scholarly journals Application of the level set method on the non-convex Hamiltonians

2009 ◽  
Vol 7 (1) ◽  
pp. 33-44
Author(s):  
B. Radjenovic ◽  
M. Radmilovic-Radjenovic ◽  
M. Mitric
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Etching Rate ◽  
Three Dimensional ◽  
Field Method ◽  
Rate Function ◽  
Wet Etching ◽  
Silicon Etching ◽  
Symmetry Properties ◽  
Interpolation Technique

Application of the level set method extended for the case of non-convex Hamiltonians is illustrated by the three dimensional (3D) simulation results of the profile evolution during anisotropic wet etching of silicon. Etching rate function is modeled on the basis of the silicon symmetry properties, by means of the interpolation technique using experimentally obtained values of the principal [100], [110], [111], and high index [311] directions in KOH solutions. The resulting level set equations are solved using an open source implementation of the sparse field method.

scholarly journals Level set simulations of the anisotropic wet etching process for device fabrication in nanotechnologies

2010 ◽  
Vol 64 (2) ◽  
pp. 93-97 ◽  
Author(s):  
Branislav Radjenovic ◽  
Marija Radmilovic-Radjenovic
Keyword(s):  
Level Set ◽  
Etching Rate ◽  
Three Dimensional ◽  
Crystal Form ◽  
Field Method ◽  
Device Fabrication ◽  
Etching Process ◽  
Semiconductor Wafer ◽  
Initial Shape ◽  
Symmetry Properties

Chemical etching is employed as micromachining manufacturing process to produce micron-size components. As a semiconductor wafer is extremely expensive due to many processing steps involved in the making thereof, the need to critically control the etching end point in an etching process is highly desirable. It was found that not only the etchant and temperature determine the exact anisotropy of etched silicon. The angle between the silicon surface and the mask was also shown to play an important role. In this paper, angular dependence of the etching rate is calculated on the base of the silicon symmetry properties, by means of the interpolation technique using experimentally obtained values of the principal <100>, <110>, <111> directions in KOH solutions. The calculations are performed using an extension of the sparse field method for solving three dimensional (3D) level set equations that describe the morphological surface evolution during etching process. The analysis of the obtained results confirm that regardless of the initial shape the profile evolution ends with the crystal form composed of the fastest etching planes, {110} in our model.

scholarly journals Evolution of Si Crystallographic Planes-Etching of Square and Circle Patterns in 25 wt % TMAH

Micromachines ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 102 ◽  
Author(s):  
Milče Smiljanić ◽  
Žarko Lazić ◽  
Branislav Radjenović ◽  
Marija Radmilović-Radjenović ◽  
Vesna Jović
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Silicon Substrate ◽  
Water Solution ◽  
Three Dimensional ◽  
Silicon Etching ◽  
3D Simulations ◽  
Circle Patterns ◽  
Crystallographic Planes ◽  
Good Agreement

Squares and circles are basic patterns for most mask designs of silicon microdevices. Evolution of etched Si crystallographic planes defined by square and circle patterns in the masking layer is presented and analyzed in this paper. The sides of square patterns in the masking layer are designed along predetermined <n10> crystallographic directions. Etching of a (100) silicon substrate is performed in 25 wt % tetramethylammonium hydroxide (TMAH) water solution at the temperature of 80 °C. Additionally, this paper presents three-dimensional (3D) simulations of the profile evolution during silicon etching of designed patterns based on the level-set method. We analyzed etching of designed patterns in the shape of square and circle islands. The crystallographic planes that appear during etching of 3D structures in the experiment and simulated etching profiles are determined. A good agreement between dominant crystallographic planes through experiments and simulations is obtained. The etch rates of dominant exposed crystallographic planes are also analytically calculated.

