Eddy Current Sensor Calibration for CMP Thickness Measurement
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Solution Overview
Problem
Existing methods for determining the thickness of conductive layers on wafers in CMP processes face challenges in accuracy, particularly at low and high thickness ranges, with eddy current sensors struggling to provide reliable measurements due to non-monotonic functions and high error rates when using modulus of impedance or polynomial curve fits.
Innovation Solution
The use of an eddy current sensor calibrated to measure magnetic flux density changes, combined with a calibration curve that correlates thickness to measured values using an analytic function with infinite order terms or smooth piecewise continuous interpolation, allowing for accurate thickness calculation within 5% error across a wide range of thicknesses from 1 kÅ to 20 kÅ.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If polynomial curve fits or modulus of impedance are used for calibration, then the calibration process is simple, but measurement precision deteriorates at low and high thickness ranges
Solution Approach 1:
The calibration curve is divided into multiple segments, each corresponding to a specific thickness range. Different mathematical functions are applied to different segments: a first function for low thickness ranges, a second function for intermediate ranges, and a third function for high thickness ranges. This segmentation allows each segment to be optimized for its specific range, resolving the contradiction by maintaining measurement precision across the entire thickness spectrum while keeping each individual calibration segment relatively simple.
Solution Approach 2:
Different mathematical functions with different characteristics are applied to different thickness ranges. The first function is optimized for low thickness measurements, the second for intermediate ranges, and the third for high ranges. This local optimization ensures that each region of the measurement spectrum has the appropriate calibration characteristics, thereby maintaining high measurement precision across all thickness values while avoiding the need for a single overly complex calibration model.
2Device complexity
If a single mathematical function is used for the entire thickness range, then the calibration model is simple, but measurement precision deteriorates across different thickness ranges
Solution Approach 1:
The calibration model is segmented into multiple functions, each valid for a specific thickness range. The system determines which segment applies based on the measured thickness value and uses the corresponding function for calculation. This approach maintains reasonable model complexity by limiting each individual function to a specific range where it performs well, while achieving high overall precision through the combination of multiple specialized functions.
Solution Approach 2:
The calibration model dynamically selects which mathematical function to apply based on the measured thickness value. The system transitions between different calibration functions as the thickness varies, allowing the model to adapt to different measurement conditions. This dynamic approach resolves the contradiction by maintaining simplicity within each local range while achieving high precision across the entire thickness spectrum through adaptive function selection.
3Speed
If eddy current sensors are used for thickness measurement, then measurement speed is fast, but measurement precision deteriorates due to non-monotonic functions and high error rates
Solution Approach 1:
The patent transforms the eddy current sensor output parameters (which exhibit non-monotonic behavior) into a different parameter space through the segmented calibration functions. By applying range-specific mathematical transformations, the system converts the complex non-monotonic impedance data into accurate thickness values. This parameter transformation maintains the fast measurement speed of eddy current sensing while eliminating the precision problems caused by non-monotonic response characteristics.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach provides accurate and reliable thickness measurements, minimizing error across a broad range of conductive layer thicknesses, enabling precise control in CMP processes and reducing the need for frequent recalibration.
Implementation Method 1
measuring a magnetic flux density change when the conductive layer on the workpiece is in a magnetic field
Implementation Method 2
when the conductive layer on the workpiece is in a magnetic field
Data Source
AI summary
Methods and apparatuses for calibrating eddy current sensors. A calibration curve is formed relating thickness of a conductive layer in a magnetic field to a value measured by the eddy current sensors or a value derived from such measurement, such as argument of impedance. The calibration curve may be an analytic function having infinite number terms, such as trigonometric, hyperbolic, and logarithmic, or a continuous plurality of functions, such as lines. High accuracy allows the omission of optical sensors, and use of eddy current sensors for endpoint detection, transition call detection, and closed loop control in which a process parameter is changed based on the measured magnetic flux density change in one or more processing zones.