To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure firstname.lastname@example.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
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.
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.
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.
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.
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.
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.
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.
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.
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 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.
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.
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.
In the previous chapter we showed that in two-dimensional hydrodynamics there can exist flows with patterns displaying symmetry and quasi-symmetry. However, the picture drawn in the previous chapter is poor compared to the one we are now going to present. Three-dimensional dynamics introduces us to a qualitatively new phenomenon – the existence of stream lines chaotically arranged in space – which is sometimes called the Lagrangian turbulence. Various forms of this phenomenon have interesting practical applications and have played an important role in our understanding of the onset of turbulence, as well. In this chapter we are going to establish the relation between the structural properties of steady-state three-dimensional flows and the chaos of stream lines in these flows. This relation will sufficiently improve our understanding of those domains of physics where a stochastic web is mentioned. At the same time, we shall notice universality in the manifestations of quasi-symmetry in physical objects as different as the phase portrait of a dynamic system in phase space and the geometrical pattern of a steady-state flow of a liquid in coordinate space.
Stream lines in space
Stream lines of two-dimensional flows have a very simple structure and coincide with lines of the level of the stream function ψ(x, y). The behaviour of stream lines in steady-state three-dimensional flows can be completely different, since three-dimensional dynamics differs drastically from two-dimensional dynamics.
How does the onset of chaos in Hamiltonian systems occur? This is one of the key questions in the modern theory of dynamic systems. However narrowly specialist this question may seem, the answer has a bearing on almost every branch of physics, including the quantum theory.
Chaos emerges as a result of specific local instability with respect to arbitrarily small perturbations of the system's orbits. It manifests itself in certain regions of phase space and within a certain range of the system's parameters. But the most remarkable feature of chaos in the fact that it is irremovable in fairly general physical situations. What is meant is the following. Under fairly typical conditions in phase space and in the space of values of parameters there always exist such regions in which the dynamics of the system is stochastic. These regions may be arbitrarily small, nevertheless, for a certain structure of the dynamic system given by its Hamiltonian, they are irremovable at any finite values of parameters. An illuminating example of this situation is Arnold's diffusion – a universal, unlimited transport of particles along the channels of a stochastic web in systems with the number of degrees of freedom exceeding two.
As we transfer from systems totally free of stochastic dynamics to systems with chaos, we encounter small regions which are seeds of chaos. In Hamiltonian systems these are stochastic layers and stochastic webs which, being the manifestation of weak chaos in these systems, at the same time perform a certain partitioning of phase space.
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).
We have shown that the phase portrait of a dynamic system with 1½ degrees of freedom can have a certain not-too-complex periodical or almost periodical structure. Such properties of the system's phase plane require quite definite conditions, which imply the existence of a stochasticity region (a stochastic web). It was this web that caused a partitioning of the phase plane either with a periodic symmetry (or simply symmetry) or with a quasi-periodic symmetry (or quasi-symmetry). This led us to a new concept of symmetries produced by dynamic systems in phase space. To what extent are symmetries of partitioning of phase space universal and are similar symmetries found in other natural objects?
We have already mentioned quasi-crystals as an example of quasi-symmetrical patterns. In this chapter we are going to show that hydrodynamic flows can also possess symmetry and quasi-symmetry similar to those displayed by the dynamic systems discussed earlier.
The formation of symmetry patterns in liquids has been known for a long time. An example of one of the simplest patterns (from the geometrical point of view) is Von Karman's vortex street. It consists of two rows of evenly spaced point vortexes arranged as on a chess board. The model of the vortex street was proposed by Von Karman to explain periodic traces behind a streamline cylinder for Reynolds numbers 30 < Re < 300. Von Karman's street is an example of a one-dimensional periodic chain, and this structural property is widely used in the analysis of its characteristics.
Among two-dimensional periodic patterns, the most famous is Benard's convective cell. This cell is formed as a result of thermal convection (the so-called Rayleigh–Benard convection).