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List of Figures
2.1 Model of a segregation effect at a material interface between silicon and silicon dioxide
2.2 Oxide growth by thermal oxidation
2.3 Model for oxide growth suggested by Deal & Grove
2.4 Model of a segregation effect at the moving interface between silicon and silicon dioxide
2.5 Segregation effects of arsenic, boron and phosphorus at the moving interface between silicon and silicon dioxide
3.1 Simulation domain subdivided into elements
3.2 Transformation of elements onto a local standard element within the limits zero and one
3.3 Linear and quadratic shape functions for one-dimensional elements
3.4 Approximation characteristics of linear and quadratic shape functions in case of h-refinement and p-refinement
3.5 Finite box discretization with assigned Voronoi box
3.6 Finite box discretization with an element-wise calculation mode to fit the analytical representation of A
MIGOS
4.1 Block structure of A
MIGOS
4.2 Several different user perspectives
4.3 Flow diagram of A
MIGOS
for a complete simulation process
4.4 Discretized solution vectors on a triangular grid element
4.5 Auxiliary calculation depending on element interconnections and weighting function
4.6 Extendible hash representing mathematical expressions such as the tree representing (a+b)*c
4.7 Insertion of a variable
b
into an existing tree (a+c+d) which needs reorganization to avoid permutation problems (resulting order: a+b+c+d)
4.8 C-code extraction for optimization purposes
4.9 Auto assembling mechanism of a one-dimensional simulation domain with linear two point elements
4.10 Two different boundary types extracted by A
MIGOS
4.11 Extracted interface grid is treated as any other grid
4.12 Global matrix assembly in case of coupled quantities
4.13 Hierarchical element decomposition for triangles, rectangles, octahedrons and tetrahedrons
4.14 Dopant distribution after 60 seconds
4.15 Dopant distribution after 600 seconds
4.16 Dopant distribution in an inhomogeneous material
4.17 Segregation effect calculated with an adaptive grid to account for a circular inhomogeneity
4.18 First approach showing forces depending on element angles
4.19 Moving boundaries for minimum restriction of freedom but preserving the geometry
4.20 Resulting optimum angles due to given connectivity
4.21 Adaptive hierarchical calculation
without
relaxation
4.22 Adaptive hierarchical calculation
with
relaxation
4.23 Hierarchical mesh adaptation calculating a change in the grid orientation along an internal topology change without and with relaxation
4.24 Hierarchical adaptation of a sphere calculated without relaxation needing 10742 points with 37482 tetrahedrons
4.25 Hierarchical adaptation of a sphere calculated with relaxation needing 7588 points with 24901 tetrahedrons
4.26 Performance comparison concerning calculation time and memory consumption
4.27 Performance comparison concerning development time
4.28 Calculated potential distribution showing the mesh of discretization
4.29 Calculated temperature distribution within the two layered interconnected structure
4.30 Calculated temperature distribution within the surrounding insulator
5.1 Maxwell body: spring and a dashpot in series
5.2 Domain and boundary settings
5.3 Parameter dependent level set function
5.4 The scanning electron micrographs show the typical effects at the the corners of a silicon step oxidized at 1100
o
C (left) and 1000
o
C (right)
5.5 Oxide growth at a temperature of 1100
o
C
5.6 Oxide growth at a temperature of 1000
o
C
5.7 Oxide growth around a nitride mask covering one quarter of the geometry
5.8 Oxide growth around a nitride mask covering three quarters of the geometry
5.9 Three-dimensional oxide growth around a thin floating nitride mask
5.10 Two-dimensional cut through the simulation result showing the materials deformation along the longer side of the mask
5.11 Two-dimensional cut through the simulation result showing the materials deformation along the shorter side of the mask
5.12 Three-dimensional oxide growth around a fat floating nitride mask
5.13 Two-dimensional cut through the simulation result showing the materials deformation along the longer side of the mask
5.14 Two-dimensional cut through the simulation result showing the materials deformation along the shorter side of the mask
5.15 Three-dimensional polysilicon growth at a temperature of 1000
o
C
5.16 Three-dimensional polysilicon growth at a temperature of 1100
o
C
5.17 Three-dimensional polysilicon growth at a temperature of 1100
o
C showing the distribution of silicon, polysilicon and silicon dioxide
5.18 Two-dimensional cut of the oxidation growth at a temperature of 1000
o
C showing the newly generated interfaces of the materials
5.19 Two-dimensional cut of the oxidation result at a temperature of 1100
o
C showing the distribution of boron and its segregation behavior at the silicon- silicon dioxide interface
Next:
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PhD - Mustafa Radi
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Acknowledgment
Mustafa Radi
1998-12-11
