Center for Quantum Devices - Most Downloaded Journal Articles

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22.	Study of Phase Transition in MOCVD Grown Ga2O3 from κ to β Phase by Ex Situ and In Situ Annealing Junhee Lee, Honghyuk Kim, Lakshay Gautam, Kun He, Xiaobing Hu, Vinayak P. Dravid and Manijeh Razeghi Photonics 2021, 8, 17. https://doi.org/10.3390/ photonics8010017 ...[Visit Journal] We report the post-growth thermal annealing and the subsequent phase transition of Ga2O3 grown on c-plane sapphire substrates by metal organic chemical vapor deposition (MOCVD). We demonstrated the post-growth thermal annealing at temperatures higher than 900 °C under N2 ambience, by either in situ or ex situ thermal annealing, can induce phase transition from nominally metastable κ- to thermodynamically stable β-phase. This was analyzed by structural characterizations such as high-resolution scanning transmission electron microscopy and x-ray diffraction. The highly resistive as-grown Ga2O3 epitaxial layer becomes conductive after annealing at 1000 °C. Furthermore, we demonstrate that in situ annealing can lead to a crack-free β-Ga2O3. [reprint (PDF)]
22.	Advances in mid-infrared detection and imaging: a key issues review Manijeh Razeghi and Binh-Minh Nguyen Rep. Prog. Phys. 77 (2014) 082401-- August 4, 2014 ...[Visit Journal] It has been over 200 years since people recognized the presence of infrared radiation, and developed methods to capture this signal. However, current material systems and technologies for infrared detections have not met the increasing demand for high performance infrared detectors/cameras, with each system having intrinsic drawbacks. Type-II InAs/GaSb superlattice has been recently considered as a promising candidate for the next generation of infrared detection and imaging. Type-II superlattice is a man-made crystal structure, consisting of multiple quantum wells placed next to each other in a controlled way such that adjacent quantum wells can interact. The interaction between multiple quantum wells offers an additional degree of freedom in tailoring the material's properties. Another advantage of type-II superlattice is the experimental benefit of inheriting previous research on material synthesis and device fabrication of bulk semiconductors. It is the combination of these two unique strengths of type-II superlattice—novel physics and easy manipulation—that has enabled unprecedented progress in recent years. In this review, we will describe historical development, and current status of type-II InAs/GaSb superlattice for advanced detection and imaging in the mid-infrared regime (λ = 3–5 µm). [reprint (PDF)]
22.	Demonstration of 256x256 Focal Plane Arrays Based on Al-free GaInAs/InP QWIP J. Jiang, K. Mi, R. McClintock, M. Razeghi, G.J. Brown, and C. Jelen IEEE Photonics Technology Letters 15 (9)-- September 1, 2003 ...[Visit Journal] We report the first demonstration of an infrared focal plane array based on aluminum-free GaInAs-InP quantum-well infrared photodetectors (QWIPs).A unique positive lithography method was developed to perform indium-bump liftoff. The noise equivalent differential temperature (NEΔT) of 29 mK was achieved at 70 K with f/2 optics. [reprint (PDF)]
22.	Long Wavelength Type-II Photodiodes Operating at Room Temperature H. Mohseni and M. Razeghi IEEE Photonics Technology Letters 13 (5)-- May 1, 2001 ...[Visit Journal] The operation of uncooled InAs-GaSb superlattice photodiodes with a cutoff wavelength of λc=8 μm and a peak detectivity of 1.2 × 10⁸ cm·Hz^½/W at zero bias is demonstrated. The detectivity is similar to the best uncooled HgCdTe detectors and microbolometers. However, the R0A product is more than two orders of magnitude higher than HgCdTe and the device is more than four orders of magnitude faster than microbolometers. These features combined with their low 1/f noise and high uniformity make these type-II photodiodes an excellent choice for uncooled high-speed IR imaging arrays [reprint (PDF)]
