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. 

C-3 電子能量損失能譜(EELS) – 同素異形體與試片厚度效應

C-3-6 成份映像 – 同素異形體與試片厚度效應

C-3-4節中，圖C-41顯示EELS能譜可以區分矽的矽元素和二氧化矽的矽元素，二者L邊刃的起始能量和近邊刃微細結構明顯不同。在半導體元件的顯微結構中有多處純矽與二氧化矽相鄰的結構，EELS的成份映像技術是否可以區分它們? 圖C-46顯示純元素矽和二氧化矽的矽的分佈在EELS成份映像是可以分離的，只要三個攝像的能窗位置和寬度設置適當。

Figure C-41 in paragraph C-3-4 shows that the Si L_2,3 edges of element Si and the oxidated Si can be clearly distinguished in EELS spectra. They are different in both threshold energy and near edge fine structure. There are many sites where Si and SiO₂ are next to each other in semiconductor devices. Can they be distinguished by EELS mapping? Figure C-46 states that the distribution of Si/Si and Si/SiO₂ can be mapped separately by adequately setting those three energy windows.

圖C-46 矽的EELS成分映像圖。(a)明場像；(b)氧元素成份映像圖；(c)單晶矽和多晶矽的矽元素成份映像圖；(d)二氧化矽的矽元素成份映像圖。Ref[1]

做EELS分析的TEM試片相對上要偏薄，盡量避免入射電子產生多重散射，造成近邊刃微細結構失真。多重散射也會影響EELS成分映像圖的品質，如圖C-47所示。圖C-47(b)明場像中的鎢栓中間的縫清晰可見，而圖C-47(a)明場中的鎢栓中間的縫則只隱約可見，經驗上得知，對應圖C-47(a)的試片比對應圖C-47(b)的試片厚。因此在鈦元素成份映像圖中，薄試片(圖C-47(d))中的TiN層和Ti層的對比清晰許多。

The thickness of TEM specimen for EELS analysis needs to be thin enough to avoid multi scattering for incident electrons. Multi scattering will smear out near edge fine structure of characteristic edges of elements. Quality of EELS elemental maps will be decreased too when multi scattering occurs, as shown in Figure C-47. The seam in Figure C-47(a) is not as clear as that in Figure C-47(b). This indicates that the specimen thickness of Figure C-47(b) is thinner than that of Figure C-47(a) by experience. The contrast between the Ti layer and the TiN layer is higher in the elemental map of the thin specimen (Figure C-47(d)) than those in the thick specimen (Figure C-47(c)).

圖C-47 EELS成分映像圖的試片厚度效應。(a)厚試片的明場像；(b)薄試片的明場像；(c)厚試片的鈦元素成份映像圖；(d)薄試片的鈦元素成份映像圖。

參考文獻

1] J. S. Bow, W. T. Chang, Y. M. Tsou, H. S. Chou, and C. Chiou, Proc. ISTFA, 101-105 (2002).

 

C-3 電子能量損失能譜(EELS) - 成份映像

 C-3-5 成份映像

成份映像圖顯示某特定區域內組成元素的二維分佈情形。在TEM/STEM的分析技術中，主要獲取成份映像圖的技術有EDS成份映像圖和EELS成份映像圖二種。EDS能譜中，元素能峰和背景的強度相差甚多，亦即P/B很高，所以在EDS元素映像圖中，只要設定包含能峰的適當能窗，即使不扣除背景，就能清楚地顯示某特定元素的分布。但是在EELS能譜中，元素特性邊刃座落在一高強度的背景上，如果只設定單一能窗，則獲取的成份映像圖中可能有超過一半的訊號是背景訊號，而不是真正的元素訊號，如圖C-44的邊刃後能窗(能窗III)所蘊含的訊號。所以獲取EELS成份映像圖，除了設定包含特性邊刃的邊刃後能窗外，必須同時設定二個邊刃前的能窗，如圖C-44中的能窗I和能窗II。由二個邊刃前能窗的訊號，推算出邊刃後能窗的訊號中的背景訊號(能窗B)，扣除後，才是真正的元素訊號(能窗IV)。

