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We have studied photoluminescence (PL) from undoped GaN films grown by HVPE technique on sapphire. Several defect-related PL bands are observed in the low-temperature PL spectrum. The concentrations of the defects responsible for these PL bands are determined from the dependence of PL intensity on excitation intensity. The RL band with a maximum at 1.8 eV is often the dominant PL band in HVPE GaN. It is caused by an unknown defect with the concentration of up to ∼1017 cm-3. The concentrations of defects responsible for other defect-related PL bands rarely exceed 1015 cm-3.
We report studies of the temperature dependence of Raman lines in high quality GaN and AlN. The temperature dependence of the phonon energies and linewidths are used to produce consistent phonon decay properties of zone center optic phonons. In GaN we observe the E22 phonon to decay into three phonons, while the A1(LO) phonon is well described according to the so-called Ridley process – one TO and one LA phonon. For AlN the E22 phonon decays by two phonon emission and the A1(LO) line also exhibits a dependence consistent with the Ridley process. Along with the phonon decay processes, it is important in each case to take into account the contribution of the thermal expansion, including the temperature dependence, to describe observed temperature shifts in the phonon properties.
Thick low defect AlN and AlGaN layers grown on ultra violet (UV) transparent substrates are considered as promising substrate materials for the UV light emitters and detectors. Electrically insulating thick AlN layers may serve as the substrates for AlGaN/GaN-based high power high electron mobility transistors (HEMTs). In this paper we report on crack-free up to 20 μm thick AlN layers grown by stress control HVPE on 2-inch sapphire substrates. As-grown surface had a characteristic pyramidal morphology. Being thick enough, AlN layers can be polished to improve surface roughness. The minimum full width at half maximum (FWHM) values of AlN ω-scan x-ray (00.2) and (10.2) rocking curves was about 500 and 1000 arcsec, respectively. The XRD analysis was applied for the threading dislocation density evaluation in grown AlN layer. Screw dislocation density was found to be (3-7)×108 cm-2 for the layers from 3 to 12 μm thick.
This paper contains results on InN growth by Hydride Vapor Phase Epitaxy (HVPE) on various substrates including sapphire, GaN/sapphire, AlGaN/sapphire, and AlN/sapphire templates. The growth processes were carried out at atmospheric pressure in a hot wall reactor in the temperature range from 500 to 650°C. Arrays of nano-crystalline InN rods with various shapes were grown directly on sapphire substrates. Continuous InN layers were grown on GaN/sapphire, AlN/sapphire and AlGaN/sapphire template substrates. X-ray diffraction rocking curves for the (00.2) InN reflection exhibit the full width at half maximum (FWHM) as narrow as 0.075 deg. for the nano-rods and 0.128 deg. for the continuous layers grown on GaN/sapphire templates.
In this paper we report p-GaN growth by hydride vapor phase epitaxy (HVPE) on sapphire substrates. Mg or Zn impurities were used for doping. Layer thickness ranged from 2 to 5 microns. For both impurities, as-grown GaN layers had p-type conductivity. Concentration NA-ND was varied from 1016 to 1018 cm−3. An annealing procedure at 750°C in argon ambient typically increased the concentration NA-ND in 1.5–3.5 times. For Mg doped GaN layers, room temperature hole mobility of 80 cm2V−1s−1 was measured by conventional Van Der Pau Hall effect technique for material having hole concentration of about 1x1018 cm−3. Initial results on highly electrically conducting p-type AlGaN/GaN heterostructures doped with Zn are also reported.
This letter reports on multi-layer submicron epitaxial device structures grown by hydride vapor phase epitaxy (HVPE). This is the first demonstration of both high electron mobility transistor (HEMT) devices and ultraviolet light emitting diodes (LED) emitting in the wavelength range from 305 to 340 nm based on AlGaN/GaN and AlGaN/AlGaN heterostructures grown by HVPE. Two unique aspects of this technological approach are the growth of Al-containing epitaxial material by HVPE and use of HVPE to form submicron multi-layer epitaxial structures. The high performance of HVPE grown devices presented in this report demonstrates the significant potential that exists for HVPE growth technology for mass production of device epitaxial wafers.
