CMP Pressure Control Using Constrained Cost Optimization
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Solution Overview
Problem
Chemical mechanical polishing (CMP) processes face challenges in achieving uniform material removal rates across substrates due to variations in initial thickness, slurry composition, polishing pad condition, relative speed, and load, leading to non-uniformity and profile inconsistencies.
Innovation Solution
A computer program product and method that utilizes an in-situ monitoring system to determine characterizing values for substrate regions, calculates polishing rates, and adjusts processing parameters in real-time using a constrained optimization algorithm to minimize a cost function, considering future pressure changes and constraints, thereby optimizing pressure differentials and achieving target thickness profiles.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional CMP control methods are used, then the polishing process is simple to operate, but within-wafer non-uniformity and edge exclusion occur due to variations in material removal rate
Solution Approach 1:
The carrier head is divided into multiple independently controllable chambers (e.g., first, second, third chambers) that can apply different pressures to different regions of the substrate. This segmentation allows localized pressure adjustments to compensate for material removal rate variations across the wafer surface, reducing within-wafer non-uniformity and edge exclusion while maintaining overall system manageability.
Solution Approach 2:
The control system dynamically adjusts chamber pressures in real-time based on monitored polishing rates. The system calculates pressure adjustments using a cost function that considers current polishing rates, target polishing rates, and future pressure changes, enabling adaptive compensation for thickness variations and slurry composition changes throughout the polishing process.
2Manufacturing precision
If frequent pressure adjustments are made to achieve target thickness profiles, then polishing uniformity improves, but pressure differentials between chambers increase causing instability
Solution Approach 1:
The control system calculates expected future polishing rates and pressure requirements in advance using a cost function that looks ahead to future time points. By anticipating future needs and preparing pressure adjustments beforehand, the system can achieve target thickness profiles more smoothly while avoiding sudden large pressure differentials that would cause instability.
Solution Approach 2:
The cost function includes terms that penalize large pressure changes and pressure differentials between chambers. This beforehand cushioning approach limits the magnitude of pressure adjustments by incorporating constraints on maximum pressure changes and differential pressures, preventing excessive pressure differentials while still achieving the desired thickness profile control.
3Manufacturing precision
If real-time monitoring and adjustment is implemented, then material removal rate variations are compensated, but computational complexity and processing time increase
Solution Approach 1:
The system transforms the complex multi-variable control problem into a parameter optimization problem by defining a cost function with specific parameters (current polishing rates, target polishing rates, pressure changes, pressure differentials). This parameter-based approach simplifies the real-time control calculations while maintaining the ability to compensate for material removal rate variations through systematic optimization of these key parameters.
Data Source
AI summary
Controlling a polishing system includes receiving from an in-situ monitoring system, for each region of a plurality of regions on a substrate being processed by the polishing system, a sequence of characterizing values for the region. For each region, a polishing rate is determined for the region, and an adjustment is calculated for at least one processing parameter. Calculation of the adjustment includes minimizing a cost function that includes, for each region, a difference between a current characterizing value or an expected characterizing value at an expected endpoint time and a target characterizing value for the region, and optimization of the cost function is subject to at least one constraint.