Spin Coating Planarization Of Integrated Circuit Topography On A Rotating Disk

MRS Proceedings ◽

10.1557/proc-227-259 ◽

1991 ◽

Vol 227 ◽

Author(s):

Roger K. Yonkoski ◽

David S. Soane

Keyword(s):

Experimental Data ◽

Fluid Flow ◽

Integrated Circuit ◽

Spin Coating ◽

Rotating Disk ◽

Momentum Conservation ◽

Flat Surfaces ◽

Determination Of Parameters ◽

Polyimide Precursor

ABSTRACTPolyimide is commonly used in the microelectronic industry for interconnection applications because of its ability to planarize features typically found on an IC chip. A mathematical model is developed to describe fluid flow on a rotating disk based on the principles of mass and momentum conservation. Constitutive relationships necessary for this model are proposed. Experimental data for polyimide precursor solutions are presented which enable the determination of parameters for the constitutive equations. This model is used to describe the film profiles over flat surfaces and near micron-sized features. Attention is focused on the coupling between mass transport and fluid flow as well as the effects of surface tension on film profiles over topographical features.

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Determination of parameters for Cauchy’s problem for systems of ODEs with application to biological modelling

BIOMATH ◽

10.11145/j.biomath.2016.04.231 ◽

2016 ◽

Vol 5 (1) ◽

pp. 1604231

Author(s):

A.N. Pete ◽

Peter Mathye ◽

Igor Fedotov ◽

Michael Shatalov

Keyword(s):

Experimental Data ◽

Mathematical Models ◽

Least Squares ◽

Numerical Method ◽

Least Squares Method ◽

Algebraic Equations ◽

Systems Of Odes ◽

Determination Of Parameters ◽

Biological Modelling

An inverse numerical method that estimate parameters of dynamic mathematical models given some information about unknown trajectories at some time is applied to examples taken from Biology and Ecology. The method consisting of determining an over-determined system of algebraic equations using experimental data. The solution of the over-determined system is then obtained using, for example the least-squares method. To illustrate the effectiveness of the method an analysis of examples and corresponding numerical example are presented.

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Selection of Adsorbents and Determination of Parameters for the Separation of Glucose, Fructose, Sucrose and Fructooligosaccharides

International Journal of Food Engineering ◽

10.2202/1556-3758.1870 ◽

2010 ◽

Vol 6 (6) ◽

Cited By ~ 2

Author(s):

Raquel Cristine Kuhn ◽

Francisco Maugeri Filho

Keyword(s):

Experimental Data ◽

Active Carbon ◽

The Other ◽

Isothermal Kinetics ◽

Nax Zeolite ◽

Selection Step ◽

Determination Of Parameters ◽

Best Fit ◽

Selection Of

This work aimed to describe the adsorption of sugars (glucose, fructose, sucrose and fructooligosaccharides) employing different adsorbents (celite, active carbon and NaX zeolite) by means of isothermal models. At the adsorbent selection step, the active carbon exhibited a higher affinity for the adsorption of fructooligosaccharides. On the other hand, the adsorbents NaX zeolite and celite presented the highest adsorption stability with glucose, giving values of 1.496 g glucose/g zeolite and 1.35 g glucose/g celite. Therefore, zeolite and celite were the adsorbents selected for the determination of isothermal kinetics and it was shown that the linear model (q*= k.C*) provided the best fit for the experimental data. The temperatures studied were 30, 40 and 50 °C, and the 50°C resulted in the highest partition coefficient (k) for glucose on celite, indicating that higher temperatures benefit sugar adsorption.

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MATHEMATICAL DEVICE FOR FORMATION OF UNITED LOADING UNITS FOR TRANSPORTATION OF GOODS

VESTNIK OF ASTRAKHAN STATE TECHNICAL UNIVERSITY SERIES MARINE ENGINEERING AND TECHNOLOGIES ◽

10.24143/2073-1574-2017-2-103-108 ◽

2017 ◽

pp. 103-108

Author(s):

Andrey Olegovich Nichiporouk

Keyword(s):

Computer Analysis ◽

Integrated Circuit ◽

Loading Capacity ◽

Large Capacity ◽

Manufacturing Plants ◽

Rational Scheme ◽

Optimum Placement ◽

Determination Of Parameters

The article substantiates the need to develop a technique of composing optimum integrated cargo units for piece goods in soft packing according to the integrated circuit "a cargo item - a transport package - a container" in their mutual coordination. The requirements and corresponding mathematical conditions of technological compatibility of transport packages and vehicles have been formulated: maximum use of loading capacity and tonnage of transport packages and vehicles, maximum use of loading capacity of the reloading equipment. Similar mathematical conditions of technological compatibility of containers and vehicles have been defined. Algorithms of carrying out computer analysis work on composing an optimum transport package have been offered: determination of parameters of a consumer (transport) package, an optimum way of location of packages in a transport package and their total number. At the same time there has been taken into account importance to maintain the standards of overall dimensions of a transport package, internal dimensions and loading capacity of a container, characteristics of loaders. The article offers the algorithm defining the rational scheme of locating the formed optimum transport packages in a container: determining net volume of a container, finding optimum placement of transport packages in a container and norms of its loading. There have been considered advantages of the developed techniques and algorithms for carrying out further researches, as well as for practical activities of cargo owners, transport and forwarding companies when planning delivery of cargo parties, forming optimum transport packages directly at manufacturing plants, deciding the best schemes of loading of large-capacity containers with transport packages.

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Interrelation of processing modes with the current parameters of the contact zone during thermofriction processing

MATEC Web of Conferences ◽

10.1051/matecconf/201822401132 ◽

2018 ◽

Vol 224 ◽

pp. 01132 ◽

Cited By ~ 1

Author(s):

Nikolay Pokintelitsa

Keyword(s):

Contact Zone ◽

Rotating Disk ◽

Flat Surfaces ◽

Material Layer ◽

Control Actions ◽

Disk Tool ◽

Processing Modes ◽

Cutting Modes

The establishment of the interrelation between the processing modes and the current parameters of the contact zone during the thermofriction processing of flat surfaces of workpieces by a rotating disk tool is considered. Dependencies are presented allowing assignment of cutting modes, prediction of the size of the removed material layer, and determination of the control actions value.

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Elastohydrodynamic Contact Model For Calculation Of Axial And Angular Stiffness In Thrust Bearing

Archive of Mechanical Engineering ◽

10.2478/v10180-012-0024-z ◽

2012 ◽

Vol 59 (4) ◽

pp. 453-467

Author(s):

Mikhail Temis ◽

Alexander Lazarev

Keyword(s):

Fluid Flow ◽

Thrust Bearing ◽

Rotating Disk ◽

Flow Calculation ◽

Sliding Surfaces ◽

Integral Characteristics ◽

Calculation Results ◽

Angular Displacements ◽

Coupled Solution

Thrust bearing model is developed for fluid flow calculation and for determination of bearing integral characteristics in the presence of sliding surfaces closure and shaft angular displacements. The model is based on the coupled solution of the problem of incompressible fluid flow between the sliding surfaces and the problem of bearing and shaft elements deformation under the action of the fluid film pressure. Verification of the bearing model results is carried out by the comparison versus the fluid flow calculation results obtained by STAR-CD software and the experimental and theoretical results represented in the certain literature. Thrust bearing characteristics are determined versus sliding surfaces closure and rotating disk (runner) angular displacements. The contribution of the sliding surfaces deformations into bearing integral characteristics is estimated.

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