Semiconductor Surface Roughness Measurement Using Multi-Gaussian Fitting
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Solution Overview
Problem
Existing optical non-contact measurement methods for surface roughness in semiconductor structures, such as those using Gaussian functions, face inaccuracies when the measurement object is curved, leading to discrepancies between calculated and actual surface roughness values.
Innovation Solution
A method involving a multiple Gaussian function fitting of reflected light distributions, where a first Gaussian function accounts for curving and a second Gaussian function accounts for surface roughness, is employed to accurately correlate parameters with the semiconductor structure's surface characteristics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a single Gaussian function is used to fit the reflected light distribution, then the measurement process is simple, but the surface roughness calculation accuracy deteriorates when the measurement object is curved
Solution Approach 1:
The reflected light distribution is segmented into multiple Gaussian functions (at least two: first and second Gaussian functions) with different standard deviations. The first Gaussian function accounts for the curving effect while the second accounts for the surface roughness, allowing separate analysis of these two factors that previously contaminated each other in a single-Gaussian approach.
Solution Approach 2:
The measurement approach changes from using a single Gaussian parameter (standard deviation) to using multiple Gaussian parameters with different standard deviations. By varying the number and standard deviations of the Gaussian functions in the fitting model, the system can distinguish between curving effects and roughness effects, thereby improving measurement accuracy without excessive complexity.
2Loss of time
If a single Gaussian function is used for fitting, then the calculation is computationally simple, but the separation of curving and roughness effects is insufficient
Solution Approach 1:
The fitting calculation is segmented into multiple Gaussian components that can be processed separately. Each Gaussian function targets a specific physical effect (curving or roughness), allowing the calculation to isolate and measure each effect independently rather than trying to extract both from a single composite parameter.
Solution Approach 2:
The patent uses at least two Gaussian functions, which is more than the single function traditionally used. This excessive action (using more functions than the minimum one) provides the additional degrees of freedom needed to separately characterize both curving and roughness, achieving better separation accuracy while keeping the computational burden manageable.
3Ease of operation
If conventional optical measurement is used on curved surfaces, then non-contact measurement is achieved, but the surface roughness value deviates from actual contact measurement values
Solution Approach 1:
The curving effect is extracted and accounted for separately using the first Gaussian function before measuring the surface roughness. By removing the curving component from the reflected light distribution analysis, the remaining analysis can accurately measure the true surface roughness without the contamination that previously caused deviation from contact measurement values.
Solution Approach 2:
The measurement model changes from a single-parameter Gaussian fit to a multi-parameter fit with different standard deviations. This parameter change allows the system to maintain non-contact measurement capability while achieving accuracy that agrees with contact measurement by properly accounting for the curving geometry through the first Gaussian function.
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 allows for high-accuracy correlation of surface roughness and curving amounts, improving the quality management of semiconductor structures by separating the influences of curving and roughness in reflected light distributions, enabling efficient detection of defective structures.
Implementation Method 1
irradiating a surface of the semiconductor structure with a light from a light source in an oblique direction to the surface, and detecting a reflected light reflected or scattered by the surface
Implementation Method 2
detecting a reflected light reflected or scattered by the surface
Data Source
AI summary
There is provided a method for manufacturing a semiconductor structure, including: preparing a plate-like semiconductor structure; and inspecting the semiconductor structure, the inspection of the semiconductor further including: performing a measurement of irradiating a surface of the semiconductor structure with a light from a light source in an oblique direction to the surface, and detecting a reflected light reflected or scattered by the surface by a two-dimensional detector, at a plurality of locations within at least a predetermined range of the surface of the semiconductor structure, to acquire a reflected light distribution that is a distribution of an integrated value obtained by integrating intensity of the reflected light measured at the plurality of locations, with respect to a position at the detector; and fitting the reflected light distribution by a multiple Gaussian function obtained by adding at least a first Gaussian function and a second Gaussian function distributed more widely than the first Gaussian function, to acquire a parameter of the second Gaussian function as an index corresponding to a surface roughness of the semiconductor structure.