相場模式在矽晶薄片垂直固化中晶粒與晶界發展之研究

Abstract

近幾年由於光電領域的蓬勃發展，多晶矽的垂直固化長晶過程一直吸引著極大的關注。在本篇論文中，吾人將利用適應性相場模式來模擬多矽晶的長晶行為。對於單晶矽而言，固液界面型態對於缺陷的生成扮演著很重要的角色。在本文的模擬中，藉由考慮高非均向性的界面能與動力學，能成功的描述在固化過程中生成的{111}奇異面，並且對於固液界面型態的發展與奇異面的生成機制，都能有效的與實驗的觀察作比較。 而對於多晶矽而言，攣生成核與晶界種類對於矽晶太陽能電池的光電特性也扮演著很重要的角色。吾人首先修改先前攣生成核機制的模式，多考慮了在晶界凹槽處成核時兩個核之間的接觸之後，有效的推導出臨界成核的過冷度和成核機率，並且能夠從實驗中估計的值作比較。然後，吾人導入了此修改後的攣生成核模式在我們的相場模擬中，並描述了非均向性的晶界能與晶界遷移率後，可用來模擬長晶時的晶粒結構與晶界發展，因此，吾人便成功的解釋了三種在實驗上觀察到的晶界間交互關係。此外，吾人也討論了初始晶界種類與晶向分佈對於長晶過程中成核速度、平均晶粒大小、晶向與晶界種類發展的影響，並且提供了較佳的初始晶種排列，使其能幫助且應用在實際的實驗上。

The directional solidification of silicon has attracted a great attention in recent years due to its booming applications in photovoltaics. In this thesis, adaptive phase field modeling is applied to simulate the crystal growth behavior of silicon in detail. For mono-crystalline silicon, the interface morphology of the solid-liquid interface plays a crucial role in defect formation. Highly anisotropic surface free energy and interfacial kinetics are considered in our simulation to form {111} facet planes during solidification, and the morphological evolution and the mechanism for facet formation are well-compared with experimental observation. For multi-crystalline silicon grown by directional solidification, the formation of the twin nucleus plays a crucial role on the electrical properties of solar cells. We revise the previous twin nucleation model by considering the interaction between two nuclei at the grain boundary groove. The predicted undercooling and twinning probability for twin nucleation based on our revised model are consistent with the estimated value from experimental observations. Then we incorporate this model in our phase field model to simulate the evolution of grain structures and grain boundaries. After we consider the anisotropic energy and mobility of grain boundaries (GBs), three basic interactions of GBs during solidification are examined and they are consistent with experiments. The effect of initial distribution of grain boundary types and grain orientations is also investigated for the twinning frequency, the evolution of grain size, grain orientation and grain boundary types. A suitable seed arrangement is proposed and it would be helpful for experiments and production.