臺灣博碩士論文加值系統

在矽/鍺超晶格中折疊聲學聲子之研究
摘 要
在這個研究中，呈現了三個以分子束磊晶法（MBE）生長在Si基底上的Si/Ge超晶格的拉曼光譜。超晶格樣本的週期數N=5，超晶格的生長條件﹕矽層的厚度均為50 nm；鍺層的厚度分別為2.2 nm、3.8 nm及5.4 nm。首先以樣品的TEM圖按比例測量，矽層的厚度為50.18 nm、48.65 nm及48.89 nm；鍺層的厚度為2.46 nm、3.78 nm及4.44 nm。
光譜中Si-Si Mode的峰線非常明顯；Ge-Ge Mode的峰線相對較弱；Si-Ge Mode的峰線則因週期數太少的關係，常溫下非常不明顯。三個超晶格的拉曼光譜在低頻(0~100 cm-1)區域，均有大量而顯著的折疊聲學聲子訊號，且其分裂的雙重線非常明顯。如以Rytov理論擬合其折疊聲子的頻率，可得矽層厚度為49.65 nm、45.98 nm及45.95 nm；鍺層的厚度為2.12 nm、3.78 nm及5.01 nm。誤差均在6%以內，可見Rytov理論是研究超晶格拉曼光譜的良好基礎。
如以彈性光學模式擬合折疊聲子的光譜強度，在遠離共振能量的波長(如476 nm)，可以得到不錯的結果。同時得到矽層對厚度週期的比值分別為0.96（632 nm）、0.93（476 nm）及0.93（476 nm），與Rytov理論擬合折疊聲子的結果：0.96、0.92及0.90相較，除了樣品N107的差異3%較大外，大致上吻合良好。
另以線性鏈模式（LCM）檢驗光譜中的Ge-Ge Mode，可以檢驗鍺層的粗糙程度，並估算其厚度為2.22 nm、3.83 nm及5.37 nm，與聲子的擬合結果相較，差異在7%以內。
由變溫下的拉曼光譜（10 K~300 K），可以看到在200 cm-1附近有連續性散射的訊號，而且發現同一樣品溫度愈低，或不同樣品鍺層厚度愈薄，其連續性散射愈明顯。經由低頻的折疊聲子及Ge-Ge Mode共振及高頻的螢光光譜，可以看出鍺層的E1能階約在2.3 eV附近，而且分佈甚廣（2.29 eV~2.35 eV）。

Raman Study of Folded Acoustic Phonons in Si/Ge Superlattices
abstract
This research presents three Raman Spectrums of Si/Ge superlattices growing on the substrate of Si by MBE. The period of superlattice samples N=5, the growing conditions of superlattice are: the Si-layer is 50nm；the Ge-layers are 2.2nm、3.8nm and 5.4nm. Measuring by TEM of samples firstly, the Si-layers are 50.18nm、48.65 nm and 48.89 nm；the Ge-layers are 2.46 nm、3.78 nm and 4.44 nm。
In the Spectrum, the peak of Si-Si mode is quite obvious；The peak of Ge-Ge mode is comparatively weak. In the room temperature, the peak of Si-Ge mode is quite unobvious due to the fewer periods.
Raman Spectrum of three superlattices shows many and obvious folded phonon signals in the low frequency (0 ~100 cm-1) area , so does the doublets of phonon are quite obvious. Fittting the frequency of folded phonons by Rytov’s theory finds that the Si-layers are 49.65nm、45.98 nm and 45.95 nm, the Ge-layers are 2.12 nm、3.78 nm and 5.01 nm. All the errors are within 6%, so Rytov’s theory is a good foundation to study Raman Spectrum of superlattice.
Fitting the intensity of folded spectrum of phonon with photoelastic mode , in the wavelength far away the energy of resonance ( As 476 nm) can get good result. Also getting the ratio of Si-layer thickness and the period of superlattice are 0.96（632 nm）、0.93（476 nm）and 0.93（476 nm）, compared with the result of fitting frequency of folded phonon by Rytov’s theory：0.96、0.92及0.90, matchs very well, except the 3% difference of sample-N107.
Besides, examining Ge-Ge mode in the spectrum with LCM, the roughness of Ge-layer can be examed, and the calculating layers are 2.22nm、3.83 nm and 5.37 nm, the difference is within 7% comparing with the result of fitting phonons.
In the various temperature (10 K~300 K) Raman Sprctrum, there are signals of continuous scattering of phonons around 200 cm-1 , and the lower the temperature, or the thinner the Ge-layer, the more obvious the continuous scattering of phonon is. We can find the phenomenon that E1 energy of Ge-layer is in the vicinity of 2.3 eV and distributed widely ,when we observe the folded phonon in low frequency, the resonance of Ge-Ge Mode, and the fluorescence in high frequency.

目 錄
第一章 緒論 ﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍ 4
參考資料
第二章 樣品製成條件及結構 ﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍ 6
參考資料
第三章 折疊聲學聲子 ﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍ 8
3.1 拉曼光譜儀
3.1.1 拉曼光譜儀的裝置
3.1.2 拉曼光譜儀的原理
3.2 拉曼散射
3.2.1 拉曼散射原理
3.2.2 樣品N105的拉曼光譜
3.2.3 樣品N106的拉曼光譜
3.2.4 樣品N107的拉曼光譜
3.3 折疊聲子的形成
3.4 由Rytov 理論計算折疊聲子模
3.5 由Rytov理論擬合折疊聲子光譜鋒值
3.6 結論
參考資料
第四章 折疊聲子的強度比 ﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍ 36
4.1 以彈性光學模式計算折疊聲子之拉曼散射強度比
4.2 折疊聲子之拉曼散射強度比擬合
4.3 結論
參考資料
第五章 超晶格中鍺層的粗糙程度 ﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍ 45
5.1 超晶格中鍺層的Ge-Ge Mode
5.2 超晶格中鍺層的厚度
5.3 結論
參考資料
第六章 超晶格中的量子井能隙 ﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍ 52
6.1 矽鍺的能帶結構
6.2 連續性散射理論
6.3 變波長的拉曼光譜
6.4 由連續性散射與螢光光譜探求共振能帶
6.5 光學、聲學聲子能帶共振現象討論
6.6結論
參考資料
第七章 結論 ﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍ 69

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