Element-local level set method for three-dimensional dynamic crack growth

2009 ◽  
Vol 80 (12) ◽  
pp. 1520-1543 ◽  
Author(s):  
Qinglin Duan ◽  
Jeong-Hoon Song ◽  
Thomas Menouillard ◽  
Ted Belytschko
Keyword(s):  
Crack Growth ◽  
Level Set Method ◽  
Level Set ◽  
Local Level ◽  
Three Dimensional ◽  
Dynamic Crack ◽  
Dynamic Crack Growth ◽  
Local Level Set

scholarly journals Computing three-dimensional two-phase flows with a mass-conserving level set method

2008 ◽  
Vol 11 (4-6) ◽  
pp. 221-235 ◽  
Author(s):  
S. P. van der Pijl ◽  
A. Segal ◽  
C. Vuik ◽  
P. Wesseling
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Three Dimensional ◽  
Two Phase Flows ◽  
Two Phase

scholarly journals A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method

2014 ◽  
Vol 1 (4) ◽  
pp. CM0039-CM0039 ◽  
Author(s):  
Hiroshi ISAKARI ◽  
Kohei KURIYAMA ◽  
Shinya HARADA ◽  
Takayuki YAMADA ◽  
Toru TAKAHASHI ◽  
...  
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Level Set Method ◽  
Level Set ◽  
Three Dimensional ◽  
Topology Optimisation ◽  
Fast Multipole ◽  
Element Method

scholarly journals The Level-Set Method for Multi-Material Wet Etching and Non-Planar Selective Epitaxy

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 115406-115422
Author(s):  
Alexander Toifl ◽  
Michael Quell ◽  
Xaver Klemenschits ◽  
Paul Manstetten ◽  
Andreas Hossinger ◽  
...  
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Wet Etching ◽  
Selective Epitaxy

scholarly journals Performance assessment of density and level-set topology optimisation methods for three dimensional heat sink design

2018 ◽  
Vol 12 (3) ◽  
pp. 273-287 ◽  
Author(s):  
Mani Sekaran Santhanakrishnan ◽  
Timothy Tilford ◽  
Christopher Bailey
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Heat Sink ◽  
Three Dimensional ◽  
Engineering Problem ◽  
Topology Optimisation ◽  
Design Quality ◽  
Advantages And Disadvantages ◽  
Computational Speed ◽  
Heat Sink Design

In this paper, two most prevalent topological optimisation approaches namely Density and Level set method are applied to a three dimensional heat sink design problem. The relative performance of the two approaches is compared in terms of design quality, robustness and computational speed. The work is original as for the first time it demonstrates the relative advantages and disadvantages for each method when applied to a practical engineering problem. It is additionally novel in that it presents the design of a convectively cooled heat sink by solving full thermo-fluid equations for two different solid-fluid material sets. Further, results are validated using a separate computational fluid dynamics study with the optimised designs are compared against a standard pin-fin-based heat sink design. The results show that the Density method demonstrates better performance in terms of robustness and computational speed, while Level-set method yields a better quality design in terms of final objective value.

Numerical Simulation of Filling Process in Vertical Centrifugal Casting Based on Projection-Level Set Method

2011 ◽  
Vol 314-316 ◽  
pp. 364-368 ◽  
Author(s):  
Jun Zhang ◽  
Jian Xin Zhou ◽  
Ming Yuan Zhang ◽  
Sheng Yong Pang ◽  
Dun Ming Liao ◽  
...  
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Centrifugal Casting ◽  
Three Dimensional ◽  
Thin Wall ◽  
Filling Process ◽  
Two Phase ◽  
Numerical Result ◽  
Complex Part ◽  
Mould Filling

A three-dimensional incompressible two phase flow model of vertical centrifugal casting is proposed to simulate the fluid flow of mould filling process accurately and effectively. The Projection method is adopted to solve the govern equation of the flow field, and the Level Set method is used to capture the free surface. The mold filling of a complex part with thin-wall is simulated. The numerical result shows that the Projection-Level Set method could simulate centrifugal casting effectively. The present study has a guiding significance to the production of vertical centrifugal casting.

An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows

2004 ◽  
Vol 126 (4) ◽  
pp. 578-585 ◽  
Author(s):  
Hiroyuki Takahira ◽  
Tomonori Horiuchi ◽  
Sanjoy Banerjee
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Interpolation Method ◽  
Density Ratio ◽  
Three Dimensional ◽  
Mass Conservation ◽  
Staggered Grid ◽  
Two Phase ◽  
Level Set Function

For the present study, we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function. It was shown that the present solver worked very well even for a density ratio of the two fluids of 1:1000. We simulated the coalescence of two rising bubbles under gravity, and a gas bubble bursting at a free surface to evaluate mass conservation for the present method. It was also shown that the volume conservation (i.e., mass conservation) of bubbles was very good even after bubble coalescence.

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