材料分析B-4-5 TEM明場像的化妝師-物鏡光圈(Objective aperture, the make up artist of TEM BF images)

TEM明場像的化妝師-物鏡光圈(Objective aperture, the make up artist of TEM BF images)

 TEM是固態微奈米材料分析的終極武器之一。TEM影像的分辨率很高，明場影像約0.4奈米，無球差的高分辨影像達0.18奈米，球差修正的高分辨影像達0.05奈米，可以解析目前半導體元件中的各層奈米薄膜結構。由於台灣本身沒有生產TEM，所以學界或工業界，對於操作上如此高精密度、高複雜性的材料分析儀器都謹慎管理，對初階(甚至中階)的使用者有許多的限制，不能調動C1光圈，不能調動C2光圈，….等等，但是一定要學會正確操作物鏡光圈。在TEM模式下，物鏡光圈是調整影像對比的樞紐。要精確地量出一、二奈米的薄膜厚度，除了TEM本身的高分辨率(或解析能力)外，各層奈米薄膜之間也要有足夠的對比。

TEM is one of the ultimate instruments for solid state micro-nano materials analysis. The resolution power of TEM image is high, BF images about 0.4 nm, HRTEM images without Cs corrector about 0.18 nm, and HRTEM images with Cs corrector 0.05 nm, enough to resolve nano thin film structures in semiconductor devices. Since there is no TEM manufacturer in Taiwan, all Taiwan TEM laboratories, academic and industry, are very carefully to manage this high precision and high complexity MA instrument, put many limit rules on junior (some even middle level) TEM users, such as do not touch the C1 aperture, do not change the C2 aperture, … etc. But, every TEM user must know how to operate the objective aperture correctly. The objective aperture is the hinge to adjust the image contrast in TEM mode. Obviously, besides the resolution power of the instrument, sufficient image contrast is another key to measure thin film thickness of 1 to 2 nano meters accurately.

TEM明場影像對比機構主要有二種：原子序對比和繞射對比。這二種影像對比機構源自入射的高能電子和試片之間的散射與繞射作用。當一束高能電子撞擊到一群原子時，入射的高能電子會被原子核散射，其分布的機率如圖B4-5-1(a)示意圖所描述。通過試片輕元素材料區域的高能電子，被散射的狀態如綠色曲線所示，集中在以光軸為中心小角度範圍內。通過試片重元素材料區域的高能電子，被散射到高角度的比例增加，如紫色曲線所示。置入物鏡光圈後，被散射到高角度的入射電子被物鏡光圈擋住，無法繼續前進成像。從圖B4-5-1(b)和(c)看出，置入物鏡光圈後，穿過輕元素材料區域和穿過重元素材料區域的高能電子被擋住的比例不同，通過輕元素材料區域的高能電子被擋的較少，成像的劑量較多，在黑白影像中呈亮區；反之亦然，重元素材料區域呈暗區。因此，置入物鏡光圈後，原子序對比提升，物鏡光圈愈小，原子序對比愈強烈。

There are two main image contrast mechanisms in TEM bright-field (BF) images: atomic contrast (or called z contrast) and diffraction contrast. These two mechanisms are caused by scattering and diffraction between incident high energy electrons and the specimen. When an electron beam strikes a bunch of atoms, the distribution of elastically scattered incident electrons is shown schematically in Figure B4-5-1(a). The green curve describes the distribution of elastically scattered high energy electrons passing through regions of light elements, centralizes around the optical axis in a small angle range. And the purple curve describes the distribution of elastically scattered high energy electrons passing through regions of heavy elements. Electrons scattered to high angles will be blocked off to contributed to the final image when an objective aperture is inserted. As shown in Figure B4-5-1(b) and (c), the number of electrons blocked by the objective aperture is different for regions consisted atoms of different atomic number. Electrons passing through regions consisted of light element will be less blocked, the corresponding pixels have high dose and show bright contrast, and vice versa, pixels corresponding to regions of heavy elements show dark contrast. The smaller objective aperture gives more atomic number contrast in TEM BF images. 

圖B4-5-1 入射高能電子被原子核散射分佈示意圖，橫軸為徑向角度，縱軸為強度。(a)輕元素和重元素散射的差異，曲線下的面積相等；(b)置入中尺寸的物鏡光圈，部分通過重元素區域的散射電子被擋掉；(c)置入小尺寸的物鏡光圈，部分通過輕元素區域的散射電子被擋住，大部分通過重元素區域的散射電子被擋掉。

當晶體試片的某個極軸和透射電子束平行時，此時該晶體在強烈繞射條件。圖B4-5-1(a)中的入射高能電子分佈狀態變成如圖B4-5-2(a)所示，電子分佈變成局部集中的狀態。類似前述的情形，圖B4-5-2(b)和B4-5-2(c)顯示，置入物鏡光圈後，部分繞射電子束的電子被擋住，無法繼續前進成像，此晶體最後成像的電子劑量因此相對低，在TEM明場影像中呈暗色。

When a zone axis (h₁ k₁ l₁) of a crystal is tilted to be parallel to the incident electron beam, the crystal is in a strong diffraction condition. The distribution of electrons passing through this crystal will change from Figure B4-5-1(a) to B4-5-2(a), electrons locate locally at some points. As described in last paragraph, parts of electrons are blocked away from the final image by the inserted objective aperture, as shown in Figure B4-5-2(b) and Figure B4-5-2(c). Thus, this crystal shows dark contrast in TEM BF images due to low electron dose.

