鍺錫半導體之能帶結構模擬與光致發光特性

Band Structure Simulation and Photoluminescence of GeSn Alloys

黃敬琮(Ching-Tsung Huang)

指導教授 ： 李峻霣

國立臺灣大學/電機資訊學院/電子工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201800486

摘要

近年來，鍺錫材料越來越受到關注，這是由於鍺錫合金在錫濃度高於8~11 %時有機會變為直接能帶材料，可製作高效能的光電元件。此外，因其同時擁有高電子與電洞的遷移率，且可跟現今的積體電路技術相容，鍺錫極有潛力被應用於下一代場效電晶體(MOSFET)的通道(channel)中。為了有效利用鍺錫合金的優點，其材料特性如能隙與等效質量必須被徹底研究與掌握。因此，在本論文中將利用第一原理計算與光致發光(photoluminescence)頻譜量測來對鍺錫的能帶結構進行深入探討。
要使鍺錫成為直接能帶材料，錫濃度必須超過某個臨界值。我們用Materials Studio軟體中的CASTEP模組，透過第一原理與密度泛函理論來模擬鍺和鍺錫半導體的能帶結構。以屬於廣義梯度近似(GGA)的RPBE為泛函，加入適當的Hubbard參數U和scissor值，可正確地模擬出鍺的能帶結構。透過建構鍺的超晶胞，並用不同數量的錫原子替換其內部的鍺原子，將可模擬不同錫濃度的鍺錫之能帶結構，鍺錫約在錫濃度為12 %時轉變為直接能帶材料。
接著為了進行光致發光實驗來研究鍺錫磊晶薄膜的光學特性而架設了一個光致發光系統，並利用室溫下矽基板和鍺基板的光致發光頻譜進行系統測試及校正。此外，透過設計支撐架將冷頭和真空腔體懸吊於光學桌上，如此可用同一套系統進行室溫與變溫的光致發光頻譜量測。當錫濃度上升時，鍺錫的光致發光頻譜有紅位移的現象，顯示鍺錫合金的能隙隨著錫濃度上升而下降。加入n型摻雜會使光致發光訊號的峰值位置往長波長方向移動，並在溫度降低時有較強的訊號，主因可能是在低溫下缺陷較不活躍。至於應變(strain)對鍺錫能隙的影響，鬆弛(relaxed)鍺錫的能隙比壓縮應變(compressive strained)的小，且可在較低的錫濃度就從間接能帶轉換成直接能帶材料。最後，由鍺錫量子井的光致發光頻譜可知，量子效應會使量子井的等效能隙大於實際能隙。透過穿透式電子顯微鏡(TEM)和倒晶格空間映射(RSM)等測量工具對鍺錫量子井結構進行詳細的分析，利用量子力學計算出的量子能階位置與實驗結果相符。比較光致發光實驗和第一原理計算的結果亦發現由兩者得到的鍺錫能隙值相當吻合。

關鍵字

鍺錫 ； 能帶結構 ； 光致發光 ； 第一原理 ； 密度泛函理論

並列摘要

Recently, GeSn alloys have attracted more and more attentions because they can become direct bandgap materials with Sn fraction of > 8~11 % for high-efficiency optoelectronic devices. In addition, due to their high electron and hole mobility, GeSn can be used as the next-generation channel material for MOSFET applications. Moreover, GeSn is compatible with the current Si VLSI technology. Therefore, the band structures of GeSn alloys were investigated in this thesis.
To investigate the critical composition of Sn for GeSn to become a direct bandgap material, we used first-principles calculation by CASTEP package in Materials Studio to simulate the band structures of Ge and GeSn. By a functional of revised Perdew-Burke-Ernzerhof (RPBE), a generalized gradient approximation, the band structure of Ge can be calculated correctly by adding Hubbard parameter U and using scissor operator. GeSn alloys of various concentrations of Sn were simulated by creating a supercell of Ge and replacing different amounts of Ge atoms with Sn atoms. The indirect-to-direct transition was predicted to occur for a GeSn alloy of Sn ~12 %.
A photoluminescence (PL) measurement system was set up for studying the bandgap of GeSn epitaxial films. Room temperature PL spectra of Si and Ge substrate were used to test and calibrate the system. Besides, a mechanical support was designed for the vacuum chamber and cold head for temperature-dependent PL experiment (300 K~18 K). As the Sn composition increases, a red-shift of PL peak position occurs, which means a reduction of bandgap. With heavily doping in GeSn films, the PL peaks shift to a longer wavelength with a stronger intensity as the temperature is reduced. The strain effect on the GeSn bandgap was also investigated. As the strain is relieved, the bandgap is reduced, and the indirect-to-direct transition would occur at a lower Sn fraction for GeSn alloys. Furthermore, the PL in the GeSn quantum well structures were studied. The effective bandgap of GeSn quantum well is larger than the bulk bandgap owing to quantum effect. A detailed analysis was offered and compared by the careful calculations of quantum subbands and material metrologies such as RSM and TEM. The bandgaps of GeSn measured by PL were also compared and well-matched to those calculated by density functional theory.

並列關鍵字

GeSn ； band structurte ； photoluminescence ； first principle ； density functional theory

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