C-2 X-光能量散佈能譜- 5/7 EDS能量解析度與能峰重疊

C-2-4 EDS能量解析度與能峰重疊

C-2-4-1  能量解析度

EDS能量解析度由能峰的半高寬定義，目前多數EDS能譜儀的能量解析度落於130 ~ 140 eV之間，最佳值為121 eV。整個EDS能譜的能量解析度並非定值，而是如圖C-22所示，在低能量區的能量解析度較佳，愈高能量區的能量解析度較差。傳統上，大家通用錳(Mn) Kα (5.898 KeV)能峰的半高寬定義該EDS能譜儀的能量解析度，如圖C-23(a)。實務上，如果一下子找不到錳金屬做試片，用鉻(Cr)或鎳(Ni)也可以替代。圖C-23(b)為一用鉻(Cr) Kα (5.414 KeV)量出的EDS能量解析度。

The energy resolution of EDS is defined by the full width of half maximum (FWHM) of energy peaks in EDS spectra. It falls the range of 130 to 140 eV, and the best resolution reported is 121 eV [1]. As shown in Figure C-22, peaks in a EDS spectrum have not the same energy resolution, peaks of higher energy have worse energy resolution. Traditionally, the EDS energy resolution is defined by the FWHM of Mn Kα (5.898 KeV), as shown in Figure C-23(a). Practically, if Mn is not available, Cr and Ni can be used in place. Figure C-23(b) shows an energy resolution 135 eV measured from a Cr Kα (5.414 KeV).

圖C-22 相同積分強度的EDS能峰隨能量的高度與寬度變化情況示意圖。

圖C-23 EDS能譜儀的能量解析度。(a) SDD EDS，錳(Mn) Kα (5.898 KeV)半高寬= 124 eV [1]； (b) Si(Li) EDS，鉻(Cr) Kα (5.414 KeV)半高寬= 135 eV。

EDS能量儀的能量解析度是可以調變的，就好像腳踏車可以換檔至省力模式或快速模式一樣。調整能譜儀的訊號脈衝處理器的時間常數( 1 ~ 50 us)可以在某範圍內調整能譜儀的能量解析度，大的時間常數有較佳的能量解析度但訊號接收率低，小的時間常數能量解析度較差，但單位時間內可接收較多的訊號。訊號脈衝處理器的時間常數在往昔是屬於設備商等級才能調整的儀器參數，隨著儀器性能與操控性的提升，目前已經看到使用者可以透過視窗介面直接更改設定的版本，因此使用者可以依實驗特性的需求，選擇要較佳的能量解析度或較高的訊號強度，做適當的調整。

The energy resolution of an EDS is not fixed, it can be modulated by changing its time constant, 1 to 50 us, of the pulse processor. Large time constant will give a better energy resolution but lower count rate, and smaller time constant gives higher count rate but low energy resolution. The time constant used to be aligned by the manufacture or agent only, now TEM/EDS users can change it through the operation window whenever the object of the EDS analysis changes.

C-2-4-2  能峰重疊

在各種電子顯微鏡的微區成份分析技術中，EDS的操作最簡單，儀器最經濟，所以被廣泛使用。但是EDS的能量解析度只有約為130 eV，和WDS的5 eV，AES的7 eV，EELS的< 1.0 eV等相比，相差甚多。低能量解析度導致EDS能譜中常有能峰重疊的現象。

EDS is the easiest one to be operated and the most economical one among all analytical techniques of electron microscopes. However, the energy resolution is only about 130 eV, very poor compared with 5 eV for WDS, 7 eV for AES, and less than 1.0 eV for EELS. This shortage results in serious problem of pathological overlap. 

