三維有限元素法應變分析應用於氮化鎵基底奈米結構發光二極體

由於能源危機，氮化鎵發光二極體因為有較好的轉換效率而越來越熱門。但氮化鎵發光二極體還是面對許多問題，其中之一就是氮化銦鎵和氮化鎵之間的晶格不匹配，在氮化銦鎵和氮化鎵之間因為晶格常數的布匹配會造成應變，這應變會造成壓電場使氮化銦鎵量子井中電子電洞的波函數分離，這種效應稱為量子侷限史塔克效性，這會降低氮化鎵發光二極體的效率，所以分析應變在研究氮化鎵發光二極體是很重要的，在很多研究中完整應變近似模型是很常被使用的，但在許多奈米尺度的問題上這是不適合的，因為在奈米尺度中整個系統會分配應變，讓系統有最小的應變能量。因此在這篇文章中，我們使用了三維有限元素法連續彈性模型來分析奈米結構的應變問題，包含銦擾動的量子井、有V形凹洞的氮化鎵發光二極體和殼型奈米柱發光二極體。在第一個問題中，我們分析了隨機銦含量分布的量子井中應變的分布，再接著算出感應的極化電荷，在我們的分析結果發現，完整應變近似模型忽略了不同銦含量分子間作用力的影響和不規則分布的銦含量所造成的剪應變這讓完整應變近似模型有比較銳利的應變分布和較高的總應變能量。我們接著分析有V形凹洞的氮化鎵發光二極體和殼型奈米柱發光二極體，有V形凹洞的氮化鎵發光二極體由於r-平面的側壁結構讓應變分佈變得非常有趣，在本篇論文的最後我們分析了一個有著不同直徑的奈米柱的應變分佈，並觀察了在這樣結構中氮化銦鎵量子井的應變變化的行為，接著得到在直徑較小的奈米柱中，有比較顯著的氮化銦鎵應變釋放。有了這個模擬模型，未來我們可以分析更多不同結構的應變分佈。

關鍵字

關鍵字:氮化鎵發光二極體；應變；有限元素法；銦元素擾動； V形凹洞；殼狀奈米柱

並列摘要

Due to the energy crisis, GaN-based light emitting diodes (LEDs) become more popular due to their better power efficiency. However, GaN-based LEDs still have many problems. One of them is the lattice mismatch between InGaN and GaN. The strain induced by lattice mismatch between InGaN and GaN layers will make the wave functions of electron and hole separate in the InGaN quantum well (QW) by induced piezoelectric field. This is called quantum confined stark effect (QCSE) and will limit the efficiency of GaN-based LED. Thus, it is important to analyze the strain distribution in the GaN-based LED. In many researches, the fully strained approximation model is widely used in lateral grown thin film. However, it is not appropriate in nano-scale structures because the system would distribute strains to reach the minimum strain energy. In this thesis, we use 3D finite element method (FEM) continuous elastic model to analyze nano-scale structures, including indium fluctuated QWs, GaN-based LED with V-pit, and core-shell nanorod. For the first case, we analyzed how the strain distributed in the random alloy fluctuation QW and then calculated the induced polarization charges in the QW. We find that the fully strained approximation model neglects the inter-molecular interactions and the shear strains caused by random distributed indium composition. These make the fully strained approximation model has sharp strain distributions and higher total strain energy. We further analyze the strain distributions in the GaN-based LED with V-pit and core-shell nanorod. Because of the r-plane sidewall structure in the V-pit, the strain distributions might be interesting and could be an example to compare the FEM strain solver with the fully strained approximation model. At the end of this thesis, we analyze the strain distributions in a core-shell nanorod with three different diameters and investigate the strain differences. The results show that a smaller diameter nanorod has an obvious strain relaxation. In the future, with this 3D FEM continuous elastic simulation program, we can exactly analyze the strain distributions for many different nano-scale structures.

並列關鍵字

Keywords:GaN-based light emitting diode ； Strian ； finite element method ； Indium fluctuation ； V-pit ； core-shell nano rod

參考文獻

[2] J. Singh, Electronic and Optoelectronic Properties of Semiconduc-

[4] S. Nakamura, T. Mukai, and M. Senoh, “Candela-class

pp. 1687–1689, 1994.

ductors Theory and Device Applications. Springer, 2010.

emitting diode with a polarization tunnel junction,” Applied

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三維有限元素法應變分析應用於氮化鎵基底奈米結構發光二極體

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