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| 12. | Background limited performance of long wavelength infrared focal plane arrays fabricated from M-structure InAs-GaSb superlattices P.Y. Delaunay, B.M. Nguyen, D. Hoffman, E.K. Huang, and M. Razeghi IEEE Journal of Quantum Electronics, Vol. 45, No. 2, p. 157-162.-- February 1, 2009 ...[Visit Journal] The recent introduction of a M-structure design improved both the dark current and R0A performances of Type-II InAs-GaSb photodiodes. A focal plane array fabricated with this design was characterized at 81 K. The dark current of individual pixels was measured between 1.1 and 1.6 nA, 7 times lower than previous superlattice FPAs. This led to a higher dynamic range and longer integration times. The quantum efficiency of detectors without antireflective coating was 74%. The noise equivalent temperature difference reached 23 mK, limited only by the performance of the testing system and the read out integrated circuit. Background limited performances were demonstrated at 81 K for a 300 K background. [reprint (PDF)] |
| 12. | InAsSb/InAsP strained-layer superlattice injection lasers operating at 4.0 μm grown by metal-organic chemical vapor deposition B. Lane, Z. Wu, A. Stein, J. Diaz, and M. Razeghi Applied Physics Letters 74 (23)-- June 7, 1999 ...[Visit Journal] We report high power mid-infrared electrical injection operation of laser diodes based on InAsSb/InAsP strained-layer superlattices grown on InAs substrate by metal-organic chemical vapor deposition. The broad-area laser diodes with 100 μm aperture and 1800 μm cavity length demonstrate peak output powers of 546 and 94 mW in pulsed and cw operation respectively at 100 K with a threshold current density as low as 100 A/cm². [reprint (PDF)] |
| 12. | Spatial Noise and Correctability of Type-II InAs/GaSb Focal Plane Arrays P.Y. Delaunay and M. Razeghi IEEE Journal of Quanutm Electronics, April 2010, Vol. 46, No. 4, p. 584-588-- April 1, 2010 ...[Visit Journal] A long wavelength infrared focal plane array based on Type-II InAs/GaSb superlattices was fabricated and characterized at 80 K. The noise equivalent temperature difference of the array was measured as low as 23 mK (f# = 2), for an integration time of 0.129 ms. The spatial noise of the array was dominated by the nonuniformity of the illumination through the circular aperture. A standard two-point nonuniformity correction improved the inhomogeneity equivalent temperature difference to 16 mK. The correctability just after calibration was 0.6. The long-term stability time was superior to 25 hours. [reprint (PDF)] |
| 12. | On the interface properties of ZnO/Si electroluminescent diodes J.L. Pau, J. Piqueras, D.J. Rogers, F. Hosseini Teherani, K. Minder, R. McClintock, and M. Razeghi Journal of Applied Physics, Vol. 107, No. 3, p. 033719-1-- February 1, 2010 ...[Visit Journal] ZnO layers grown on n−–Si(100), n+–Si(100), and n––Si(111) substrates by pulsed-laser deposition were found to give electroluminescence. Light emission was observed in the form of discrete spots for currents over 1 mA with a white appearance to the naked eye. The intensity of these spots showed an erratic behavior over time, appearing and disappearing at random, while showing an associated random telegraph noise in the current signal. Regardless the substrate used, the electroluminescence spectra had a main broadband emission centered at about 600 nm and a relatively small peak at around 380 nm which corresponds to the energy of ZnO near band edge emission. Furthermore, the devices exhibited rectifying characteristics, whose current blocking direction depended on the substrate orientation. Optimization of ZnO conductivity and performing sample growth in N2 ambient were found to be critical to enhance the emission intensity. Rutherford backscattering characterization revealed the existence of an intermixed region at the interface between ZnO and Si. To study the electronic properties at the interface, frequency dependent capacitance measurements were carried out. The junction capacitance became frequency dependent at the bias voltages at which light emission occurs due to the relatively slow trapping and generation processes at deep centers. These centers are believed to play an important role in the mechanism of light emission. [reprint (PDF)] |
