An Analytical Model of Contact Pressure Distribution Caused by 3-D Wafer Topography in Chemical-Mechanical Polishing Processes

2012 ◽  
Vol 159 (3) ◽  
pp. H266-H276 ◽  
Author(s):  
Lixiao Wu
2011 ◽  
Vol 215 ◽  
pp. 217-222 ◽  
Author(s):  
Y.S. Lv ◽  
Nan Li ◽  
Jun Wang ◽  
Tian Zhang ◽  
Min Duan ◽  
...  

In order to make the contact pressure distribution of polishing wafer surface more uniform during chemical mechanical polishing (CMP), a kind of the bionic polishing pad with sunflower seed pattern has been designed based on phyllotaxis theory, and the contact model and boundary condition of CMP have been established. Using finite element analysis, the contact pressure distributions between the polishing pad and wafer have been obtained when polishing silicon wafer and the effects of the phyllotactic parameter of polishing pad on the contact pressure distribution are found. The results show that the uniformity of the contact pressure distribution can be improved and the singularity of the contact pressure in the boundary edge of polished wafer can be decreased when the reasonable phyllotactic parameters are selected.


2010 ◽  
Vol 135 ◽  
pp. 84-89
Author(s):  
Yu Shan Lu ◽  
Qi Lin Shu ◽  
Jun Wang

In order to obtain the contact pressure distribution between the hard disc substrate and the polishing pad and its effects on the profile of polished substrate surface, the elastic contact mechanical model and mathematical equations on the chemical mechanical polishing of the hard magnetic disc substrate are established, and also the relevant boundary conditions are put forward. The contact pressure distribution is calculated with FEM, the polishing experiments are carried out and the surface profiles of polished substrates are obtained. The study results show that the contact pressure distribution on the substrate surface is non-uniformity and the contact pressure in the substrate edge present biggish undulation. Choosing properly the Young’s modulus of the polishing pads and decreasing its Poisson’s ratios can make the uniform area of the contact pressure distribution enlarging and improve the flatness of polished substrate.


2006 ◽  
Vol 34 (1) ◽  
pp. 38-63 ◽  
Author(s):  
C. Lee

Abstract A tire slips circumferentially on the rim when subjected to a driving or braking torque greater than the maximum tire-rim frictional torque. The balance of the tire-rim assembly achieved with weight attachment at certain circumferential locations in tire mounting is then lost, and vibration or adverse effects on handling may result when the tire is rolled. Bead fitment refers to the fit between a tire and its rim, and in particular, to whether a gap exists between the two. Rim slip resistance, or the maximum tire-rim frictional torque, is the integral of the product of contact pressure, friction coefficient, and the distance to the wheel center over the entire tire-rim interface. Analytical solutions and finite element analyses were used to study the dependence of the contact pressure distribution on tire design and operating attributes such as mold ring profile, bead bundle construction and diameter, and inflation pressure, etc. The tire-rim contact pressure distribution consists of two parts. The pressure on the ledge and the flange, respectively, comes primarily from tire-rim interference and inflation. Relative contributions of the two to the total rim slip resistance vary with tire types, depending on the magnitudes of ledge interference and inflation pressure. Based on the analyses, general guidelines are established for bead design modification to improve rim slip resistance and mountability, and to reduce the sensitivity to manufacturing variability. An iterative design and analysis procedure is also developed to improve bead fitment.


1995 ◽  
Vol 23 (2) ◽  
pp. 116-135 ◽  
Author(s):  
H. Shiobara ◽  
T. Akasaka ◽  
S. Kagami ◽  
S. Tsutsumi

Abstract The contact pressure distribution and the rolling resistance of a running radial tire under load are fundamental properties of the tire construction, important to the steering performance of automobiles, as is well known. Many theoretical and experimental studies have been previously published on these tire properties. However, the relationships between tire performances in service and tire structural properties have not been clarified sufficiently due to analytical and experimental difficulties. In this paper, establishing a spring support ring model made of a composite belt ring and a Voigt type viscoelastic spring system of the sidewall and the tread rubber, we analyze the one-dimensional contact pressure distribution of a running tire at speeds of up to 60 km/h. The predicted distribution of the contact pressure under appropriate values of damping coefficients of rubber is shown to be in good agreement with experimental results. It is confirmed by this study that increasing velocity causes the pressure to rise at the leading edge of the contact patch, accompanied by the lowered pressure at the trailing edge, and further a slight movement of the contact area in the forward direction.


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