實驗及理論探討奈米結構之氧化鋅光學性質研究

Abstract

我們運用實驗及理論探討在有限結構下的氧化鋅的光學性質特性。首先在實驗部份，我們利用溶膠-凝膠法製備氧化鋅量子點，由拉曼散射與光激發光實驗研究氧化鋅量子點的晶格動力學、激子相關特性在不同量子點尺寸的變化情形。我們藉由高解析度穿透顯微鏡與x-光繞射估計在調配不同溶液濃度下的氧化鋅奈米晶粒尺寸。而在具有量子尺寸的材料中，電子與電洞的交互影響會隨著尺寸變小變得越顯著;而電子與聲子的耦合作用亦會隨著尺寸而變化。在拉曼光譜中，我們發現隨著氧化鋅奈米晶粒尺寸變小E2 (high) mode有明顯的紅位移與不對稱光譜，再由modified spatial correlation model探討在不同奈米晶粒尺寸下的拉曼光譜隨尺寸變化的形為；而此理論模型概念考慮聲子受到奈米晶粒的邊界與尺寸分布的影響。我們發現在拉曼光譜的紅位移與不對稱光譜都是來自於optical phonon在空間中被局限所造成的結果。經由共振拉曼量測，發現電子與聲子耦合作用亦隨著奈米晶粒尺寸變小而有減緩的趨勢，而其中Fröhlich interaction在電子與聲子交互作用中具有決定性的影響能力。另外，在光吸收光譜與光激發光譜中發現氧化鋅奈米晶粒有明顯的藍位移現象，再利用有效質量模型可粗略估計其量子侷限效應在不同氧化鋅奈米晶粒尺寸下的結果。經由低溫光激發光譜探討激子束縛能、激子與縱模聲子的耦合作用在氧化鋅量子點下所受到的影響，我們發現隨著氧化鋅量子點變小直接影響到激子波爾半徑變小而使得激子的極化現象變弱，進而導致激子與縱模聲子的Fröhlich interaction作用能力變小。經由上面的實驗，有效質量模型雖可以初步斷定光譜的藍位移現象來自於量子侷限效應；而有效質量模型在量子點尺寸越小時，過分地計算晶體週遭的位能，而且也無法得知在具有量子尺寸下詳細的電子行為。因此，我們利用sp3緊束縛理論計算氧化鋅在奈米尺寸下的電子結構與其表面能量。 首先，我們計算氧化鎂鋅在不同鎂含量下的電子結構與電子能態密度。發現隨著鎂含量變高能隙寬度與電子有效質量皆會有效的提升，這現象與實驗量測到得趨勢相當吻合。由電子能態密度計算結果發現額外鎂的3s與3p電子軌域造成陽離子間波函數耦合作用增加，使得電子有效質量變大。另外，我們亦由計算電子軌域的波函數權重發現氧原子的2p 電子軌域侷限在氧原子的現象趨緩，因此減弱了氧原子本身的負電性；而陽離子電子軌域的波函數則有輕微的侷限現象產生。最後，我們利用sp3緊束縛理論計算氧化鋅在奈米尺寸下延著極化面<0001>與非極化面<1-100>的電子結構與其表面能量。在表面上的dangling bonds會在電子結構中形成各自的表面能帶，而其波函數有明顯侷限在表面的趨勢。另外，延著<1-100>方向的非極化面，發現表面的dangling bonds的波函數會隨著尺寸變小而有增大的趨勢，進而導致其表面能帶的energy splitting增大。在我們的計算當中亦發覺到延著極化面的量子侷限效應比其他方向較更為明顯。

We studied optical properties in finite crystallize ZnO nanostructures with Experimental and theoretical method. In experimental part, ZnO quantum dots were successfully synthesized from 3.5 to 12 nm via a simple sol-gel method. The average size of quantum dots can be tailored using well-controlled concentration of zinc precursor. In the lattice dynamics, the measured Raman spectral shift and asymmetry for the E2 (high) mode caused by localization of optical phonons agree well with that calculated by using the modified spatial correlation model. From the resonant Raman scattering, the coupling strength between electron and longitudinal optical phonon, deduced from the ratio of the second- to the first-order Raman scattering intensity, diminishes with reducing the ZnO QD diameter. The size dependence of electron-phonon coupling is principally a result of the Fröhlich interaction. Size-dependent blue shifts of photoluminescence and absorption spectra revealed the quantum confinement effect. Additionally, the exciton-longitudinal-optical-phonon (LO-phonon) interaction was observed to decrease with reducing ZnO particle size to its exciton Bohr radius (aB). The unapparent LO-phonon replicas of free exciton (FX) emission and the smaller FX energy difference between 13 and 300 K reveal decreasing weighting of exciton-LO phonon coupling strength. The diminished Fröhlich interaction mainly results from the reducing aB with size due to the quantum confinement effect that makes the exciton less polar. According to the above experiment data, the effective-mass approximation apparently gives a good understanding of the blue shift of the optical absorption threshold. However, this approach fails for the smallest crystallite sizes because of the oversimplified description of the crystal potential as a spherical well of infinite depth. A better description of the band structure can be obtained from a tight-binding (TB) framework. Since the atomic structure is implicitly considered, this method is more adequate for small crystallites. In our theoretical part, we used sp3 TB model to calculate the electronic structure and surface states in in ZnO finite crystallize. Firstly, calculating the electronic structure and the density of states in the wurtzite structure of Zn1-xMgxO (ZMO) alloys using sp3 semi-empirical tight-binding model, we observed increases of both band gap and electron effective mass that agree with the experimental results as increasing Mg composition up to x = 0.3. From the calculated total density of states, the increasing electron effective mass is a result of localized orbital overlap of cation sites due to extra density of modes coming from Mg3s and Mg3p orbitals as introducing more Mg composition. Additionally, reducing electronegative characteristic of oxygen was caused by the O2p was less localized around the oxygen atom. Finally, the electronic band structures and surface states were investigated for ZnO finite wells or slabs grown along <0001> and <1-100> directions using tight binding representation. The dangling bonds on two end-surfaces caused surface bands for different directions grown slabs, of which the wavefunctions tend to localize at the end surfaces. The increasing splitting of the degenerate surface bands at the Γ point was observed decreasing with the thickness of the nonpolar [1-100] slab. And, we also found that the enhancing the band gap along [0001] polar due to more effective carrier confinement in c-axis.