Digital Twin Wafer Temperature Estimation with Minimal Sensors
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Solution Overview
Problem
Existing methods for measuring temperature distribution during rapid thermal processing of semiconductor wafers are inaccurate and costly, requiring numerous sensors that introduce thermal resistance and emissivity changes, leading to non-uniform temperature calculations and increased production costs.
Innovation Solution
A digital twin-based method and apparatus that builds a numerical model for thermal behavior, adjusts noise with regularization parameters, generates a sensitivity coefficient matrix, and estimates temperature distribution using minimal point measurement data, allowing for precise temperature uniformity calculation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If numerous thermocouple sensors are used to measure the entire temperature of a wafer, then temperature measurement coverage is improved, but thermal resistance error increases and production cost rises
Solution Approach 1:
The patent creates a virtual copy (digital twin) of the physical wafer that replicates its thermal behavior. Instead of measuring temperature at multiple physical points, the system uses a single physical sensor's data to drive a numerical model that generates temperature values for the entire wafer surface, effectively copying the measurement capability to all locations without additional sensors
Solution Approach 2:
The patent replaces the mechanical/physical measurement system (multiple thermocouple sensors) with a computational system. A numerical model based on heat transfer equations processes data from a single sensor to estimate temperatures across the entire wafer, substituting physical measurement infrastructure with mathematical modeling
2Ease of operation
If a pyrometer is used to measure temperature distribution, then non-contact measurement is achieved, but measurement precision deteriorates due to changing emissivity during rapid thermal processing
Solution Approach 1:
The patent introduces a numerical model as an intermediary between the single physical sensor and the wafer temperature field. The model acts as a mediator that translates the limited sensor data into comprehensive temperature distribution information, overcoming the limitations of both direct pyrometer measurement and multiple sensor approaches
Solution Approach 2:
The patent changes the approach from directly measuring temperature at multiple points to measuring at one point and computationally deriving other temperatures. The system transforms the measurement problem by changing from spatial distribution measurement to temporal measurement at a single location combined with mathematical modeling
3Device complexity
If point measurement temperature data is used, then sensor requirements are reduced, but temperature distribution estimation accuracy deteriorates
Solution Approach 1:
The patent performs preliminary actions by pre-building a numerical model of the wafer's thermal characteristics before actual measurement. The model is prepared in advance with known thermal properties and geometry, enabling accurate temperature distribution estimation from minimal measurement data during 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
Enables accurate estimation of temperature distribution with reduced sensor usage, improving production quality and yield by maintaining uniformity and reducing measurement costs.
Implementation Method 1
In measuring the entire temperature distribution with a pyrometer, an amount of photons is measured from a point or points of a wafer
Data Source
AI summary
The temperature distribution estimating method of the disclosure includes a building operation to build a numerical model for a form and thermal behavior of a substrate; a setting operation to set a regularization parameter to adjust noises of a temperature of the substrate measured by a temperature sensor; a generating operation to generate a sensitivity coefficient matrix that estimates a heat source received by the substrate from a plurality of heaters; a condensing operation to condense the sensitivity coefficient matrix based on a power ratio input in the heaters respectively; and estimating operation to estimate an entire temperature distribution of the substrate based on the numerical model, the regularization parameter, and the condensed sensitivity coefficient matrix, when predetermined temperature data are input.