Topography Simulation Using Discrete Time Steps
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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 and inaccuracies, especially when predicting complex topographies or high-aspect semiconductor devices, due to the complexity of calculating surface segment flux and movement speed without contradiction, and the transition from two-dimensional to three-dimensional simulations further prolongs calculation time.
Innovation Solution
A topography simulation apparatus and method that sets material topographies at multiple times within a calculation region, allowing independent time development calculations of surface movement amounts to predict the final topography, simplifying the process by dividing time development calculations into smaller, parallelizable steps and using level set functions to calculate surface movement speeds and amounts, thereby enhancing accuracy and reducing calculation time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional topography simulation methods are used to calculate surface segment flux and movement speed, then the simulation can predict material topography changes, but the calculation time becomes excessively long
Solution Approach 1:
The patent segments the continuous topography evolution process into discrete time steps (T1 to TN). By dividing the simulation into N separate calculations at different time points and using interpolation to determine intermediate topographies, the method avoids the need for continuous complex flux calculations, thereby reducing calculation time while maintaining prediction accuracy.
Solution Approach 2:
The patent performs preliminary calculations of topography at N discrete time points T1 to TN before the final simulation completion. These pre-calculated topography states are then used to determine intermediate topographies through interpolation, eliminating the need for real-time complex calculations during the simulation process and significantly reducing overall computation time.
2Measurement precision
If three-dimensional simulations are used to accurately predict complex topographies, then prediction accuracy is improved, but calculation time increases significantly
Solution Approach 1:
The patent segments the three-dimensional topography simulation into discrete time-step calculations. By calculating topography at N specific time points and using interpolation for intermediate states, the method maintains three-dimensional accuracy where needed while avoiding continuous complex computations, thus improving simulation efficiency without sacrificing prediction accuracy.
Solution Approach 2:
The patent applies full three-dimensional simulation only at N critical time points rather than continuously. For intermediate topographies between these time points, simpler interpolation methods are used. This partial application of complex simulation maintains accuracy for critical predictions while significantly reducing overall calculation time and improving productivity.
3Measurement precision
If continuous time development calculations are performed to track surface movement, then accurate topography prediction is achieved, but computational complexity and time increase
Solution Approach 1:
The patent segments continuous surface movement tracking into discrete snapshots at time points T1 to TN. By calculating surface movement between these discrete points and using linear interpolation for intermediate positions, the method achieves accurate surface movement prediction while dramatically reducing calculation complexity compared to continuous tracking.
Solution Approach 2:
The patent performs preliminary calculation of surface movement amounts between discrete time points T1 to TN. These pre-calculated movement data are then used to determine intermediate topographies through simple interpolation, avoiding the need for complex real-time movement calculations and reducing overall computational complexity.
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 topographies of a material at N times T1 to TN (N is an integer of two or more) within a calculation region. The memory further stores instructions executable by the processor to develop the topographies of the material at the times T1 to TN over time independently, calculate first to N-th values respectively representing a change in a topography of the material from the times T1 to TN to times T1′ to TN′, and calculate a topography of the material at time TN+1, based on the first to N-th values.