Multi-Point Probe Position Correction for Finite Samples
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Solution Overview
Problem
Current position correction methods for multi-electrode probe measurements fail when measuring non-infinite or multi-layered samples, especially near boundaries or when the sample size is comparable to the probe, leading to geometrical errors and distorted measurements.
Innovation Solution
A method and system using a multi-point probe with multiple probe arms and electrodes to perform resistance measurements, establishing a resistance model that accounts for finite or multi-layered samples, and using data fitting to determine precise electrode positions by minimizing an error function based on measured and predicted resistance differences.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If prior art position correction methods (van der Pauw, Worledge) are used, then measurement is simple for infinite single-layer samples, but measurement accuracy deteriorates for finite or multi-layered samples near boundaries
Solution Approach 1:
The invention changes the fundamental parameters of the resistance model from assuming infinite single-layer samples to accounting for finite sample dimensions and multi-layered structures. The model incorporates sample boundary conditions, layer thicknesses, and inter-layer spacing as variable parameters that are fitted to measurement data, enabling accurate measurements for samples of any geometry or layer structure.
Solution Approach 2:
The invention introduces a dynamic, adaptive modeling approach where the resistance model is not fixed but is instead fitted to the specific sample configuration being measured. The model parameters (sample dimensions, layer properties, electrode positions) are dynamically determined through non-linear least squares fitting of measured resistance values, allowing the same model to accurately represent different sample types.
2Reliability
If ideal infinite single-layer sample assumption is made, then position correction works adequately, but measurement reliability deteriorates when sample size is comparable to probe or near boundaries
Solution Approach 1:
The invention creates a universal resistance model that can handle multiple sample configurations (infinite, finite, single-layer, multi-layered, near-boundary conditions) within a single framework. The model automatically adapts to the specific sample type through parameter fitting, eliminating the need for different correction methods for different sample geometries.
Solution Approach 2:
The invention performs preliminary characterization of the sample by fitting the resistance model to measurement data before final parameter extraction. This preliminary fitting step determines accurate electrode positions and sample geometry parameters, which then serve as the basis for reliable electrical parameter measurement, ensuring the model is properly calibrated to the specific sample being measured.
3Adaptability or versatility
If multi-layered samples or finite samples are measured, then measurement versatility is improved, but measurement accuracy deteriorates due to boundary effects and current redistribution
Solution Approach 1:
The invention explicitly incorporates sample boundary conditions and multi-layer structure parameters into the resistance model. Instead of ignoring these effects, the model includes terms for finite sample dimensions, sample boundaries, layer thicknesses, and inter-layer resistances, allowing accurate measurement of samples with these complex geometries.
Solution Approach 2:
The invention uses an iterative feedback process where measured resistance values are compared to model predictions, and the model parameters are adjusted through non-linear least squares fitting to minimize the difference between measured and calculated resistances. This feedback loop ensures the model accurately represents the actual sample configuration, compensating for boundary effects and current redistribution in multi-layered structures.
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 accurate position correction and precise electrical parameter determination for multi-layered samples and samples near boundaries, improving measurement accuracy and reducing geometrical errors.
Implementation Method 1
A method of establishing specific electrode positions by providing a multi-point probe and a test sample... performing at least four different resistance measurements... applying a current propagating through the test sample between the first pair of electrodes... detecting an voltage induced between the second pair of electrodes
Data Source
AI summary
The present invention relates to a method of establishing specific electrode positions by providing a multi-point probe and a test sample. The method comprises the measuring or determining of a distance between two of the electrodes of the multi-point probe and establishing a resistance model representative of the test sample. The method further comprises the performing of at least three different sheet resistance measurements and establishing for each of the different sheet resistance measurement a corresponding predicted sheet resistance based on the resistance model. Thereafter the method comprises the establishment of a set of differences constituting the difference between each of the predicted sheet resistance and its corresponding measured sheet resistance, and deriving the specific electrode positions of the multi-point probe on the surface of the test sample by using the distance and performing a data fit by minimizing an error function constituting the sum of the set of differences.