- 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 AMIGOS
- 4.1 Block structure of AMIGOS
- 4.2 Several different user perspectives
- 4.3 Flow diagram of AMIGOS 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 AMIGOS
- 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

1998-12-11