A Dishing Model for STI CMP Process

2005 ◽  
Vol 867 ◽  
Author(s):  
Shih-Hsiang Chang
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Closed Form ◽  
Contact Mechanics ◽  
Closed Form Solution ◽  
Form Solution ◽  
Experimental Results ◽  
Quantitative Prediction ◽  
Comparison With Experimental Data

AbstractIt is well known that oxide dishing occurring in STI CMP leads to considerable sidewall and edge-parasitic conduction. Thus, a closed-form solution for quantitative prediction of oxide dishing is needed. A contact-mechanics-based approach to describe the steady-state oxide dishing occurring in STI CMP process is presented. The theory is validated through comparison with experimental data in the literature. Once validated, the model is used to quantify the effect of pattern geometry on oxide dishing. It is shown that the predictions of the model agree reasonably well with the experimental results measured in overpolishing time.

A Dishing Model for Chemical Mechanical Polishing of Plug Structures

2010 ◽  
Vol 126-128 ◽  
pp. 276-281
Author(s):  
Shih Hsiang Chang
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Chemical Mechanical Polishing ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mechanical Polishing ◽  
Quantitative Prediction ◽  
Wafer Surface ◽  
Maximum Value ◽  
Pattern Density

It is well known that dishing occurring in chemical mechanical polishing of plug structures leads to considerable wafer surface non-planarity and reduces the current/charge conduction. Thus, a closed-form solution for quantitative prediction of dishing is needed. A contact-mechanics-based approach to describe the steady-state dishing occurring in chemical mechanical polishing of plug structures is presented. The model is then applied to investigate the effect of pattern geometry on dishing in details. It was shown that plug dishing strongly depends on plug size, but minimally on pattern density. In addition, the maximum value of dishing occurs at a critical pattern density for fixed pitch.

scholarly journals Rotation Estimation: A Closed-Form Solution Using Spherical Moments

Sensors ◽  
2019 ◽  
Vol 19 (22) ◽  
pp. 4958
Author(s):  
Hicham Hadj-Abdelkader ◽  
Omar Tahri ◽  
Houssem-Eddine Benseddik
Keyword(s):  
Image Processing ◽  
Closed Form ◽  
Synthetic Data ◽  
Closed Form Solution ◽  
Form Solution ◽  
Unified Model ◽  
Experimental Results ◽  
Motion Information ◽  
Vision Sensors ◽  
Spherical Projection

Photometric moments are global descriptors of an image that can be used to recover motion information. This paper uses spherical photometric moments for a closed form estimation of 3D rotations from images. Since the used descriptors are global and not of the geometrical kind, they allow to avoid image processing as features extraction, matching, and tracking. The proposed scheme based on spherical projection can be used for the different vision sensors obeying the central unified model: conventional, fisheye, and catadioptric. Experimental results using both synthetic data and real images in different scenarios are provided to show the efficiency of the proposed method.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

Design and Analysis of Automotive Serpentine Belt Drive Systems for Steady State Performance

1997 ◽  
Vol 119 (2) ◽  
pp. 162-168 ◽  
Author(s):  
R. S. Beikmann ◽  
N. C. Perkins ◽  
A. G. Ulsoy
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Parameters ◽  
Belt Drive ◽  
Automotive Engine ◽  
Theoretical Predictions ◽  
Serpentine Belt ◽  
Drive Systems

Serpentine belt drive systems with spring-loaded tensioners are now widely used in automotive engine accessory drive design. The steady state tension in each belt span is a major factor affecting belt slip and vibration. These tensions are determined by the accessory loads, the accessory drive geometry, and the tensioner properties. This paper focuses on the design parameters that determine how effectively the tensioner maintains a constant tractive belt tension, despite belt stretch due to accessory loads and belt speed. A nonlinear model predicting the operating state of the belt/tensioner system is derived, and solved using (1) numerical, and (2) approximate, closed-form methods. Inspection of the closed-form solution reveals a single design parameter, referred to as the “tensioner constant,” that measures the effectiveness of the tensioner. Tension measurements on an experimental drive system confirm the theoretical predictions.

scholarly journals Closed form solution of the SIR model for the COVID-19 outbreak in Italy

2020 ◽  
Author(s):  
Riccardo Giubilei
Keyword(s):  
Experimental Data ◽  
Closed Form ◽  
Closed Form Solution ◽  
Sir Model ◽  
Form Solution ◽  
Model Equations

AbstractThe CODIV-19 outbreak in early 2020 generated a tremendous effort of epidemiologists and researchers to fit the experimental data with the solutions of the SIR model equations [1] or with more sophisticated models. In this paper we show that under same hypotheses, a closed form solution exists that reasonably fits the experimental data for Italy, and the results can be extended to any other area.

Moving Load on a Fluid-Solid Interface: Supersonic Regime

1973 ◽  
Vol 40 (1) ◽  
pp. 137-142 ◽  
Author(s):  
T. C. Kennedy ◽  
G. Herrmann
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
Steady State Response ◽  
Entire Space ◽  
State Response ◽  
Supersonic Regime

The steady-state response of a semi-infinite solid with an overlying semi-infinite fluid subjected at the plane interface to a moving point load is determined for supersonic load velocities. The exact, closed-form solution valid for the entire space is presented. Some numerical results for the displacements at the interface are calculated and compared to the results obtained when no fluid is present.

Sign in / Sign up

Export Citation Format

Share Document