Center for Quantum Devices - Most Downloaded Journal Articles

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2.	Surface leakage reduction in narrow band gap type-II antimonide-based superlattice photodiodes E.K. Huang, D. Hoffman, B.M. Nguyen, P.Y. Delaunay and M. Razeghi Applied Physics Letters, Vol. 94, No. 5, p. 053506-1-- February 2, 2009 ...[Visit Journal] Inductively coupled plasma (ICP) dry etching rendered structural and electrical enhancements on type-II antimonide-based superlattices compared to those delineated by electron cyclotron resonance (ECR) with a regenerative chemical wet etch. The surface resistivity of 4×10⁵ Ω·cm is evidence of the surface quality achieved with ICP etching and polyimide passivation. By only modifying the etching technique in the fabrication steps, the ICP-etched devices with a 9.3 µm cutoff wavelength revealed a diffusion-limited dark current density of 4.1×10⁻⁶ A/cm² and a maximum differential resistance at zero bias in excess of 5300 Ω·cm² at 77 K, which are an order of magnitude better in comparison to the ECR-etched devices. [reprint (PDF)]
2.	A review of the growth, doping, and applications of β-Ga₂O₃ thin films Manijeh Razeghi, Ji-Hyeon Park , Ryan McClintock, Dimitris Pavlidis, Ferechteh H. Teherani, David J. Rogers, Brenden A. Magill, Giti A. Khodaparast, Yaobin Xu, Jinsong Wu, Vinayak P. Dravid Proc. SPIE 10533, Oxide-based Materials and Devices IX, 105330R -- March 14, 2018 ...[Visit Journal] β-Ga₂O₃ is emerging as an interesting wide band gap semiconductor for solar blind photo detectors (SBPD) and high power field effect transistors (FET) because of its outstanding material properties including an extremely wide bandgap (Eg ~4.9eV) and a high breakdown field (8 MV/cm). This review summarizes recent trends and progress in the growth/doping of β-Ga₂O₃ thin films and then offers an overview of the state-of-the-art in SBPD and FET devices. The present challenges for β-Ga₂O₃ devices to penetrate the market in real-world applications are also considered, along with paths for future work. [reprint (PDF)]
2.	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)]
2.	QEPAS based ppb-level detection of CO and N₂O using a high power CW DFB-QCL Y. Ma, R. Lewicki, M. Razeghi and F. Tittel Optics Express, Vol. 21, No. 1, p. 1008-- January 14, 2013 ...[Visit Journal] An ultra-sensitive and selective quartz-enhanced photoacoustic spectroscopy (QEPAS) sensor platform was demonstrated for detection of carbon monoxide (CO) and nitrous oxide (N₂O). This sensor used a stateof-the art 4.61 μm high power, continuous wave (CW), distributed feedback quantum cascade laser (DFB-QCL) operating at 10°C as the excitation source. For the R(6) CO absorption line, located at 2169.2 cm⁻¹, a minimum detection limit (MDL) of 1.5 parts per billion by volume (ppbv) at atmospheric pressure was achieved with a 1 sec acquisition time and the addition of 2.6% water vapor concentration in the analyzed gas mixture. For the N₂O detection, a MDL of 23 ppbv was obtained at an optimum gas pressure of 100 Torr and with the same water vapor content of 2.6%. In both cases the presence of water vapor increases the detected CO and N₂O QEPAS signal levels as a result of enhancing the vibrational-translational relaxation rate of both target gases. Allan deviation analyses were performed to investigate the long term performance of the CO and N2O QEPAS sensor systems. For the optimum data acquisition time of 500 sec a MDL of 340 pptv and 4 ppbv was obtained for CO and N₂O detection,respectively. To demonstrate reliable and robust operation of the QEPAS sensor a continuous monitoring of atmospheric CO and N₂O concentration levels for a period of 5 hours were performed. [reprint (PDF)]
