C-2 X-光能量散佈能譜儀-1/7 X-光能量散佈能譜儀簡介

C-2-1 X-光能量散佈能譜儀簡介

X-光能量散佈能譜儀(X-ray Energy Dispersive Spectroscope)是一種能譜儀，收集高能電子(電子束)撞擊試片後產生的X-光訊號，形成一如圖C-11的能譜，橫軸為能量(KeV)，縱軸為訊號強度(counts)，一般簡稱EDS。依能峰所在的能量位置，鑑定元素的種類；再從各能峰的強度，算出組成元素的比例。這種成份分析技術，稱之為能量散佈能譜學 (X-ray Energy Dispersive Spectroscopy, EDS or EDX or XEDS)。

X-ray energy dispersive spectroscope (EDS) is an spectroscope of energy type, collecting X-ray signals generated from a specimen after being hit by high energy electrons to form a spectrum as shown in Figure C-11, the x-axis is energy axis with unit KeV and y-axis is intensity with counts. Elements are identified by their corresponding energy peaks, and composition ratio is calculated by calculating intensity of energy peaks. This kind of analytical technique is called X-ray energy dispersive spectroscopy (EDS or EDX or XEDS)

圖C-11 典型能量散佈能譜。橫軸是能量單位，KeV，最常顯示範圍為0 ~ 10 KeV；縱軸是訊號強度，Counts。

由於操作簡單，EDS成為目前電子顯微鏡系統(SEM, TEM, STEM)中最廣泛被使用的成份分析附屬設備。舊型的EDS使用鋰漂移矽偵測器(lithium drifted silicon detectors, Si(Li)-detectors)將X-光訊號轉換成電子訊號，由於鋰原子遠小於矽原子，鋰漂移矽晶體內摻雜的鋰原子在工作狀態下的電場，會被逐漸推出晶體。因此，EDS必須在攝氏零下一百度以下運作，才能將偵測晶體內的鋰原子凍在晶格位置上。因為從室溫降溫至工作溫度的時間長(將近4小時)，為了隨時可以使用EDS，必須持續保持液態氮不間斷。因為液態氮桶容積的限制，每4 ~ 5天必須添加一次液態氮，是使用該設備麻煩的地方。新型的EDS使用矽漂移偵測器(Si drift detector, SDD)將X-光訊號轉換成電子訊號，矽漂移晶體內沒有摻雜異質原子，同時改善後接於偵測晶體的場效電晶體(FET)的設計，使用冷卻器(chiller)冷卻至攝氏零下廿度即可。冷卻器開機10分鐘後就可達到穩定的工作狀態，因此，新型EDS不使用狀態下是關機的。SDD EDS訊號接收率提升至每秒750000。更優的性能和更方便的操作，使得SDD EDS逐漸全面汰換Li-drift EDS。

Because of simple operation, EDS has become the most popular analytic instruments for electron microscopes, including SEM, TEM, and STEM. Traditional EDS used a Li drift silicon detector (Si(Li)-Detector) to transfer X-ray signals to electronic signals. Since the volume of the lithium atom is much smaller than that of the Si atom, these doped Li atoms will be driven out of the crystal under an applied electrical field at room temperature. The EDS detector thus has to work at temperatures below -100 ^oC to freeze Li atoms at lattice sites. It takes about 4 hours to stabilize the cooling procedure from room temperature down to liquid nitrogen temperature and let EDS work normally. Thus, we always keep liquid nitrogen in the tank and let the EDS be turn-on condition. It is an annoying job to fill out liquid nitrogen every 4 ~ 5 days. New EDS uses a Si drift detector (SDD), without extrinsic atoms in the silicon crystal, to transfer X-ray signals to electronic signals, and new designed field effect transistor (FET) which can process signals more than 750000 cps. The cooling temperature now is only – 20 ^oC, and it takes only about 10 minutes to reach the stable working condition. SDDs have largely displayed Si(Li) detectors based on better performance and more convenient operation.

