探討半導體量子點U型結構之電子能帶問題

Abstract

隨著製造技術的進步，電子元件的尺寸越來越小，以目前的金屬氧化物場效應電晶體的通道長度就已短至0.12mm的尺寸。這造成量子效應越來越明顯，因此近幾年來很多量子井，量子線，量子點的研究越來越多。這篇論文主要是將量子點中的位能分佈設定成U形的結構，然後求出哈密頓運算符的特徵值（能量）和特徵函數（波函數）。並且分析半導體內能量對波數空間的分佈情況。

The size of electronic devices can be scaled down more small with more advanced process. For examples, the channel length of MOSFET has been scaled down to 0.12μm. However the quantum effect is observed obviously. Recently more and more researches are related to the quantum effect of devices, such as quantum wells, quantum wires, and quantum dots. In this thesis, the potential structure is set as U shape, and one may calculate the eigenvalue (energy) and eigenfunction (wave function) of Hamiltonian oparator. One can also analyze the relationship between energy E and wave vector k of electrons in semiconductor.