2.	Extended short-wavelength infrared nBn photodetectors based on type-II InAs/AlSb/GaSb superlattices with an AlAsSb/GaSb superlattice barrier A. Haddadi, R. Chevallier, A. Dehzangi, and M. Razeghi Applied Physics Letters 110, 101104-- March 8, 2017 ...[Visit Journal] Extended short-wavelength infrared nBn photodetectors based on type-II InAs/AlSb/GaSb superlattices on GaSb substrate have been demonstrated. An AlAsSb/GaSb H-structure superlattice design was used as the large-bandgap electron-barrier in these photodetectors. The photodetector is designed to have a 100% cut-off wavelength of ∼2.8 μm at 300 K. The photodetector exhibited a room-temperature (300 K) peak responsivity of 0.65 A/W at 1.9 μm, corresponding to a quantum efficiency of 41% at zero bias under front-side illumination, without any anti-reflection coating. With an R × A of 78 Ω·cm² and a dark current density of 8 × 10⁻³ A/cm² under −400 mV applied bias at 300 K, the nBn photodetector exhibited a specific detectivity of 1.51 × 10¹⁰ Jones. At 150 K, the photodetector exhibited a dark current density of 9.5 × 10⁻⁹ A/cm² and a quantum efficiency of 50%, resulting in a detectivity of 1.12 × 10¹³ Jones. [reprint (PDF)]
2.	High Detectivity GaInAs/InP Quantum Well Infrared Photodetectors Grown on Si Substrates J. Jiang, C. Jelen, M. Razeghi and G.J. Brown IEEE Photonics Technology Letters 14 (3)-- March 1, 2002 ...[Visit Journal] In this letter, we report an improvement in the growth and the device performance of GaInAs-InP quantum well infrared photodetectors grown on Si substrates. Material growth techniques, like low-temperature nucleation layers and thick buffer layers were used to grow InP on Si. An in situ thermal cycle annealing technique was used to reduce the threading dislocation density in the InP-on-Si. Detector dark current was reduced 2 orders of magnitude by this method. Record high detectivity of 2.3 × 10⁹ cm·Hz^½·W^-1 was obtained for QWIP-on-Si detectors in the 7-9 μm range at 77 K [reprint (PDF)]
2.	Surface leakage investigation via gated type-II InAs/GaSb long-wavelength infrared photodetectors G. Chen, E.K. Huang, A.M. Hoang, S. Bogdanov, S.R. Darvish, and M. Razeghi Applied Physics Letters, Vol. 101, No. 21, p. 213501-1-- November 19, 2012 ...[Visit Journal] By using gating technique, surface leakage generated by SiO₂ passivation in long-wavelength infrared type-II superlattice photodetector is suppressed, and different surface leakage mechanisms are disclosed. By reducing the SiO₂ passivation layer thickness, the saturated gated bias is reduced to −4.5 V. At 77 K, dark current densities of gated devices are reduced by more than 2 orders of magnitude, with 3071 Ω·cm² differential-resistance-area product at −100 mV. With quantum efficiency of 50%, the 11 μm 50% cut-off gated photodiode has a specific detectivity of 7 × 10¹¹ Jones, and the detectivity stays above 2 × 10¹¹ Jones from 0 to −500 mV operation bias. [reprint (PDF)]
2.	High Temperature Continuous Wave Operation of ~8 μm Quantum Cascade Lasers S. Slivken, A. Matlis, C. Jelen, A. Rybaltowski, J. Diaz, and M. Razeghi Applied Physics Letters 74 (2)-- January 11, 1999 ...[Visit Journal] We report single-mode continuous-wave operation of a λ∼8 μm quantum cascade laser at 140 K. The threshold current density is 4.2 kA/cm² at 300 K in pulsed mode and 2.5 kA/cm² at 140 K in continuous wave for 2 mm long index-guided laser cavities of 20 μm width. Wide stripe (W ∼ 100 μm), index-guided lasers from the same wafer in pulsed operation demonstrate an average T₀ of 210 K with other wafers demonstrating a T₀ as high as 290 K for temperatures from 80 to 300 K. This improvement in high-temperature performance is a direct result of three factors: excellent material quality, a low-loss waveguide design, and a low-leakage index-guided laser geometry. [reprint (PDF)]
