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).