C-2-8 STEM/EDS分析上的假訊 (Artifacts in STEM/EDS Analysis)
由於STEM/EDS硬體的性能與軟體的功能大幅提升，近幾年來，在半導體元件的TEM分析中，EDS分析已成不可或缺的資料。目前所有的EDS分佈都在STEM模式下，用能譜影像(spectrum image)技術分析，先做出一組成份映像圖(elemental maps)，如圖C2-34所示。成份映像圖顯示元素的二維分佈狀況，每一元素映像圖內的訊號明暗度，可以顯示元素濃度的相對高低，但無法告知絕對的濃度值，而不同元素映像圖內的明暗度不能代表濃度的相對高低。元素絕對的濃度值必須選取局部區域運算，或從直線成份分佈圖，才能讀出線上各點的濃度值。
Due to significant improvements in the performance of hardware and functions of software, EDS analysis has become a necessary and routine item in TEM analysis of semiconductor devices recently. An EDS analysis is performed by spectrum image technique in STEM mode. A set of elemental maps are then extracted from this spectrum image, as shown in Figure C2-34. EDS elemental maps tell the distribution of elements in two-dimension, and relative concentration by brightness in the same elemental map, but no values of concentration, and the difference in brightness in different elemental map does not means high or low in concentration. Values of concentration of elements are available by extracting EDS spectra from local regions, or from EDS line profiles from this spectrum image.
圖C2-34 STEM HAADF image and elemental maps of nano particles extracted from a spectrum image
製程工程師往往希望拿到的EDS成份直線分佈圖，圖中元素曲線非常平滑好看。但是由於EDS訊號收集效率和能譜影像像素數目的因素，能譜影像中每一像素內的EDS訊號強度不高，從奈米層次的相拉出的EDS原子百分比成份直線分佈圖中的元素曲線通常是上下震盪的。為了滿足客戶的要求，TEM分析實驗室常對原始數據做一些後續的平滑處理，如下面各圖所示。圖(a) 是EDS原始強度line profiles，在標示 I 的區域內，各元素的訊號強度為背景值，物理上是沒有試片的區域。但是將其換算成圖(b)的EDS at%成份直線分佈圖後，雖然氮和氧的曲線震盪幅度很大，代表氮和氧的濃度變化很大，因此圖(b)圖面上的意義顯示區域I 為一含氮和氧的區域。雖然數學上，7/10和700/1000值相等，但是物理上(或統計學上或統計學上)，二者的意義完全不同。將類似區域I的訊號放入EDS at% line profiles或EDS wt% line profiles運算中，除了造成可能誤導的訊息外，物理上完全沒有意義的是。將圖(b)平滑處理成圖(c)或圖(d)之後，這些曲線平滑處理造成的假象，更容易誤導許多不知整個分析歷史的看圖者，導致工程師製程調整方向錯誤。
Process engineers always like elemental curves in EDS line profiles are smooth. However, due to the limit of EDS collection efficiency and large pixel number in spectrum images, the signal intensity is low in each pixel in spectrum images. EDS at% line profiles of phases in nano scale are usually fuzzy. To meet requirements of customers, many TEM service laboratories do some off-line data process to make EDS line profiles smooth. Some artifacts in these processed EDS line profiles may mislead engineers in process tuning, as plots shown below. Region I in EDS intensity line profiles, Figure (a), is a region with no physical specimen. But, when the y axis is transferred to at% as shown in Figure (b), it looks region I is a region consisting of N and O with large variation. Both 7/10 and 700/1000 are identical mathematically, but significantly different in physics (or statistically). It is meaningless to put region I into EDS at% line profiles or EDS wt% line profiles calculation physically, except to result in misleading information. Those fuzzy elemental curves, especially N and O in region I, in Figure (b) can be improved by data smoothing process. They are changed to Figure (c) and Figure (d) by 3-points and 5-points smoothing respectively. Those elemental curves look better compared with them in Figure (b). This will mislead people who do not know the history of these data in detail, and even guide process engineers to tune processes in wrong directions.
圖C2-24 EDS line profiles. (a) EDS intensity line profiles, (b) EDS at% line profiles, (c) EDS at% line profiles, 3-points smoothing, (c) EDS at% line profiles, 5-points smoothing.
除了引起前述的錯誤外，數據平滑處理對於只有幾奈米厚度薄膜的濃度也頗有影響。從圖(b)量得的鉭/氮化鉭薄膜約為9.2奈米，最高濃度約為71.4 at%；經三點平滑處理後，鉭訊號曲線從非對稱變成高斯對稱，半高寬為8.3奈米，最高濃度降為58.4 at%；經五點平滑處理後，鉭訊號曲線也是成高斯對稱，半高寬為10奈米，最高濃度降為48.6 at%。而IV區的銅的最高濃度始終保持在77 at%左右，平均濃度也保持在70 ~ 75 at% 之間。顯見平滑處理對於大尺寸的物體，元素曲線確實可以變得較好看，真實濃度也變化不大。但是對奈米尺寸的物體，其組成的濃度和濃度分佈都會明顯失真。
Besides errors induced as stated before, smoothing process will affect the concentration of thin films of several nano meters in thickness. The thickness of Ta/TaN is about 9.2 nm, maximum Ta concentration is 71.4 at% in Figure (b). The distribution of Ta becomes Gaussian symmetry after 3-points smoothing, the full width of half maximum is about 8.3 nm, and its maximum concentration drops to 58.4 at%. The maximum Ta concentration becomes to 48.6 at% and the FWHM is about 10 nm if a 5-points smoothing is processed. Obviously, smoothing EDS line profiles is good for objects of large scale but may cause misleading errors in objects of several nano meters.
沒有留言:
張貼留言