高能電子撞擊試片後，產生的X-光有兩大類：連續X-光和特性X-光。連續X-光是因入射的高能電子受試片原子的原子核庫倫電場減速而損失動能，損失的能量以X-光的形式輻射出來，如圖C-12所示，某一高能電子從位置1移到位置2時，動能受原子核庫倫電場減速由E1降至E2。連續X-光又名剎車X-光，是由入射電子發出的，能量是連續的，在EDS能譜內形成背景，在0.5 ~ 3.0 KeV範圍內特別明顯，同樣的電鏡操作條件下，重元素試片有較高的背景強度。特性X-光則是入射的高能電子撞擊並游離試片內原子的內層電子，外層電子填補內層電子空位時，多餘的能量以X-光釋出，如圖C-13所示。特性X-光是由樣品發出的，能量是量子化的，且有特定的能量，可以用來鑑定元素。EDS能譜是由特性X-光和連續X-光加總而成，如圖C-14解析圖C-11中的特性X-光和連續X-光。

Two kinds of X-rays, continuum X-ray and characteristic X-ray, generated from the specimen after being hit by high energy electrons. Continuum X-ray is released when the incident electron is decelerated by the Coulomb field of the nucleus, as shown in Figure C-12. The high energy electron travel from position 1 to position 2, its corresponding kinetic energy drops from E1 to E2. Continuum X-ray also known as Bremsstrahlung X-ray is emitted from the incident electron, and can be any amount of energy below the energy of primary beam. It forms the background of an EDS spectrum, and significant in the range of 0.5 ~ 3.0 KeV. For same electron microscope conditions, the background intensity of specimens of heavy elements is higher than that of light elements. When a high energy electron penetrates the outer electron shells and knocks out of one inner shell electron, a hole will be left in the inner shell, and the atom is in an excited state. One of outer shell electron will jump to fill the hole in the inner shell to return to the lowest energy state of the atom, and emits an X-ray of specified energy equaling to the difference of the outer shell and the inner shell, as shown in Figure C-13. The X-ray of this type is called characteristic X-ray, emits from the specimen, is quantization, and can be used to characterize elements in a specimen. An EDS spectrum is the sum of characteristic X-ray superimposing on continuum X-ray, as displayed in Figure C-14 which resolves the EDS spectrum shown in Figure C-11.

   

圖C-12 連續X-光產生機構的示意圖。高能電子從位置1移到位置2時，動能受原子核庫倫電場減速由E1降至E2

圖C-13 特性X-光產生機構的示意圖。(a)基態原子狀態；(b)一內層電子被入射電子撞擊出原子，在內層軌域留下一電洞；(c) 一外層電子躍下填補電洞，並將多餘的能量以X-光的形式釋出。

圖C-14 圖C-11中的EDS能譜分解成特性X-光和連續X-光。

材料與材料分析(Materials and Materials Analysis): C-1 表面分析儀 – 2/2 X射線光電子能譜儀 & 二次離子質譜儀

材料與材料分析(Materials and Materials Analysis): C-1 表面分析儀 – 2/2 X射線光電子能譜儀 & 二次離子質譜儀: C-1-2  X 射線光電子能譜儀 (XPS) X 射線光電子能譜儀 (X-ray Photoelectron Spectroscope, XPS) 又稱化學分析電子能譜儀 (Electron Spectroscope for Chemical Analysis, ESCA...

C-1 表面分析儀 – 2/2 X射線光電子能譜儀 & 二次離子質譜儀

C-1-2  X射線光電子能譜儀(XPS)

X射線光電子能譜儀(X-ray Photoelectron Spectroscope, XPS)又稱化學分析電子能譜儀(Electron Spectroscope for Chemical Analysis, ESCA)，也是必須在超高真空的環境下操作的表面分析儀。由於能量解析度考量，XPS最常用的X射線光源是Mg Kα和Al Kα。光電子的能量範圍和和部分歐傑電子的能量範圍重疊，因此，XPS和AES可以共用球扇電子能量分析器。XPS分析有二種模式：全能譜快速分析和局部能譜慢速分析。全能譜快速分析主要用於定性分析和半定量分析，鑑定試片的組成元素種類，典型的XPS全能譜如圖C-6所示，一般能量範圍從0至800或1000 eV，最高元素訊號能峰值將近二萬。全能譜經常會包含一、二個歐傑能峰，如圖C-6的Na KLL能峰。局部能譜慢速分析則主要用於定量分析和化學鍵結分析，只針對包含特定能峰的10 ~ 30 eV做慢速掃描，得到十幾萬以上的訊號強度，然後根據程式資料庫內儲存的資料做曲線配湊(Curve fitting)運算，在算出最佳配湊後，可以決定某特定元素各種化態離子的比值，如圖C-7所示。