| 12. | Reliable GaN-based resonant tunneling diodes with reproducible room-temperature negative differential resistance C. Bayram, D.K. Sadana, Z. Vashaei and M. Razeghi SPIE Proceedings, Vol. 8268, p. 826827-- January 22, 2012 ...[Visit Journal] negative differential resistance (NDR). Compared to other negative resistance devices such as (Esaki) tunnel and transferred-electron devices, RTDs operate much faster and at higher temperatures. III-nitride materials, composed of AlGaInN alloys, have wide bandgap, high carrier mobility and thermal stability; making them ideal for high power high frequency RTDs. Moreover, larger conduction band discontinuity promise higher NDR than other materials (such as GaAs) and room-temperature operation. However, earlier efforts on GaN-based RTD structures have failed to achieve a
reliable and reproducible NDR. Recently, we have demonstrated for the first time that minimizing dislocation density and eliminating the piezoelectric fields enable reliable and reproducible NDR in GaN-based RTDs even at room
temperature. Observation of NDR under both forward and reverse bias as well as at room and low temperatures attribute the NDR behaviour to quantum tunneling. This demonstration marks an important milestone in exploring III-nitride quantum devices, and will pave the way towards fundamental quantum transport studies as well as for high frequency
optoelectronic devices such as terahertz emitters based on oscillators and cascading structures. [reprint (PDF)] |
| 12. | Gain-length scaling in quantum dot/quantum well infrared photodetectors T. Yamanaka, B. Movaghar, S. Tsao, S. Kuboya, A. Myzaferi and M. Razeghi Virtual Journal of Nanoscale Science & Technology-- September 14, 2009 ...[Visit Journal][reprint (PDF)] |
| 12. | 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)] |
| 12. | Ultraviolet avalanche photodiodes Ryan McClintock ; Manijeh Razeghi Proc. SPIE 9555, Optical Sensing, Imaging, and Photon Counting: Nanostructured Devices and Applications, 95550B -- August 28, 2015 ...[Visit Journal] The III-Nitride material system is rapidly maturing; having proved itself as a material for LEDs and laser, and now finding use in the area of UV photodetectors. However, many UV applications are still dominated by the use of photomultiplier tubes (PMT). PMTs are capable of obtaining very high sensitivity using internal electron multiplication gain (typically ~106). It is highly desirable to develop a compact semiconductor-based photodetector capable of realizing this level of sensitivity. In principle, this can be obtained in III-Nitrides by taking advantage of avalanche multiplication under high electric fields – typically 2.7 MV/cm, which with proper design can correspond to an external reverse bias of less than 100 volts.
In this talk, we review the current state-of-the-art in III-Nitride solar- and visible-blind APDs, and present our latest results on GaN APDs grown on both conventional sapphire and low dislocation density free-standing c- and m-plane GaN substrates. Leakage current, gain, and single photon detection efficiency (SPDE) of these APDs were compared. The spectral response and Geiger-mode photon counting performance of UV APDs are studied under low photon fluxes, with single photon detection capabilities as much as 30% being demonstrated in smaller devices. Geiger-mode operation conditions are optimized for enhanced SPDE. [reprint (PDF)] |
| 12. | Stranski-Krastanov growth of InGaN quantum dots emitting in green spectra C. Bayram and M. Razeghi Applied Physics A: Materials Science and Processing, Vol. 96, No. 2, p. 403-408-- August 1, 2009 ...[Visit Journal] Self-assembled InGaN quantum dots (QDs) were grown on GaN templates by metalorganic chemical vapor deposition. 2D–3D growth mode transition through Stranski–Krastanov mode was observed via atomic force microscopy. The critical thickness for In0.67Ga0.33N QDs was determined to be four monolayers. The effects of growth temperature, deposition thickness, and V/III ratio on QD formation were examined. The capping of InGaN QDs with GaN was analyzed. Optimized InGaN quantum dots emitted in green spectra at room temperature. [reprint (PDF)] |
