半導體奈米物質的人工複合材料的集體磁光特性

Abstract

在這篇博士論文中，我們理論研究了半導體奈米物質的人工複合材料的集體磁光特性，這些半導體奈米物質包含量子點分子與奈米環，我們模擬了這些嵌埋的量子點分子的量子能階與磁光響應的相關性，我們也研究了非對稱奈米環群體的磁響應與三重共圓心奈米環群體的激子能量的非同質擴張。 我們設計複合的分裂-連續模型去普遍性的模擬任意形態的半導體奈米物質的磁光響應，我們的普遍複合模型模擬被奈米物質侷限的電子與電洞的量子能階的同調操作，並且用實驗上全體磁光響應分析量測印證(包含反射、穿透、吸收)，這個操作是在外加磁場的情況下，我們的三維模型使我們可以施加任意方向的磁場模擬，這個技術的最大突破是可以建構任意形狀與尺寸的奈米物質並施加任意方向外加磁場。只要我們知道個別單一奈米物質的磁光響應，我們就可以使用此模型進行群體奈米物質的磁光響應模擬。我們藉由添加極化率參數來特徵化奈米物質的磁光響應，這個極化率包含穩態與動態部分，因此我們同時需要一個多階電動態與量子機制描述。穩態部分利用波松等式計算，動態部分(包含物質發光的能量與機率)利用量子機制計算，我們使用 K•P近似數值計算(包含 2+2 與 2+4非線性迴圈法的能帶模型)計算被奈米物質侷限的電子與電洞的能量與波函數。為了實現模型，我們考慮了非對稱量子點分子(包含兩個或者三個量子點)的電子能階的同相操作和一層分子結構的全體磁光特性，我們的模擬結果顯示了量子點分子的量子機制組態可以藉由監控橢圓儀結果觀察到，這個磁場橢圓儀資料清楚的展現量子點分子的量子機制資訊。 我們提出網格方法來有效率的模擬不同尺寸大小的半導體奈米物質的量子機制特性，藉由網格法，我們可以探索因為奈米環的尺寸大小差異造成的磁性與光性的非同質擴張。我們的三維侷限位能考慮了奈米物質的真實的幾何外型、結構、材料組成，並計算被奈米物質侷限的電子與電洞的能階。然後我們模擬奈米物質群體的激子發光與磁響應的非同質擴張。一般而言，我們的模型可以模擬任意形狀的奈米物質群體。然而在這篇論文，為了實行我們的模型，我們進行模擬 詳細解釋了非對稱奈米環的磁響應的溫度穩定性，和同心三重奈米環的寬的非對稱激子發光頻譜。我們的模擬結果顯示磁化率的量對半導體奈米奈米環的集合與組成很敏感。因為非同質擴張，群體非對稱奈米環的不同磁化率造成了溫度穩定性。我們也觀察了同心三重奈米環的激子發光頻譜的非同質擴張，結果顯示非同質擴張主要來自奈米環的內層高度差異。這個模擬結果再現並解釋了實驗寬的非對稱的螢光頻譜。計算的激子頻譜波峰位置和實驗觀察到的相符。 所以，我們實現了網格法能有效率的對複雜外貌的奈米環群體的磁性光性進行模擬與模型。群體奈米環的計算結果協助我們了解與解釋實驗結果。

In this dissertation, we theoretically studied the collective magneto-optical properties of artificial composite materials made from semiconductor nano-objects such as quantum dot molecules and nano-rings. We present results of simulations on relations between quantum mechanical states in semiconductor quantum dot molecules and the magneto-optical response of embedded layers of these nano-objects. We also study the effect of the inhomogeneous broadening on the magnetic response of ensembles of asymmetrical nano-rings and excitonic peaks in triple concentric nano-rings ensembles. We have generalized hybrid discrete-continuum model to simulate magneto-optical response of systems of embedded semiconductor nano-objects with arbitrary shapes. Our generalized hybrid model allows us to simulate the coherent manipulation of quantum states of electrons and holes confined in nano-objects and monitor that by means of analysis of the collective magneto-optical response (reflectance, transmittance, absorbance) from the systems. The manipulation is performed by an external magnetic field applied upon the systems. Our description is done in three-dimensions which allows us to consider arbitrary directions of the external magnetic field. The great advantage of our approach is flexibility in modeling of systems with arbitrary shapes, sizes and directions of the external field in contrast to most of the calculations done before. Using the generalized hybrid model the magneto-optical response of layers of semiconductor nano-objects can be found once we know the responses of individual nano-objects. In the hybrid description the response of a nano-object is characterized by the excess polarizability. This polarizability includes a static part and dynamic part. Therefore, our approach requires for a simultaneous multi-scale electrodynamic and quantum mechanical description. The static part is determined electromagnetically by solving the Poison’s equation. The dynamic part (requiring for energies and probabilities of the optical transitions in the object) is determined quantum mechanically. To calculate this part the energies and wave functions of electrons and holes confined in the semiconductor nano-objects are obtained numerically within the k.p approximation including 2+2, and 2+4 band models by the nonlinear iterative method. To demonstrate our model we consider the coherent manipulation of the electronic states of asymmetrical quantum dot molecules (triple and double quantum dot molecules) and the collective magneto-optical properties of a layer of the molecules. Our simulation results show that changes in the quantum mechanical configuration of the quantum dot molecules can be observable by monitoring changes in the ellipsometric data obtained for layers made from them. The magnetoellipsometric data can reproduce an important and clear information on the quantum mechanics of the molecules. We proposed mapping method which allows us to efficiently simulate quantum mechanical properties of semiconductor nano-objects with variations of their sizes and shapes. Using our mapping method we have investigated the inhomogeneous broadening of magnetic response and optical properties of ensembles of nano-rings due to size and shape dispersion. In our method three-dimensional confinement potential is mapping the actual geometrical, structural, and material composition of nano-objects. Using this potential, we find energy states of electrons and holes confined in the nano-objects. Then we simulate the inhomogeneous broadening of the magnetic response and excitonic peaks of ensembles of nano-objects. Generally, our method can be applied to simulate the inhomogeneous broadening effect in ensembles of nano-objects with arbitrary shapes. However, in this dissertation, to implement our method, we perform simulations to explain in detail the temperature stability of magnetic response of asymmetrical nano-rings and the appearance of wide asymmetrical excitonic peaks in ensembles of concentric triple nano-rings. Our simulation results show that the amplitude of the differential magnetic susceptibility is sensitive to geometry and composition of semiconductor nano-rings. Because of the inhomogeneous broadening effect the differential magnetic susceptibility of the ensembles of wobbled nano-rings demonstrates the temperature stable behavior. We also investigated the inhomogeneous broadening effect on excitonic peak in triple concentric nano-rings ensembles. It has been shown that the broadening is preferably caused by variation of the inner height of the ring. The simulation results have reproduced and explained the appearance of the wide and asymmetrical excitonic peak in the experimental photoluminescence spectra. The calculated position of the excitonic peak in the optical spectrum is in good agreement with the experimental observation as well. We have managed to demonstrate that our mapping method is very efficient for simulation and modeling of magnetic and optical properties of ensembles of nano-rings with sophisticated shape. The calculation results for ensembles of nano-rings help us to explain and understand clearly experimental data.