具缺陷超晶格之聲子散射特性

Scattering of Acoustic Phonons in Superlattice with a Defect

陳榮峰(Rueng-Feng Chen)

指導教授 ： 薛文証

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.10372

摘要

本篇論文主要目的在於分析聲頻聲子在半導體超晶格結構下的能帶與缺陷態特性，針對聲頻聲子分為垂直入射之縱向聲頻聲子與斜向入射之橫向聲頻聲子作探討。本文利用傳輸矩陣法推導其兩層與四層的能帶結構色散關係式與缺陷態特徵方程式；改變其材料排列與厚度變化，觀察在垂直入射之縱向聲頻聲子與斜向入射之橫向聲頻聲子的能帶結構與缺陷態的特性，結果發現材料排列與厚度完全相反時，能帶結構會相同。固定摻雜濃度並增加第二層厚度時，在相同的頻率範圍下會使得能隙變多，在四層超晶格結構下，單純增加第四層的厚度也會得到相同的結果，但兩層超晶格的能帶結構的變化較明顯；此外，在固定厚度下，當摻雜濃度變大時，能隙的頻率會變大；最後，改變厚度比例、摻雜濃度、與材料排列觀察缺陷態的變化，會發現缺陷態都會侷限在能隙裡面，也可觀察其奇模態與偶模態分佈的特色。

關鍵字

聲子 ； 超晶格 ； 傳輸矩陣法 ； 能帶結構 ； 缺陷態

並列摘要

The purpose of this thesis is to analyze the characteristics of band structure and defect modes for acoustic phonons in semiconductor superlattice. The acoustic phonons can be separated into two parts, one is the longitudinal acoustic phonon and the other is transverse one. I use transfer matrix method to derive the dispersion relation and the defect mode equations of two-layered and four-layered semiconductor superlattice. In order to observe the characteristic of band structures and defect modes for longitudinal and transverse acoustic phonon, I change material arrangement and width. Then I find that if material arrangement and width are reversed, the band structures will be the same. Moreover, fixing doping concentration and increasing the width of the second layer, in the same range of frequency, the number of band gap will be increased. I can observe the same phenomenon in four-layered semiconductor superlattice, but the variation of the band structure in two-layered superlattice is more obvious. Furthermore, fixing the total width of the superlattice and adding the doping concentration, the frequency of the band gap will be increased. Finally, changing the width ratio of superlattice, doping concentration, and material arrangement, I can observe not only the defect modes are all localized in band gap but also the distributive characteristic of even and odd defect modes.

並列關鍵字

Phonon ； Superlattice ； Transfer Matrix Method ； Band structure ； Defect mode

參考文獻

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