Edge Detection in Line-and-Space Patterns Using Second Derivative Profiles
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Solution Overview
Problem
Existing methods for measuring line and space patterns using scanning electron microscopes struggle to accurately distinguish between lines and spaces when their widths are nearly equal, leading to potential misjudgment due to similar tone information.
Innovation Solution
A pattern measurement apparatus and method that creates a line profile, differentiates it twice to generate a second derivative profile, and uses peak positions and values to determine whether an edge is a rising or falling edge, allowing for reliable detection of line patterns even when tones are reversed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the width of line pattern and space pattern are approximately equal, then it is possible to detect edges, but it is difficult to judge whether intervals between edges constitute the line pattern or the space pattern
Solution Approach 1:
The patent changes the parameter used for pattern identification from luminance (tone) information to the shape of the first derivative waveform. By analyzing whether the waveform exhibits a peak or valley at the edge position, the system can reliably distinguish lines from spaces even when their widths are equal and luminance information is ambiguous or reversed.
2Reliability
If luminance information is used to judge line pattern, then it is possible to identify patterns with different tones, but there is a risk of misjudgment when tones are similar or reversed
Solution Approach 1:
The patent introduces the first derivative waveform as an intermediary between the original luminance information and the final pattern identification. This intermediary transformation converts ambiguous luminance differences into distinct waveform characteristics (peak vs. valley), providing a more reliable basis for distinguishing lines from spaces regardless of luminance conditions.
3Measurement precision
If the method of determining edge position by maximum slope or minimum secondary electron signal is used, then edge positions can be detected, but accurate distinction between line and space patterns cannot be achieved when widths are equal
Solution Approach 1:
The patent changes the parameter for pattern type identification from the magnitude of secondary electron signal (luminance) to the shape characteristic of its first derivative. By examining whether the derivative waveform shows a peak or valley at the edge position, the system achieves accurate pattern type identification while maintaining precise edge position measurement capability.
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
Enables accurate identification and measurement of line patterns in line-and-space patterns with equal widths, improving measurement accuracy and reducing errors caused by reversed tone information.
Implementation Method 1
a scanning electron microscope is configured to scan an electron beam scanning range by irradiating incident electrons, to acquire secondary electrons emitted from a sample
Data Source
Figure 1A~1C
Figure 2
Figure 3A~3C
AI summary
A pattern measurement apparatus (100) includes a line profile creating unit (21) for creating a line profile of a pattern formed on a sample (7) by scanning with a charged particle beam (9), a derivative profile creating unit (22) for creating a second derivative profile by differentiating twice the line profile, and an edge detecting unit (23) for judging whether an edge in the pattern is a rising edge or a falling edge by use of two peak positions and two peak values appearing in the vicinity of an edge position of the pattern obtained from the second derivative profile. Assuming that the two peak positions appearing in the vicinity of the edge position of the pattern obtained from the second derivative profile are defined as X1 and X2 , X2 being larger than X1, the edge detecting unit (23) judges that the edge is a rising edge when a signal amount in the peak position X1 is larger than a signal amount in the peak position X2.