相場模式在含雙晶面的小面化枝晶之研究

Phase Field Modeling of Twin-related Faceted Dendrites

陳冠穎(Kuan-Ying Chen)

指導教授 ： 藍崇文

國立臺灣大學/工學院/化學工程學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201603324

摘要

因為半導體枝晶(例如矽和鍺)獨特的生長形貌，其生長行為受到重視。此種枝晶被稱為小面化枝晶(Faceted dendrite)，其外觀由晶癖面(Habit plane)所組成，且在枝晶中心可發現至少兩個平行的雙晶面(Twin plane)。小面化枝晶的生長方向和液體中的過冷有關，但現存的理論還不能完美的解釋此現象。本文主旨為使用相場模式(Phase field model)研究小面化枝晶生長。在此研究中，我們首先探討在平衡形狀以及生長過程中奇異面形成的條件。我們提出一個新的介面能非均向函數，應用於三維相場模擬，同時引入負的韌性(Stiffness)。我們接著使用相場模式進行矽的枝晶生長模擬。模擬的<112>和<110>枝晶形貌和實驗上的發現相符，我們亦發現枝晶的生長方向和凹角以及凸角的長速相關。我們更進一步提出新的小面化枝晶生長模式，其中凹角生長會導致<112>枝晶生長，而連續生長會導致<110>枝晶生長。長速於凹角、凸角之比值Vre-entrant/Vridge決定生長方向的轉變，我們提出Vre-entrant/Vridge 之解析解並和實驗比較。

關鍵字

相場模式 ； 小面化枝晶 ； 雙晶面凹入棱機制

並列摘要

Dendritic growth behaviors of semiconductors (e.g. Si and Ge) have attracted much attention due to their unique crystal morphologies. The appearance of the dendrite is bounded by habit planes, and more than two parallel twin planes can be found at the center of these dendrites. The growth orientation of twin-related faceted silicon dendrites depends on the undercooling ΔT in the melt, which cannot be explained by the existing models. The aim of this thesis is to investigate the faceted dendrite growth via our phase field model.
In this study, we first investigate the faceting condition for equilibrium shapes and dynamic situations. We propose a new anisotropic function of surface energy for the phase-field simulations in three dimensions, and negative stiffness is further considered. Then we investigate the growth of a twin-related silicon dendrite through a novel phase field model. The correctness of the model for an equilibrium twined crystal is examined first before we model the faceted dendrite growth. The simulated morphologies of <112> and <110> faceted dendrites are consistent with experimental observations. The growth orientation of the simulated dendrite depend on the growth rates at the ridges and the re-entrant corners. Moreover, we propose a model to explain the growth behavior showing that the re-entrant corners would lead to the growth of <112> dendrites, while the <110> branch is due to continuous growth. Such a selection could be determined by the velocity ratio Vre-entrant/Vridge that is a function of ΔT. An analytical expression for this ratio is derived and compared to the experimental observations.

並列關鍵字

Phase field model ； faceted dendrite ； Twin-Plane-Reentrant-Edge mechanism (TPRE)

參考文獻

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