利用有限差分法計算自組式量子點電子結構

Three dimensional finite difference simulation for the electronic structures of self-assembled quantum dots

徐燁(Hsu, Yeh)

指導教授 ： 鄭舜仁

國立交通大學/理學院/電子物理系所/碩士(2010年)

https://doi.org/10.6842/NCTU.2010.00636

摘要

本論文主要是探討(InGaAs/GaAs)自組式量子點中載子的電子結構。文章中利用單能帶有效質量理論以及三維非均勻格點有限差分法計算自組式量子點中載子的電子結構。
我們利用自行發展的數值程式探討截角金字塔量子點中擴散、應變等效應對量子點的有效能隙、能階量化、波函數分布範圍的影響。
當量子點受到量子點中擴散和應變效應影響時束縛位能會減弱，特別在量子點很小時，我們模擬結果顯示隨著量子點變小，電子態的束縛越來越弱，當量子點底部長度小於12奈米時，電子波函數分布範圍的趨勢出現明顯的反轉與實驗相符合[1]

關鍵字

自組式量子點 ； 非均勻格點 ； 截角金字塔 ； 電子結構

並列摘要

This thesis presents a theoretical study of electronic structures of InGaAs/GaAs self-assembled quantum dots by using finite difference method in the single-band effective mass approximation. Throughout this work, truncated-pyramid shaped quantum dots subject to strain and Ga-diffusion are considered in the simulation.
For the study, we develop a 3D non-uniform grid finite difference simulator to calculate the effective energy gap, the level energy quantizations and wave functions of single electron and hole confined in 3D-confining quantum dots. We show that the confining potential of quantum dot for electron is substantially softened by strain and Ga-interdiffusion, especially pronounced in small quantum dots. Our simulated results reveal the formation of weakly bound electron states in the small dots with the base length shorter than 12nm and the resulting significant extent of electron wave has been recently confirmed experimentally[1].

並列關鍵字

self-assembled quantum dots ； non-uniform grid ； truncated pyramid ； electronic structure

參考文獻

[1]M.-F. Tsai, H. Lin, C.-H. Lin, S.-D. Lin, S.-Y. Wang, S.-J. Cheng, M.-C. Lee, W.-H Chang, “Diamagnetic Response of Exciton Complexes in Semiconductor Quantum Dots”,Phys. Rev. Lett. 101, 267402 (2008)

[2]M. Califano and P. Harrison, Phys. Rev. B 61, 10959 (2000).

[3]M. Grundmann, O. Stier, and D. Bimberg, Phys. Rev. B 52, 11969 (1995).

[4]M. A. Kastner, Phys. Today 46, 24 (1993).

[5]S. Tarucha, D. G. Austing, and T. Honda, Phys. Rev. Lett. 77, 3613 (1996).