The structural, optical, and electrical properties of HVPE-grown GaN-on-sapphire templates were studied. The c and a lattice constants of the GaN layers were measured by x-ray diffraction. It was observed that the c and a lattice constants vary non-monotonically with Si-doping. The proper selection of Si-doping level and growth conditions resulted in controllable strain relaxation, and thus, influenced defect formation in GaN-on-sapphire templates. It was also observed that HVPE homoepitaxial GaN layers grown on the templates have better crystal quality and surface morphology than the initial templates.
Deep levels studies on a set of n-GaN films grown by MOCVD and HVPE reveal the presence of electron traps with levels near Ec−0.25 eV, Ec−0.55 eV, Ec−0.8 eV, Ec−1 eV, hole traps with levels near Ev+0.9 eV and a band of relatively shallow states in the lower half of the bandgap. The total density of these latter states was estimated to be some 1016 cm−3 and they were tentatively associated with dislocations in GaN based on their high concentration and band-like character. None of the electron or hole traps could be unambiguously related with strong changes of diffusion lengths of minority carriers in various samples. It is proposed that such changes occur due to different surface recombination velocities. An important role of Ec−0.55 eV traps in persistent photoconductivity phenomena in n-GaN has been demonstrated.
Deep levels studies on a set of n-GaN films grown by MOCVD and HVPE reveal the presence of electron traps with levels near Ec-0.25 eV, Ec-0.55 eV, Ec-0.8 eV, Ec-1 eV, hole traps with levels near Ev+0.9 eV and a band of relatively shallow states in the lower half of the bandgap. The total density of these latter states was estimated to be some 1016 cm−3 and they were tentatively associated with dislocations in GaN based on their high concentration and band-like character. None of the electron or hole traps could be unambiguously related with strong changes of diffusion lengths of minority carriers in various samples. It is proposed that such changes occur due to different surface recombination velocities. An important role of Ec-0.55 eV traps in persistent photoconductivity phenomena in n-GaN has been demonstrated.
Thick AlGaN layers and GaN/AlGaN heterostructures were grown by low pressure MOCVD on (0001) sapphire substrates utilizing a low temperature AlGaN buffer layer. The distribution of Al in the thick AlGaN layers was observed to be non-uniform as a function of depth. The Al content gradually increases from the substrate towards the epilayer surface. Moreover, fluctuations of Al content are also noticeable. The saturation of impurity-related emission with increasing current density was observed in EL spectra of LEDs consisting of AlGaN/GaN/AlGaN DH sandwiched by a 2 μm-thick bottom layer of GaN:Si and 0.5 μm-thick layer of GaN:Mg. The dominant near-band edge emission of the GaN active layer was found to be strongly absorbed in the thick bottom layer. Utilizing a 2 μm-thick AlGaN bottom layer instead of the GaN one allowed the absorption edge to be shifted towards higher energies. A single peak at 362 nm with FWHM of 14 nm was observed in this type of LED. Luminescence properties of various types of heterostructures are also discussed.
Undoped and Si-doped GaN films were grown by low pressure MOCVD on (0001) sapphire substrates. The angular distribution of the X-ray diffraction corresponding to the (0002), (0004), (100), (200), and (114) reflections has been measured by means of double- and triple -crystal diffractometry with Mo Kα1 and Cu Kα1 radiation under conditions of symmetrical and asymmetrical Bragg- and Laue-geometry. In our experiments a non-coplanar geometry was also applied. On the basis of the performed studies, five independent components of the tensor of microdistortion were evaluated and the average grain-size in two directions was determined. The type, position, and density of dislocations were established as well. The role of dislocations in strain relaxation and their influence on the optical and electrical properties are discussed.
In this study, both single undoped GaN epilayers and GaN-based device structures was treated by electrochemical etching in the dilute water solution of KOH or NaOH. Our investigations showed that in the undoped GaN epilayers grown by MOCVD the electrical and optical properties were nonuniform in depth. In this case, high defective and high conductive sublayer adjacent to the substrate was revealed by the electrochemical etching. This high conductive region was proved to condition the results of Hall effect measurements. Electrolyte etching of i-n GaN-based device structures grown by HVPE gave rise to significant increasing of the electroluminescence intensity. Influence of electrochemical etching on luminescence properties of the device structure is discussed.
