Semiconductor Defect Density Modeling for Real-Scale Pattern Prediction
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Solution Overview
Problem
Existing methods struggle to predict crystal defect distribution in actual pattern sizes within realistic calculation time, particularly for low-density defects, which affects the accuracy of transistor and pixel characteristics in semiconductor devices.
Innovation Solution
A defect density calculation method and apparatus that utilize an arithmetic function based on activation energy, processing temperature, and time to predict the temporal change of defect density distribution in semiconductor layers, enabling accurate prediction within realistic time frames.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If simulation is used to predict crystal defect distribution, then prediction capability is improved, but calculation time becomes excessively long for actual pattern sizes
Solution Approach 1:
The patent changes the fundamental parameters of the calculation model by switching from atomistic simulation parameters to continuum mechanics parameters. The defect density distribution is calculated using partial differential equations with parameters such as defect generation rate, recombination rate, and diffusion coefficient, rather than simulating individual atom movements. This parameter transformation enables calculation of actual pattern sizes within realistic time frames while maintaining prediction accuracy.
Solution Approach 2:
The patent replaces the mechanical simulation system (atomistic modeling) with a mathematical field theory system (continuum mechanics). Instead of mechanically tracking each atom's position and interaction, the system uses field-based partial differential equations to describe defect density distribution evolution, achieving the same predictive goal with dramatically reduced computational complexity.
2Measurement precision
If detailed distribution of low-density crystal defects is measured, then measurement precision is improved, but measurement difficulty increases significantly
Solution Approach 1:
The patent creates a mathematical model (copy) of the defect density distribution evolution process based on continuum mechanics. Instead of directly measuring the difficult-to-detect low-density defects, the system calculates a model that replicates the defect distribution behavior under various conditions, providing indirect but accurate information about the defect patterns without the measurement difficulties.
Data Source
AI summary
A defect density calculation method according to one embodiment of the present disclosure is a method of calculating a temporal change of the defect density distribution in a semiconductor layer. The method includes calculating the temporal change of the defect density distribution on the basis of an arithmetic function using at least the activation energy of a detect included in the semiconductor layer, the processing temperature of the semiconductor layer, and the processing time of the semiconductor layer as arguments.