Mechanical and Optoelectronic Properties of Self-Assembled Quantum Dots

本文旨在研究自聚式量子點奈米結構的機械與光電耦合性質。文中以線性彈性力學理論與k•p理論，配合有限元素法分析砷化銦鎵量子點的成份、形狀、大小，以及堆疊層對應變、壓電等效應之影響，進而探討自聚式砷化銦鎵/砷化鎵量子點奈米結構的機械與光電性質。 本文首先，以彈性力學的起始應變理論模擬量子點異質磊晶結構因材料晶格不匹配引致的彈性變形。應變計算結果與文獻上使用高解析影像處理法測得的應變分佈吻合。本文並依循量子點的製程順序，提出二階段應變模擬法以分析覆蓋型量子點結構的應變場；並分別經由變形位能理論與壓電位能理論，求得量子點的應變效應及壓電效應，以修正穩定狀態有效質量之薛丁格方程式的位能函數。 最後，以有效質量的薛丁格方程式來估算量子點結構的特徵能量及對應之波形函數。本文的應變場、壓電場，以及薛丁格方程式的解皆以有限元素法分析求得。數值結果清楚地顯示，二階段模擬法與其他兩種忽略量子點製程的模擬方法結果明顯的不同；且二階段模擬法計算的發光波長與文獻的光致螢光實驗數據一致。另外，本文亦發現壓電效應導致了第一激發態p類型簡併態分裂，且電子波形函數產生異向性化；這些結果與文獻的磁力穿遂光譜實驗結果吻合。The coupling mechanical strain and opto-electronic properties in self-assembled quantum-dot nanostructures are studied. A model, based on the theories of linear electricity and k•p, is developed to analyze chemical composition effects, shape effects, size effects, and multiple layers effects on mechanical and opto-electronic properties of the self-assembled InGaAs /GaAs quantum dots by means of finite element analysis. At first, the strain fields of surface quantum dots induced by mismatch of lattice constants between the quantum-dot material and substrate material are analyzed. For cases of indium concentrations , The calculated results of strain relaxations have good agreement with what are taken experimentally through HREM imaging by others. On the other hand, a new two-step model is proposed to analyze strain fields of buried quantum dots. The model takes into account of the sequence of the fabrication process of buried quantum dots. Then strain-induced as well as piezoelectric effects are considered by modifying the carrier confinement potential in Schrödinger equation. The strain-induced potential is determined from deformation potential theory. Also, the piezoelectric potential is analyze by solving Poisson’s equation. After that, the steady-state effective-mass Schrödinger equation is adopted to find confined energy levels as well as wave functions both for electrons and holes of the quantum-dot nanostructures. Finally, energies of interband optical transitions are acquired in numerical experiments. The numerical results show that the strain field from this new two-step model is significantly different from models where the sequence of the fabrication process is completely omitted. The calculated optical wavelength from this new model agrees well with previous experimental photoluminescence data from other studies. Piezoelectric effect, on the other hand, splits the p-like degeneracy for the electron first excited state about 1~7 meV, and leads to anisotropy on the wave function. The effect was also experimentally observed through magnetotunneling spectroscopy by others.目錄 i 表目錄 iv 圖目錄 vi 第一章 緒論 1 1-1研究動機 1 1-2量子點製程 3 1-3研究內容 7 第二章 量子點應變理論分析 10 2-1起始應變模擬法 13 2-2材料的組成律 15 2-3平衡方程式與邊界條件 18 2-4起始應變與等效熱應變模擬的ㄧ致性 20 2-5裸露型量子點應變分析 24 2-5-1裸露型量子點的應變場 24 2-5-2裸露型量子點的應變結果比較 26 2-6覆蓋型量子點應變場的模擬 28 2-6-1覆蓋型量子點應變場傳統模擬法 29 2-6-2覆蓋型量子點應變場簡化模擬法 30 2-6-3覆蓋型量子點應變場二階段模擬法 31 第三章 量子點光電性質理論分析 34 3-1薛丁格方程式 37 3-2 理論 39 3-2-1微擾理論 39 3-2-2有效質量 42 3-3量子點結構的位能函數 45 3-3-1量子點結構的能隙效應 46 3-3-2量子點結構的應變效應 47 3-3-3量子點結構的壓電效應 51 3-4裸露型量子點光電性質分析 54 第四章 量子點應變與壓電效應 58 4-1砷化銦量子點應變效應 59 4-1-1砷化銦量子點應變場 59 4-1-2砷化銦量子點光電性質 62 4-2砷化銦鎵量子點壓電效應 65 4-2-1砷化銦鎵量子點應變場 67 4-2-2砷化銦鎵量子點壓電場 68 4-2-3砷化銦鎵量子點光電性質 69 第五章 量子點形狀與層狀堆疊效應 73 5-1砷化銦量子點的形狀效應 74 5-1-1砷化銦量子點應變場 74 5-1-2砷化銦量子點壓電場 75 5-1-3砷化銦量子點光電性質 76 5-2砷化銦量子點的層狀堆疊效應 80 5-2-1多層砷化銦量子點應變場 80 5-2-2多層砷化銦量子點光電性質 81 第六章 結論 83 參考文獻 9