2.	High-temperature high-power continuous-wave operation of buried heterostructure quantum-cascade lasers A. Evans, J.S. Yu, J. David, L. Doris, K. Mi, S. Slivken, and M. Razeghi Applied Physics Letters, 84 (3)-- January 19, 2004 ...[Visit Journal] We report cw operation of buried heterostructure quantum-cascade lasers (λ=6 µm) using a thick electroplated Au top contact layer and epilayer-up bonding on a copper heat sink up to a temperature of 333 K (60 °C). The high cw optical output powers of 446 mW at 293 K, 372 mW at 298 K, and 30 mW at 333 K are achieved with threshold current densities of 2.19, 2.35, and 4.29 kA/cm² respectively, for a high-reflectivity-coated, 9-µm-wide and 3-mm-long laser [reprint (PDF)]
2.	Anomalous Hall Effect in InSb Layers Grown by MOCVD on GaAs Substrates C. Besikci, Y.H. Choi, R. Sudharsanan, and M. Razeghi Journal of Applied Physics 73 (10)-- May 15, 1993 ...[Visit Journal] InSb epitaxial layers have been grown on GaAs substrates by low‐pressure metalorganic chemical vapor deposition. A 3.15 μm thick film yielded an x‐ray full width at half maximum of 171 arcsec. A Hall mobility of 76 200 cm²/V· s at 240 K and a full width at half maximum of 174 arcsec have been measured for a 4.85 μm thick epilayer. Measured Hall data have shown anomalous behavior. A decrease in Hall mobility with decreasing temperature has been observed and room‐temperature Hall mobility has increased with thickness. In order to explain the anomalous Hall data, and the thickness dependence of the measured parameters, the Hall coefficient and Hall mobility have been simulated using a three‐layer model including a surface layer, a bulklike layer, and an interface layer with a high density of defects. Theoretical analysis has shown that anomalous behavior can be attributed to donor-like defects caused by the large lattice mismatch and to a surface layer which dominates the transport in the material at low temperatures. [reprint (PDF)]
2.	Buried heterostructure quantum cascade lasers with high continuous-wave wall plug efficiency A. Evans, S.R. Darvish, S. Slivken, J. Nguyen, Y. Bai and M. Razeghi Applied Physics Letters, Vol. 91, No. 7, p. 071101-1-- August 13, 2007 ...[Visit Journal] The authors report on the development of ~4.7 µm strain-balanced InP-based quantum cascade lasers with high wall plug efficiency and room temperature continuous-wave operation. The use of narrow-ridge buried heterostructure waveguides and thermally optimized packaging is presented. Over 9.3% wall plug efficiency is reported at room temperature from a single device producing over 0.675 W of continuous-wave output power. Wall plug efficiencies greater than 18% are also reported for devices at a temperature of 150 K, with continuous-wave output powers of more than 1 W. [reprint (PDF)]
2.	A lifetime of contributions to the world of semiconductors using the Czochralski invention M. Razeghi Vacuum Vol. 9934, 993406-1-- February 8, 2017 ...[Visit Journal] Over the course of my career, I have made numerous contributions related to semiconductor crystal growth and high performance optoelectronics over a vast region of the electromagnetic spectrum (ultraviolet to terahertz). In 2016 this cumulated in my receiving the Jan Czochralski Gold Medal award from the European Materials Research Society. This article is designed to provide a historical perspective and general overview of these scientific achievements, on the occasion of being honored by this award. These achievements would not have been possible without high quality crystalline substrates, and this article is written in honor of Jan Czochralski on the 100th anniversary of his important discovery. [reprint (PDF)]
2.	First room‐temperature cw operation of a GaInAsP/InP light‐emitting diode on a silicon substrate M. Razeghi; R. Blondeau; M. Defour; F. Omnes; P. Maurel; F. Brillouet Appl. Phys. Lett. 53, 854–855 (1988)-- July 4, 1988 ...[Visit Journal] We report in this letter the first successful fabrication of an InP-GalnAsP light-emitting diode, emitting at 1.15 pm grown by low-pressure metalorganic chemical vapor deposition on a silicon substrate. The device has been operated under continuous wave operation at room temperature for 24 h (with an injection current of 200 rnA), and showed no degradation. [reprint (PDF)]