Elemental maps display two dimensional distributions of elements in local interested regions. EDS mapping and EELS mapping are two main analysis techniques in TEM/STEM systems. Peaks of elements, especially major elements, in EDS spectra have high P/B ratio, elemental maps show the distributions of elements clearly once proper energy windows are set, with or without background subtraction. On the contrary, all characteristic edges fall on high background in EELS spectra, the map obtained from an energy window including part of characteristic edge will include background noise as well as true element signal, as shown in the post edge window (window III) in Figure C-44. It is necessary to set two more pre-edge windows to calculate out the background (window B) in the post edge window to obtain the true signal (window IV). 

圖C-44 EELS能譜示意圖顯示運算成份映像圖需要設定三能窗，二個邊刃前能窗: 能窗I和能窗II，和一個邊刃後能窗(能窗III)。能窗III包含背景訊號(能窗B)和真正元素訊號(能窗IV)。

圖C-45顯示一組典型TEM模式下拍攝的EELS三能窗影像和演算後的成份映像圖。圖C-45(a)為TEM明場像顯示一分析區域，此區域的組成元素包含Ti, Ni, Zr, Sb等四元素。圖C-45(b)相當於圖44中能窗IV的影像，顯示富鈦相呈一近橫躺的T字形。圖C-45(e)的邊刃後能窗影像相當於圖44中能窗III的影像，和圖C-45(c)和圖C-45(d)相比，雖然隱約顯示富鈦相的區域比周圍他相稍亮，但影像的亮度變化，會被誤認為鈦的分佈幾乎涵蓋整個區域，而且都有相當的濃度。透過二個邊刃前能窗影像算出背景影像(能窗B)，再從能窗III影像中扣除後，才能得到圖C45(b)的鈦成份映像圖。

A typical set of energy-selected images acquired in TEM mode and the final processed elemental map are shown in Figure C-45. Figure 45(a) is a TEM BF image showing an interested region being consisted of Ti, Ni, Zr, and Sb. Figure C-45(b) is the elemental map corresponding the image of energy IV in Figure 44 and indicates that the shape of the Ti-rich phase look like a lying down T. Figure C-45(e) is the Ti post-edge image corresponding to the image of window III in Figure C-44. The region of Ti-rich phase in this image is a little brighter compared with corresponding regions in Figure C-45(c) and Figure C-45(d), but is not distinguishable. A true Ti map, as shown in Figure C-45, is only obtained after background subtracted from the post-edge image.

圖C-45 EELS成分映像圖的演算。(a)明場像；(b)鈦元素成份映像圖；(c) pre-edge 1影像；(d) pre-edge 2影像；(e) post-edge影像。

C-3 電子能量損失能譜(EELS)-元素鍵結化態

 C-3-4 元素鍵結化態

原子的鍵結能和在鍵結方向的電子分布密度會因周圍原子的不同而改變。元素鍵結能的改變大概在0 ~ 7 eV的範圍內，常見的固態材料分析技術中，能解析鍵結能位移的有歐傑(AES)、電子能量損失譜(EELS)、X光吸收光譜(XAS)和X射線光電子能譜(XPS)四種。其中AES、EELS、XAS三種分析技術能同時解析電子分布密度的改變。其中，EELS和XAS的能量解析度可小於1.0 eV，而EELS的特點在於空間解析度高，可以解析小於1奈米的微區。

Both chemical bonding energy and the density of states of electrons along the bond of the atoms change with the surrounding atoms. The change in bonding energy of atoms falls in the range of 0 ~ 7 eV. There are four typical material analysis techniques for solid state materials can resolve the shift in bonding energy, they are Auger electron spectroscopy (AES), electron energy loss spectroscopy (EELS), X-ray absorption spectroscopy (XAS), and X-ray photon spectroscopy (XPS). AES, EELS, and XAS also can resolve the change in the density of states of electrons. The energy resolution of both EELS and XAS is better than 1.0 eV. Besides high energy resolution, the spatial resolution of EELS can be smaller than 1.0 nm.

