Single-Crystal Substrate Bowing Measurement via X-ray Flux Width Variation
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Solution Overview
Problem
Conventional methods for measuring the bowing of single-crystal substrates are inadequate as they either observe only the exterior appearance or require moving the substrate, leading to errors due to deviations in movement direction and distance, and do not accurately measure the crystal lattice plane bowing.
Innovation Solution
The method involves changing the width of the X-ray flux incident on the specimen to measure the rocking curve width, allowing for the determination of the curvature radius without translating the substrate, by plotting the X-ray irradiation width and rocking curve width on a coordinate system and calculating the gradient of the resulting shift line.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Area of stationary object
If the substrate is moved to measure bowing at multiple positions, then measurement coverage is improved, but measurement precision deteriorates due to deviations in movement direction and distance
Solution Approach 1:
Instead of moving the substrate to measure different positions, the invention inverts the approach by keeping the substrate stationary and moving the X-ray measurement system. This eliminates positioning errors associated with substrate movement while achieving comprehensive measurement coverage through systematic scanning of the measurement beam across the substrate surface.
Solution Approach 2:
The invention introduces a collimated X-ray beam as an intermediary measurement tool that can be precisely positioned and scanned across the substrate without moving the substrate itself. This intermediary measurement system enables accurate bowing measurement at multiple virtual positions while the substrate remains stationary, avoiding mechanical positioning errors.
2Device complexity
If exterior appearance is observed using laser beams, then measurement simplicity is improved, but measurement precision deteriorates because crystal lattice plane bowing is not measured
Solution Approach 1:
The invention replaces mechanical/optical observation methods (laser beams reflecting off the surface) with X-ray diffraction measurement. X-rays interact with the crystal lattice planes themselves, enabling direct measurement of lattice plane bowing rather than just surface appearance, thereby achieving higher measurement precision while maintaining reasonable system complexity.
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 improves the reliability of bowing measurement by eliminating the need for substrate movement and provides accurate evaluation of the curvature radius, enhancing the sensitivity and precision of the measurement process.
Implementation Method 1
irradiating a surface of a target object with X-rays in a position under measurement to acquire a rocking curve
Data Source
AI summary
At least two values of an X-ray irradiation width are set for a single specimen. A rocking curve is measured for each of the X-ray irradiation widths. A rocking curve width value is determined for each of the rocking curves. The values of the X-ray irradiation width and the values of the rocking curve width are plotted on a planar coordinate system having a vertical axis representing the rocking curve width value and a horizontal axis representing the X-ray irradiation width value, and a rocking curve width shift line is determined based on the plotted points. A gradient of the rocking curve width shift line is determined. A curvature radius of the specimen is determined based on the gradient. The amount of bowing of a single-crystal substrate under measurement can be measured without a need to move the single-crystal substrate for reliable measurement with a small amount of error.