矽基半導體材料系統最常見的能峰重疊有二組。第一組是Si Kα (1.740 KeV)-Ta Mα  (1.710 KeV)和Si Kα-W Mα (1.775 KeV)，能量差分別為30 eV和35 eV，如圖C-24。很明顯的，在同一EDS能譜中很難區分Si Kα-Ta Mα-W Mα 三能峰。這類EDS能譜分析另外有一個問題，以圖C-24(a)下半部的EDS能譜為例，依教科書的準則，高能量的Ta Lα能峰存在，證實位於1.7 KeV的能峰有Ta Mα能峰，可是此能峰究竟是純Ta Mα能峰?還是Si Kα + Ta Mα能峰? 運用材料學的知識，資料庫的比對，和細用現代EDS軟體的功能等技術都可解決此問題。

There are two sets of energy peak overlap observed commonly in semiconductor material system. The first set is Si Kα (1.740 KeV) - Ta Mα (1.710 KeV) and Si Kα -W Mα (1.775 KeV), as shown in Figure C-24. Their energy difference is 30 eV and 35 eV respectively. Obviously, it is hard to distinguish energy peaks of Si Kα, Ta Mα, and W Mα, when they show up in the same EDS spectrum. There is another problem in these EDS spectra. Let us take the low EDS spectrum in Figure C-24(a) for example. As taught in textbooks, we know Ta Mα must be there since Ta Lα is observed. However, we do not know that the peak locating at 1.7 KeV is a pure Ta Mα peak or a combination Si Kα and Ta Mα peaks. This problem can be solved by using knowledge of the materials system, comparison with database, and using the EDS software deeply.

圖C-24 EDS能峰重疊問題。(a) 上: 矽的EDS能譜，下: 二氧化矽和钽的EDS能譜；(b) 上: 矽的EDS能譜，下: 二氧化矽、氮化鈦、鈦、鎢的EDS能譜。Si Kα (1.740 KeV), Ta Mα (1.710 KeV), W Mα (1.775 KeV)，從貫穿上下二個EDS能譜的紅色虛線指出Si Kα能峰-Ta Mα能峰 和Si Kα能峰-W Mα能峰 在同一EDS能譜時完全重疊的情形。

第二組是N Kα (0.392 KeV)和Ti Lα (0.452 KeV)，能量差為60 eV。圖C-25(a)是金屬鈦的EDS能譜，此時Ti Lα能峰和Ti Kα能峰的強度比約為0.14。圖C-25(b)是二氧化矽和氮化鈦的EDS能譜，此時Ti Lα能峰和Ti Kα能峰的強度比約為0.51，遠高於0.14，此資料顯示這裡的Ti Lα能峰不是純Ti Lα能峰而是N Kα 加Ti Lα能峰。從圖C-25(b)中的低能量區，可以看出氧能峰(0.525 KeV)和鈦L (0.452 KeV)能峰是可分離的，二者的能量差為73 eV。從此結果推估，在0.5 KeV處的能量解析度約為65 eV。

The second set is N Kα (0.392 KeV) and Ti Lα (0.452 KeV), their difference is 60 eV. Figure C-25(a) is an EDS spectrum of metal Ti, the peak intensity ratio of Ti Lα to Ti Kα is 0.14. Figure C-25(b) is an EDS spectrum of SiO₂/TiN, the peak intensity ratio of Ti Lα to Ti Kα is 0.51, significantly higher than 0.14, so the peak at 0.45 KeV is a combined peak of N K and Ti Lα rather than a pure peak of Ti Lα. From the low energy region in Figure C-25(b), energy peaks of O K (0.525 KeV) and Ti Lα (0.452 KeV) are distinguishable. This indicates that the energy resolution at 0.5 KeV is around 65 eV.