21.	320x256 Solar-Blind Focal Plane Arrays based on Al_xGa_1-xN R. McClintock, K. Mayes, A. Yasan, D. Shiell, P. Kung, and M. Razeghi Applied Physics Letters, 86 (1)-- January 3, 2005 ...[Visit Journal] We report AlGaN-based back-illuminated solar-blind ultraviolet focal plane arrays operating at a wavelength of 280 nm. The electrical characteristics of the individual pixels are discussed, and the uniformity of the array is presented. The p–i–n photodiode array was hybridized to a 320×256 read-out integrated circuit entirely within our university research lab, and a working 320×256 camera was demonstrated. Several example solar-blind images from the camera are also provided. [reprint (PDF)]
21.	High performance photodiodes based on InAs/InAsSb type-II superlattices for very long wavelength infrared detection A. M. Hoang, G. Chen, R. Chevallier, A. Haddadi, and M. Razeghi Appl. Phys. Lett. 104, 251105 (2014)-- June 23, 2014 ...[Visit Journal] Very long wavelength infrared photodetectors based on InAs/InAsSb Type-II superlattices are demonstrated on GaSb substrate. A heterostructure photodiode was grown with 50% cut-off wavelength of 14.6 μm. At 77 K, the photodiode exhibited a peak responsivity of 4.8 A/W, corresponding to a quantum efficiency of 46% at −300 mV bias voltage from front side illumination without antireflective coating. With the dark current density of 0.7 A/cm², it provided a specific detectivity of 1.4 × 10¹⁰ Jones. The device performance was investigated as a function of operating temperature, revealing a very stable optical response and a background limited performance below 50 K. [reprint (PDF)]
21.	Shortwave quantum cascade laser frequency comb for multi-heterodyne spectroscopy Q. Y. Lu, S. Manna, D. H. Wu, S. Slivken, and M. Razeghi Applied Physics Letters 112, 141104-- April 3, 2018 ...[Visit Journal] Quantum cascade lasers (QCLs) are versatile light sources with tailorable emitting wavelengths covering the mid-infrared and terahertz spectral ranges. When the dispersion is minimized, frequency combs can be directly emitted from quantum cascade lasers via four-wave mixing. To date, most of the mid-infrared quantum cascade laser combs are operational in a narrow wavelength range wherein the QCL dispersion is minimal. In this work, we address the issue of very high dispersion for shortwave QCLs and demonstrate 1-W dispersion compensated shortwave QCL frequency combs at λ~5.0 μm, spanning a spectral range of 100 cm⁻¹. The multi-heterodyne spectrum exhibits 95 equally spaced frequency comb lines, indicating that the shortwave QCL combs are ideal candidates for high-speed high-resolution spectroscopy [reprint (PDF)]
21.	Pulse Autocorrelation Measurements Based on Two- and Three-Photon Conductivity in a GaN Photodiode A. Streltsov, K.D. Moll, A. Gaeta, P. Kung, D. Walker, and M. Razeghi Applied Physics Letters 75 (24)-- December 13, 1999 ...[Visit Journal] We characterize the performance of a GaN p-i-n photodiode as a nonlinear sensor for second- and third-order femtosecond pulse autocorrelation measurements in the visible and near-infrared regimes, respectively. The two- and three-photon absorption coefficients for GaN are also determined. [reprint (PDF)]
21.	Very Long Wavelength GaAs/GaInP Quantum Well Infrared Photodetectors C. Jelen, S. Slivken, G.J. Brown, and M. Razeghi SPIE Conference, San Jose, CA, -- February 12, 1997 ...[Visit Journal] We demonstrate long wavelength quantum well infrared photodetectors with GaAs quantum wells and GaInP barriers grown using gas-source molecular beam epitaxy. Wafers were grown with varying well widths. The optimum well width was 75 angstrom, which resulted in a detection peak at 13 μm and a cutoff wavelength of 15 μm. Dark current measurements of the samples with 15 μm cutoff wavelength show low dark current densities. The dark current characteristics have been investigated as a function of temperature and electron density in the well and compared to a model which takes into account thermionic emission and thermally assisted tunneling. The model is used to extract a saturation velocity of 1.5 x 10⁵ cm/s for electrons. The photoelectron lifetime before recapture has been deduced from this carrier velocity and photoconductive gain measurements. The lifetime is found to be approximately 5 ps. Preliminary focal plane array imaging is demonstrated. [reprint (PDF)]
