scholarly journals On the Relationship Between the Thin Film Equation and Tanner's Law

2020 ◽  
Author(s):  
M. G. Delgadino ◽  
A. Mellet
Keyword(s):  
Thin Film ◽  
Thin Film Equation ◽  
The Relationship

scholarly journals Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise

2021 ◽  
Author(s):  
Konstantinos Dareiotis ◽  
Benjamin Gess ◽  
Manuel V. Gnann ◽  
Günther Grün
Keyword(s):  
Thin Film ◽  
Energy Estimates ◽  
Approximation Procedure ◽  
Thin Film Flow ◽  
Thin Film Equations ◽  
Scalar Conservation Law ◽  
Thin Film Equation ◽  
Degenerate Parabolic ◽  
Scalar Conservation ◽  
Martingale Solutions

AbstractWe prove the existence of non-negative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range of mobilites including the cubic one which occurs under the assumption of a no-slip condition at the liquid-solid interface. Since their introduction more than 15 years ago, by Davidovitch, Moro, and Stone and by Grün, Mecke, and Rauscher, the existence of solutions to stochastic thin-film equations for cubic mobilities has been an open problem, even in the case of sufficiently regular noise. Our proof of global-in-time solutions relies on a careful combination of entropy and energy estimates in conjunction with a tailor-made approximation procedure to control the formation of shocks caused by the nonlinear stochastic scalar conservation law structure of the noise.

Improvement of Thermal Conductivity of Electroplated Copper Thin-Film Interconnections by Controlling Their Micro Texture

2014 ◽  
Author(s):  
Pornvitoo Rittinon ◽  
Ken Suzuki ◽  
Hideo Miura
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Thermal Conductivity ◽  
Grain Boundaries ◽  
Diffraction Method ◽  
Electron Back Scatter Diffraction ◽  
High Resistivity ◽  
Copper Thin Film ◽  
Electroplated Copper ◽  
The Relationship

Copper thin films are indispensable for the interconnections in the advanced electronic products, such as TSV (Trough Silicon Via), fine bumps, and thin-film interconnections in various devices and interposers. However, it has been reported that both electrical and mechanical properties of the films vary drastically comparing with those of conventional bulk copper. The main reason for the variation can be attributed to the fluctuation of the crystallinity of grain boundaries in the films. Porous or sparse grain boundaries show very high resistivity and brittle fracture characteristic in the films. Thus, the thermal conductivity of the electroplated copper thin films should be varied drastically depending on their micro texture based on the Wiedemann-Franz’s law. Since the copper interconnections are used not only for the electrical conduction but also for the thermal conduction, it is very important to quantitatively evaluate the crystallinity of the polycrystalline thin-film materials and clarify the relationship between the crystallinity and thermal properties of the films. The crystallinity of the interconnections were quantitatively evaluated using an electron back-scatter diffraction method. It was found that the porous grain boundaries which contain a significant amount of vacancies increase the local electrical resistance in the interconnections, and thus, cause the local high Joule heating. Such porous grain boundaries can be eliminated by control the crystallinity of the seed layer material on which the electroplated copper thin film is electroplated.

Analytical Treatment of Field-Effect Conduction in Polysilicon thin film Transistors

1997 ◽  
Vol 471 ◽  
Author(s):  
W. Eccleston
Keyword(s):  
Thin Film ◽  
Grain Size ◽  
Thin Film Transistors ◽  
Field Effect ◽  
Drain Current ◽  
High Current ◽  
Analytical Treatment ◽  
Channel Mobility ◽  
Current Region ◽  
The Relationship

ABSTRACTThe drift of electrons in the channels of Thin Film Transistors is analysed for discrete grains separated by grain boundaries containing amorphous silicon. The model provides the relationship channel mobility and grain size. The relationship between drain current and the terminal voltages is also predicted. The model relates to normal high current region of transistor operation.

scholarly journals Global existence for a thin film equation with subcritical mass

2017 ◽  
Vol 22 (4) ◽  
pp. 1461-1492 ◽  
Author(s):  
Jian-Guo Liu ◽  
◽  
Jinhuan Wang ◽  
Keyword(s):  
Thin Film ◽  
Global Existence ◽  
Thin Film Equation

Unstable sixth-order thin film equation: II. Global similarity patterns

Nonlinearity ◽  
2007 ◽  
Vol 20 (8) ◽  
pp. 1843-1881 ◽  
Author(s):  
J D Evans ◽  
V A Galaktionov ◽  
J R King
Keyword(s):  
Thin Film ◽  
Sixth Order ◽  
Thin Film Equation ◽  
Global Similarity
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