圖C-25 EDS能峰重疊問題。(a) 金屬鈦的EDS能譜；(b)二氧化矽和氮化鈦的EDS能譜。

C-2 X-光能量散佈能譜- 4/7 EDS分析形式II - 定點分析/線掃描/成分映像

C-2-3-2  定點分析/線掃描/成分映像

從成份分析的形式來說，EDS成份分析有三種：定點分析、線掃描、成分映像。定點分析通常先將特徵物移到螢光屏中心，然後將電子束精確地微移到待分析特徵物上，即可開始分析。定點分析可以在TEM模式或在STEM模式下進行。在STEM模式下進行只能用聚焦的電子束，在TEM模式下進行則可以用聚焦電子束，也可以用非聚焦電子束。如果待分析的特徵物夠大，個人建議使用TEM模式非聚焦電子束進行分析，一來取樣空間較大，二來減小輻射損傷和局部積碳效應。線掃描和成分映像則必須在STEM模式下進行，才能自動化逐點等距收集訊號。

From forms of analysis, EDS analysis can be divided into three types: position resolved, line scan, and mapping. For position resolved analysis, we usually move the feature to the screen center, accurately position the electron beam on the feature, and start to analyze it. Position resolved analysis can be performed either in TEM mode or in STEM mode. In STEM mode, only a focused electron beam is used. Either a focused electron beam or a non-focused electron beam can be used in TEM mode. It is suggested to use TEM mode and a non-focused electron if the feature is large enough. Advantages of this method include large sampling space, less electron beam radiation damage, and less local carbon contamination. Both line scan and mapping must be performed in STEM mode to keep positions and distances accurately and automatically.

由於現代TEM都兼備STEM功能，而且非常容易切換，因此演變成新TEM機台的EDS分析都在STEM模式用能譜影像(spectrum image)技術進行。能譜影像技術意指對一特徵區域掃描，在攝取一張STEM影像的同時，每一像素內包含一個對應的EDS能譜。能譜影像除了提供組成元素的成分映像圖外，也可從中拉出直線成份分佈圖(line profiles)，如同線掃描一般；也可以選定一微區，萃取出該微區的EDS能譜，如同定點分析一般。能譜影像成份分析上有許多便利的地方，使TEM/EDS成份分析變得容易許多，唯一的缺點是訊號強度比起線掃描和定點分析弱了許多。如圖C-20所示，對於四層薄膜材料的定點分析，如果每點收集20秒，得到的EDS能譜，其中最大能峰的尖峰強度達到8000，總收集時間為80秒。改用線掃描通過此四層薄膜，假設共設定100點，每點訊號收集時間為2秒，則每點的EDS能譜中，最大能峰的尖峰強度約為800，總收集時間為200秒。這樣的分析方法會花費較長的時間，而且每個EDS能譜的訊號強度降低，好處是可以看到所有元素通過界面的變化。改用成分映像法掃描一包含此四層薄膜的區域，假設共設定3000 (100 x 30)點，每點訊號收集時間只能為0.2秒，則每點的EDS能譜中，最大能峰的尖峰強度約為80，總收集時間為600秒。這樣的分析方法會花費更長的時間，每個EDS能譜的訊號強度更低，好處是可以看到所有元素的二維分佈，如圖C-21(c) ~ (e)所示。

Currently, all TEMs have STEM functions, and switch between two modes is only a finger job. All new TEM users are used to performing EDS analysis by using STEM spectrum image. Spectrum image means once an area including the interested feature is scanned, EDS spectra for all pixels as well as the STEM image are stored. Besides elemental maps, line profiles and EDS spectra of any specific area can all be extracted from a set of data file. STEM/EDS spectrum image makes the composition analysis job easier and more powerful. However, the intensity extracted one pixel or a line of pixel is somehow less than that obtained from position resolved or line scan analysis. As illustrated in Figure C-20, if we use position resolved method to analyze the composition of each thin film layer and set the dwell time for each point to be 20s. Four EDS spectra are obtained and the maximum peak intensity can reach 8000 counts. The total acquisition time is 80s. When line scan is used, 100 points in the line crossing four layers of thin films are set and the dwell time for each point is 2s. The total acquisition time becomes 200s, and the maximum peak intensity is around 800 counts. We can see the composition change cross these films with the scarify of time and intensity. When EDS mapping is used. 3000 points are set to scan an area covering four layers of thin films. The dwell time for each point can be only 0.2s, the total acquisition time is 600s. The maximum peak intensity is now 80 counts only. However, the distribution of elements in two dimensions can be observed, as shown in Figure C-21.