21.	Free-space optical communication using mid-infrared or solar-blind ultraviolet sources and detectors R. McClintock, A. Haddadi and M. Razeghi SPIE Proceedings, Vol. 8268, p. 826810-- January 22, 2012 ...[Visit Journal] Free-space optical communication is a promising solution to the “last mile” bottleneck of data networks. Conventional near infrared-based free-space optical communication systems suffer from atmospheric scattering losses and scintillation effects which limit the performance of the data links. Using mid-infrared, we reduce the scattering and thus can improve the quality of the data links and increase their range. Because of the low scattering, the data link cannot be intercepted without a complete or partial loss in power detected by the receiver. This type of communications provides ultra-high bandwidth and highly secure data transfer for both short and medium range data links. Quantum cascade lasers are one of the most promising sources for mid-wavelength infrared sources and Type-II superlattice photodetectors are strong candidates for detection in this regime. The same way that that low scattering makes mid-wavelength infrared ideal for secure free space communications,high scattering can be used for secure short-range free-space optical communications. In the solar-blind ultraviolet (< 280 nm) light is strongly scattered and absorbed. This scattering makes possible non-line-of-sight free-space optical communications. The scattering and absorption also prevent remote eavesdropping. III-Nitride based LEDs and photodetectors are ideal for non-line-of-sight free-space optical communication. [reprint (PDF)]
21.	Performance enhancement of GaN ultraviolet avalanche photodiodes with p-type delta-doping C. Bayram, J.L. Pau, R. McClintock and M. Razeghi Applied Physics Letters, Vol. 92, No. 24, p. 241103-1-- June 16, 2008 ...[Visit Journal] High quality delta-doped p-GaN is used as a means of improving the performance of back-illuminated GaN avalanche photodiodes (APDs). Devices with delta-doped p-GaN show consistently lower leakage current and lower breakdown voltage than those with bulk p-GaN. APDs with delta-doped p-GaN also achieve a maximum multiplication gain of 5.1×10⁴, more than 50 times higher than that obtained in devices with bulk p-GaN. The better device performance of APDs with delta-doped p-GaN is attributed to the higher structural quality of the p-GaN layer achieved via delta-doping. [reprint (PDF)]
21.	Room Temperature Terahertz and Frequency Combs Based on Intersubband Quantum Cascade Laser Diodes: History and Future Manijeh Razeghi , and Quanyong Lu Photonics 2025, 12(1), 79; ...[Visit Journal] : The year 2024 marks the 30-year anniversary of the quantum cascade laser (QCL), which is becoming the leading laser source in the mid-infrared (mid-IR) range. Since the first demonstration, QCL has undergone tremendous development in terms of the output power, wall plug efficiency, spectral coverage, wavelength tunability, and beam quality. Owing to its unique intersubband transition and fast gain features, QCL possesses strong nonlinearities that makes it an ideal platform for nonlinear photonics like terahertz (THz) difference frequency generation and direct frequency comb generation via fourwave mixing when group velocity dispersion is engineered. The feature of broadband, high-power, and low-phase noise of QCL combs is revolutionizing mid-IR spectroscopy and sensing by offering a new tool measuring multi-channel molecules simultaneously in the µs time scale. While THz QCL difference frequency generation is becoming the only semiconductor light source covering 1–5 THz at room temperature. In this paper, we will introduce the latest research from the Center for Quantum Devices at Northwestern University and briefly discuss the history of QCL, recent progress, and future perspective of QCL research, especially for QCL frequency combs, room temperature THz QCL difference frequency generation, and major challenges facing QCL in the future. [reprint (PDF)]
