An Analytical Dishing and Step Height Reduction Model for Chemical Mechanical Planarization (CMP)

2002 ◽  
Author(s):  
Guanghui Fu ◽  
Abhijit Chandra
Keyword(s):  
Chemical Mechanical Planarization ◽  
Design Tool ◽  
Step Height ◽  
Wafer Surface ◽  
Surface Geometry ◽  
Height Reduction ◽  
Proposed Model ◽  
Model Predictions ◽  
Feature Scale ◽  
Good Agreement

An analytical model for dishing and step height reduction in chemical mechanical planarization (CMP) of copper is presented. The model is based on the assumption that at the feature scale, high areas on the wafer experience higher pressure than low areas. The slurry is assumed to be Prestonian. The model delineates how dishing and step height reduction depend on slurry properties (selectivity and Preston’s constants), pad characteristics (stiffness and bending ability), polishing conditions (pressure, relative velocity and overpolishing) and wafer surface geometry (linewidth, pitch and pattern density). Model predictions are in good agreement with existing experimental observations. The present model facilitates understanding of the CMP process at the feature scale. Based on the proposed model, design avenues for decreasing dishing and increasing the speed of step height reduction may be explored through modification of appropriate parameters for slurry, pad and polishing conditions. The proposed model may also be used as a design tool for pattern layout to optimize the performance of the CMP process.

On the Pattern Dependency and Substrate Effects During Chemical-Mechanical Planarization for Ulsi Manufacturing

1999 ◽  
Vol 566 ◽  
Author(s):  
Wei-Tsu Tseng ◽  
James Jong-Lin Niu ◽  
Chi-Fa Lin
Keyword(s):  
Chemical Mechanical Planarization ◽  
Reduction Rate ◽  
Surface Profile ◽  
Step Height ◽  
Substrate Effects ◽  
Height Reduction ◽  
Pattern Density

The change of surface profile during chemical-mechanical planarization (CMP) is monitored continuously in this study. The influences from pattemn dependency and substrate effects are discussed. Step height reduction rate is a function of pattern density and down force. The rate decreases with time until planarization is achieved. As the polish approaches the patterns underneath, the interaction between substrate effects and pattern dependency results in the resurgence of step height. The implication of this newly found phenomenon is discussed.

A COMPREHENSIVE MODEL FOR CAPILLARY PRESSURE DIFFERENCE ACROSS A DROP/BUBBLE FLOWING THROUGH A CONSTRICTED CAPILLARY

2015 ◽  
Vol 22 (06) ◽  
pp. 1550077 ◽  
Author(s):  
MINGCHAO LIANG ◽  
JUNHONG WEI ◽  
HONGMEI HAN ◽  
CHENGGUO FU ◽  
JIANJUN LIU
Keyword(s):  
Capillary Pressure ◽  
Pressure Difference ◽  
Chemical Engineering ◽  
Bubble Formation ◽  
Comprehensive Model ◽  
Science And Engineering ◽  
Proposed Model ◽  
Model Predictions ◽  
Interface Science ◽  
Good Agreement

The capillary pressure is one of the crucial parameters in many science and engineering applications such as composite materials, interface science, chemical engineering, oil exploration, etc. The drop/bubble formation and its mechanisms that affect the permeability of porous media have steadily attracted much attention in the past. When a drop/bubble moves from a larger capillary to a smaller one, it is often obstructed by an additional pressure difference caused by the capillary force. In this paper, a comprehensive model is derived for the capillary pressure difference when a drop/bubble flows through a constricted capillary, i.e. a geometrically constricted passage with an abrupt change in radius. The proposed model is expressed as a function of the smaller capillary radius, pore-throat ratio, contact angle, surface tension and length of the drop/bubble in the smaller capillary. The model predictions are compared with the available experimental data, and good agreement is found between them.