X-ray Photoelectron Spectroscope (XPS) is also known as Electron Spectroscope for Chemical Analysis (ESCA)。XPS also works in an ultra-high vacuum environment. Mg Kα and Al Kα X-rays are generally used in XPS, because of their high energy resolution. Energy of X-ray photoelectrons overlaps with part of Auger electrons, so some Auger peaks show up in XPS spectra. There are two analysis mode for XPS, full spectrum with fast scan and partial spectrum with slow scan. The full spectrum is for qualitative and semi-quantitative analyses, a typical XPS spectrum of this mode is shown in Fig. C-6, the energy range is from 0 to 800 or 1000 eV with a maximum peak intensity close to 20000 counts, and a Na KLL Auger peak included. Composition of the specimen can be quickly identified. The partial spectrum is for quantitative and chemical bonding shift analyses. Only 10 to 30 eV energy range is scanned, the speed of energy scan is slow, and high intensity, over 100K, is collected. Curve fitting is then performed by repeated calculation using database built in the program. All chemical bonding states of a specified element can be determined after a best curve fitting is obtained, as shown in Fig. C-7.

XPS的缺點是空間解析度差，也就是探束(probe)很大，舊型的通常是直徑3 ~ 5釐米，產生訊號的體積很大，訊號強度很高，可達十幾萬，比EDS的數千高百倍，所以相對上定量分析的結果較準確。近代科學工程利用光纖聚焦，目前XPS的光源可縮小至7微米。當然，訊號強度也下降。XPS的另一優點是試片不必是導體。加裝適當的離子束後，XPS也可以做成分份縱深分析。

The disadvantage of XPS is its poor spatial resolution (big probe size). The probe is about 3 ~ 5 mm in diameter for old generation XPS. However, the volume excited is large and the intensity of the signal can be over 100 K counts, which is much higher than that of EDS. This makes XPS be more accurate in composition quantitative analysis. Current science and engineering use optical fibers to focus X-ray down to 7 um in diameter. Of course, the signal intensity drops with probe size inevitably. Another advantage of XPS is that no conduct specimen is required. XPS can perform composition depth profile when a suitable ion gun is available. 

圖C-6 典型XPS全能譜，能譜中包含有歐傑電子的能峰。

圖C-7 典型XPS局部能譜與曲線配湊。

C-1-3  二次離子質譜儀(SIMS)

二次離子質譜儀(Secondary Ion Mass Spectrometer)簡稱SIMS，係利用1 ~ 20 keV的主離子(通常是O₂⁺或者Cs⁺)撞擊固態試片的表面，靠近試片表面1 ~ 2 nm內的原子或分子得到足夠的能量，脫離試片表面形成濺射粒子(sputtered particles)，濺射粒子以中性粒子為主和一小部份二次離子(secondary ions)，如圖C-8所示。將二次離子收集至質譜儀(mass spectrometer)後，經質譜儀分析離子的質荷比(m/q)，而達到分析試片表面元素的目的(圖C-9)。由於主離子束對試片表面有濺射的作用，所以重複間隔一定時間收集暨分析二次離子，可以得到成份縱深分布曲線(圖C-10)，這是半導體界最常做的分析，用來分析離子佈植的深度。如果將首次離子聚焦成一離子探束(ion probe)並掃瞄試片表面，則可作二維成份影像分析，再搭電腦軟體控制與訊號收集和重建，則可進一步獲得3-D成份映像圖。

When a solid sample is sputtered by primary ions (O₂⁺ or Cs⁺ generally) of 1 ~ 20 keV, a fraction of the sputtered particles emitted from the target is ionized, as shown in Fig. C-8, from the surface to a depth of 1 to 2 nm. SIMS collects all ions into the mass spectrometer and identify elements by measuring their ratio of mass to charge (m/q). The primary ion beam itself can sputter the specimen, thus when secondary ions are collected and analyzed repeatedly at a constant rate, a depth profile can be obtained. An elemental map can be obtained by focusing the primary ions to scan the specimen. Further, a 3D map can be obtained by ions collection and reconstruction process using a program.   

