General Relationship for the Thermal Oxidation of Silicon
01 Dec 1965-Journal of Applied Physics (American Institute of Physics)-Vol. 36, Iss: 12, pp 3770-3778
TL;DR: In this paper, the thermaloxidation kinetics of silicon are examined in detail based on a simple model of oxidation which takes into account the reactions occurring at the two boundaries of the oxide layer as well as the diffusion process, the general relationship x02+Ax0=B(t+τ) is derived.
Abstract: The thermal‐oxidation kinetics of silicon are examined in detail. Based on a simple model of oxidation which takes into account the reactions occurring at the two boundaries of the oxide layer as well as the diffusion process, the general relationship x02+Ax0=B(t+τ) is derived. This relationship is shown to be in excellent agreement with oxidation data obtained over a wide range of temperature (700°–1300°C), partial pressure (0.1–1.0 atm) and oxide thickness (300–20 000 A) for both oxygen and water oxidants. The parameters A, B, and τ are shown to be related to the physico‐chemical constants of the oxidation reaction in the predicted manner. Such detailed analysis also leads to further information regarding the nature of the transported species as well as space‐charge effects on the initial phase of oxidation.
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TL;DR: In this article, the authors compare the performance of SiC, GaN, and ZnSe for high-temperature electronics and short-wavelength optical applications and conclude that SiC is the leading contender for high temperature and high power applications if ohmic contacts and interface state densities can be further improved.
Abstract: In the past several years, research in each of the wide‐band‐gap semiconductors, SiC, GaN, and ZnSe, has led to major advances which now make them viable for device applications. The merits of each contender for high‐temperature electronics and short‐wavelength optical applications are compared. The outstanding thermal and chemical stability of SiC and GaN should enable them to operate at high temperatures and in hostile environments, and also make them attractive for high‐power operation. The present advanced stage of development of SiC substrates and metal‐oxide‐semiconductor technology makes SiC the leading contender for high‐temperature and high‐power applications if ohmic contacts and interface‐state densities can be further improved. GaN, despite fundamentally superior electronic properties and better ohmic contact resistances, must overcome the lack of an ideal substrate material and a relatively advanced SiC infrastructure in order to compete in electronics applications. Prototype transistors have been fabricated from both SiC and GaN, and the microwave characteristics and high‐temperature performance of SiC transistors have been studied. For optical emitters and detectors, ZnSe, SiC, and GaN all have demonstrated operation in the green, blue, or ultraviolet (UV) spectra. Blue SiC light‐emitting diodes (LEDs) have been on the market for several years, joined recently by UV and blue GaN‐based LEDs. These products should find wide use in full color display and other technologies. Promising prototype UV photodetectors have been fabricated from both SiC and GaN. In laser development, ZnSe leads the way with more sophisticated designs having further improved performance being rapidly demonstrated. If the low damage threshold of ZnSe continues to limit practical laser applications, GaN appears poised to become the semiconductor of choice for short‐wavelength lasers in optical memory and other applications. For further development of these materials to be realized, doping densities (especially p type) and ohmic contact technologies have to be improved. Economies of scale need to be realized through the development of larger SiC substrates. Improved substrate materials, ideally GaN itself, need to be aggressively pursued to further develop the GaN‐based material system and enable the fabrication of lasers. ZnSe material quality is already outstanding and now researchers must focus their attention on addressing the short lifetimes of ZnSe‐based lasers to determine whether the material is sufficiently durable for practical laser applications. The problems related to these three wide‐band‐gap semiconductor systems have moved away from materials science toward the device arena, where their technological development can rapidly be brought to maturity.
2,514 citations
TL;DR: In this paper, the authors present the current state of experimental data for basic parameters such as point-defect diffusivities and equilibrium concentrations and address a number of questions regarding the mechanisms of dopant diffusion.