圖C-41顯示單晶矽、碳化矽、二氧化矽三者物質中的矽的扣除背景後的EELS特性邊刃。圖C-41(b)是圖C-41(a)的低能量區域的局部放大圖，清楚顯示三種矽L特性邊刃的起始能量的不同，元素態的矽是共價鍵，鍵結能為99 eV；碳化矽中的矽和碳接近共價鍵，矽鍵結能增強為101 eV；二氧化矽中的矽為離子鍵，其鍵結能增強為103 eV。二氧化矽中矽的近邊刃微細結構明顯和其他二者不同，顯示Si-O鍵明顯和Si-Si與Si-C鍵不同。圖C-42顯示金屬鋁、氮化鋁、三氧化二鋁，和藍寶石的鋁的扣除背景後的EELS特性邊刃，有著類似圖C-41中的變化。所以只要有足夠的資料庫，從EELS扣除背景後的元素特性邊刃，即可判斷該元素的鍵結化態(chemical bonding state)。目前最常用的EELS 特性邊刃的資料庫是Gatan 建立的EELS Atalas^[1]。

Figure C-41 shows three kinds of background subtracted Si L edges, Si of Si, Si of SiC, and Si of SiO₂. Figure C-41(b), magnification of the low energy region of Figure C-41(a), shows the different threshold energy of Si L edges, 99 eV for Si/Si, 101 eV for Si/SiC, and 103 eV for Si/SiO₂. The near edge fine structure of Si of SiO₂ is obviously different from the other two, indicating that Si-O bonds is significantly different from Si-Si and Si-C. Figure C-42 shows four kinds of background subtracted Al L edges, Al of Al, Al of Al₂O₃, Al of AlN, and Al of sapphire. All these Al L edges show similar variation with those Si L edges in Figure C-41. The chemical bonding state of any element can be identified from its background subtracted characteristic edge once data base of all elements is established. The EELS Atlas^[1] edited by Gatan is most popular at present.

圖C-41 正常化後的三種Si L特性邊刃。紅線是元素Si的Si，藍線是元素6H-SiC的Si，綠線是元素SiO₂的Si，

圖C-42 正常化後的三種Si L特性邊刃。紅線是元素Si的Si，藍線是元素6H-SiC的Si，綠線是元素SiO₂的Si，

TEM電子源能量解析度愈高，EELS的能量解析度愈高，近邊刃微細結構也會愈清楚，對應的材料電子物理特性也被解析地愈透徹。圖C-43顯示鈷用不同能量解析度的電子源解析出來的L特性邊刃微細結構。

The energy resolution of EELS increases with the energy resolution of the TEM electron beam. The near edge fine structure resolved by TEM/EELS system with better energy resolution will tell electronic properties more detail and exact. Figure C-43 shows the near edge fine structure of Co L₂₃ edge from TEM/EELS system with different energy resolution.

圖C-43 CoO內Co L₂₃的近邊刃微細結構和TEM能量分辨率的關係。(a)能量分辨率 ~ 0.8 eV；(b)能量分辨率 ~ 0.5 eV；(c)能量分辨率 ~ 0.2 eV。ref. [2] (Courtesy of FEI Dr. Bert Freitag and Dr. Peter Tiemeijer)

參考文獻

1] EELS Atlas, edited by C. C. Ahn, O. L. Krivanek. Gatan, 1983.

2] 鮑忠興和劉思謙，近代穿透式電子顯微鏡實務，第18頁，第二版，台中 (2012).