21.	Planar nBn type-II superlattice mid-wavelength infrared photodetectors using zinc ion-implantation Arash Dehzangi, Donghai Wu, Ryan McClintock, Jiakai Li, and Manijeh Razeghi Appl. Phys. Lett. 116, 221103 https://doi.org/10.1063/5.0010273-- June 2, 2020 ...[Visit Journal] In this Letter, we report the demonstration of zinc ion-implantation to realize planar mid-wavelength infrared photodetectors based on type-II InAs/InAs1−xSbx superlattices. At 77 K, the photodetectors exhibit a peak responsivity of 0.68 A/W at 3.35 μm, corresponding to a quantum efficiency of 23.5% under Vb = −80 mV, without anti-reflection coating; these photodetectors have a 100% cutoff wavelength of 4.28 μm. With an R0 × A value of 1.53 × 104 Ω cm2 and a dark current density of 1.23 × 10−6 A/cm2 under an applied bias of −80 mV at 77 K, the photodetectors exhibit a specific detectivity of 9.12 × 1011 cm·Hz1/2/W. [reprint (PDF)]
21.	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)]
21.	Type-II InAs/GaSb Superlattices and Detectors with Cutoff Wavelength Greater Than 18 μm M. Razeghi, Y. Wei, A. Gin, G.J. Brown and D. Johnstone Proceedings of the SPIE, San Jose, CA, Vol. 4650, 111 (2002)-- January 25, 2002 ...[Visit Journal] The authors report the most recent advances in Type-II InAs/GaSb superlattice materials and photovoltaic detectors. Lattice mismatch between the substrate and the superlattice has been routinely achieved below 0.1%, and less than 0.0043% as the record. The FWHM of the zeroth order peak from x-ray diffraction has been decreased below 50 arcsec and a record of less than 44arcsec has been achieved. High performance detectors with 50% cutoff beyond 18 micrometers up to 26 micrometers have been successfully demonstrated. The detectors with a 50% cut-off wavelength of 18.8 micrometers showed a peak current responsivity of 4 A/W at 80K, and a peak detectivity of 4.5¹⁰ cm·Hz^½·W^-1 was achieved at 80K at a reverse bias of 110 mV under 300 K 2(pi) FOV background. Some detectors showed a projected 0% cutoff wavelength up to 28~30 micrometers . The peak responsivity of 3Amp/Watt and detectivity of 4.25¹⁰ cm·Hz^½·W^-1 was achieved under -40mV reverse bias at 34K for these detectors. [reprint (PDF)]
21.	Demonstration of Zn-Diffused Planar Long-Wavelength Infrared Photodetector Based on Type-II Superlattice Grown by MBE Rajendra K. Saroj, Van Hoang Nguyen, Steven Slivken, Gail J. Brown and Manijeh Razeghi IEEE Journal of Quantum Electronics ...[Visit Journal] We report on a planar long-wavelength infrared photodetector based on InAs/InAs1−xSbx type-II superlattice with zinc diffusion. The superlattice structures were grown by molecular beam epitaxy, followed by a post-growth Zinc diffusion process in a metal-organic chemical vapor deposition reactor. The planar photodetectors showed a peak responsivity of 2.18 A/W, under an applied bias of −20 mV, with a corresponding quantum efficiency of 44.5%, without any anti-reflection coating, and had a 100% cut-off wavelength of 8.5 μm at 77 K temperature. These photodetectors exhibit a specific peak detectivity of 3.0×10^12 cm.Hz^1/2/W, with a dark current density of 1.5 × 10−5 A/cm2 and the differential-resistance-area product of ∼8.6 × 10−1 Ω.cm2, under an applied bias of −20 mV at 77 K. A comparative study between the planar and conventional mesa isolated photodetectors was also carried out. [reprint (PDF)]