圖B4-5-2 入射高能電子和晶體產生繞射後電子分佈示意圖，橫軸為徑向角度，縱軸為強度。(a)電子集中在幾個局部的區域；(b)置入中尺寸的物鏡光圈，小部分繞射電子被擋掉；(c)置入小尺寸的物鏡光圈，繞射電子都被擋掉。

除了調整影像的對比外，物鏡光圈也可以降低球面像差效應造成的疊影。圖B4-5-3顯示一組TEM明場像，分別為(a)沒有物鏡光圈，(b)100微米的物鏡光圈，(b)30微米的物鏡光圈。很明顯的，使用30微米以下的物鏡光圈，可幾乎完全消除球面像差效應造成的疊影，避免TEM明場像內含有可能造成誤解的訊息。

Besides adjusting the image contrast, the objective aperture can minimize the shadow caused by the spherical aberration. As shown in Figure B4-5-3, (a)TEM BF image without objective aperture, (b)TEM BF image with an objective aperture of 100 um, (c)TEM BF image with an objective aperture of 30 um. Obviously, an objective aperture of 30 um is enough to eliminate any visible shadow caused by the spherical aberration.

圖B4-5-3 TEM明場像。(a)無物鏡光圈，試片內有多餘的亮影(紅色箭頭)，試片邊緣有多餘的輪廓亮影(藍色箭頭)；(b)100 um的物鏡光圈，試片內仍有多餘的亮影(紅色箭頭)，試片邊緣仍有多餘的輪廓亮影(藍色箭頭)；(c)30 um的物鏡光圈，無多餘的亮影。

EDS與EELS的競爭與比較

 C-3-7 EDS與EELS的競爭與比較

由於幾何位置的關係，傳統的TEM/EDS系統中，從試片發出的特性X-光，其中只有4%被EDS偵測器接收。也就是說EDS的偵測效率很差；另外EDS能量解析度約為130電子伏特(eV)。相對地，EELS的偵測效率可以高達90%以上，而且在使用場效電子鎗穿透式電鏡的條件下，能量解析度優於1.0電子伏特(eV)。因此在1980年代中期，EELS由SEELS演進到PEELS後，許多TEM使用者預測EDS在TEM應用領域將會逐漸被EELS取代[1]。三十幾年過去，EDS不但沒有被EELS取代，反而隨著超薄窗型和無窗型的偵測器問世，逐漸蠶食EELS分析碳、氮、氧的領域。當然，EELS能譜儀最大製作公司- Gatan也不會坐視TEM成份分析的生意大餅被吞食，近幾年開發出新型的EELS能譜儀，大幅提升在重元素的偵測能力，也就是能量損失大於1000電子伏特能區的收集能力。

Due to the geometric relationship of signals and the detector, only about 4% of characteristic X-rays emitted from the specimen can enter the traditional EDS detector. It means that the collection efficiency of the EDS detector is quite low. Besides, the energy resolution of EDS is about 130 eV. On the contrary, the collection efficiency of EELS can be over 90%, and its energy resolution can be better than 1.0 eV when a FEG TEM is used. Thus, in the mid 1980s, many TEM users predicted that EDS was going to be phased out of the TEM applications [1]. However, more than 30 years passed, EDS is not replaced by EELS in the TEM market, but blooms more and more. Currently, most of TEM users have used STEM/EDS of ultra-thin-window type detectors or windowless type detectors to map C, N, O contained phases widely. Gatan, the main manufacture of EELS spectrometers, of course, is not able to stand for the loss in the market of TEM composition analysis. The developed new generation EELS spectrometers which are more efficiently in collecting electrons suffering large energy loss, more than 1000 eV, by striking atoms of heavy elements.

圖C3-15比較三組同一個MOS結構的氮和氧的成份映像圖。(a)使用單一超薄窗EDS偵測器STEM/EDS系統，訊號收集時間90分鐘；(b)使用四無窗EDS偵測器STEM/EDS系統，訊號收集時間30分鐘；(c)使用TEM/GIF系統，攝像時間約3分鐘。明顯地，從訊號收集時間和訊號強度來說，EELS對輕元素的成份映像能力還是遠優於EDS。但是EDS的價格優勢遠大於EELS，加上EELS的操作程序遠比EDS複雜。因此，目前台灣裝設在TEM上的EDS的數目遠大於EELS。

Three sets of N and O elemental maps are shown in Figure C3-15, (a)an STEM/EDS system with mono ultra-thin-window EDS detector, collection time is 90 minutes, (b)an STEM/EDS system with four windowless EDS detectors, collection time is 30 minutes, (c) a TEM/GIF system, total imaging time is about 3 minutes. Obviously, EELS is better than EDS when collection time and the intensity of signal are considered only. However, the price of EDS is much lower than that of EELS, and the operation of EELS is much complicate compared with EDS. Therefore, the number of TEM equipped with EDS overwhelms that of TEM equipped with EELS. 

圖C3-15 MOS的EDS和EELS氮和氧成分映像圖。(a)單一超薄窗EDS偵測器 STEM/EDS系統；(b) 四無窗EDS偵測器 STEM/EDS系統；(c)TEM/GIF系統。訊號收集時間分別為90分鐘，60分鐘，3分鐘。

參考文獻

1] E. Van Cappellen, “Energy Dispersive X-ray Microanalysis in Scanning and Conventional Transmission Electron Microscopy”, in the book “X-ray Spectrometry: Recent Technological Advances”, edited by Kouichi Ysuji, Jasna Injuk, and René Van Grieken, published by John Wiley & Sons Ltd. (2004).

C-2 X-光能量散佈能譜- STEM/EDS分析上的假訊 (Artifacts in STEM/EDS Analysis)

 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.