Subrmicron heteroepitaxial GaAs and GaN films were grown by both conventional MOCVD and «capillary epitaxy» technique on (001) and (111) fianit (YSZ)substrates. A preliminary annealing of the substrates under vakuum was made in order to stabilize the surface by removing of some amount of oxygen. Conditions of single crystalline growth of GaAs submicron films (50–500nm) have been determined. The films had mirror-like surface morphology and high structural perfection. The distribution of Zr, O, Y across the film-substrate interface was sharp and doping impurities contents were uniform over the film. PL spectra of undoped GaN films on YSZ were studied.
It is shown that slopes of p(R) = Ω(R) ± κ(R)/m curves at Lindblad resonances determine the widths of resonance regions. The ability of galactic disks to respond to torques exerted at ILRs by perturbers (bar, density wave, galaxy-satellite, etc.) is determined by the widths of inner Lindblad resonances (ILRs). Widths of ILRs vary along the Hubble sequence of normal and barred galaxies. Galaxies having the bulge to disk ratio of masses and radii similar to the Milky Way could have wide ILRs if they are formed at the region of 2-4 kpc from their centers. A wide range of possible perturbers with pattern speeds 4≤ Ωp ≤ 26 km s≤1 kpc−1 could excite an ILR at this region of the Milky Way. Probably, the ILR of Milky Way’s grand design is located in the same region. The hole in the galactic H2 disk is also located in this region. The mechanism responsible for the origin of this hole could be similar to that opening gaps in planetary rings.
The equations of motion in classical physics differ considerably depending upon the subject they describe: a particle, an electromagnetic field, or a fluid. However our natural yearning for unification in the description of different phenomena has long since led to the development of universal formalisms. Among these the Lagrangian and Hamiltonian formalisms are the most advanced. This can be explained by the nature of the phenomena discussed. The popularity of each method varied at different stages in the development of physics. Throughout the whole period of advancement of relativistically invariant theories, preference was chiefly given to Lagrangian formalism (this was most conspicuous in field theory and the theory of a continuous medium). To a large extent, it was not before the generalization of the concepts of Hamiltonian formalism and introduction of Poisson's brackets that the Hamiltonian method of analysis was able to compete with the Lagrangian one.
The formation of new ideas and possibilities triggered recently by the discovery of the phenomenon of dynamic stochasticity (or simply, chaos) have brought the methods of Hamiltonian dynamics to the fore. Liouville's theorems on the conservation of phase volume and on the integrability of systems with a complete set of integrals of motion have determined both the formulation of many problems of dynamics and the methods of their study. The Hamiltonian method turned out to be of extreme importance for the theory of stability, which was advanced in this direction by Poincaré. Numerous subsequent studies have shown that Hamiltonian systems (i.e., systems which can be described by Hamiltonian equations of motion) demonstrate fundamental physical differences from other (non-Hamiltonian) systems. This chapter provides the most necessary information on Hamiltonian systems.
So far, we have been discussing various kinds of pattern with regular or almost regular symmetry. They emerged either in phase space of dynamic systems or in coordinate space of hydrodynamic flows. Common to all these cases was the method of obtaining or revealing patterns. Such patterns emerged not as the result of some artificial formal algorithm but as an expression of natural laws. In ancient times, however, people did not possess the level of knowledge available to us today. Perhaps it was the attempt to penetrate into the laws of creation of regular patterns, that gave rise to the art of ornament. Or perhaps this form of human activity had nothing to do with what was observed in nature. In either event, it would be interesting to make a number of comparisons between ancient ornaments and the pictures drawn by the trajectory of a real particle under certain conditions.
Two-dimensional tilings in art
Byzantine mosaic is one of the oldest examples of symmetrical periodic tilings of a plane (Fig. 10.1.1). Although the periodicity condition might have arisen as an independent problem, practical aims of architectural design required exactly this kind of ornament. Tiles of one shape (or of several different shapes) were to form the elementary components of a tiling. The element of an ornament was to be reproduced as many times as need, so that eventually any chosen portion of the plane could be paved.
The ornamental technique reached its peak of development in Muslim art. Elementary cells of an ornament became far more complex (Figs. 10.1.2 to 10.1.4).