2.	Bias-selectable three-color short-, extended-short-, and mid-wavelength infrared photodetectors based on type-II InAs/GaSb/AlSb superlattices Abbas Haddadi, and Manijeh Razeghi Optics Letters Vol. 42, Iss. 21, pp. 4275-4278-- October 16, 2017 ...[Visit Journal] A bias-selectable, high operating temperature, three-color short-, extended-short-, and mid-wavelength infrared photodetector based on InAs/GaSb/AlSb type-II superlattices on GaSb substrate has been demonstrated. The short-, extended-short-, and mid-wavelength channels’ 50% cutoff wavelengths were 2.3, 2.9, and 4.4μm, respectively, at 150K. The mid-wavelength channel exhibited a saturated quantum efficiency of 34% at 4μm under +200 mV bias voltage in a front-side illumination configuration and without any antireflection coating. At 200mV, the device exhibited a dark current density of 8.7×10⁻⁵ A/cm² providing a specific detectivity of ∼2×10¹¹ cm·Hz^1/2/W at 150K. The short-wavelength channel achieved a saturated quantum efficiency of 20% at 1.8μm. At −10 mV, the device’s dark current density was 5.5×10⁻⁸ A/cm². At zero bias, its specific detectivity was 1×10¹¹ cm·Hz^1/2/W at 150K. The extended short-wavelength channel achieved a saturated quantum efficiency of 22% at 2.75 μm. Under −2 V bias voltage, the device exhibited a dark current density of 1.8×10⁻⁶ A/cm² providing a specific detectivity of 6.3×10¹¹ cm·Hz^1/2/W at 150K. [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.	Solar-blind avalanche photodiodes R. McClintock, K. Minder, A. Yasan, C. Bayram, F. Fuchs, P. Kung and M. Razeghi SPIE Conference, San Jose, CA, Vol. 6127, pp. 61271D-- January 23, 2006 ...[Visit Journal] There is a need for semiconductor based UV photodetectors to support avalanche gain in order to realize better performance and more effectively compete with existing photomultiplier tubes. However, there are numerous technical issues associated with the realization of high-quality solar-blind avalanche photodiodes (APDs). In this paper, APDs operating at 280 nm, within the solar-blind region of the ultraviolet spectrum, are investigated. [reprint (PDF)]
2.	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)]
2.	High-Performance InP-Based Mid-IR Quantum Cascade Lasers M. Razeghi IEEE Journal of Selected Topics in Quantum Electronics, Vol. 15, No. 3, May-June 2009, p. 941-951.-- June 5, 2009 ...[Visit Journal] Quantum cascade lasers (QCLs) were once considered as inefficient devices, as the wall-plug efficiency (WPE) was merely a few percent at room temperature. But this situation has changed in the past few years, as dramatic enhancements to the output power andWPE have been made for InP-based mid-IR QCLs. Room temperature continuous-wave (CW) output power as high as 2.8 W and WPE as high as 15% have now been demonstrated for individual devices. Along with the fundamental exploration of refining the design and improving the material quality, a consistent determination of important device performance parameters allows for strategically addressing each component that can be improved potentially. In this paper, we present quantitative experimental evidence backing up the strategies we have adopted to improve the WPE for QCLs with room temperature CW operation. [reprint (PDF)]