圖C-20 (a)定點分析，(b)線掃描，(c)成分映像 三種EDS分析法的示意圖。比較在訊號收集時間和能峰訊號強度方面的差異。

圖C-21 III-V半導體元件STEM/EDS分析。(a)STEM HAADF影像；(b)從能譜影像中萃取出來的EDS直線成份分佈圖(line profiles)，萃取位置是由(a)中紅色粗線箭頭所示，而加總平均的側向範圍則如紅色細線矩形所示；(c)從能譜影像中萃取出來的Al map；(d)從能譜影像中萃取出來的Ga map；(e)從能譜影像中萃取出來的As map。

如前段所述，能譜影像中單一像素對應的EDS能譜訊號強度太弱。改善的方法是將同相材料內的像素加總，例如:將圖-C20(c)第二層薄膜中10像素的EDS訊號加總，則最高能峰的尖峰高度就可達到800；若將該層薄膜中100像素的EDS訊號加總，則最高能峰的尖峰高度就可達到8000。同樣地，在萃取EDS直線成份分佈曲線時，也不限於只用單一行像素的訊號，側向增加10 ~ 50行的訊號做加總平均，才能得到平滑的直線成份分佈曲線。如圖C-21(b)所示，這組EDS直線成份分佈曲線的萃取位置是如圖C-21(a)中紅色粗線箭頭所示，而加總平均的側向像素數則如紅色細線矩形所示。

As stated in the last paragraph, the intensity of the EDS spectrum corresponding to each pixel in the spectrum image is very weak. Improvement can be reached by summing the intensity of several pixels, for examples, when EDS spectra of 10 pixels in the #2 layer thin film, the peak intensity of the maximum peak can reach 800 counts, and 8000 counts by summing 100 pixels. Similarly, the EDS line profiles of one line of pixels is very rough, then becomes smother and smother when the width of the line becomes wider and wider. Usually, lateral 10 to 50 pixels are integrated to be one value in the line. As shown in Figure C-21(b), this set of EDS line profiles are extracted from the position indicated by the red thick straight arrow and the width illustrated by the red thin rectangle.

早期的能譜影像只能一次掃描，此時每一點的停留時間(dwell time, τ)約為10 ~ 100毫秒，進階的能譜影像技術具有快速掃描的功能，每一點的停留時間可降至10 微秒，多重掃描後再將訊號加總。快速掃描可降低試片的電子輻射損傷，積碳速率，和電子束擴展等效應。

Old versions of spectrum image can scan the interested area one time only, the dwell time for each pixel is set to be about 10 to 100 ms. Gradually, some spectrum image techniques developed fast scan mode and reduced the dwell time for each pixel to be 10 us. For each pixel, multi-scan occurs and signals for all scanning are summed. Advantages of fast include less radiation damage, less carbon contamination, and less beam broadening effect.

無論是一次掃描還是快速掃描，一次能譜影像的資料蒐集都是10分鐘以上的工作，此時試片漂移問題就會很明顯，因此能譜影像技術都附有漂移修正的功能，可設定每隔一定的時間，快速掃描一下試片，和初始影像做比對，如果發現有試片漂移，會自動偏折電子束掃描區域，修正後續掃描區域和初始掃描區域吻合。

It usually takes more than ten minutes to acquire a set of spectrum image data, no matter fast scan or slow scan methods. The specimen drift becomes significant, and functions of drift correction is necessary for spectrum image techniques. The program fast scans the specimen and compares the scanned image with the initial scanned image in a period of time as set, a compensate current is sent to the deflection coils to make the following scanning as matching the initial area as possible if any specimen drift is detected.