Abstract: Diffusion in silicon of elements from columns III and V of the Periodic Table is reviewed in theory and experiment. The emphasis is on the interactions of these substitutional dopants with point defects (vacancies and interstitials) as part of their diffusion mechanisms. The goal of this paper is to unify available experimental observations within the framework of a set of physical models that can be utilized in computer simulations to predict diffusion processes in silicon. The authors assess the present state of experimental data for basic parameters such as point-defect diffusivities and equilibrium concentrations and address a number of questions regarding the mechanisms of dopant diffusion. They offer illustrative examples of ways that diffusion may be modeled in one and two dimensions by solving continuity equations for point defects and dopants. Outstanding questions and inadequacies in existing formulations are identified by comparing computer simulations with experimental results. A summary of the progress made in this field in recent years and of directions future research may take is presented.
1,155 citations
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01 Jan 2004
TL;DR: In this thesis, the existence and uniqueness of gradient trajectories near an A2singularity are analysed and it is proved that the two Lagrangian vanishing cycles associated to these critical points intersect transversally in exactly one point in all regular fibres along a straight line.
Abstract: In this thesis, the existence and uniqueness of gradient trajectories near an A2singularity are analysed. The A2-singularity is called a birth-death critical point in the real case. The birth-death critical point appears in a one-parameter family of functions. Such a family of functions has precisely two Morse critical points of index difference one, on the birth side. The result of the real case states that these two critical points are joined by a unique gradient trajectory up to time-shift. Here the gradient flow is defined with respect to any family of Riemannian metrics. This can be viewed as a converse to Smale’s cancellation theorem. We also look at the complex analogue of the result in Picard–Lefschetz theory. This analogue considers a holomorphic one-parameter family with an A2-singularity. Such a family has two critical Morse critical points near the singularity for every small non-zero parameter. We prove that the two Lagrangian vanishing cycles associated to these critical points intersect transversally in exactly one point in all regular fibres along a straight line. The result is obtained by analysing the gradient trajectories of the real part of these functions. Both proofs start with a normal form in local coordinates for such families of functions. The gradient equations in these coordinates can be rescaled into a fast-slow system of non-linear differential equation. Existence will rely on an adiabatic limit analysis whereas uniqueness follows from a Conley index pair construction. The latter construction will also show that connecting gradient trajectories cannot leave the local charts. Even though the proof of these two results follow from similar lines of argument, the real case cannot be reduced to the complex case and vice versa.
1,061 citations
959 citations
TL;DR: Due to high permittivity, the magnetic dipole resonance is observed in the visible spectral range for Si nanoparticles with diameters of ∼200 nm, thereby opening a way to the realization of isotropic optical metamaterials with strong magnetic responses in thevisible region.
Abstract: Strong resonant light scattering by individual spherical Si nanoparticles is experimentally demonstrated, revealing pronounced resonances associated with the excitation of magnetic and electric modes in these nanoparticles. It is shown that the low-frequency resonance corresponds to the magnetic dipole excitation. Due to high permittivity, the magnetic dipole resonance is observed in the visible spectral range for Si nanoparticles with diameters of ∼200 nm, thereby opening a way to the realization of isotropic optical metamaterials with strong magnetic responses in the visible region.
932 citations
References
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01 Jan 1955
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.
17,321 citations
2,540 citations
TL;DR: In this paper, the authors measured the permeation of gaseous oxygen through vitreous silica over the temperature range 950°-1,080° C. in a permeation cell constructed with two portions separated by a thin-walled spherical bulb with a short neck.
Abstract: THE permeation of gaseous oxygen through vitreous silica has been measured over the temperature-range 950°–1,080° C. in a permeation cell constructed with two portions separated by a thin-walled spherical bulb with a short neck. The bulb was 25 mm. outside diameter, and served as the membrane of vitreous silica ; its area was 18.9 cm.2 and thickness 0.27 mm. The thickness was determined from electrical capacitance measurements. The silica was used as blown ; and no cleaning was done with hydrofluoric acid. The oxygen pressure, 300–800 mm. mercury, was applied to the convex side of the bulb. The low-pressure side led directly to a mass spectrometer with no leak intervening. The rate of permeation of gas was measured1, in this case by the peak height of mass 32. It was assured that true permeation, and not merely degassing, was being measured by : (1) observing the slow rise of the oxygen peak after application of oxygen to the high-pressure side, (2) attainment of steady-state flow and then, (3) slow decay of the peak after the gas was removed from the high-pressure side.
273 citations