在半導體工業降低成本聲浪中，積體元件之微細化與晶圓的大型化備受關切。
本文提供一個三維熱流分析技巧，模擬矽品體成表過程，以應大型柴可斯基矽品體成長系統設計篩選分析之用。本模型包含矽熔融液、矽晶體、與矽坩堝。基于熔融液之穩態、黏性、非壓縮性層流，本文利用有限元素法來解析整個模型之熱流非線式基本方程式。其結果可用于最佳設計之依據。晶體大小之控制依晶體／熔融液的溫度分佈，而決定于拉晶速度與加熱條件。求得之溫度分佈、壓力分佈與重力旋即加諸于「應力次模型」計算應力分量；進而根據塑性分析，確保不會產生「差排」現像。除了影響溫度分佈，流場也影響摻質之均勻性。本模型尤其適於參數分析，以得晶體成長系統之最佳設計。利用「多溶質傳遞」選項，本模型也可供摻質分析之用。更詳細的邊界層分析可以用本模型之「次結構」來進行。根據本文之分析，我們可以確定：用柴可斯基拉晶法製造直徑 300 mm以上之大晶體是可行的。我們也知道如何去改進。運用本文所提供的技巧，進行設計分析，經濟效益又高，實為矽晶體成長設備設計上絕佳的工具。
A model is proposed for a detail three dimensional thermo fluid flow analysis of large silicon crystal growth systems composed of the silicon melt, silicon crystal, and silica crucible, by first solving the coupled not-1inear governing equation for a steady, viscous, laminar flow, using the finite element method. The temperature, presssure, and gravitational fields thus obtained are 'loaded' into the stress sub-model for calculation of stresses to ascertain a 'dislocation-free' crystal grown. The model is particularly suitable for parametric studies to arrive at an optimum design of the system The model also provides options for a 'multiple species transport' analysis and for a more detailed local analysis, such as a boundary layer analysis at the crystal-melt interface, by sub-structuring part of the model. Based on results obtained from the current example, it is also concluded that a large dislocation-free crystal of 300 mm diameter or larger is obtainable functionally by the Czochralski technique, with a room for improvement', and economically using technique presented in this paper.
