Liquid-Solid Interface Morphology Calculation via Resistivity
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Solution Overview
Problem
Current methods for calculating the liquid-solid interface morphology during crystal growth, such as the Czochralski method, are complex, costly, and time-consuming, especially when dealing with curved interfaces, which are common in semiconductor crystal production.
Innovation Solution
A method involving the detection of electrical resistivity at multiple sampling locations on a wafer, calculation of doping concentrations and height differences, and illustration of the liquid-solid interface morphology using these measurements, which allows for the determination of the interface shape without the need for invasive procedures like slicing and polishing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional methods (slicing and polishing) are used to analyze liquid-solid interface morphology, then measurement precision can be achieved, but device complexity and manufacturing cost increase significantly
Solution Approach 1:
The patent replaces mechanical slicing and polishing operations with electrical resistivity measurement and mathematical calculation. Instead of physically cutting the crystal to expose the interface, the method uses electrical probes to measure resistivity at different radial positions on the crystal surface, then calculates the interface morphology through doping concentration distributions and segregation coefficient relationships. This substitution eliminates complex mechanical processing while achieving equivalent or superior measurement precision.
2Measurement precision
If conventional slicing and polishing methods are employed, then interface morphology can be observed, but production time and cost increase
Solution Approach 1:
The patent creates an electrical resistivity map of the crystal surface that serves as a proxy for the physical interface morphology. By measuring resistivity at multiple radial positions and using the known relationship between doping concentration, segregation coefficient, and interface position, the method reconstructs the interface shape without physical destruction. This copying approach through electrical properties enables rapid, non-destructive measurement that preserves the crystal while providing accurate morphology data.
3Ease of operation
If electrical resistivity measurement method is used, then operation simplicity and cost reduction are achieved, but measurement precision may be compromised
Solution Approach 1:
The patent transforms the measurement parameter from direct physical geometry (interface shape) to electrical property (resistivity distribution). By measuring resistivity at multiple radial positions and using the established relationship between resistivity, doping concentration, and interface position through the segregation coefficient, the method converts an complex geometric measurement problem into a series of simple electrical measurements combined with mathematical calculation, maintaining precision while improving ease of operation.
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 method simplifies the process, reduces costs, and provides a more efficient way to analyze the morphology of liquid-solid interfaces during crystal growth, enabling the production of high-quality ingots with curved interfaces by using electrical resistivity measurements and doping concentration calculations.
Implementation Method 1
detecting electrical resistivity at the plural sampling locations
Implementation Method 2
The wafer comprises a dopant
Implementation Method 3
k0 is the segregation coefficient of the dopant in the silicon
Data Source
AI summary
The present invention provides a method for calculating the liquid-solid interface morphology during growth of the ingot. The method comprises providing a wafer, selecting plural sampling locations on the wafer and detecting electrical resistivity at the plural sampling locations, calculating height differences between the sampling locations based on the detected electrical resistivity, and illustrating the morphology of the liquid-solid interface based on the calculated height differences. The method of the invention has advantages including easy operation and low cost.