLs with thick carrier injection barriers within the semi-classical formalism. A self-consistent solution is obtained by iteratively solving the Schrödinger-Poisson equation with this transport model. Carrier-light coupling is also included to simulate the current behavior arising from stimulated emission. As a quasi-ab initio model, intermediate parameters such as pure dephasing time and optical linewidth are dynamically calculated in the convergence process, and the only fitting parameters are the interface roughness correlation length and height. Good agreement has been achieved by comparing the simulation results of various designs with experiments, and other models such as density matrix Monte Carlo and non-equilibrium Green’s function method that, unlike here, require important computational resources. The accuracy, compatibility, and computational efficiency of our model enables many application scenarios, such as design optimization and quantitative insights into THz QCLs. Finally, the source code of the model is also provided in the supplementary material of this article for readers to repeat the results presented here, investigate and optimize new designs. [reprint (PDF)]
14.	GaInAs/InP nanopillar arrays for long wavelength infrared detection A. Gin, Y. Wei, A. Hood, D. Hoffman, M. Razeghi and G.J. Brown SPIE Conference, Jose, CA, Vol. 5732, pp. 350-- January 22, 2005 ...[Visit Journal] Nanopillar devices have been fabricated from GaInAs/InP QWIP material grown by MOCVD. Using electron beam lithography and reactive ion etching techniques, large, regular arrays of nanopillars with controllable diameters ranging from 150 nm to less than 40 nm have been reproducibly formed. Photoluminescence experiments demonstrate a strong peak wavelength blue shift for nanopillar structures compared to the as-grown quantum well material. Top and bottom metal contacts have been realized using a polyimide planarization and etchback procedure. I-V and noise measurements have been performed. Optical measurements indicate photoconductive response in selected nanopillar arrays. Device peak wavelength response occurs at about 8 µm with peak device responsivity of 420 mA/W. Peak detectivity of 3×10⁸ cm·Hz^½/W has been achieved at -1V bias and 30 K. [reprint (PDF)]
14.	Gain and recombination dynamics in photodetectors made with quantum nanostructures: the quantum dot in a well and the quantum well B. Movaghar, S. Tsao, S. Abdollahi Pour, T. Yamanaka, and M. Razeghi Virtual Journal of Nanoscale Science & Technology, Vol. 18, No. 14-- October 6, 2008 ...[Visit Journal][reprint (PDF)]
14.	Photoluminescence Study of AlGaN-based 280 nm Ultraviolet Light-Emitting Diodes A. Yasan, R. McClintock, K. Mayes, D.H. Kim, P. Kung, and M. Razeghi Applied Physics Letters, 83 (20)-- November 17, 2003 ...[Visit Journal] We investigated optical properties of single quantum well AlGaN-based UV 280 nm light-emitting diodes using temperature-dependent photoluminescence (PL) measurement. We found an "S-shaped" temperature dependence of the peak energy. From the Arrhenius plot of integrated PL intensity, we speculate that dislocations as well as thermal emission of carriers out of the quantum well are responsible for the PL quenching behavior. Also a second nonradiative channel with much lower activation energy was found, the origin of which we believe to be quenching of the bound excitons [reprint (PDF)]
14.	Investigation of MgZnO/ZnO heterostructures grown on c-sapphire substrates by pulsed laser deposition D. J. Rogers ; F. Hosseini Teherani ; P. Bove ; A. Lusson ; M. Razeghi Proc. SPIE 8626, Oxide-based Materials and Devices IV, 86261X (March 18, 2013)-- March 18, 2013 ...[Visit Journal] MgZnO thin films were grown on c-sapphire and ZnO-coated c-sapphire substrates by pulsed laser deposition from a ZnMgO target with 4 at% Mg. The MgZnO grown on the ZnO underlayer showed significantly better crystal quality than that grown directly on sapphire. AFM studies revealed a significant deterioration in surface morphology for the MgZnO layers compared with the ZnO underlayer. Optical transmission studies indicated a MgZnO bandgap of 3.61eV (compared with 3.34eV for the ZnO), which corresponds to a Mg content of about 16.1 at%. The MgZnO/ZnO heterojunction showed an anomalously low resistivity, which was more than two orders of magnitude less than the MgZnO layer and an order of magnitude lower than that for the ZnO layer. It was suggested that this may be attributable to the presence of a 2D electron gas at the ZnMgO/ZnO heterointerface. [reprint (PDF)]