C-3 電子能量損失能譜(EELS) - EELS能譜背景扣除

 C-3-3 EELS能譜背景扣除[2021/06/08更新]

C-3-1節中述及EELS在儀器操作和後續資料處理的複雜度都遠大於EEDS，C-3-2節已闡明EELS儀器操作上的複雜性，本章節將簡介如何後續處理EELS能譜。

In section C-3-1, we mentioned that the complexity of EELS in both operation and data process is much more than that of EDS. The complexity of operation has been discussed in section C-3-2, and this section will introduce how to process acquired EELS spectra. 

在材料科學與工程領域的成份分析應用，主要使用EELS的核損失區域。圖C3-3-1為一典型的核損失區域EELS能譜，此能譜內包含一小段邊刃前背景，邊刃起始點(threshold)，近邊刃微細結構區(NEFS or ELNES)，邊刃延伸結構區(EXELFS)等，各有其物理意義和用途。邊刃前背景主要用於做曲線契合，找出特性邊刃下的背景訊號。邊刃起始點代表此元素的鍵結能，用來判別特性邊刃對應的元素。近邊刃微細結構區內能量強度的變化特性，代表此被分析元素的化學鍵結型態，元素的每一種化態都有其如指紋般唯一對應的微細結構。邊刃延伸結構區內能量強度的變化特性受元素化態影響較小，用來做定量分析。

Core loss regions in EELS spectra are mainly used for applications of composition analysis for the field of materials of science and engineer. Some features, including pre-edge background, threshold, near-edge-fine-structure (NESF) or energy-loss near-edge structure (ELNES), and extended energy-loss fine structure (EXELFS), in a typical EELS spectrum, as shown in Figure C3-3-1, have their own uses and physical meanings. The pre-edge background is used for fitting the background under the characteristic edge. The element can be identified from the threshold energy which stands for the bonding energy of the element. The variation of intensity in the energy range of 50 eV behind the threshold energy is called near edge fine structure which indicates the chemical bonding state of the element analyzed and is finger-print unique. The intensity variation of EXELFS is little affected by neighbor atoms and used for quantitative analysis.

圖C3-3-1 典型核損失區域的EELS能譜。包含一小段邊刃前背景，邊刃起始點(threshold)，近邊刃微細結構區(NEFS)，邊刃延伸結構區(EXELFS)。

EELS能譜中，元素的特性邊刃座落在一高強度的背景訊號上，唯有將背景訊號扣除後，才能看到元素特性邊刃的真正形貌，尤其是近邊刃微細結構。從累積的EELS能譜分析結果中，發現背景訊號的變化近似一指數函數，y = ax^b。由於EELS能譜的橫軸是能量損失，而且訊號強度隨能量損失的增加而降低，所以背景訊號強度可以下面的式子近似:

I = A E^-r   ------------------------- (C 3-3-1)

Elemental characteristic edges mount on a high intensity background in EELS spectra. The true shape of an elemental characteristic edge, especially the ELNES is only visible after its corresponding background is removed. The intensity variation of background was found to approximate an exponential function, y = ax^b. The x-axis of EELS spectra is energy loss, and the intensity drops with increasing energy loss, so the background intensity can be approximated by the equation below:

I = A E^-r   ------------------------- (C 3-3-1)

C3-3-1式二邊取對數後，變成一直線方程式 y = a + bx的形式

ln(I) = ln(A) – r ln(E) ------------------------- (C 3-3-2)

其中A和r二個常數在EELS能譜中都並非是固定單一值，隨著試片厚度，收集角度(由TEM相機長度和EELS能譜儀入口光圈決定)，和損失能量的大小而變化。常數r的值大概落在 2 ~ 5之間，而常數A的值則落在10 ~ 30之間，而且每一組A，r值只適用在某能量範圍內^[1]。每個元素特性邊刃下背景訊號對應的A，r值都不同，因此無法像EDS一樣，一次將全能譜的背景契合出來，EELS能譜中每個元素對應的背景都需個別契合運算。

