Point Defect Simulator for Silicon Crystal Thermal Stress

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Solution Overview

Problem

Current methods fail to accurately determine the distribution of point defects, such as vacancies and interstitial silicon atoms, in silicon single crystals considering thermal stress during the Czochralski process, which is crucial for producing defect-free silicon wafers for semiconductor devices.

Innovation Solution

A point defect simulator using convection-diffusion equations with stress coefficients to calculate concentration profiles of vacancies and interstitial silicon atoms, taking into account thermal stress, and a simulation method to design a single crystal pulling apparatus that produces defect-free silicon crystals.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If conventional methods are used to determine point defect distribution, then the calculation is simpler, but the accuracy is insufficient because thermal stress is not considered

Engineering Contradiction:

Improveaccuracy of point defect distribution determinationVSAvoidcomplexity of simulation model

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent incorporates thermal stress as an additional parameter into the convection-diffusion equations for point defects. The equilibrium concentrations of vacancies and interstitial silicon atoms are modified to include stress terms: Cv_eq = C0v * exp(-(Ev + avf*P)/(kB*T)) and Ci_eq = C0i * exp(-(Ei + aIf*P)/(kB*T)), where P is stress and avf, aIf are stress coefficients. This parameter change enables accurate determination of point defect distribution under thermal stress conditions.

Inventive Principle:

Principle #35Parameter changes

2Manufacturing precision

If the range of pulling speed for critical v/G is narrowed to ensure defect-free crystals, then the manufacturing precision improves, but the productivity decreases

Engineering Contradiction:

Improvedefect-free crystal productionVSAvoidpulling speed control range

Core Design Contradiction:

Manufacturing precisionVSProductivity

Solution Approach 1:

The patent uses a point defect simulator to perform preliminary calculations of vacancy and interstitial silicon atom concentration profiles under various pulling conditions before actual crystal growth. By simulating different stress conditions and pulling speeds, the optimal pulling speed range can be determined in advance, allowing for broader operational margins while ensuring defect-free crystal production.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The simulation model provides feedback on the relationship between pulling speed, thermal stress, and point defect distribution. This feedback mechanism allows for optimization of pulling speed ranges by showing how changes in pulling conditions affect defect formation, enabling broader operational windows while maintaining defect-free crystal quality.

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

Enables precise determination of point defect distribution in silicon single crystals, ensuring the production of defect-free silicon wafers by optimizing the pulling process based on thermal stress considerations.

Implementation Method 1

a convection-diffusion equation having a concentration Cveq of vacancies in thermal equilibrium

Methodology Applied

Scientific EffectConvection: Convection

Implementation Method 2

a convection-diffusion equation having a concentration Cveq of vacancies in thermal equilibrium

Methodology Applied

Scientific EffectDiffusion: Diffusion

Implementation Method 3

it has been suggested that the thermal stress in a crystal near the solid-liquid interface influences the distribution of vacancies V and interstitial silicon atoms I in the crystal

Methodology Applied

Scientific EffectThermal stress: Stress Relaxation

Implementation Method 4

a convection-diffusion equation having a concentration Cveq of vacancies in thermal equilibrium represented by an equation (A)

Methodology Applied

Scientific EffectThermal equilibrium:

Data Source

PatentUS12258675B2Method of producing a silicon single crystal based on concentration profiles of vacancies and interstitial silicon atoms during pulling of a silicon single crystal by the Czochralski process

Publication Date: 2025.03.25 SUMCO CORP

AI summary

Provided is a point detect simulator which makes it possible to determine the distribution of point defects in a silicon single crystal in consideration of the thermal stress of the silicon single crystal being grown. A point defect simulator 1 is a point defect simulator calculating the concentration profiles of vacancies and interstitial silicon during pulling of a silicon single crystal using a convection-diffusion equation reflecting the consideration of thermal stress in the silicon single crystal, and includes an analysis unit used to fit calculation results to experimental results using stress coefficients that are the coefficients of stress terms as a fitting parameter.