Biophysical Model of the Coupled Mechanisms of Cell Adhesion, Contraction and Spreading

2012 ◽  
Author(s):  
Franck J. Vernerey
Keyword(s):  
Actin Polymerization ◽  
Mathematical Formulation ◽  
Cell Spreading ◽  
Fiber Formation ◽  
Biophysical Model ◽  
Self Assembling ◽  
Cell Substrate ◽  
Proposed Model ◽  
Model Predictions ◽  
Good Agreement

Recent research has shown that cell spreading is highly dependent on the contractility of its cytoskeleton and the mechanical properties of its surrounding environment. This extended abstract introduces a mathematical formulation of cell spreading and contraction that couples the processes of stress fiber formation, protrusion growth through actin polymerization at the cell edge and dynamics of cross-membrane protein (integrins) enabling cell-substrate attachment. The evolving cell’s cytoskeleton is modeled as a mixture of fluid, proteins and filaments that can exchange mass and generate contraction. In particular, besides self-assembling into stress fibers, actin monomers are able to polymerize into an actin meshwork at the cell’s boundary in order to push the membrane forward and generate protrusion. These processes are possible via the development of cell-substrate attachment complexes that arise from the mechano-sensitive equilibrium of membrane proteins, known as integrins. Numerical simulations show that the proposed model is able to capture the dependency of cell spreading and contraction on substrate stiffness and chemistry. The very good agreement between model predictions and experimental observations suggests that mechanics plays a strong role into the coupled mechanisms of contraction, adhesion and spreading of adherent cells.

scholarly journals Compact Modelling of Electrical, Optical and Thermal Properties of Multi-Colour Power LEDs Operating on a Common PCB

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1286
Author(s):  
Krzysztof Górecki ◽  
Przemysław Ptak
Keyword(s):  
Integrated Circuits ◽  
Optical Model ◽  
Printed Circuit Board ◽  
Circuit Board ◽  
Junction Temperature ◽  
Optical Parameters ◽  
Spice Simulation ◽  
Light Emitting ◽  
Proposed Model ◽  
Good Agreement

This paper concerns the problem of modelling electrical, thermal and optical properties of multi-colour power light-emitting diodes (LEDs) situated on a common PCB (Printed Circuit Board). A new form of electro-thermo-optical model of such power LEDs is proposed in the form of a subcircuit for SPICE (Simulation Program with Integrated Circuits Emphasis). With the use of this model, the currents and voltages of the considered devices, their junction temperature and selected radiometric parameters can be calculated, taking into account self-heating phenomena in each LED and mutual thermal couplings between each pair of the considered devices. The form of the formulated model is described, and a manner of parameter estimation is also proposed. The correctness and usefulness of the proposed model are verified experimentally for six power LEDs emitting light of different colours and mounted on an experimental PCB prepared by the producer of the investigated devices. Verification was performed for the investigated diodes operating alone and together. Good agreement between the results of measurements and computations was obtained. It was also proved that the main thermal and optical parameters of the investigated LEDs depend on a dominant wavelength of the emitted light.

Static and Dynamic Structure of Molecular Monomers and Dimers of the Rare-earth Fluorides

2001 ◽  
Vol 56 (5) ◽  
pp. 381-385
Author(s):  
Z. Akdeniz ◽  
M . Gaune-Escard ◽  
M. P. Tosi
Keyword(s):  
Rare Earth ◽  
Bond Length ◽  
Geometrical Structure ◽  
Vibrational Mode ◽  
Dynamic Structure ◽  
Molecular Shape ◽  
Proposed Model ◽  
Infrared Studies ◽  
Charged Clusters ◽  
Good Agreement

Abstract We determine a model of the ionic interactions in RF3 compounds, where R is a rare-earth element in the series from La to Lu, by an analysis of data on the bond length and the vibrational mode frequencies of the PrF3, GdF3 and HoF3 molecular monomers. All RF3 monomers are predicted to have a pyramidal shape, displaying a progressive flattening of the molecular shape in parallel with the lanthanide contraction of the bond length. The vibrational frequencies of all monomers are calculated, the results being in good agreement with the data from infrared studies of matrix-isolated molecules. We also evaluate the geometrical structure and the vibrational spectrum of the La2F6 and Ce2F6 dimers, as a further test of the proposed model. -PACS 36.40.Wa (Charged clusters)

