标题: 奈米尺度场效电晶体随机电报讯号:三维统计异变模式及缺陷捉放动力学分析
Random Telegraph Signals in Nanoscale FETs: 3D Statistical Variability Models and Trapping/De-trapping Kinetics Analysis
作者: 涂宫强
陈明哲
Tu, Kong-Chiang
电子工程学系 电子研究所
关键字: 随机电报讯号;统计变异;渗透理论;偏压温度不稳定性;Random Telegraph Signals;Statistical Varibility;Percolation;Bias Temperature Instability
公开日期: 2016
摘要: 对于未来的电路设计而言,奈米尺度下元件开发的统计变异性至关重要。本文从平面式金氧半场效电晶体中的随机电报讯号研究出发,探讨通道中电子分布在均匀和非均匀状态下受到随机电报讯号影响时,元件的电流及临界电压所表现出来的扰动行为。我们参考穆勒和舒尔茨教授的数学解析模型,进一步推导出在均匀通道下,当元件受到随机电报讯号影响时,电流扰动的统计分布解析式。经由比对文献中实验和模拟结果以及我们的模拟统计结果,可证明我们解析式的正确性。另外,针对非均匀通道的元件,我们藉由建立应用准则,可将穆勒-舒尔茨渗透理论中标准差和平均值明确界定出允许的范围,因此确立了对标准差和平均值正确的使用方式。使用标准差和平均值并搭配我们提出的图形化方法,可以快速建立不同渗透型态下受随机电报讯号影响时电流扰动的统计分布曲线。每一组的标准差和平均值都意谓着某一种的渗透型态,且可视为一渗透型态指标,协助我们分析元件在制程变异,大小变化及闸极结构改变下,非均匀通道中的渗透型态模式。非均匀通道下随机电报引致临界电压偏移的统计分布模型进一步延伸应用于偏压温度不稳定性所造成的临界电压偏移统计分布,并成功地重现了文献中偏压温度不稳定性临界电压偏移的统计分布曲线。建立此均匀和非均匀两种通道状态下,电流和临界电压偏移的统计分布模型,可以大幅减少透过实验或数值模拟所需要的时间和限制。
考量工业界主流采用三维鳍式场效电晶体结构,我们推导出适用于鳍式场效电晶体下电流扰动的统计分布模型。对于均匀通道而言,透过比较文献数据和我们的模拟统计结果可以证明统计解析公式的正确性。对于非均匀通道的元件,我们也建立了适用于鳍式电晶体结构下所对应的应用准则,并成功重现文献中的统计分布曲线。透过此一统计模型也可发现在鳍式场效电晶体元件中的渗透型态与制程有关,和元件的大小无明显相关。此外,此一统计模型也证明同样适用于偏压温度不稳定引致临界电压偏移之统计分布,并可推估对应的缺陷密度。因此,本研究对为下一世代元件开发中的电流及临界电压扰动,,提供了一个可靠及有效率的分析方式。
另外,电子进出缺陷产生随机电报讯号的过程对电路中的时域分析是很重要的。我们可以使用多声子穿隧理论来模拟抓取时间,且以组态座标图加以描述对应的能量关系。透过外加应力的方式,确立了电子进出缺陷间之能量关系及其所对应的唯一组态座标图。同时我们也发现在外加伸张应力之下,缺陷能量、热活化能和晶格弛豫能量皆会增加。
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.
URI: http://etd.lib.nctu.edu.tw/cdrfb3/record/nctu/#GT079611818
http://hdl.handle.net/11536/138679
显示于类别:Thesis