Determination of the displacements of structures on foundations represented by a layer of finite thickness

1971 ◽  
Vol 5 (7) ◽  
pp. 636-639 ◽  
Author(s):  
B. I. Kogan ◽  
O. A. Yurchenko
Keyword(s):  
Finite Thickness

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%

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

THEORY OF A RESONANCE METHOD TO MEASURE THE ACOUSTIC PROPERTIES OF SEDIMENTS

Geophysics ◽  
1956 ◽  
Vol 21 (2) ◽  
pp. 299-304 ◽  
Author(s):  
W. J. Toulis
Keyword(s):  
Finite Thickness ◽  
Resonance Method ◽  
Acoustic Properties ◽  
Velocity Of Sound ◽  
Attenuation Constant ◽  
Cylindrical Chamber ◽  
Sediment Samples ◽  
Pressure Release ◽  
Acoustic Losses

The theory of resonance for a pressure release cylindrical chamber is explored and equations are derived for determining absolute values of the velocity of sound and the attenuation constant in sediment samples. The essential measurements that need to be made are the determination of the frequencies of the lower modes of resonance and the associated sharpness of resonance. Corrections are derived also for the finite thickness and the acoustic losses in the chamber walls.

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