2.	Well Resolved Room Temperature Photovoltage Spectra of GaAs-GaInP Quantum Wells and Superlattices Xiaoguang He and Manijeh Razeghi Applied Physics Letters 62 (6)-- February 8, 1993 ...[Visit Journal] We report the first well resolved room‐temperature photovoltage spectra due to the sublevel transitions in the GaInP‐GaAs superlattices and multiquantum wells grown by low pressure metalorganic chemical vapor deposition. Sharp well resolved peaks attributed to exciton absorption of the electron‐to‐light hole and electron‐to‐heavy hole have been observed at room temperature. This indicates that GaAs‐GaInP is a promising material for the application of the modulators, optical switches, and optical bistable divices. Satisfactory agreements between experimental measurements and theoretical results have been obtained. These results demonstrate that photovoltage spectroscopy is a simple, but very powerful tool to study quantum confinement structures. [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.	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)]
2.	*A Crystallographic Model of (001) Aluminum Nitride Epitaxial Thin Film Growth on (001) Sapphire Substrate* C.J. Sun, P. Kung, A. Saxler, H. Ohsato, M. Razeghi, and K. Haritos Journal of Applied Physics 75 (8)-- April 15, 1994 ...[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 (011-bar 2) sapphire substrates by metalorganic chemical vapor deposition. Better crystallinity with fine ridgelike facets is obtained on the (011-bar 2) sapphire. Also lower carrier concentration and higher mobilities indicate both lower nitrogen vacancies and less oxygen incorporation on the (011-bar 2) sapphire. The results of this study show better physical properties of GaN thin films achieved on (011-bar 2) sapphire. [reprint (PDF)]
2.	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)]
2.	Quantum Dot Infrared Photodetectors: Comparison Experiment and Theory H. Lim, W. Zhang, S. Tsao, T. Sills, J. Szafraniec, K. Mi, B. Movaghar, and M. Razeghi Physical Review B, 72-- August 17, 2005 ...[Visit Journal] We present data and calculations and examine the factors that determine the detectivities in self-assembled InAs and InGaAs based quantum dot infrared photodetectors (QDIPs). We investigate a class of devices that combine good wavelength selectivity with “high detectivity.” We study the factors that limit the temperature performance of quantum dot detectors. For this we develop a formalism to evaluate the optical absorption and the electron transport properties. We examine the performance limiting factors and compare theory with experimental data. We find that the notion of a phonon bottleneck does not apply to large-diameter lenslike quantum dots, which have many closely spaced energy levels. The observed strong decrease of responsivity with temperature is ultimately due to a rapid thermal cascade back into the ground states. High temperature performance is improved by engineering the excited state to be near the continuum. The good low temperature (77 K) performance in strongly bound QDIPs is shown to be due to the high gain and the low noise achievable in these micron size devices. [reprint (PDF)]
2.	SOLID-STATE DEEP UV EMITTERS/DETECTORS: Zinc oxide moves further into the ultraviolet David J. Rogers; Philippe Bove; Eric V. Sandana; Ferechteh Hosseini Teherani; Ryan McClintock; Manijeh Razeghi Laser Focus World. 2013;49(10):33-36.-- October 10, 2013 ...[Visit Journal] Latest advancements in the alloying of zinc oxide (ZnO) with magnesium (Mg) can offer an alternative to (Al) GaN-based emitters/detectors in the deep UV with reduced lattice and efficiency issues. The emerging potential of ZnO for UV emitter and detector applications is the result of a long, concerted, and fruitful R&D effort that has led to more than 7000 publications in 2012. ZnO is considered to be a potentially superior material for use in LEDs and laser diodes due to its larger exciton binding energy, as compared with 21 meV for GaN. Wet etching is also possible for ZnO with nearly all dilute acids and alkalis, while GaN requires hydrofluoric (HF) acid or plasma etching. High-quality ZnO films can be grown more readily on mismatched substrates and bulk ZnO substrates have better availability than their GaN equivalents.

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