Determination of the horizontal displacements of rigid structures resting on elastic foundation of finite thickness

1972 ◽  
Vol 6 (4) ◽  
pp. 396-397
Author(s):  
S. N. Yagolkovskii
Keyword(s):  
Elastic Foundation ◽  
Finite Thickness ◽  
Horizontal Displacements

scholarly journals Determination of Stresses in Incrementally Deposited Films From Wafer-Curvature Measurements

2020 ◽  
Vol 87 (10) ◽  
Author(s):  
Zhaoxia Rao ◽  
Hanxun Jin ◽  
Alison Engwall ◽  
Eric Chason ◽  
Kyung-Suk Kim
Keyword(s):  
Residual Stress ◽  
Finite Thickness ◽  
Deposition Process ◽  
Wafer Curvature ◽  
Curvature Measurement ◽  
Stressed Layer ◽  
Relaxation Stress ◽  
Curvature Measurements ◽  
Deposited Films

Abstract We report closed-form formulas to calculate the incremental-deposition stress, the elastic relaxation stress, and the residual stress in a finite-thickness film from a wafer-curvature measurement. The calculation shows how the incremental deposition of a new stressed layer to the film affects the amount of the film/wafer curvature and the stress state of the previously deposited layers. The formulas allow the incremental-deposition stress and the elastic relaxation to be correctly calculated from the slope of the measured curvature versus thickness for arbitrary thicknesses and biaxial moduli of the film and the substrate. Subtraction of the cumulative elastic relaxation from the incremental-deposition stress history results in the residual stress left in the film after the whole deposition process. The validities of the formulas are confirmed by curvature measurements of electrodeposited Ni films on substrates with different thicknesses.

A variational–Green's function approach to theoretical treatment and applications of the capacitance of three-dimensional geometries

1982 ◽  
Vol 60 (2) ◽  
pp. 179-195 ◽  
Author(s):  
Andreas Mandelis
Keyword(s):  
Thin Film ◽  
Spatial Distribution ◽  
Green’S Function ◽  
Green's Function ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Function Approach ◽  
Theoretical Treatment ◽  
One Dimensional

A combined variational–Green's function approach to the determination of the capacitance of various useful three-dimensional geometries is developed. This formalism leads to general, exact expressions for the capacitance, which can be used with all geometries provided the spatial distribution of the charge can be determined. In particular, the theory takes into account the finite thickness and unequal areas of the capacitor plates. Specific applications of the theory include circular capacitors with disc and ring-shaped charged plate geometries. Such geometries are commonly encountered in experimental set-ups for capacitive measurements of thin film thicknesses in the field of microelectronics. Numerical results indicate that the values of thin film thicknesses calculated via simplified one-dimensional formulae for the capacitance may be incorrect by more than 10%

Inverse determination of the loading source of the infinite beam on elastic foundation

2008 ◽  
Vol 22 (12) ◽  
pp. 2350-2356 ◽  
Author(s):  
T. S. Jang ◽  
H. G. Sung ◽  
S. L. Han ◽  
S. H. Kwon
Keyword(s):  
Elastic Foundation ◽  
Infinite Beam ◽  
Beam On Elastic Foundation

Determination of Diffusion Length for the Finite Thickness Normal-Collector Configuration Using EBIC Technique

2013 ◽  
Vol 60 (10) ◽  
pp. 3541-3547 ◽  
Author(s):  
Chee Chin Tan ◽  
Vincent K. S. Ong ◽  
K. Radhakrishnan ◽  
Siti Hairunnisah Bte Sunar
Keyword(s):  
Diffusion Length ◽  
Finite Thickness
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