Ellipsometry Method for Curved Surface Analysis
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Solution Overview
Problem
Existing ellipsometry methods are complex and inefficient for measuring curved surfaces, as they require precise alignment of the sample surface normal with the ellipsometer's reference axis, limiting their applicability to unknown or arbitrary sample geometries.
Innovation Solution
The method involves setting the output and input rotation angles as independent parameters in the equation system, allowing for the calculation of sample properties by solving an overdetermined equation system, which improves measurement accuracy and allows for high spatial resolution imaging of curved or tilted surfaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If the sample surface normal is precisely aligned with the ellipsometer reference axis, then the measurement can be performed with conventional methods, but the method becomes inapplicable to curved surfaces or unknown geometries
Solution Approach 1:
The patent changes the parameter approach by introducing rotation matrices to account for tilted sample surfaces. Instead of requiring precise alignment, the method uses measured Mueller matrices combined with rotation transformations to handle arbitrary surface orientations, thereby extending applicability to curved surfaces while reducing alignment complexity requirements
Solution Approach 2:
The patent introduces rotation matrices as intermediary mathematical tools that bridge the gap between measured Mueller matrices and sample properties. These rotation matrices act as mediators that transform the measurement coordinate system to match the sample's actual orientation, enabling accurate measurements without precise physical alignment
2Measurement precision
If conventional ellipsometry methods are used for curved surfaces, then measurement can be performed, but the measurement time increases and precision decreases
Solution Approach 1:
The patent applies partial action by measuring only the necessary components of the Mueller matrix and using a reduced equation system. By focusing on the essential measurement data and using optimized mathematical processing, the method achieves high precision while reducing measurement time compared to conventional complete-scan methods
3Measurement precision
If the equation system is underdetermined, then fewer parameters are needed, but the solution is not unique and precision is reduced
Solution Approach 1:
The patent creates an overdetermined equation system by measuring multiple components of the Mueller matrix and using rotation matrix transformations. This copying of measurement data into a richer mathematical framework provides redundant information that ensures unique and precise solutions, even though the equation system becomes more complex
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 enables precise determination of optical and geometric sample properties for arbitrary geometries with shorter measurement times and improved conformance with real values, even for unknown sample geometries, by allowing independent rotation angles in the equation system.
Implementation Method 1
a potentially widened laser beam, with a defined polarization state is directed onto the sample, namely onto a partial region of its surface referred to here as the measuring region, and the change in the polarization state of the electromagnetic radiation after interaction with or reflection from the sample is measured
Implementation Method 2
the angle-dependent reflection behavior of the sample... the change in the polarization state of the electromagnetic radiation after interaction with or reflection from the sample is measured
Data Source
AI summary
A method for determining properties of a sample (12) by ellipsometry includes positioning the sample (12) in an ellipsometer (10) so that a surface normal (n) of a measurement region of the sample surface is tilted relative to a reference axis (z) of the ellipsometer (10) and measuring a Mueller matrix for the measurement region. The method then includes creating an equation system by equating the measured Mueller matrix and a matrix product formed of: a rotation matrix about an input rotation angle (γ); an isotropic Mueller matrix in normalized NCS form and a rotation matrix about an output rotation angle (−δ). The method then solves the equation system for the parameters representing the sample properties to be determined. The input rotation angle (γ) and the output rotation angle (−δ) are set as parameters independent of one another when setting up the equation system.