Atomic-Scale Uniform Grid for Moving Semiconductor Boundaries
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for modeling temporal processes in CAD and EDA systems, such as semiconductor fabrication, face challenges with irregular grids near boundaries, leading to increased computing time and difficulty in parallelization, especially for moving-boundary problems like silicon-silicon oxide interfaces during oxide growth.
Innovation Solution
A system that imposes a uniform grid of nodes with spacing less than the quantum separation distance in silicon, allowing for efficient simulation of temporal processes by iterating through time steps and representing boundary movement by changing particle types assigned to nodes, applicable to both partial differential equations and discrete time probability equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If an irregular grid of nodes is used to fit curved boundaries, then the accuracy of boundary representation is improved, but the computing time increases and parallelization becomes difficult
Solution Approach 1:
The patent changes the grid structure from irregular to regular/uniform, transforming the problem from geometric fitting to numerical approximation. This parameter change allows the use of standard numerical methods on structured grids while maintaining sufficient accuracy through appropriate grid spacing and boundary condition handling.
2Measurement precision
If a new grid of nodes is generated for each time step in moving-boundary problems, then the accuracy of moving boundary representation is improved, but the computational complexity and time consumption increase
Solution Approach 1:
The patent performs preliminary action by establishing a fixed regular grid once at the beginning of the simulation. Instead of regenerating the grid at each time step, the method tracks material boundaries and updates particle types within the pre-established grid framework, significantly reducing computational complexity.
Solution Approach 2:
The patent applies dynamics by allowing the material boundaries and particle types to evolve dynamically within the static grid framework. As the simulation progresses, particles change types based on boundary movement and material transformations, enabling accurate representation of moving boundaries without grid regeneration.
3Measurement precision
If an irregular matrix is used to solve continuity equations on irregular grids, then the accuracy of boundary modeling is improved, but the difficulty of parallelization increases
Solution Approach 1:
The patent transforms the problem from irregular to regular by changing the grid structure parameter. This allows the use of structured matrices and standard numerical linear algebra techniques that are well-suited for parallel computation, while boundary accuracy is maintained through appropriate boundary condition implementation and grid spacing selection.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
Roughly described, a system for simulating a temporal process in a body includes a meshing module to impose a grid of nodes on the body, the grid having a uni-form node spacing which is less than the quantum separa-tion distance in silicon. A system of node equations is provided, including at least one node equation for each of a plurality of nodes of the grid. The node equations describe behavior of at least one physical quantity at that node through each time step of the process. An iterati ng module iterates through the time steps to determi ne val ues for physical quantities of the body at the end of the simulation peri-od. Preferably one particle of the body is assigned to each node of the grid. For moving boundary processes, boundary movement can be represented simply by changing the particle type assigned to various nodes of the grid as the boundary advances.