奈米尺度場效電晶體隨機電報訊號:三維統計異變模式及缺陷捉放動力學分析

Abstract

對於未來的電路設計而言，奈米尺度下元件開發的統計變異性至關重要。本文從平面式金氧半場效電晶體中的隨機電報訊號研究出發，探討通道中電子分布在均勻和非均勻狀態下受到隨機電報訊號影響時，元件的電流及臨界電壓所表現出來的擾動行為。我們參考穆勒和舒爾茨教授的數學解析模型，進一步推導出在均勻通道下，當元件受到隨機電報訊號影響時，電流擾動的統計分佈解析式。經由比對文獻中實驗和模擬結果以及我們的模擬統計結果，可證明我們解析式的正確性。另外，針對非均勻通道的元件，我們藉由建立應用準則，可將穆勒-舒爾茨滲透理論中標準差和平均值明確界定出允許的範圍，因此確立了對標準差和平均值正確的使用方式。使用標準差和平均值並搭配我們提出的圖形化方法，可以快速建立不同滲透型態下受隨機電報訊號影響時電流擾動的統計分布曲線。每一組的標準差和平均值都意謂著某一種的滲透型態，且可視為一滲透型態指標，協助我們分析元件在製程變異，大小變化及閘極結構改變下，非均勻通道中的滲透型態模式。非均勻通道下隨機電報引致臨界電壓偏移的統計分佈模型進一步延伸應用於偏壓溫度不穩定性所造成的臨界電壓偏移統計分佈，並成功地重現了文獻中偏壓溫度不穩定性臨界電壓偏移的統計分布曲線。建立此均勻和非均勻兩種通道狀態下，電流和臨界電壓偏移的統計分佈模型，可以大幅減少透過實驗或數值模擬所需要的時間和限制。 考量工業界主流採用三維鰭式場效電晶體結構，我們推導出適用於鰭式場效電晶體下電流擾動的統計分佈模型。對於均勻通道而言，透過比較文獻數據和我們的模擬統計結果可以證明統計解析公式的正確性。對於非均勻通道的元件，我們也建立了適用於鰭式電晶體結構下所對應的應用準則，並成功重現文獻中的統計分布曲線。透過此一統計模型也可發現在鰭式場效電晶體元件中的滲透型態與製程有關，和元件的大小無明顯相關。此外，此一統計模型也證明同樣適用於偏壓溫度不穩定引致臨界電壓偏移之統計分布，並可推估對應的缺陷密度。因此，本研究對為下一世代元件開發中的電流及臨界電壓擾動，，提供了一個可靠及有效率的分析方式。 另外，電子進出缺陷產生隨機電報訊號的過程對電路中的時域分析是很重要的。我們可以使用多聲子穿隧理論來模擬抓取時間，且以組態座標圖加以描述對應的能量關係。透過外加應力的方式，確立了電子進出缺陷間之能量關係及其所對應的唯一組態座標圖。同時我們也發現在外加伸張應力之下，缺陷能量、熱活化能和晶格弛豫能量皆會增加。

For the design of future circuits, it is essential to examine the statistical variability associated with the development of nanoscale devices. In this thesis, we study such current and threshold voltage disturbances due to the random telegraph signals (RTS) in planar metal-oxide-semiconductor field-effect transistors (MOSFETs) taking into account the percolation-free channel and percolative channel. We quote the analytical formula developed by Muller and Schulz to further deduce analytic statistical models for the MOSFETs with a uniform channel subject to RTS. We can validate these analytic models through comparison with existing experiment and simulation results as well as our simulated ones. In addition, for the case of non-uniform channel, the standard deviation (loc) and mean (mloc) of the Iloc/Id distribution in the Muller-Schulz percolation theory are clearly defined, leading to design guidelines. For the first time, the statistical distributions for the non-uniform channels can be quickly created through our devised graphical method with allowed sets of mloc and loc. A set of mloc and loc is representative of a kind of percolation pattern and a useful indicator to help us analyze percolation patterns under the process variations, different device sizes and gate stack types. The statistical model for non-uniform channel is further extended to the calculation of the threshold voltage shift statistical distribution caused by bias temperature instability (BTI). The ability to reproduce threshold voltage shift distributions by BTI provides us an efficient way to predict stressing reliability. Briefly, the created statistical models can significantly reduce the time-consuming demand in the experimental and simulation works. Considering the mainstream 3-D fin field-effect transistors (FinFETs) structure in industry, we derive corresponding statistical models for current and threshold voltage shift disturbances in FinFETs. Literature results and our simulation ones confirm the validity of the proposed statistical analytic model in the uniform channel. For the non-uniform channel, the design guidelines for FinFETs are created and the statistical distribution curves are reproduced successfully. The percolation patterns of FinFETs witnessed by statistical model resemble each other due to the same or similar manufacturing process, without significant correlation with the device size. Furthermore, the models are also utilized in BTI induced threshold voltage shift distributions and thus the corresponding defect density can be obtained. Therefore, RTS statistical model provides a reliable and efficient method to examine the current and threshold voltage shift variation for the next generation devices. In addition, the RTS capture/emission time constants due to electron trapping/de-trapping process are crucial in the kinetic analysis for circuit design. We utilize multi-phonon tunneling theory to simulate capture time and describe the corresponding energies via a configuration coordinate diagram. The unambiguous configuration coordinate diagram and energy levels before and after electron trapping are crucially confirmed by the externally applied mechanical stress. We found that the trap energy, thermal activation energy and lattice relaxation energy are all increased after tensile stress.