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)
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