| 12. | AlGaN-based deep UV light emitting diodes with peak emission below 255 nm A. Yasan, R. McClintock, K. Mayes, P. Kung, and M. Razeghi SPIE Conference, Jose, CA, Vol. 5732, pp. 197-- January 22, 2005 ...[Visit Journal] We report on the growth and fabrication of AlGaN-based deep ultraviolet light-emitting diodes (LEDs) with peak emission of below 255 nm. In order to achieve such short wavelength UV LEDs, the Al mole fractions in the device layers should be greater than ~60%. This introdues serious challenges on the growth and doping of AlxGa1-xN epilayers. However, with the aid of a high-quality AlN template layer and refinement of the growth conditions we have been able to demonstrate UV LEDs emitting below 255 nm. [reprint (PDF)] |
| 12. | Roadmap of Semiconductor Infrared Lasers and Detectors for the 21st Century M. Razeghi SPIE Conference, San Jose, CA, -- January 27, 1999 ...[Visit Journal] Since the first discovery, semiconductor infrared lasers and detectors have found many various applications in military, communications, medical, and industry sections. In this paper, the current status of semiconductor infrared lasers and detectors will be reviewed. Advantages and disadvantages of different methods and techniques is discussed later. Some basic physical limitations of current technology are studied and the direction to overcome these problems will be suggested. [reprint (PDF)] |
| 12. | Suppression of surface leakage in gate controlled type-II InAs/GaSb mid-infrared photodetectors G. Chen; B.-M. Nguyen; A.M. Hoang; E.K. Huang; S.R. Darvish; M. Razeghi Proc. SPIE 8268, Quantum Sensing and Nanophotonic Devices IX, 826811 (January 20, 2012)-- January 20, 2012 ...[Visit Journal] One of the biggest challenges of improving the electrical performance in Type II InAs/GaSb superlattice photodetector is suppressing the surface leakage. Surface leakage screens important bulk dark current mechanisms, and brings difficulty and uncertainty to the material optimization and bulk intrinsic parameters extraction such as carrier lifetime and mobility. Most of surface treatments were attempted beyond the mid-infrared (MWIR) regime because compared to the bulk performance, surface leakage in MWIR was generally considered to be a minor factor. In this work, we show that below 150K, surface leakage still strongly affects the electrical performance of the very high bulk performance p-π-M-n MWIR photon detectors. With gating technique, we can effectively eliminate the surface leakage in a controllable manner. At 110K, the dark current density of a 4.7 μm cut-off gated photon diode is more than 2 orders of magnitude lower than the current density in SiO2 passivated ungated diode. With a quantum efficiency of 48%, the specific detecivity of gated diodes attains 2.5 x 1014 cm·Hz1/2/W, which is 3.6 times higher than that of ungated diodes. [reprint (PDF)] |
| 12. | Back-illuminated separate absorption and multiplication GaN avalanche photodiodes J.L. Pau, C. Bayram, R. McClintock, M. Razeghi and D. Silversmith Applied Physics Letters, Vol. 92, No. 10, p. 101120-1-- March 10, 2008 ...[Visit Journal] The performance of back-illuminated avalanche photodiodes with separate absorption and multiplication regions is presented. Devices with an active area of 225 µm2 show a maximum multiplication gain of 41,200. The calculation of the noise equivalent power yields a minimum value of 3.3×10−14 W·Hz−1/2 at a gain of 3000, increasing to 2.0×10−13 W·Hz−1/2 at a gain of 41,200. The broadening of the response edge has been analyzed as a function of bias. [reprint (PDF)] |
| 12. | LEO of III-Nitride on Al2O3 and Si Substrates M. Razeghi, P. Kung, P. Sandvik, K. Mi, X. Zhang, V.P. Dravid, J. Freitas, and A. Saxler SPIE Conference, San Jose, CA, -- January 26, 2000 ...[Visit Journal] Lateral epitaxial overgrowth (LEO) has recently become the method of choice to reduce the density of dislocations in heteroepitaxial GaN thin films, and is thus expected to lead to enhanced performance devices. We present here the LEO growth and characterization of GaN films by low pressure metalorganic chemical vapor deposition. Various substrates were used, including basal plane sapphire and oriented Si substrates. The steps in the LEO growth technology will be briefly reviewed. The characterization results will be discussed in detail. The structural, electrical and optical properties of the films were assessed through scanning, atomic and transmission electron microscopy, x-ray diffraction, capacitance-voltage, deep level transient spectroscopy, photoluminescence, and scanning cathodoluminenscence measurements. Single-step and double- step LEO GaN was achieved on sapphire. Similarly high quality LEO grown GaN films were obtained on sapphire and silicon substrates. Clear and dramatic reduction in the density of defects are observed in LEO grown materials using the various characterization techniques mentioned previously. [reprint (PDF)] |