現在的能譜影像軟體可賦予成份映像圖各種顏色，但是各種顏色的映像圖中的明暗度只代表該元素的濃度的高低，無法看出元素濃度的真正值，例如圖C-21(d) and (e)。而且成份映像圖中的明暗度是可以調整的，因此二張成份映像圖中的明暗度無法明確顯示此二種元素的濃度。要知道元素間濃度值必須從EDS直線成份分佈圖，圖C-21(b)，才能看出。

Current spectrum image software can assign various colors to elemental maps, but the brightness of these colorful maps indicates high or low concentration only, not concentration value, as shown in Figure C-21(d) and (e). The brightness can be tuned manually, so the difference in brightness of two maps is not corresponding to the difference in concentration. A set of line profiles, as shown in Figure C-21(b), are extracted to show variation in concentration through layers of thin films.

C-2 X-光能量散佈能譜儀- 3/7 EDS分析形式 I - EDS定性分析與定量分析

C-2-3 EDS分析形式

C-2-3-1  EDS定性分析與定量分析

從成份分析的目的來說，成份分析有二大類型：定性分析和定量分析。定性分析的目的是要鑑定試片的組成元素那幾種，而定量分析則是進一步分析各元素間的比例關係。

By the object of composition analysis, EDS analysis can be divided into two main types: qualitative analysis and quantitative analysis. Qualitative analysis means to determine what kinds of elements in the analyzed volume, and quantitative analysis goes further to calculate out of the ratio of elements interested

.

EDS定性分析

X-光能量散佈能譜儀的儀器特性非常適合做成份定性分析，電子束打到試片後，該分析區域組成元素的特性X-光全部都被激發出來。超薄窗式的EDS，可以偵測週期表內原子序大於等於6的元素，而無窗式的EDS，可以偵測週期表內原子序大於等於5的元素。幾秒鐘就可以完成鑑定待分析物質的組成元素。目前EDS的軟體都含有自動鑑定能峰的功能，但是由於EDS的能量解析度差(約為130 eV左右)的問題(Auger (7 eV), EELS (<1.0 eV))，產生許多能峰重疊的問題，元素A的K能峰可能會和元素 B的L能峰重疊，此時EDS軟體會在該能峰上方同時顯示可能的元素，分析者必須用自己相關的材料知識與經驗判斷能峰的歸屬。

EDS is very suitable for qualitative composition analysis, since all elements can be checked in a few seconds. When a UTW detector is used, elements with atomic number larger than six can be detected. When a windowless detector is used, elements with atomic number larger than five can be detected. Once a EDS spectrum is collected, all energy peaks in it can be identified automatically. However, peaks overlap occurs from time to time because its poor energy resolution (~ 130 eV) (the energy resolution of Auger is ~ 7eV, and the energy resolution of EELS can be less than 1.0 eV). When K peak of element A overlaps with L peak of element B, the software will display all possible peaks on the peak, the engineer has to pick up the right one by his/her knowledge of material and experience of analysis.  

另一個影響EDS定性分析結果是迷走X-光 (Spurious X-ray)，迷走X-光產生額外的能峰，導致成份誤判。產生迷走X-光的機構是電子散射，電子散射效應引入部分來自非電子探束直接照射區域的X-光訊號。這類X-光訊號稱為迷走X-光，可分成二大類型：來自試片本身和來自試片外部。如圖C-18所示，入射電子束(綠色粗直線箭)打到試片，從電子探束直接照射的區域產生特性X-光(紅色波浪線箭)。部分入射電子束被試片反射(綠色細直線箭)後打到上半部的物鏡，從物鏡產生特性X-光(粉紅色波浪線箭頭)，此為試片外部迷走X-光，也稱系統X-光，在試片強烈繞射狀態下很容易產生，如圖C-19(a)所示。部分入射電子束被試片散射(藍色粗直線箭)打到下半部的物鏡，再被反射打到試片其他區域(藍色細直線箭)，產生電子探束直接照射區域外的特性X-光(橘色波浪線箭)，是試片本身的迷走X-光。另外一部分散射-反射電子束會打到承載試片的銅環，因此即使試片本身不含銅，EDS能譜中仍可看到明顯的Cu-Kα和Κβ能峰，如圖C-19(b)所示。這種Cu-Kα和Κβ能峰屬試片外部迷走X-光。

