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).

C-3 電子能量損失能譜(EELS) - 3-2 電子能量損失能譜攝取

 C-3-2 電子能量損失能譜攝取 [2021/06/03更新] 

        前面章節提到EELS的操作的複雜度遠大於EDS的。以定點分析為例，當電子束已定位待分析區域後，EDS分析只要按下EDS控制軟體中的“開始”按鈕，待訊號足夠後，再按下“停止”按鈕即可，或預設收集時間，時間到自動停止。但是EELS分析，卻必須先完成一套調整與測試，才能按下EELS控制軟體中的“開始”按鈕。

        I mentioned that the operation of EELS is much more complicate than that of EDS in last paragraph. Let us take the position analysis for an example. For EDS analysis, we only have to press the “start” button in the EDS control software, wait for enough intensity acquired, then press the “stop” button, or set a live time and wait for automatic stop. For EELS analysis, a set of tuning and test must be performed before pressing the “start” button in the EELS control software.

        要攝取良好的EELS能譜，總共有6個重要的調整和設定步驟: (1)切換至繞射模式；(2)能譜歸零；(3)選定散佈值；(4)設定適當的能譜偏移；(5)設定適當的單次能譜攝取時間；(6)設定加總攝取次數。當TEM工程師充分瞭解每一步驟的物理意義，並靈活運用時，才能攝取正確與良好的EELS能譜。

        There are six important steps of tuning and setting to acquire good EELS spectra: (1) switch to diffraction, (2) zero set the zero loss peak, (3) select an adequate dispersion, (4) set an adequate energy offset, (5) set an adequate acquisition time for a single EELS spectrum, (6) to set the accumulation number. Correct and good EELS spectra can only be acquired when TEM engineers fully understand the physical mechanisms in steps and operate them flexibly.

繞射模式：影像模式時，穿過試片後不同能量損失的電子，通過投射透鏡後聚焦位置有所不同，    

                    如圖C3-2-1所示，造成進入EELS能譜儀的訊號的比例和試片發出的訊號比例不同，引

                    起定量分析上很大的誤差。

Diffraction mode: In image mode, high energy electrons suffering energy losses after penetrating the 

                             specimen will be focused at different height after the projector lenses, as shown in 

                             Figure C3-2-1. This makes the ratio of signals into the EELS spectroscope be different 

                             from that emitted from the specimen, which will cause big error in quantitative analysis.

能譜歸零：調整零損失峰落在能譜零點的位置，以確定其他特性邊刃在能譜上的能量位移是源自

                    化學鍵結，而不是能譜偏移造成的。

Zero set: Tuning the zero loss peak right at the “zero” channel in the spectrum to make sure that any shift 

                in a characteristic edge is due to chemical bonding shift instead of spectrum shift.

 

圖C3-2-1 不同能量損失的電子通過投射透鏡後聚焦在不同的平面，噵致後續進入EELS能譜儀的

                比例改變。

散佈值：能譜的散佈值相當於影像的倍率。散佈值為1.0 eV/ch時，倍率最小(最小能量解析度)；散

                佈值為0.05 eV/ch時倍率最大(最大能量解析度)。一般成份分析選擇1.0 eV/ch，分析化學

                鍵結則選擇0.2或0.1 eV/ch，測量EELS能譜儀的能量解析度則用0.05 eV/ch。

Dispersion: The dispersion to spectra is like magnification to images. The minimum magnification (the 

                    smallest energy resolution) is dispersion equaling 1.0 eV/ch, and the maximum magnification 

                    is dispersion equaling 0.05 eV/ch (the highest energy resolution). We use 1.0 eV/ch dispersion 

                    for composition analysis, 0.1 or 0.2 eV/ch for chemical bonding analysis, 0.05 eV/ch for 

                    measuring the energy resolution of the EELS system.

能譜偏移：將高劑量的零損失峰，低損失能峰，和部分低能量損失區域等移出訊號偵測器(閃爍器)

                    範圍，以避免過高劑量的電子損傷閃爍器，同時可讓最低能量損失特性邊刃的單次能

                    譜攝取時間盡量提高。

Energy offset: This is to move high dose parts, including zero loss peak, low loss region, and some parts 

                        of the core loss region, of the spectrum out of the scintillator to protect it from high dose 

                        electron beam damage. This offset can also raise the acquisition time of a single spectrum 

                        of the interested region.

單次能譜攝取時間：適當的單次能譜攝取時間()並非唯一，而是一個範圍。在此時間範圍內，最

                                    低能量損失特性邊刃與其前面的背景區不會過飽和，而高能量損失特性邊刃

                                    也能被有效偵測。

Acquisition time of a single spectrum: 

        The acquisition time of a single spectrum (t) is an optimum range instead of a single value. The 

        intensity of the edge of the lowest energy loss and its pre-background is not saturated, and the edge of 

        the highest energy loss is visible in this time range.

加總攝取次數：最長的單次能譜攝取時間受限於最低能量損失特性邊刃的能量位置，可能導致高

                            能量損失特性邊刃的訊號不足。藉由多次攝取能譜後加總，可以補強此問題，同

                            時提高整個能譜的訊號強度。總訊號收集時間等於加總次數(N)乘以t，N大小的

                            限制以總訊號收集時間後，不造成明顯的試片飄移和試片輻射損傷為原則。

Accumulation number: The characteristic edge of high energy loss in the spectrum may be weak due to 

                                       the limit in acquisition time for the edge of low energy loss. This can be 

                                       compensated by summing several spectra from multi-acquisition. Total collection 

                                      time is N x t, where N is the accumulation number. There should not be 

                                      detectable specimen shift and electron beam damage in total collection time.

