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Showing papers by "Rakesh K. Jain published in 1974"


Journal ArticleDOI
TL;DR: In this paper, a small perturbation applied to the free interface generates motions in the film, and the assumption is made that the Navier-Stokes equations can be used to describe them.
Abstract: The rupture of a liquid film on a solid surface and of a free liquid film have been studied using hydrodynamic stability theory. The films are not thicker than several hundred Angstrom. A small perturbation applied to the free interface generates motions in the film, and the assumption is made that the Navier–Stokes equations can be used to describe them. The difference in forces acting upon an element of liquid in a thin film and in a bulk fluid is accounted for by introducing a body force in the Navier–Stokes equations. This force is calculated from the potential energy per unit volume in the liquid caused by the London–van der Waals interactions with the surrounding molecules of the liquid and with those of the solid. If the perturbation grows, it leads to the rupture of the film. The range of wavelengths of the perturbation for which instability occurs is established and the time of rupture is evaluated. The effect of insoluble and soluble surface active agents is analyzed. Available experimental data concerning condensation on a solid surface and coalescence of bubbles are explained on the basis of the obtained results.

476 citations


Journal ArticleDOI
TL;DR: In this paper, the Fermi level in lightly and heavily compensated phosphorus doped silicon, at normal diffusion temperatures, was calculated numerically from the charge neutrality condition, taking into account the heavy doping effects (i.e., band tailing and impurity band formation).
Abstract: Taking into account the heavy doping effects (i.e., band tailing and impurity band formation) and high temperature effects, the Fermi level in lightly and heavily compensated phosphorus doped silicon, at normal diffusion temperatures is calculated numerically from the charge neutrality condition. The effective intrinsic carrier concentration is a function of the doping level and of the degree of compensation. Above discussed impurity concentration dependent results are used to calculate the impurity activity coefficient, the vacancy activity coefficient, and the concentration of the total number of vacancies as a function of doping and temperature.

34 citations


Journal ArticleDOI
TL;DR: In this article, it is shown that high concentrations of boron or phosphorus impurities are diffused into silicon single crystals, an elastic stress is suffered by the silicon lattice due to the mismatch sizes of the solute and solvent atoms.
Abstract: When high concentrations of boron or phosphorus impurities are diffused into silicon single crystals, an elastic stress is suffered by the silicon lattice due to the mismatch sizes of the solute and solvent atoms. This diffusion induced stress is relieved by the generation and movement of dislocations. Moving dislocations cause the anomalous diffusion which in turn is related to the plastic deformation of the silicon crystal. Maximum stresses developed at the beginning of the process caused by boron and phosphorus are calculated and studied as a function of diffusion temperature. It is found that these stresses are sufficient to cause plastic flow. Attempts are made using well developed theories of plasticity in metals to calculate the range of phosphorus diffusion induced stresses necessary to cause plastic deformation in silicon crystals; they are found to be of the order 2.6 × 107 to 7.2 × 107 dyn/cm2. Durch Eindiffusion hoher Bor- oder Phosphorbeimischungskonzentrationen in Silizium-einkristalle wird das Siliziumgitter elastisch verspannt, da eine Fehlanpassung in der Grose der gelosten und der Wirtsgitteratome vorliegt. Diese diffusionsbedingte Spannung ist begleitet von der Erzeugung und Bewegung von Versetzungen. Wandernde Versetzungen verursachen die anomale Diffusion, die wiederum mit der plastischen Deformation des Siliziumgitters zusammenhangt. Die sich zu Beginn des Prozesses entwickelnden maximalen Spannungen werden berechnet und als Funktion der Diffusionstemperatur untersucht. Es wird gefunden, das diese Spannungen ausreichen, um plastisches Fliesen hervorzurufen. Unter Benutzung bekannter Theorien der Plastizitat in Metallen wird versucht, den durch Phosphordiffusion bedingten Bereich der Spannungen zu berechnen, der notig ist, um plastische Deformation in Siliziumkristallen zu erzeugen. Es ergibt sich, das dieser Bereich in der Grosenordnung von 2,6 × 107 bis 7,2 × 107 dyn/cm2 liegt.

25 citations