| 12. | III-Nitride Optoelectronic Devices: From Ultraviolet Toward Terahertz M. Razeghi IEEE Photonics Journal-Breakthroughs in Photonics 2010, Vol. 3, No. 2, p. 263-267-- April 26, 2011 ...[Visit Journal] We review III-Nitride optoelectronic device technologies with an emphasis on recent breakthroughs. We start with a brief summary of historical accomplishments and then report the state-of-the-art in three key spectral regimes: (1) Ultraviolet (AlGaN-based avalanche photodiodes, single photon detectors, focal plane arrays, and light emitting diodes), (2) Visible (InGaN-based solid state lighting, lasers, and solar cells), and (3) Near-, mid-infrared, and terahertz (AlGaN/GaN-based gap-engineered intersubband devices). We also describe future trends in III-Nitride optoelectronic devices. [reprint (PDF)] |
| 12. | Growth and Characterization of Type-II Non-Equilibrium Photovoltaic Detectors for Long Wavelength Infrared Range H. Mohseni, J. Wojkowski, A. Tahraoui, M. Razeghi, G. Brown and W. Mitche SPIE Conference, San Jose, CA, -- January 26, 2000 ...[Visit Journal] Growth and characterization of type-II detectors for mid-IR wavelength range is presented. The device has a p-i-n structure is designed to operate in the non-equilibrium mode with low tunneling current. The active layer is a short period InAs/GaSb superlattice. Wider bandgap p-type AlSb and n-type InAs layers are used to facilitate the extraction of both electronics and holes from the active layer for the first time. The performance of these devices were compared to the performance of devices grown at the same condition, but without the AlSb barrier layers. The processed devices with the AlSb barrier show a peak responsivity of about 1.2 A/W with Johnson noise limited detectivity of 1.1 X 1011 cm·Hz½/W at 8 μm at 80 K at zero bias. The details of the modeling, growth, and characterizations will be presented. [reprint (PDF)] |
| 12. | High Thermal Stability of κ-Ga2O3 Grown by MOCVD Junhee Lee, Honghyuk Kim, Lakshay Gautam and Manijeh Razeghi Lee, J.; Kim, H.; Gautam, L.; Razeghi, M. High Thermal Stability of κ-Ga2O3 Grown by MOCVD. Crystals 2021, 11, 446. https://doi.org/ 10.3390/cryst11040446 ...[Visit Journal] We report a high thermal stability of kappa gallium oxide grown on c-plane sapphire substrate by metal organic chemical vapor deposition. Kappa gallium oxide is widely known as a metastable polymorph transitioning its phase when subjected to a high temperature. Here, we show the kappa gallium oxide whose phase is stable in a high temperature annealing process at 1000 °C. These oxide films were grown at 690 °C under nitrogen carrier gas. The materials showed high electrical resistivity when doped with silicon, whereas the film conductivity was significantly improved when doped with both indium and silicon. This work provides a pathway to overcoming limitations for the advance in utilizing kappa gallium oxide possessing superior electrical characteristics. [reprint (PDF)] |
| 12. | High operating temperature midwave infrared photodiodes and focal plane arrays based on type-II InAs/GaSb superlattices S. Abdollahi Pour, E.K. Huang, G. Chen, A. Haddadi, B.M. Nguyen and M. Razeghi Applied Physics Letters, Vol. 98, No. 14, p. 143501-1-- April 4, 2011 ...[Visit Journal] The dominant dark current mechanisms are identified and suppressed to improve the performance of midwave infrared InAs/GaSb Type-II superlattice photodiodes at high temperatures. The optimized heterojunction photodiode exhibits a quantum efficiency of 50% for 2 μm thick active region without any bias dependence. At 150 K, R0A of 5100 Ω·cm² and specific detectivity of 1.05×1012 cm·Hz0.5·W-1 are demonstrated for a 50% cutoff wavelength of 4.2 μm. Assuming 300 K background temperature and 2π field of view, the performance of the detector is background limited up to 180 K, which is improved by 25 °C compared to the homojunction photodiode. Infrared imaging using f/2.3 optics and an integration time of 10.02 ms demonstrates a noise equivalent temperature difference of 11 mK at operating temperatures below 120 K. [reprint (PDF)] |