        對一理想做EELS分析的TEM試片，得到的EELS能譜強度分佈如圖C3-2-2示意圖所示。設零損失峰的強度是Io，低損失能峰的強度約為0.01Io，矽特性邊刃的最高點強度約為1 x 10-3 Io，碳特性邊刃的最高點強度約為0.1 x 10-3Io，而氧特性邊刃的最高點強度約為0.04 x 10-3Io。隨著能量損失的增加，能譜訊號強度迅速大幅降低。此EELS能譜強度變化的特性使EELS的攝取無法像EDS那樣的簡單。

        For a thin enough TEM specimen for EELS analysis, a schematic full EELS spectrum is shown in Figure C3-2-2. Let the intensity of zero loss peak to be Io, then the intensity of low loss peak is about one percent of Io, the maximum of Si characteristic edge is about 1 x 10-3 Io, the maximum of C characteristic edge is about 0.1 x 10-3 Io, and the maximum of O characteristic edge is about 0.04 x 10-3 Io. The intensity drops quickly with increasing energy loss. This characteristic of variation in intensity with energy loss makes the job of EELS spectrum acquisition more complicate than EDS does.

        用數毫秒的攝取時間，可以攝取到完整的零損失峰，但是低損失能峰和特性損失能峰邊刃的強度則不足，泯沒於背景訊號中。增長攝取時間使矽特性邊刃有足夠的訊號強度，此時零損失峰和低損失能峰則會過飽和，而氧特性邊刃的強度則尚稍嫌不足。因此做EELS分析，在正式攝取能譜之前必須先做一些測試，根據測試結果設定適當的單次能譜攝取時間，和對應的能譜偏移使過飽和的訊號移出偵測器的範圍，避免過高劑量損傷偵測器。

        A zero loss peak can be acquired with an acquisition time of several milliseconds, but the intensity of low loss peak and characteristic edges of elements are not distinguishable with this short acquisition time. When the intensity of Si characteristic edge is adequate by aligning a suitable acquisition time, the intensity of zero loss peak and low loss peak will be saturated, while characteristic edge of oxygen are weak. So, some tests before formal acquiring must be performed to evaluate an adequate acquisition time of a single EELS spectrum, and an adequate energy offset to shift signals with oversaturated intensity out of the detector, which protects the detector from high dose damage.

 

圖C3-2-2 典型EELS能譜訊號強度變化示意圖。

        單次攝取EELS能譜時間是攝取EELS能譜實驗中一非常重要的設定。圖C3-2-3顯示一組攝取矽的EELS能譜。攝取零損失峰時，所需要的單次攝取時間很短，通常為0.01秒，也可以降至0.004秒，仍可以攝取到訊號，因為單次攝取時間很短，加總次數就可以很多次。圖C3-2-3 (a)顯示50次加總的結果，總有效收集時間為0.2秒。因為單次攝取時間太短，只有零損失峰可見，在100 eV處並沒有看到Si L特性邊刃。將單次能譜攝取時間提到0.2秒，即可看到明顯的Si L2,3特性邊刃，如圖C3-2-3 (b)所示。當單次能譜攝取時間超過元素特性邊刃的臨界攝取時間後，再經由多次攝取加總後，訊號強度就可以線性增加，如圖C3-2-3 (c)所示，經10次加總後，Si L2,3的強度接近80000。同時，Si L2,3的能譜輪廓線也明顯變得較平滑。

        The acquisition time for a single EELS spectrum is an important setting in EELS spectrum acquisition. A set of EELS spectra of Si in Figure C3-2-3 explains this. The acquisition time is usually about 0.01s when zero loss peak is included, but also can be as short as 0.004s, and the accumulation number can be 50 for this short time acquisition. Figure C3-2-3 (a) shows that there is only zero loss peak visible, Si L2,3 edges at around 100 eV are not visible even the total acquisition 0.2s. When the acquisition for a single EELS spectrum is 0.2s, the Si L2,3 edge is clear visible, as shown in C3-2-3 (b). The maximum intensity of Si L2,3 is ten times when 10 spectra are accumulated, as shown in C3-2-3 (c), and the Si L2,3 spectrum is much smooth.

圖C3-2-3  攝取時間對EELS能譜訊號的影響。(a)攝取時間= 0.004s，加總次數= 50；

                  (b) 攝取時間= 0.2s，加總次數= 1；(c) 攝取時間= 0.2s，加總次數= 10。

        為了能進行特性邊刃的背景扣除，攝取EELS能譜時，通常會在特性邊刃前預留一小段能量區，通常為50 eV，最小為30 eV。待攝取的EELS能譜的最小損失能量愈大，所需要的單次攝取時間就愈大。例如: 前述的Si L特性邊刃(99 eV)對應的單次攝取時間為0.2秒，同樣的機台狀況和試片厚度條件下，則攝取C K特性邊刃(284 eV)對應的單次攝取時間約需1.0秒；攝取O K特性邊刃(532 eV)對應的單次攝取時間約需3.0秒。

        The acquisition time becomes longer when the minimum loss energy of the specified spectrum goes higher. For example, under the same condition of TEM and specimen thickness of the previous Si L2,3 edge (99 eV), the acquisition times for C K edge (284 eV) and O K edge (532 eV) are about 1.0s and 3.0s respectively.