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.

scholarly journals Etching of Uncompensated Convex Corners with Sides along and in 25 wt% TMAH at 80 °C

Micromachines ◽  
2020 ◽  
Vol 11 (3) ◽  
pp. 253 ◽  
Author(s):  
Milče M. Smiljanić ◽  
Žarko Lazić ◽  
Vesna Jović ◽  
Branislav Radjenović ◽  
Marija Radmilović-Radjenović
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Water Solution ◽  
Wet Etching ◽  
Tetramethylammonium Hydroxide ◽  
Convex Corner ◽  
Crystallographic Planes ◽  
Good Agreement

This paper presents etching of convex corners with sides along <n10> and <100> crystallographic directions in a 25 wt% tetramethylammonium hydroxide (TMAH) water solution at 80 °C. We analyzed parallelograms as the mask patterns for anisotropic wet etching of Si (100). The sides of the parallelograms were designed along <n10> and <100> crystallographic directions (1 < n < 8). The acute corners of islands in the masking layer formed by <n10> and <100> crystallographic directions were smaller than 45°. All the crystallographic planes that appeared during etching in the experiment were determined. We found that the obtained types of 3D silicon shape sustain when n > 2. The convex corners were not distorted during etching. Therefore, no convex corner compensation is necessary. We fabricated three matrices of parallelograms with sides along crystallographic directions <310> and <100> as examples for possible applications. Additionally, the etching of matrices was simulated by the level set method. We obtained a good agreement between experiments and simulations.

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.

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 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.

Computation of a Propagating Interface in Multiphase Flows Using an Adaptive Coupled Level Set Method

2002 ◽  
Author(s):  
Ruquan Liang ◽  
Satoru Komori
Keyword(s):  
Surface Tension ◽  
Level Set Method ◽  
Level Set ◽  
Multiphase Flows ◽  
Surface Tension Force ◽  
Numerical Results ◽  
Passive Transport ◽  
Effect Of Surface ◽  
Good Agreement ◽  
Numerical Strategy

We present a numerical strategy for a propagating interface in multiphase flows using a level set method combined with a local mesh adaptative technique. We use the level set method to move the propagating interface in multiphase flows. We also use the local mesh adaptative technique to increase the grid resolution at regions near the propagating interface and additionally at the regions near points of high curvature with a minimum of additional expense. For illustration, we apply the adaptive coupled level set method to a collection of bubbles moving under passive transport. Good agreement has been obtained in the comparision of the numerical results for the collection of bubbles using an adaptative grid with those using a single grid. We also apply the adaptive coupled level set method to a droplet falling on a step where it is important to accurately model the effect of surface tension force and the motion of the free-surface, and the numerical results agree very closely with available data.

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