CMP Polishing Frequency Analysis via Binary Matrix Conversion
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Solution Overview
Problem
Conventional methods for evaluating polishing frequency and number of polishing times in chemical mechanical planarization (CMP) are complex and difficult to apply, especially for non-circular polishing pads and planet paths, leading to uneven wafer surface planarization and limited endpoint detection capabilities.
Innovation Solution
A method involving image processing to convert polishing pad and wafer drawings into pixel arrays, then binary matrices, allowing for coordinate transformation and superposition of effective polishing times across different polishing pad profiles and paths, enabling the evaluation of effective polishing frequency and number of polishing times.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional finite element method is used to evaluate pressure field distribution and speed distribution, then polishing process can be analyzed, but the evaluation becomes complex involving complicated integration and difficult to implement for non-circular polishing pads
Solution Approach 1:
The patent creates a simplified mathematical model that copies the essential geometry of the polishing pad and wafer, representing them as overlapping circular regions defined by center coordinates and radii. This simplified model replaces the complex finite element geometry while preserving the key spatial relationships needed for polishing frequency calculation, making the evaluation tractable for non-circular and irregular polishing pad profiles
Solution Approach 2:
The patent transforms the evaluation from a complex spatial integration problem into a parameter-based calculation by defining polishing frequency as a function of key parameters: polishing pad radius, wafer radius, rotation speeds, and center positions. This parameterization approach allows efficient calculation of effective polishing frequency without performing complicated integration over complex geometries
2Manufacturing precision
If planet path with identical rotating speeds is used for CMP, then mechanical polishing can be performed, but the polishing pad incompletely covers the wafer resulting in uneven distribution of polishing times
Solution Approach 1:
The patent introduces differential rotation where the polishing pad and wafer rotate at different speeds (ωp ≠ ωw), creating a dynamic scanning motion that ensures every point on the wafer surface is visited by the polishing pad over time. This dynamic approach replaces the static identical-speed planet path, achieving uniform polishing time distribution across the entire wafer surface while maintaining complete coverage
Solution Approach 2:
The patent utilizes periodic relative motion between the polishing pad and wafer, where the differential rotation creates a periodic scanning pattern that systematically covers all points on the wafer surface. This periodic action ensures that each point receives the required number of polishing passes, achieving uniform effective polishing times across the wafer while maintaining complete coverage
3Measurement precision
If compensating CMP with wafer disposed above pad is used, then direct measurement during polishing is helped, but the available number of measurement positions is still limited and global planarization detection is not easily achieved
Solution Approach 1:
The patent develops a universal evaluation method that can assess effective polishing frequency and time distribution across the entire wafer surface simultaneously, rather than requiring multiple separate measurements at different positions. This multi-functional approach enables both local endpoint detection and global planarization assessment through a single integrated framework, overcoming the limitation of limited measurement positions
Data Source
AI summary
A method for analyzing polishing frequency and number of polishing times for chemical planarization polishing wafer with different polishing pad profiles is disclosed. First, drawings of a wafer and a polishing pad are provided and then are converted into pixel arrays. Pixel arrays are processed to be black/white images. The black/white images are converted into binary matrices. The effective polishing frequencies of all points in the binary matrix are calculated. Following the calculated polishing frequencies, the coordinates of all binary matrices are redefined according to a displacement condition, and then new coordinates of all points and corresponding effective numbers of polishing times for a time increment are calculated so as to form an effective polishing times matrix for the time increment. Further, all effective numbers of polishing times within a total polishing time interval are added together.