Step height removal mechanism of chemical mechanical planarization (CMP) for sub-nano-surface finish

Wear ◽  
2010 ◽  
Vol 268 (3-4) ◽  
pp. 505-510 ◽  
Author(s):  
Ji Chul Yang ◽  
Dong Won Oh ◽  
Gae Won Lee ◽  
Chang Lyung Song ◽  
Taesung Kim
Keyword(s):  
Surface Finish ◽  
Chemical Mechanical Planarization ◽  
Step Height ◽  
Removal Mechanism

Effects of Alkaline Nano-SiO2 Abrasive on Planarization of 300mm Copper Patterned Wafer

2013 ◽  
Vol 634-638 ◽  
pp. 2949-2954
Author(s):  
Xin Liang Tang ◽  
Yu Ling Liu ◽  
Hong Yuan Zhang ◽  
Jie Bao
Keyword(s):  
Removal Rate ◽  
Chemical Mechanical Planarization ◽  
Initial Step ◽  
Step Height ◽  
Copper Removal ◽  
Copper Wafers

Silica abrasive plays an important role in chemical mechanical planarization (CMP) of copper. In this paper, effect of different silica abrasive concentrations on copper removal rate and planarization performance of copper was investigated. The results show that the copper removal rate was increased as the concentration of silica abrasive increase. However, excessive abrasive will lead to a decreased copper removal rate. The initial step height values of the multilayer copper wafers were all about 2500Å, and after being polished for 30s, the remaining values of step height of slurry A, B, C and D were 717 Å, 906 Å, 1222 Å and 1493 Å. It indicates that alkaline copper slurries with different abrasive concentrations all had a good planarization performance on copper patterned wafer CMP. As the abrasive concentration increased, the planarization capability was enhanced.

Rigid-Plastic Impact of Single Angular Particles

2021 ◽  
Author(s):  
Sandeep Dhar
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Orientation Dependence ◽  
Particle Orientation ◽  
Rigid Plastic ◽  
Plastic Model ◽  
Model Predictions ◽  
Good Agreement ◽  
Angular Particles

The trajectory of an angular particle as it cuts a ductile target is, in general, complicated because of its dependence not only on particle shape, but also on particle orientation at the initial instant of impact. This orientation dependence has also made experimental measurement of impact parameters of single angular particles very difficult, resulting in a relatively small amount of available experimental data in the literature. The current work is focused on obtaining measurements of particle kinematics for comparison to rigid plastic model developed by Papini and Spelt. Fundamental mechanisms of material removal are identified, and measurements of rebound parameters and corresponding crater dimensions of single hardened steel particles launched against flat aluminium alloy targets are presented. Also a 2-D finite element model is developed and a dynamic analysis is performed to predict the erosion mechanism. Overall, a good agreement was found among the experimental results, rigid-plastic model predictions and finite element model predictions.

Viscosity Models Based on Network Theory for Polymer Melts

2010 ◽  
Vol 129-131 ◽  
pp. 1244-1247
Author(s):  
Hai Hang Xu ◽  
Lei Zhong
Keyword(s):  
Experimental Data ◽  
Kinetic Equation ◽  
Constitutive Equation ◽  
Polymer Composites ◽  
Network Theory ◽  
Polymer Melts ◽  
Structure Parameter ◽  
Viscosity Models ◽  
Model Predictions ◽  
Good Agreement

New shear and extensional viscosity models based on Fredrickson kinetic equation coupled with Dewitt constitutive equation were established to predict viscosities of polymer melts. The experimental data of 125°C LDPE and LDPE filled with 35% glass beads reported from references were compared with the model predictions. The predictions showed good agreement with the measurements. The models are simple and easy to use. Because they contain no structure parameter, they are capable to describe the viscosities of pure polymer and polymer composites.

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