| 12. | High-performance, continuous-wave operation of λ ~ 4.6 μm quantum-cascade lasers above room temperature J.S. Yu, S. Slivken, A. Evans and M. Razeghi IEEE Journal of Quantum Electronics, Vol. 44, No. 8, p. 747-754-- August 1, 2008 ...[Visit Journal] We report the high-performance continuous-wave (CW) operation of 10-μm-wide quantum-cascade lasers (QCLs) emitting at λ ~ 4.6 μm, based on the GaInAs–AlInAs material without regrowth, in epilayer-up and -down bonding configurations. The operational characteristics of QCLs such as the maximum average power, peak output power, CW output power, and maximum CW operating temperature are investigated, depending on cavity length. Also, important device parameters, i.e., the waveguide loss, the transparency current density, the modal gain, and the internal quantum efficiency, are calculated from length-dependent results. For a high-reflectivity (HR) coated 4-mm-long cavity with epilayer-up bonding, the highest maximum average output power of 633 mW is measured at 65% duty cycle, with 469 mW still observed at 100%. The laser exhibits the maximum wall-plug efficiencies of 8.6% and 3.1% at 298 K, in pulsed and CW operatons, respectively. From 298 to 393 K, the temperature dependent threshold current density in pulsed operation shows a high characteristic temperature of 200 K. The use of an epilayer-down bonding further improves the device performance. A CW output power of 685 mW at 288 K is achieved for the 4-micron-long cavity. At 298 K, the output power of 590 mW, threshold current density of 1.52 kA / cm2, and maximum wall-plug efficiency of 3.73% are obtained under CW mode, operating up to 363 K (90 °C). For HR coated 3-micron-long cavities, laser characteristics across the same processed wafer show a good uniformity across the area of 2 x 1 cm2, giving similar output powers, threshold current densities, and emission wavelengths. The CW beam full-width at half-maximum of far-field patterns are 25 degree and 46 degree for the parallel and the perpendicular directions, respectively. [reprint (PDF)] |
| 12. | Recent advances in III-Nitride materials, characterization and device applications M. Razeghi, X. Zhang, P. Kung, A. Saxler, D. Walker, K.Y. Lim, and K.S. Kim SPIE Conference: Solid State Crystals in Optoelectronics and Semiconductor Technology; Proceedings 3179-- October 7, 1996 ...[Visit Journal] High-quality AlN, GaN, AlGaN have been grown on sapphire substrate by low-pressure metalorganic chemical vapor deposition (LP-MOCVD). The x-ray rocking curve of AlN and GaN were 100 arcsecs and 30 arcsecs respectively with Pendelloesung oscillations, which are the best reported to date. GaN with high crystallinity simultaneously exhibited high optical and electrical quality. Photoluminescence linewidth of GaN at 77K was as low as 17 meV, which is the best reported to date. Si-doped GaN had a mobility higher than 300 cm²/V·s. GaN has been also successfully grown on LiGaO2 substrate with LP-MOCVD for the first time. AlGaN for the entire composition range has been grown. These layers exhibited the lowest x-ray FWHM reported to date. The excellent optical quality of these layers have been characterized by room temperature UV transmission and photoluminescence. N-type doping of AlGaN with Si has ben achieved up to 60 percent Al with mobility as high as 78 cm²/V·s. AlxGa1-xN/AlyGa1-yN superlattice with atomically sharp interface have been demonstrated. Optically-pumped stimulated emission in GaN:Ge and GaN:Si has been observed with threshold optical power density as low as 0.4 MW/cm². AlGaN photoconductors with cut-off wavelengths from 200 nm to 365 nm have been achieved for the first time. GaN p-n junction photovoltaic detector with very selective photoresponse have been demonstrated and theoretically modeled. Ti/AlN/Si metal-insulator- semiconductor capacitor with high capacitance-voltage performances at both low and high frequencies and low interface trap level density have been demonstrated for the first time in this material system. [reprint (PDF)] |