Equation C3-3-1 becomes a linear equation (y = a + bx) as shown below, after logarithm for both sides being taken.

ln(I) = ln(A) – r ln(E) ------------------------- (C 3-3-2)

Values of both constants, A and r, are not unique for all EELS spectra, they vary with specimen thickness, collection angles (depending on the cameral length and the spectrometer entrance aperture), and energy loss. The value of r falls in the range of 2 to 5, while A in the range of 10 to 30, and each set of r and A is only valid over a specified energy range^[1]. Unlike EDS spectra which one set of background is fitted for the whole spectrum, the background of each characteristic edge in any EELS spectrum must be fitted seperately.

圖C3-3-2解說傳統上如何處理EELS能譜。先對EELS能譜取對數，找到最契合背景訊號的直線，然後從EELS能譜中將背景扣除後。除了是TEM數位相機的主要生產公司外，Gatan也是生產柱體後形式EELS能譜儀的最主要公司，因此其影像控制與處理軟體DigitalMicrograph，也是控制能譜儀和處理EELS能譜與影像的軟體。在DigitalMicrograph中，EELS能譜背景扣除法有三個選項，一般以冪函數為主要方法。如圖C3-3-3所示，先在特性邊刃前設置一10 ～ 60 eV的能窗，然後前後移動，找出最佳的背景契合曲線。

Figure C3-3-2 shows how to process an EELS spectrum traditionally, including taking logarithm, linear fitting, background subtraction. Gatan is the main manufacture for post-columnar EELS spectrometers as well as TEM digital cameras, its image process program, DigitalMicrograph, can control EELS spectrometers and process EELS spectra too. There are three models to fit the background in DigitalMicrograph EELS module, and power law is the one most used. As shown in Figure C3-3-3, a pre-edge window of 10 to 60 eV is set and moved forward and backward to find the best background fitting.    

圖C3-3-2 EELS能譜扣除背景運算。(a)原始EELS能譜；(b)取對數後的EELS能譜；(c)找出各元素的背景契合直線；(d)去除背景後的Si特性邊刃；(e)去除背景後的C特性邊刃。

圖C3-3-3 Gatan DigitalMicrograph對EELS能譜扣除背景運算。Ref [2]

扣除背景訊號後的EELS特性邊刃才能顯示出其真正的近邊刃微細結構。前段提及特性邊刃的微細結構是唯一對應，所以被分析物的化學鍵結狀態，可以通過和資料庫內已儲存的能譜做比對而鑑定。圖C3-3-4中顯示一典型的例子，圖C3-3-4(a)從半導體元件中的缺陷區得到的碳特性邊刃，圖C3-3-4(b)和圖C3-3-4(c)則分別為銅環碳膜和low k介電材料中的碳特性邊刃。比對之後，可以推斷此缺陷區域的碳應是low k介電材料。

The true NEFS of a characteristic edge can only be viewed after background subtraction. Since the NEFS is unique, it can be used to identify the chemical bonding state of an analyzed material by comparison with corresponding characteristic edges in database. A typical example is shown in Figure C3-3-4. The characteristic C edge shown in Figure C3-3-4(a) is obtained from a defect in a semiconductor device, while Figure C3-3-4(b) and Figure C3-3-4(c) are characteristic C edges of carbon film of Cu grid and the low k dielectric respectively. The carbon in the defect can thus be deduced to be the low k material by comparing the spectra in Figure C3-3-4(a) with those in Figure C3-3-4(c) and Figure C3-3-4(c).

圖C3-3-4 扣除背景後的碳特性邊刃。(a)來自試片的缺陷區域；(b)來自銅環碳膜；(a)來自low k材料。

參考文獻

1] David B. Williams and C. Barry Carter, Transmission Electron Microscopy, Microscopy, vol.1 Spectroscopy, chapter 35, Plenum Press, New York (2009).

2] Handout of Gatan EELS school (2007).