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  • 學位論文

氮化銦鎵/氮化鎵多重量子井之光電特性之數值分析

Numerical Analysis of Optoelectronic Properties of InGaN/GaN Multiple Quantum Well

指導教授 : 吳育任

摘要


在本篇論文中,我們討論了氮化銦鎵/氮化鎵多重量子井中的銦含量、溫度、井寬、井與井之間的厚度、井的層數與注入載子濃度對自發發光頻譜的影響。我們利用了帕松和薛丁格方程來求解多重量子井中的位能以及電子電洞在量子井中的分佈,並且利用了疊代的方法來求出帕松和薛丁格方程在此系統中的解,進而來求解在氮化銦鎵/氮化鎵多重量子井中自發發光強度的大小。而從計算自發發光強度的公式中,我們發現電子和電洞波函數復合的機率,以及電子電洞個別的費米分佈函數對於自發發光的強度有相當大的影響,因此我們將分別討論當我們改變了量子井的物理條件時,那種情況會是造成發光頻譜不同的主因。 而經由模擬的結果我們發現,當我們固定了所有的條件,而分別的改變量子井中的銦含量、溫度、井寬、井與井之間的厚度以及井的層數時、電子與電洞復合機率的大小在多重量子井的發光效率中扮演了一個決定性的角色。而我們認為這主要是由於當我們改變了量子井的結構時所產生的壓電效應,因而影響了載子在量子井中的分佈的關係。然而,當我們固定量子井的結構以及注入的載子濃度,僅僅改變溫度時,電子電洞的費米分佈反而是造成了發光強度不同的主因。而從我 們所發展的程式以及所得到的資訊,我們將能夠去設計或是改善元件的效能。 關鍵詞:氮化銦鎵、氮化鎵、量子井、帕松方程、薛丁格方程、自發發光、發光二極體。

並列摘要


In this thesis, we studied the spontaneous emission rate in InGaN/GaN mutiple quantum well (MQW) when we change the indium composition, temperature, well number, well width, barrier length, and injection carrier density. We used the Poisson equation to find out the band structure of the MQW and the Schrodinger equation to obtain the carrier distribution in the MQW. The Poisson and Schrodinger equation are solved self-consistently to get a converged solution of the system. We use the solution to calculate the spontaneous emission rate in an InGaN/GaN MQW LED. From the formula for calculating spontaneous emission rate, we find the overlap of electron and hole wavefunction, and the fermi distribution function of electrons and holes is strongly related to the strength of emission rate. The main factors influencing the emission rate will be discussed in this thesis. From the simulation results, we find that when we change the indium composition, well width, barrier width, and the well number, the overlap of electrons and holes wavefunction play an important role. We think that due to the influence of piezoelectric polarization and the quantum confined Stark effect, the change of quantum well structures will affect the carrier distribution in the quantum well structures. Also, the influence of the temperature to the spontaneous emission rate is closely related to the Fermi-Dirac distribution of the carriers. With these information and the program we have developed, it is possible for us to design and improve the device performance. Keywords : InGaN, GaN, quantum well, Poisson equation, Schr"{o}di- nger equation, spontaneous emission, LED.

參考文獻


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