Besides overlap, spurious X-rays also affect the result of EDS qualitative analysis. Spurious X-rays will introduce extra energy peaks and give wrong composition of the analyzed volume. The mechanism of generating spurious X-rays results from electron scattering. Spurious X-rays can be generated from the specimen and outside the specimen. As shown in Figure C-16, X-rays are generated (red wave arrow) from an interested region where hit by the focused electron beam (green thick straight arrow). Some X-rays generated from the bottom of upper pole pieces when some electrons are back scattered (green thin straight arrow) by the specimen and hit the bottom of the objective lenses. This is one of spurious X-rays outside the specimen, also named system X-rays easily observed when the analyzed crystal is in strong diffraction condition, as shown in Figure C-19(a). Some incident electrons are scattered (blue thick straight arrows) and reflected by the top of lower pole pieces (blue thin straight arrows), then strike regions away from the interested region. Finally, characteristic X-rays (orange wave arrow), spurious X-rays from the specimen, are generated from these non-interested regions. Some scattered electrons strike the copper ring, it is why Cu peaks are observed in EDS spectra even no Cu contained in the specimen, as shown in Figure C-19(b). These Cu-Kα and Cu-Κβ peaks result from spurious X-rays outside the specimen.

圖C-18 TEM EDS迷走X-光來源示意圖。綠色粗直線箭頭：入射電子束。紅色波浪線箭頭：試片分析區域產生的特性X-光。綠色細直線箭頭：反射電子束。粉紅色波浪線箭頭：物鏡產生的特性X-光(試片外迷走X-光，也稱系統X-光)。藍色粗直線箭頭：散射電子束。藍色細直線箭頭：被物鏡反射的電子束。橘色波浪線箭頭：試片分析區域外產生的特性X-光(試片本身產生的迷走X-光)。參考文獻[1]

圖C-19 典型EDS能譜中的迷走X-光。(a)矽晶片在[1 1 0]正極軸繞射狀態，源自TEM物鏡的系統X-光，Fe Kα和Co Kα，和少量源自承載試片銅環的迷走X-光，Cu Kα和Cu Kβ；(b)源自承載試片銅環的迷走X-光Cu Kα和Cu Kβ。

EDS定量分析

定性分析是成份分析的第一步，進一步當然要做定量分析。傳統理論，做定量分析需要標準試片在幾乎相同的電鏡操作條件下做比對，但是因為標準試片製作不易，而且昂貴，所以很多人直接用能峰強度的尖峰強度或能峰積分強度運算，稱為半定量分析。隨著技術的演進，Cliff和Lorimer於1975年提出K因子概念[2]，用礦石中最常用的矽元素當作的K因子當1，其他元素和矽比對，衍伸一組K因子。這種用K因子運算的定量分析稱為無標準片定量分析法。因為無標準片的需求，加上大數據的累積，K因子法愈來愈準確，無標準片定量分析法現在廣被接受，包括各大學術專業期刊發表論文都接受。

Quantitative analysis is now usually required after qualitative analysis is finished. For traditional theories, quantitative analysis always needs a standard specimen acquired at almost identical electron microscope conditions. However, standard specimens are expensive and not easily to be prepared. Some people performed quantitative analysis just integrating peak intensity or using the peak heights directly. This was called semi-quantitative analysis. Cliff and Lorimer proposed the concept of K factors [2]. K-factors of elements are calculated with respect to Si experimentally. This method is called standardless quantitative analysis. Since no standard specimen is required, TEM/EDS standardless quantitative analysis is getting more and more popular, even publishing papers technical journals.     