21.	Investigation of impurities in type-II InAs/GaSb superlattices via capacitance-voltage measurement G. Chen, A. M. Hoang, S. Bogdanov, A. Haddadi, P. R. Bijjam, B.-M. Nguyen, and M. Razeghi Applied Physics Letters 103, 033512 (2013)-- July 17, 2013 ...[Visit Journal] Capacitance-voltage measurement was utilized to characterize impurities in the non-intentionally doped region of Type-II InAs/GaSb superlattice p-i-n photodiodes. Ionized carrier concentration versus temperature dependence revealed the presence of a kind of defects with activation energy below 6 meV and a total concentration of low 10¹⁵ cm⁻³. Correlation between defect characteristics and superlattice designs was studied. The defects exhibited a p-type behavior with decreasing activation energy as the InAs thickness increased from 7 to 11 monolayers, while maintaining the GaSb thickness of 7 monolayers. With 13 monolayers of InAs, the superlattice became n-type and the activation energy deviated from the p-type trend. [reprint (PDF)]
21.	GalnAs AND GaInAsP MATERIALS GROWN BY LOW PRESSURE MOCVD FOR MICROWAVE AND OPTOELECTRONIC APPLICATIONS J.P. Duchemin, J.P. Hirtz, M. Razeghi, M. Bonnet , S.D. Hersee J.P. Duchemin, J.P. Hirtz, M. Razeghi, GaInAs and GaInAsP materials grown by low pressure MOCVD for microwave and optoelectronic applications, Journal of Crystal Growth, 55, 1, 1981, Pages 64-73,-- August 1, 1981 ...[Visit Journal] The low pressure MOCVD technique has been successfully used to grow GaInAsP, lattice-matched to InP, for the complete compositional range between InP (λ=0.91 μm) and the ternary compound Ga0.47In0.53As (λ=1.67 μm). By contrast to LPE growth it has been found that during the MOCVD growth of double heterostructures InP can be grown directly onto the ternary or quaternary with no disturbance of the active layer, i.e. there is no effect equivalent to “melt back”. The compositional grading on both sides of the active layer was measured by scanning Auger spectroscopy on bevelled samples. It was found that the graded regions were typically less than 100 Å wide for GaInAsP active layers and less than 50 Å wide for GaInAs active layers. Single layers of undoped GaInAs exhibited a typical mobility of 6700 cm2 V-1s-1 at 1.5×1017 cm-3. The compositional uniformity of the ternary layers was characterised by measurement of the photoluminescence wavelength at various points on a large sample. The wavelength varied by <3 nm over 95% of the area, which was approximately 8 cm2. Our early MOCVD grown GaInAsP/InP DH lasers exhibited high thresholds due to a poor interface between the p-InP and the active layer. However, recently fabricated broad area lasers emitting at 1.27 μm show an average threshold current density of 1.5 kA cm-2 with a T0 of between 70 to 80 K. Stripe geometry lasers have being fabricated from this material and CW operation has been obtained. [reprint (PDF)]
21.	Short Wavelength (λ~ 4.3 μm) High-Performance Continuous-Wave Quantum-Cascade Lasers J.S. Yu, A. Evans, S. Slivken, S.R. Darvish, and M. Razeghi IEEE Photonics Technology Letters, 17 (6)-- June 1, 2005 ...[Visit Journal] We report continuous-wave (CW) operation of a 4.3-μm quantum-cascade laser from 80 K to 313 K. For a high-reflectivity-coated 11-μm-wide and 4-mm-long laser, CW output powers of 1.34 W at 80 K and 26 mW at 313 K are achieved. At 298 K, the CW threshold current density of 1.5 kA/cm² is observed with a CW output power of 166 mW and maximum wall-plug efficiency of 1.47%. The CW emission wavelength varies from 4.15 μm at 80 K to 4.34 μm at 298 K, corresponding to a temperature-tuning rate of 0.87 nm/K. The beam full-width at half-maximum values for the parallel and the perpendicular far-field patterns are 26° and 49° in CW mode, respectively. [reprint (PDF)]
21.	Very High Average Power Quantum Cascade Lasers by GasMBE S. Slivken and M. Razeghi SPIE Conference, San Jose, CA, Vol. 4999, pp. 59-- January 27, 2003 ...[Visit Journal] Very high average power QCLs are demonstrated within the 5.8 - 9 µm wavelength range. At longer wavelengths, scaling of the power is demonstrated by increasing the number of emitting regions in the waveguide core. At λ = 9 µm, over 3.5 W of peak power per facet has been demonstrated at room temperature for a single 25 µm by 3 mm diode, with an average power of 150 mW at 6% duty cycle. At shorter wavelengths, highly strain-balanced heterostructures are used to create a high coduction band offset and minimize leakage current. At λ = 6 µm, utilizing a high reflective coating and epilayer-down mounting of the laser, we demonstrate 225 mW of average power from a single facet at room temperature. Increasing the conduction band offset further and optimizing the doping in the injector region has led to demonstration of > 250 mW average power (λ = 5.8 µm) at > 50% duty cycle for a 20 µm by 2 mm HR coated diode bonded epilayer-down to a copper heatsink. Also at room temperature, use of Au electroplating and wider ridges has allowed us to further demonstrate without epilayer-down bonding, 0.67 W average power at 17% duty cycle from a single 40 µm by 2 mm HR coated laser. [reprint (PDF)]
