Effective thermal conductivity of poly-silicon chunks and its size dependence in a melting process of silicon Czochralski crystal growth: Part 2. Numerical simulations and comparison with measurements
{"title":"Effective thermal conductivity of poly-silicon chunks and its size dependence in a melting process of silicon Czochralski crystal growth: Part 2. Numerical simulations and comparison with measurements","authors":"Michio Kida, Toshinori Taishi","doi":"10.1016/j.jcrysgro.2024.127703","DOIUrl":null,"url":null,"abstract":"<div><p>In the article Part 1, experimental relation of a temperature distribution and a poly-silicon size in a melting process of silicon Czochralski (CZ) method is investigated. In this work, numerical simulations are performed to obtain temperature distributions in a crucible of a silicon CZ melting process. And applicability of International Atomic Energy Agency (IAEA) formula of effective thermal conductivity to poly-silicon chunks is examined. Calculations are done with a two-dimensional symmetric axis system and an explicit finite difference method. Samples are poly-silicon chunks of two sizes and small cylindrical graphite pellets of three sizes. Temperatures at 6 points in a crucible have been simulated. Simulations using IAEA formula give a good agreement with measured temperatures in the article Part 1. The experimental relation of temperature and a sample size is reproduced by simulations. Though IAEA formula is constructed for sphere particles, it serves in predicting an effective thermal conductivity of poly-silicon chunks. When applying the formula to chunks, a measured value of the porosity and an average size are used as parameters. The method of estimating an effective thermal conductivity is hoped to be applied to a large diameter silicon CZ growth.</p></div>","PeriodicalId":353,"journal":{"name":"Journal of Crystal Growth","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Crystal Growth","FirstCategoryId":"88","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022024824001386","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CRYSTALLOGRAPHY","Score":null,"Total":0}
引用次数: 0
Abstract
In the article Part 1, experimental relation of a temperature distribution and a poly-silicon size in a melting process of silicon Czochralski (CZ) method is investigated. In this work, numerical simulations are performed to obtain temperature distributions in a crucible of a silicon CZ melting process. And applicability of International Atomic Energy Agency (IAEA) formula of effective thermal conductivity to poly-silicon chunks is examined. Calculations are done with a two-dimensional symmetric axis system and an explicit finite difference method. Samples are poly-silicon chunks of two sizes and small cylindrical graphite pellets of three sizes. Temperatures at 6 points in a crucible have been simulated. Simulations using IAEA formula give a good agreement with measured temperatures in the article Part 1. The experimental relation of temperature and a sample size is reproduced by simulations. Though IAEA formula is constructed for sphere particles, it serves in predicting an effective thermal conductivity of poly-silicon chunks. When applying the formula to chunks, a measured value of the porosity and an average size are used as parameters. The method of estimating an effective thermal conductivity is hoped to be applied to a large diameter silicon CZ growth.
期刊介绍:
The journal offers a common reference and publication source for workers engaged in research on the experimental and theoretical aspects of crystal growth and its applications, e.g. in devices. Experimental and theoretical contributions are published in the following fields: theory of nucleation and growth, molecular kinetics and transport phenomena, crystallization in viscous media such as polymers and glasses; crystal growth of metals, minerals, semiconductors, superconductors, magnetics, inorganic, organic and biological substances in bulk or as thin films; molecular beam epitaxy, chemical vapor deposition, growth of III-V and II-VI and other semiconductors; characterization of single crystals by physical and chemical methods; apparatus, instrumentation and techniques for crystal growth, and purification methods; multilayer heterostructures and their characterisation with an emphasis on crystal growth and epitaxial aspects of electronic materials. A special feature of the journal is the periodic inclusion of proceedings of symposia and conferences on relevant aspects of crystal growth.