EDS做定量分析時，下列幾個關鍵步驟必須注意：

(1)攝取足夠強度的X-光訊號。統計學上，訊號強度愈高代表取樣數目愈多，訊號的可信度愈高，精確度愈佳。做SEM/EDS定量分析，最高強度的能峰最少要大於5000劑量(counts)，超過10000劑量更佳。因為TEM的試片是小於100奈米的薄片，產生X-光訊號的體積比SEM試片小很多，因此做TEM/EDS定量分析，只要最高強度的能峰大於1000劑量就足夠 [4?]。

(2)排除加成能峰，矽逸能峰，和迷走X-光形成的能峰後，只保留分析區域內組成元素對應的能鋒進行定量分析運算。

(3)背景扣除。將連續X-光形成的背景訊號扣除，只留下特徵X-光的淨訊號。背景訊號調適( fitting)優劣對定量分析的結果有很大的影響，尤其是小於2.0 KeV的低能量區的調適。

(4)能峰積分強度。用尖峰強度運算的最佳準確度是1.6%，用能峰半高寬積分強度運算的最佳準確度是0.59%，用1.2能峰半高寬積分強度運算的最佳準確度是0.56%，用能峰全高寬積分強度運算的最佳準確度是0.53%[3]。最通常用的積分強度是半高寬積分強度。

(5)K因子運算。省去ZAF修正，直接將元素對應的K因子和該元素的積分強度帶入方程式中運算，即可得到組成元素的比例。此法只適用於TEM/EDS，使用薄片(thin foil)試片的系統。目前，EDS設備商都對該公司各種型式的EDS搭配TEM設備建置一套K因子表。個人的使用經驗，布魯克和牛津二大系統的 K因子都有相當的準確度。

To do EDS quantitative analysis, engineers should pay attention to some key steps list below.

(1)Acquiring high enough intensity of X-ray signals. Statistically, high intensity means high sampling number, and gives high reliability and high accuracy. For SEM/EDS, the intensity of the maximum peak should be higher than 5000 counts, and it will be better if the intensity of the maximum peak is over 10000 counts. The thickness of TEM specimens is typical less than 100 nm, the volume of X-rays generation is much smaller than that of SEM, the intensity of the maximum peak for TEM/EDS is thus enough for quantitative analysis when it is higher than 1000 counts. 

(2)Excluding sum peaks, escape peaks, and spurious peaks. Only elements in the interested region are put into calculation.

(3)Background subtraction. The background formed by continuous X-rays has to be subtracted first. The background fitting, especially in regions lower than 2.0 KeV, is critical for EDS quantitative analysis.

(4)Integrating intensity under the energy peaks. Several kinds of intensity can be used for quantitative analysis. They give different accuracy. The best accuracy is 1.6% when peak intensity is used. The best accuracy can be 0.59 %, 0.56%, and 0.53% when integrated intensity of FWHM, 1.2 FWHM, and FWTM are used respectively [3]. 

(5)K factors. For thin foil specimens, such TEM/EDS analysis, we can neglect ZAF correction, put integrated intensity of elements and corresponding K factors into the equation, and calculate out the concentration for all interested elements. EDS manufacturers have established tables of k factors for TEMs of different model and coupled EDS. According to personal experience, k factors established by Bruker and Oxford are good for TEM standardless quantitative analysis.

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] Cliff G. and Lorimer G. W., J. Microscopy, vol. 103, 275 (1975)

3] Robert Edward Lee, Scanning Electron Microscopy and X-ray Microanalysis, P T R Prentice-Hall Inc., New Jersey (1993)