| 12. | Ga/sub 0.51/In/sub 0.49/P/GaAs HEMT's exhibiting good electrical performance at cryogenic temperatures Y.-J. Chan; D. Pavlidis; M. Razeghi; F. Omnes IEEE TRANS. ELEC.DEVICES. 77. IO. 1990-- October 1, 1990 ...[Visit Journal] The DC and microwave characteristics of Ga/sub 0.51/In/sub 0.49/P/GaAs HEMTs grown by metalorganic chemical vapor deposition (MOCVD) are presented. Devices with 1- mu m-long gates show transconductances of 163 and 213 mS/mm at 300 and 77 K, respectively. Their maximum cutoff frequency is 17.8 GHz. Deep traps in the doped layer are evaluated at low temperature by the threshold voltage shift and current collapse phenomena. GaInP/GaAs HEMTs show no current collapse and have almost zero threshold voltage shift compared to AlGaAs/GaAs and InAlAs/InGaAs where the corresponding values are 0.5 and 0.25 V, respectively. [reprint (PDF)] |
| 12. | Quantum-Cascade Lasers Operating in Continuous-Wave Mode Above 90°C at λ ~5.25 µm A. Evans, J. Nguyen, S. Slivken, J.S. Yu, S.R. Darvish, and M. Razeghi Applied Physics Letters 88 (5)-- January 30, 2006 ...[Visit Journal] We report on the design and fabrication of λ~5.25 μm quantum-cascade lasers (QCLs) for very high temperature continuous-wave (CW) operation. CW operation is reported up to a maximum temperature of 90 °C (363 K). CW output power is reported in excess of 500 mW near room temperature with a low threshold current density. A finite element thermal model is used to investigate the Gth and maximum CW operating temperature of the QCLs. [reprint (PDF)] |
| 12. | High Performance Quantum Cascade Laser Results at the Centre for Quantum Devices M. Razeghi and S. Slivken Physica Status Solidi, 195 (1)-- January 1, 2003 ...[Visit Journal] In this paper, we review some of the history and recent results related to the development of the quantum cascade laser at the Center for Quantum Devices. The fabrication of the quantum cascade laser is described relative to growth, characterization, and processing. State-of-the-art testing results for 5-11 μm lasers will be then be explored, followed by a future outlook for the technology. [reprint (PDF)] |
| 12. | Room temperature continuous wave, monolithic tunable THz sources based on highly efficient mid-infrared quantum cascade lasers Quanyong Lu, Donghai Wu, Saumya Sengupta, Steven Slivken, Manijeh Razeghi Nature Scientific Reports 6, Article number: 23595-- March 24, 2016 ...[Visit Journal] A compact, high power, room temperature continuous wave terahertz source emitting in a wide frequency range (ν ~ 1–5 THz) is of great importance to terahertz system development for applications in spectroscopy, communication, sensing, and imaging. Here, we present a strong-coupled strain-balanced quantum cascade laser design for efficient THz generation based on intracavity difference frequency generation. Room temperature continuous wave emission at 3.41 THz with a side-mode suppression ratio of 30 dB and output power up to 14 μW is achieved with a wall-plug efficiency about one order of magnitude higher than previous demonstrations. With this highly efficient design, continuous wave, single mode THz emissions with a wide frequency tuning range of 2.06–4.35 THz and an output power up to 4.2 μW are demonstrated at room temperature from two monolithic three-section sampled grating distributed feedback-distributed Bragg reflector lasers. [reprint (PDF)] |
| 12. | The correlation between x-ray diffraction patterns and strain distribution inside GaInP/GaAs superlattices X.G. He, M. Erdtmann, R. Williams, S. Kim, and M. Razeghi Applied Physics Letters 65 (22)-- November 28, 1994 ...[Visit Journal] Strong correlation between x‐ray diffraction characteristics and strain distribution inside GaInP/GaAs superlattices has been reported. It is found that the symmetry of (002) diffraction patterns can be used to evaluate the interface strain status. A sample with no interfacial strains has a symmetric (002) diffraction pattern and weak (004) diffraction pattern. It is also demonstrated that strain distribution in superlattices can be readily estimated qualitatively by analyzing x-ray diffraction patterns. [reprint (PDF)] |
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