Topography Simulation Using Level Set Function Updates
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Solution Overview
Problem
Current topography simulation methods for materials processed by chemical vapor deposition (CVD) or reactive ion etching (RIE) face long calculation times due to the need to process multiple surface segments and repeatedly calculate time development, which can be inefficient, especially when using methods like Radiosity or direct simulation Monte Carlo (DSMC).
Innovation Solution
A topography simulation apparatus and method that sets a function indicating the position relationship between points in a calculation region and a material surface, determines particle collisions with the surface, and updates the function value upon collision, allowing for faster calculation of topography changes using a level set function and direct simulation Monte Carlo (DSMC) method, reducing calculation time by updating the function only when collisions occur.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional methods (Radiosity or DSMC) are used to process multiple surface segments and repeatedly calculate time development, then topography simulation accuracy is maintained, but calculation time becomes excessively long
Solution Approach 1:
The patent divides the material surface into multiple surface segments and assigns a level set function value to each segment. This segmentation allows the simulation to track topography changes at discrete locations independently, enabling efficient calculation while maintaining accuracy. Each surface segment's level set function value is updated based on particle collision events, avoiding the need to process all segments at every time step.
Solution Approach 2:
The patent implements time development calculation by periodically updating level set function values at discrete time intervals. Instead of continuous calculation, the system updates the level set function values at surface segments at specific time steps, and particle trajectories are recalculated between updates. This periodic action significantly reduces computation time while preserving the essential topography evolution.
2Manufacturing precision
If the level set function is updated at every time step for all surface segments, then topography change accuracy is improved, but computation cost increases significantly
Solution Approach 1:
The patent applies local quality by updating level set function values only at surface segments where particle collisions occur, rather than uniformly updating all segments at every time step. The level set function value at each surface segment is updated based on the local particle flux and collision events at that specific location. This localized update approach maintains topography accuracy at critical regions while minimizing unnecessary computations elsewhere.
Solution Approach 2:
The simulation system automatically identifies which surface segments require level set function updates by detecting particle collision events. The system self-adapts the calculation effort to match the actual physical activity - updating only where particles interact with the surface, and skipping updates at segments experiencing no collisions. This self-service mechanism eliminates wasted computation on inactive regions.
3Measurement precision
If particle trajectories are calculated continuously without optimization, then collision detection accuracy is maintained, but calculation efficiency decreases
Solution Approach 1:
The patent performs preliminary calculation of particle trajectories from the source to the material surface before detailed collision analysis. By pre-calculating the paths particles would take based on the initial topography, the system can efficiently determine which surface segments are likely to be hit. This preliminary trajectory calculation allows the simulation to focus computational resources on relevant collision events rather than exhaustively checking all possible particle-surface interactions.
Data Source
AI summary
A topography simulation apparatus includes a processor and a memory connected to the processor. The memory stores instructions executable by the processor to set a function indicating a position relationship between a point in a calculation region and a material surface in the calculation region. The memory stores further instructions executable by the processor to determine whether or not a particle moving in the calculation region collides with the material surface, and update a value of the function, responsive to determining that the particle collides with the material surface.