本論文主要是利用光激發螢光光譜( Photoluminescence spectrum，PL ) 研究半導體砷化銦鎵( InGaAs )、砷化銦( InAs )量子井( Quantum well，QW )、量子點( Quantum dot，QD)結構的光電特性，包括電子能階、激子( Exciton )的反磁性位移( diamagnetic shift )、量子點隨溫度變化的躍遷情形等。首先我們用高強度的光激發樣品取得螢光光譜，發現可以從光譜波峯的偏移情形判讀半導體結構的維度，如波峯紅位移( redshift )屬於二維量子井結構，藍位移( blueshift )則是零維量子點結構。接下來解外加磁場的薛丁格方程式，獲得激子躍遷能量偏移與磁場的關係，然後在低溫量取各不同磁場強度下的光激螢光譜，擬合得到激子的反磁位移係數，進一步求得電子的展開波函數，所得與k.p計算結果一致，再利用展開波函數估計量子點側向尺寸~14nm及高度~6nm和從原子力顯微鏡 ( atomic force microscopy，AFM ) 掃描的結果一致。利用Makado model的氫原子理論模擬，得到量子井中激子的束縛能~5meV。
　　本文的第二部份是針對在不同溫度下成長的InAs/GaAs量子點內電子電洞能階的分布、躍遷能量受溫度的影響等特性加以討論。假設量子點的高度是基底長的一半，根據單粒子在三維結構中侷域變化且有效質量非各向同性的薛丁格方程式計算，推算量子點在不同基底長度下所對應的躍遷能量及其中應包含的電子電洞能階。量測樣品在不同激發光強度下的螢光光譜，隨著激發光源功率增強，被激發的載子數量增加，多餘的載子在基態能階填滿後開始佔據激發態能階，基態與激發態躍遷的結果與理論計算一致，基態能階隨光強度增加的藍位移歸因於量子尺寸效應。另外我們量測量子點在不同溫度下的光激發螢光光譜，在中溫區的快速紅位移約為Varshni law的三倍有別於塊材及量子井結構，且光譜線寬隨溫度的增加而減少，歸因於載子的穿遂效應。

Photoluminescence spectroscopy was employed to investigated electro-optical properties of InGaAs/GaAs , InAs/GaAs quantum well and quantum dots structures, including the electronic state, the diamagnetic shift, and the temperature dependent transition energy of quantum dots. In the first part of this dissertation the photoluminescence (PL) peak shift under high excitation intensity is used to distinguish QW from QD structures. It is redshift in quantum well and blueshift in quantum dot structure under high excitation intensity, which was attributed to the band gap renormalization and quantum size effect, respectively. Then a magneto optical characterization of InGaAs/GaAs quantum well (QW) and quantum dot (QD) structures grown on (111)B GaAs substrates was studied. The extent of confined wave function obtained from the diamagnetic shift of the PL peak energy is consistent with the result calculated by the k.p method. The InGaAs/GaAs QD lateral confinement energy and the dot size are also estimated from the diamagnetic shift of the PL lines. The mean radius of the InGaAsQD is about 14nm and the dot height is about 6nm, which is in good agreement with the results as revealed in AFM imaging. The binding energy derived from Makado model in (111) InGaAs/GaAs QW is about 5meV.
Second part we investigated the InAs/GaAs quantum dots (QDs) grown at different temperature by the excitation- and temperature-dependent photoluminescence (PL). The relationship between QDs transition energy and baselength can be solved based on the three-dimensional single particle effective mass Schrodinger equation using a locally varying, anisotropic effective mass. Under the excitation dependent photoluminescence experiment, all the ground states of the QDs are filled as the excitation intensity increased, and the surplus carriers starts to occupy the excited state. The ground and excited state transition energy is in consistent with the theoretical calculation. The blueshift of the ground state energy with increasing excitation intensity was attributed to the quantum size effect. The QDs transition energy shift with temperature is different from the behavior of bulk and quantum well. The transition energy in temperature-dependent PL spectra shows a rapid redshift as the temperature is higher than the critical temperature. The redshift rate is about three times larger than the values calculated by Varshni’s law. The higher redshift rate and decreased FWHM can be explained by the tunneling effect.

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