14.	ZnO Thin Films & Nanostructures for Emerging Optoelectronic Applications D.J. Rogers, F. Hosseini Teherani, V.E. Sandana, and M. Razeghi SPIE Proceedings, San Francisco, CA (January 22-28, 2010), Vol. 7605, p. 76050K-1-- January 27, 2010 ...[Visit Journal] ZnO-based thin films and nanostructures grown by PLD for various emerging optoelectronic applications. AZO thin films are currently displacing ITO for many TCO applications due to recent improvements in attainable AZO conductivity combined with processing, cost and toxicity advantages. Advances in the channel mobilities and Id on/off ratios in ZnO-based TTFTs have opened up the potential for use as a replacement for a-Si in AM-OLED and AM-LCD screens. Angular-dependent specular reflection measurements of self-forming, moth-eye-like, nanostructure arrays grown by PLD were seen to have <0.5% reflectivity over the whole visible spectrum for angles of incidence between 10 and 60 degrees. Such nanostructures may be useful for applications such as AR coatings on solar cells. Compliant ZnO layers on mismatched/amorphous substrates were shown to have potential for MOVPE regrowth of GaN. This approach could be used as a means to facilitate lift-off of GaN-based LEDs from insulating sapphire substrates and could allow the growth of InGaN-based solar cells on cheap substrates. The green gap in InGaN-based LEDs was combated by substituting low Ts PLD n-ZnO for MOCVD n-GaN in inverted hybrid heterojunctions. This approach maintained the integrity of the InGaN MQWs and gave LEDs with green emission at just over 510 nm. Hybrid n-ZnO/p-GaN heterojunctions were also seen to have the potential for UV (375 nm) EL, characteristic of ZnO NBE emission. This suggests that there was significant hole injection into the ZnO and that such LEDs could profit from the relatively high exciton binding energy of ZnO. [reprint (PDF)]
14.	Molecular beam epitaxial growth of InSb p-i-n photodetectors on GaAs and Si E. Michel, R. Peters, S. Slivken, C. Jelen, P. Bove, J. Xu, I. Ferguson, and M. Razeghi Optoelectronic Integrated Circuit Materials, Physics and Devices, SPIE Conference, San Jose, CA; Proceedings, Vol. 2397-- February 6, 1995 ...[Visit Journal] High quality InSb has been grown by Molecular Beam Epitaxy and optimized using Reflection High Energy Electron Diffraction. A 4.8 micrometers InSb layer grown on GaAs at a growth temperature of 395 degree(s)C and a III/V incorporation ratio of 1:1.2 had an X-ray rocking curve FWHM of 158 arcsec and a Hall mobility of 92300 cm2V-1s-1 at 77 K, the best reported to date for InSb nucleated directly onto GaAs. InSb p-i-n structures of 5.8 micrometers grown under the same conditions demonstrated a X-ray Full Width at Half Maximum of 101 arcsec and 131 arcsec for GaAs and Si substrates, respectively, and exhibited excellent uniformity of +/- 3 arcsec over a 3' substrate. Prototype InSb p-i-n detectors on Si have been fabricated and have demonstrated photovoltaic response at 6.5 micrometers up to 200 K. These p-i-n detectors have also exhibited the highest D* for a device grown onto Si. [reprint (PDF)]
14.	Monolithic integration of a short‐length GaInAs photoconductor with a GaAs/GaAlAs optical waveguide on a GaAs semi‐insulating substrate F. Mallecot; J. F. Vinchant; M. Razeghi; D. Vandermoere; J. P. Vilcot; D. Decoster Appl. Phys. Lett. 53, 2522–2524 (1988)-- December 19, 1988 ...[Visit Journal] We report the first fabrication of a GaO. 47 Inn. 53 As planar photoconductive detector, associated with a GaAs/GaAIAs rib waveguide grown on a semi-insulating GaAs substrate, which needs a short-length absorbing layer to detect the optical signal. Because of the GaAIAs epilayer, a GalnAs length of about 100 tl1n only is needed to detect 90% of the opticai signal, accordingly to results predicted using a four-layer model with complex refractive indices in each layer. [reprint (PDF)]
14.	Relaxation kinetics in quantum cascade laser S. Slivken, V. Litvinov, M. Razeghi, and J.R. Meyer Journal of Applied Physics 85 (2)-- January 15, 1999 ...[Visit Journal] Relaxation kinetics in a quantum cascade intersubband laser are investigated. Distribution functions and gain spectra of a three-subband double-quantum-well active region are obtained as a function of temperature and injection current. The potentially important role of the nonequilibrium phonons at lasing threshold is shown and discussed in details. It is shown that the threshold current is strongly dependent of the power dissipated in the active region in steady state. The numerical calculations for an 8.5 μm laser illustrate the general issues of relaxation kinetics in quantum cascade lasers. Temperature dependence of the threshold current is obtained in a good agreement with the experiments. [reprint (PDF)]
14.	Evaluation of the Band Offsets of GaAs-GaInP Multilayers by Electroreflectance Razeghi M., D. Yang, J.W. Garland, Z. Zhang, D. Xue SPIE Proceedings, Vol. 1676, pp. 130-- January 1, 1992 ...[Visit Journal] We report the first band offset measurement of GaAs/Ga_0.51In_0.49P multiquantum wells and superlattices by electrolyte electroreflectance spectroscopy. The conduction and valence band discontinuities (Delta) Ec equals 159 ± 4 meV and (Delta) Ev equals 388 ± 6 meV have been measured. The values found for the conduction band, heavy-hole and light-hole masses in the GaInP barriers and GaAs wells and for the split-off well mass are in excellent agreement with the literature. The intraband, intersubband transition energies, which are important for III - V infrared detection devices, also were directly measured. [reprint (PDF)]