21.	-- November 30, 1999
21.	Polarity inversion of Type-II InAs/GaSb superlattice photodiodes B.M. Nguyen, D. Hoffman, P.Y. Delaunay, M. Razeghi and V. Nathan Applied Physics Letters, Vol. 91, No. 10, p. 103503-1-- September 3, 2007 ...[Visit Journal] The authors demonstrated the realization of p-on-n Type-II InAs/GaSb superlattice photodiodes. Growth condition for high quality InAsSb layer lattice matched to GaSb was established for the use of an effective n-contact layer. By studying the effect of various GaSb capping layer thicknesses on the optical and electrical performances, an optimized thickness of 160 nm was determined. In comparison to as grown n-on-p superlattice photodiodes, this inverted design of p on n has shown similar quality. Finally, by analyzing Fabry-Perot interference fringes in the front side illuminated spectral measurement, the refractive index of the superlattice was determined to be approximately 3.8. [reprint (PDF)]
21.	Growth and characterization of InAs/GaSb Type-II superlattices for long-wavelength infrared detectors H. Mohseni, E. Michel, M. Razeghi, W. Mitchel, and G. Brown SPIE Conference, San Jose, CA, -- January 28, 1998 ...[Visit Journal] We report the molecular beam epitaxial growth and characterization of InAs/GaSb superlattices grown on semi- insulating GaAs substrate for long wavelength IR detectors. Photoconductive detectors fabricated from the superlattices showed 80% cut-off at 11.6 μm and peak responsivity of 6.5 V/W with Johnson noise limited detectivity of 2.36 x 10⁹ cm·Hz^½/W at 10.7 μm at 78 K. The responsivity decreases at higher temperatures with a T^-2 behavior rather than exponential decay, and at room temperature the responsivity is about 660 mV/W at 11 μm. Lower Auger recombination rate in this system provides comparable detectivity to the best HgCdTe detectors at 300K. Higher uniformity over large areas, simpler growth and the possibility of having read-out circuits in the same GaAs chip are the advantages of this system over HgCdTe detectors for near room temperature operation. [reprint (PDF)]
20.	Optoelectronic Devices Based on III-V Compound Semiconductors Which Have Made a Major Scientific and Technological Impact in the Past 20 Years M. Razeghi IEEE Journal of Selected Topics in Quantum Electronics 6 (6), pp.1344 - 1354 -- November 1, 2000 ...[Visit Journal] This paper reviews some of our pioneering contributions to the field of III–V compound semiconductor materials and low-dimensional optoelectronic devices. These contributions span from the ultraviolet (200 nm) up to the far-infrared (25 μm) portion of the electromagnetic spectrum and have had a major scientific and technological impact on the semiconductor world in the past 20 years. [reprint (PDF)]
20.	Comparison of Trimethylgallium and Triethylgallium for the Growth of GaN A. Saxler, D. Walker, P. Kung, X. Zhang, M. Razeghi, J. Solomon, W. Mitchel, and H.R. Vydyanath Applied Physics Letters 71 (22)-- December 1, 1997 ...[Visit Journal] GaN films grown by low-pressure metalorganic chemical vapor deposition using trimethylgallium and triethylgallium as gallium precursors are compared. The films were characterized by x-ray diffraction, Hall effect, photoluminescence, secondary ion mass spectroscopy, and etch pit density measurements. GaN layers grown using triethylgallium exhibited superior electrical and optical properties and a lower carbon impurity concentration. [reprint (PDF)]

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