Silicon Crystal Pulling Condition Calculation for Defect-Free Growth

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Solution Overview

Problem

Conventional methods for growing monocrystalline silicon lack the ability to determine optimal hot zone geometry and pulling conditions, leading to suboptimal defect-free regions due to unknown specific hot zone geometry and interface geometry.

Innovation Solution

A monocrystalline silicon pulling condition calculation program is developed to determine optimal pulling conditions by calculating heat flux, crystal surface temperature, and in-crystal temperature distribution, using a reference temperature and solid-liquid interface geometry as boundary conditions, to maximize the defect-free region.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If conventional monocrystalline silicon growing methods are used with controlled V/G profile, then the effect of thermomechanical stress field is compensated, but the specific hot zone geometry and interface geometry for controlling the V/G profile remain unknown

Engineering Contradiction:

Improvedefect-free regionVSAvoidhot zone geometry and interface geometry

Core Design Contradiction:

ReliabilityVSLoss of information

Solution Approach 1:

The invention changes the parameters of hot zone geometry (heat shield plate distance Gap and heater power P) and interface geometry (solid-liquid interface height h) to optimize the V/G profile. By systematically varying these parameters and evaluating their impact on defect formation, the invention identifies optimal parameter combinations that maximize the defect-free region while controlling thermomechanical stress effects.

Inventive Principle:

Principle #35Parameter changes

2Manufacturing precision

If numerical analysis is used to determine interface geometry, then a method is provided for controlling V/G profile, but the determined interface geometry is not always the same as the actual solid-liquid interface geometry

Engineering Contradiction:

Improveinterface geometry controlVSAvoidinterface geometry accuracy

Core Design Contradiction:

Manufacturing precisionVSMeasurement precision

Solution Approach 1:

The invention implements feedback by using sensors to detect the actual solid-liquid interface geometry during crystal growth and comparing it with the target geometry. This real-time information is fed back to adjust the hot zone parameters (heat shield plate position, heater power) to ensure the actual interface geometry matches the optimal geometry required for defect-free crystal growth, thereby improving both manufacturing precision and measurement accuracy.

Inventive Principle:

Principle #23Feedback

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

The program effectively identifies optimal solid-liquid interface height and distance between the heat shield plate and silicon melt, stabilizing the growth of monocrystalline silicon with reduced influence from pulling velocity, thereby maximizing the defect-free region.

Implementation Method 1

calculating a heat flux q (W/m2) and a crystal surface temperature T(K) in the pull-up apparatus by global heat transfer analysis

Methodology Applied

Scientific EffectHeat transfer: Conduction (thermal)

Implementation Method 2

recalculating an in-crystal temperature distribution in the monocrystalline silicon based on the defined boundary conditions

Methodology Applied

Scientific EffectThermal conduction: Conduction (thermal)

Implementation Method 3

calculating a mean stress σmean caused in the monocrystalline silicon by structure analysis based on the recalculated in-crystal temperature distribution

Methodology Applied

Scientific EffectThermomechanical stress: Thermomechanical Effect

Data Source

PatentUS10920339B2Silicon single crystal pulling condition calculation program, silicon single crystal hot zone improvement method, and silicon single crystal growing method

Publication Date: 2021.02.16 SUMCO CORP

AI summary

A pulling condition calculation program enables a computer to perform the steps of: setting a plurality of sets of pulling conditions based on solid-liquid interface height and distance between a surface of a silicon melt and a heat shield plate; performing, for each set of the pulling conditions, the steps of: calculating a heat flux (q) (W/m2) and a crystal surface temperature (T); defining a reference temperature (Tref) given by an equation (1) below and a geometry of the solid-liquid interface as boundary conditions, recalculating an in-crystal temperature distribution; calculating a mean stress in the monocrystalline silicon; calculating a defect distribution in a pulling direction based on the mean stress and the in-crystal temperature distribution; determining a defect-free region in the pulling direction; and drawing a contour line showing a dimension of the defect-free region on a two-dimensional map defined by the distance and the solid-liquid interface height.Tref=T4-qɛσ4(1)