14.	Two‐dimensional electron gas in a In0.53Ga0.47As‐InP heterojunction grown by metalorganic chemical vapor deposition Y. Guldner; J. P. Vieren; P. Voisin; M. Voos; M. Razeghi; M. A. Poisson Y. Guldner, J. P. Vieren, P. Voisin, M. Voos, M. Razeghi, M. A. Poisson; Two‐dimensional electron gas in a In0.53Ga0.47As‐InP heterojunction grown by metalorganic chemical vapor deposition. Appl. Phys. Lett. 15 May 1982; 40 (10): 877–879.-- April 15, 1982 ...[Visit Journal] We report, from Shubnikov-de Haas and cyclotron resonance experiments, the first observation of a two-dimensional, high-mobility electron gas in a selectively doped 1110.53 G~l.47 As-InP heterojunction grown by metalorganic chemical vapor deposition. Several parameters of the electronic system under consideration are determined. [reprint (PDF)]
14.	Engineering Multi-Section Quantum Cascade Lasers for Broadband Tuning Steven Slivken and Manijeh Razeghi Photonics 3, 41-- June 27, 2016 ...[Visit Journal] In an effort to overcome current limitations to electrical tuning of quantum cascade lasers, a strategy is proposed which combines heterogeneous quantum cascade laser gain engineering with sampled grating architectures. This approach seeks to not only widen the accessible spectral range for an individual emitter, but also compensate for functional non-uniformity of reflectivity and gain lineshapes. A trial laser with a dual wavelength core is presented which exhibits electroluminescence over a 750 cm⁻¹ range and discrete single mode laser emission over a 700 cm⁻¹ range. Electrical tuning over 180 cm⁻¹ is demonstrated with a simple sampled grating design. A path forward to even wider tuning is also described using more sophisticated gain and grating design principles. [reprint (PDF)]
14.	Comparison of the Physical Properties of GaN Thin Films Deposited on (0112) and (0001) Sapphire Substrates C.J. Sun and M. Razeghi Applied Physics Letters 63 (7)-- August 16, 1993 ...[Visit Journal] A direct comparison of the physical properties of GaN thin films is made as a function of the choice of substrate orientations. Gallium nitride single crystals were grown on (0001) and (0112) sapphire substrates by metalorganic chemical vapor deposition. Better crystallinity with fine ridgelike facets is obtained on the (0112) sapphire. Also lower carrier concentration and higher mobilities indicate both lower nitrogen vacancies and less oxygen incorporation on the (0112) sapphire. The results of this study show better physical properties of GaN thin films achieved on (0112) sapphire. [reprint (PDF)]
14.	InAs/InAs_1-xSb_x type-II superlattices for high performance long wavelength infrared detection M. Razeghi, A. Haddadi, A. M. Hoang, R. Chevallier, S. Adhikary, A. Dehzangi Proc. SPIE 9819, Infrared Technology and Applications XLII, 981909-- May 20, 2016 ...[Visit Journal] We report InAs/InAs1-xSbx type-II superlattice base photodetector as high performance long-wavelength infrared nBn device grown on GaSb substrate. The device has 6 μm-thick absorption region, and shows optical performance with a peak responsivity of 4.47 A/W at 7.9 μm, which is corresponding to the quantum efficiency of 54% at a bias voltage of negative 90 mV, where no anti-reflection coating was used for front-side illumination. At 77K, the photodetector’s 50% cut-off wavelength was ~10 μm. The device shows the detectivity of 2.8x10¹¹ cm•Hz^½/W at 77 K, where RxA and dark current density were 119 Ω•cm² and 4.4x10^-4 A/cm² , respectively, under -90 mV applied bias voltage [reprint (PDF)]
14.	Band edge tunability of M-structure for heterojunction design in Sb based Type-II superlattice photodiodes B.M. Nguyen, D. Hoffman, P.Y. Delaunay, E.K. Huang, M. Razeghi, and J. Pellegrino Applied Physics Letters, Vol. 93, No. 16, p. 163502-1-- October 20, 2008 ...[Visit Journal] We present theoretically and experimentally the effect of the band discontinuity in Type-II misaligned InAs/GaSb superlattice heterodiodes. Calculations using the empirical tight binding method have shown the great flexibility in tuning the energy levels of the band edge in M-structure superlattice as compared to the standard InAs/GaSb superlattice. Through the experimental realization of several p-pi-M-n photodiodes, the band discontinuity alignment between the standard binary-binary superlattice and the M-structured superlattice was investigated via optical characterization. The agreement between the theoretical predictions and the experimental measurement confirms the capability of controlling the M-structure band edges and suggests a way to exploit this advantage for the realization of heterostructures containing an M-structured superlattice without bias dependent operation. [reprint (PDF)]

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