C-2 X-光能量散佈能譜儀 - 2/7 EDS偵測器晶體的靈敏係數

C-2-2 EDS偵測器晶體的靈敏係數

EDS偵測器前端的分隔窗，晶體前端的金屬電極與dead layer，對通過的X-光有衰減的作用，而且對愈低能量的X-光衰減作用愈大。所以EDS偵測器對所有X-光的靈敏度並非單一定植，而是如圖C-15(a)和(b)所示，低於4.0 KeV後，靈敏係數開始緩緩下降，在低於1.74 KeV的低能量區，靈敏係數會迅速下降，對於鈹窗、高分子超薄窗、超薄窗、無窗等型式的EDS偵測器分別在0.7, 0.32, 0.24, 0.16 KeV時降至零，在4.0 ~ 19.0 KeV之間靈敏係數保持0.95定值，超過19.0 KeV後靈敏係數又逐漸緩緩下降(圖C-15(a))。EDS通常用的能量區間是0 ~ 10.0 KeV。

Three components, including the window at the front end of the EDS detector, the 20 nm thick gold electrode and the dead layer ahead at the front side of the Si crystal, as shown in Figure C-15c, will decay X-rays when they pass through them. The sensitivity curve of the Si(Li) crystal is shown in Figure C-15a and b. The sensitive factor starts to drop slowly when the energy is lower than 4.0 KeV, then drops quickly when the energy is lower than 1.74 KeV. The sensitive factor drops zero at 0.7, 0.32, 0.24, and 0.16 KeV for Be-window, polymer UTW, UTV, and windowless respectively. The sensitive factor is a constant value, 0.95, at the energy range 4.0 ~ 19.0 KeV. The sensitive factor drops slowly again when the energy is higher than 19.0 KeV (Figure C15(a)). The most used energy region for EDS spectra is 0 ~ 10 KeV.

圖C-15 EDS偵測器的靈敏係數曲線。(a)0 ~ 30 KeV範圍的EDS偵測器的靈敏係數曲線；(b)低能量區 0 ~ 4 KeV範圍的EDS偵測器的靈敏係數曲線；(c) EDS偵測器結構示意圖，矽晶體本質區前面三層結構都會衰減通過的X-光。

EDS能譜中的能峰高度並不完全直接對應元素的濃度，而是元素的原始能峰高度和靈敏係數曲線的卷積(convolution)結果。由於EDS靈敏係數曲線在小於1.74 KeV的低能量區急速下降的特性，所以碳、氮、氧等常見輕元素的能峰高度遠低於它們應有的高度。圖C-16(a)中虛線能峰代表從三氧化二鋁試片產生的EDS訊號應有的能峰高度和靈敏係數曲線，二者卷積後的實際SEM/EDS能譜如圖C-16(b)所示，即使氧的濃度為鋁的1.5倍，氧的能峰仍遠低於鋁的能峰。類似的情形常見於其他含有輕元素的EDS能譜，例如圖C-17中的氮化矽和氧化矽。所以要簡略地從能峰高度判斷二元素的相對濃度時，必須先將能峰高度除以對應的靈敏係數。

The heights of energy peaks in EDS spectra are not completely corresponding to the concentration of elements directly. All peaks shown in an EDS spectrum are a convolution of original peaks with the sensitivity curve. Because the sensitivity of EDS drops quickly in energy regions less than 1.74 KeV, the peak height of typical light elements, such as C, N, and O, is always much lower than it should be. Figure C-16(a) illustrates ideal energy peaks of oxygen and aluminum from an Al₂O₃ specimen and the sensitivity curve, their convolution is shown in Figure C-16(b). The O peak height is much lower than that of Al, even the intensity ratio of O to Al should be 1.5. Similar situations are commonly observed in EDS spectra with light elements, for examples, EDS spectra of Si₃N₄ and SiO₂ shown in Figure C-17. Thus, to simply estimate the relative concentration of two elements, we have to divide the peak height by its corresponding sensitivity factor first.

圖C-16 三氧化二鋁的EDS能譜。(a)氧和鋁理論上能峰高度示意圖以及靈敏係數曲線；(b)三氧化二鋁真正的SEM/EDS能譜。

圖C-17 含輕元素的EDS能譜。(a)氮化矽的TEM/EDS能譜；(b)氧化矽的TEM/EDS能譜。