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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Optimization of Graphical Parameter Extraction Algorithm for Chip-Level CMP Prediction Model Based on Effective

Bowen Ren1,2, Lan Chen1, Rong Chen1

  • 1The EDA Center, Institute of Microelectronics of Chinese Academy of Sciences, Beijing 100029, China.

Micromachines
|April 27, 2024
PubMed
Summary
This summary is machine-generated.

Chemical mechanical polishing (CMP) faces challenges with pattern effects impacting chip thickness. This study introduces a density correction and line contact deformation profile to enhance CMP prediction models, significantly improving accuracy.

Keywords:
HKMGdensity correctiondie-scale CMP modeleffective planarization length (EPL)layout extractionlayout-dependent effects

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Area of Science:

  • Materials Science
  • Semiconductor Manufacturing
  • Computational Modeling

Background:

  • Chemical Mechanical Polishing (CMP) is crucial for semiconductor planarization but suffers from pattern-dependent variations in material thickness.
  • These variations, known as layout-dependent effects (LDE), significantly impact integrated circuit performance and manufacturing yield.
  • Current models for predicting post-CMP morphology often rely on graphic parameter extraction, which inadequately captures complex layout pattern interactions.

Purpose of the Study:

  • To develop an improved method for predicting post-CMP chip morphology by addressing limitations in existing layout-dependent effect (LDE) models.
  • To enhance the accuracy of CMP prediction models by incorporating a novel density correction and weighting function.
  • To validate the effectiveness of the proposed optimization method against experimental silicon data.

Main Methods:

  • Calculated average density as a density correction factor to account for pattern effects.
  • Introduced a one-dimensional line contact deformation profile as a weighting function to better describe pattern interactions.
  • Applied the density correction method to a high-K metal gate-CMP prediction model based on density step-height.
  • Compared surface prediction results with and without the optimization against silicon data.

Main Results:

  • The optimized CMP prediction model demonstrated a significant reduction in prediction errors.
  • Achieved a 40.1% decrease in mean squared error (MSE) for oxide height predictions.
  • Achieved a 35.2% decrease in MSE for aluminum (Al) height predictions compared to pre-optimization results.
  • Validated the improved accuracy through direct comparison with experimental silicon data.

Conclusions:

  • The proposed density correction and line contact deformation profile effectively enhance CMP prediction models.
  • The optimization method significantly improves the accuracy of predicting post-CMP chip morphology.
  • This advancement is critical for design verification and manufacturing development in the semiconductor industry.