圖C-8 二次離子的生成機制示意圖。

圖C-9 二次離子的靜態能譜圖。(黃悉雅博士提供(1999))

圖C-10 SIMS縱深分析圖。(黃悉雅博士提供(1999))

SIMS的有如下的特性

(1)可偵測週期表上所有的元素，而且可鑑別同位素。

(2)高偵測零敏度，可達ppm，甚至可達ppb (1 x 10¹² to 10¹⁶ atom/cm³ )。

(3)偵測濃度範圍(Dynamic range)可達10⁶，是常用材料分析儀器中最大動態範圍者。

(4)屬破壞性分析，樣品只有一次分析的機會。

(5)搭配標準試片可精準定量分析。

Characteristics of SIMS include 

(1) Capability of analyzing all elements, including their isotopes, in the periodic table. 

(2) High sensitivity, concentration as low as ppm, even ppb (1 x 10¹² to 10¹⁶ atom/cm³ ) can be detected.

(3) High dynamic range, ~ 10⁶, the highest one among routinely used materials analysis instruments. 

(4) A type of destructive analysis, the feature is gone once analyzed.

(5) Accurate quantitative analysis is possible with the use of standards.

目前常用的二次離子質譜儀有三種型式。(1)四極質譜儀：特點為對低質量元素靈敏，適用於超淺接面分析。(2)磁場質譜儀：特點為質量解析度高。(3)飛行式質譜儀：特點為偵測速率快，高靈敏度，入射主離子流小。

There are three main types of SIMSs. (1) Quadrupole mass spectrometer: sensitive to light elements, suitable for ultra-shallow junctions. (2) Magnetic mass spectrometer: high mass resolution. (3) Time of flight (TOF) mass spectrometer: high detection rate, high sensitivity, and small primary ion current.

參考文獻:

1] 凌永健，“二次離子質譜儀分析”，材料科學叢書2-材料分析，第二版，汪建民主編(2014)。

2] Secondary ion mass spectrometry – Wikipedia, https://en.wikipedia.org/wiki/Secondary_ ion_mass_ spectrometry (2020)

材料分析 Part C-1 表面分析儀 – 1/2 歐傑電子能譜儀(AES)

C-1表面分析儀

      高能粒子(電子，離子，中子，光子)撞擊試片後，在試片內部產生許多訊號。這些在試片內部產生的訊號，部分訊號逸出試片，部分訊號在試片內部穿梭中被吸收，最終成為熱能。用適當的偵測器收集這些訊號逸出試片的訊號就可以做成份分析。表面分析儀偵測的幾種訊號有一共通的特性，它們在固態試片內的自由平均行程都很短，只有在試片上表面起往試片內部5奈米內的深度內產生的訊號才有機會逸出試片；10奈米深度後，逸出試片的機率幾乎為零。因此物理學上將這些儀器劃分為表面分析儀器，一般材料分析實驗室常用的有歐傑電子能譜儀(AES)，X射線光電子能譜儀(XPS)，二次離子質譜儀(SIMS)。

High energy particles, such as electrons, ions, neutrons, and photons, will generate signals from a specimen after striking the specimen. Parts of these generated signals can escape from the specimen, parts of them will be absorbed during traveling in the specimen and be transferred to heat finally. When those escaped signals are collected by suitable detectors, information of composition of the specimen can be extracted. Signals collected by surface analyzers have a common characteristics: their mean free paths in the solid sample are very short, less than 10 nm, 5 nm averagely. So, only those generated in the depth less than 5 nm have chance to escape from the specimen. There is rarely signal from depth below 10 nm. That is the reason why we call instruments of this sort to be surface analyzers. Auger electron microscopes (AES), X-ray photon spectroscopes (XPS), and Secondary ion mass spectroscopes (SIMS) are three most used surface analyzers in materials analysis laboratories.

表面分析儀的工作腔必須是超高真空，也就是說其真空度優於 1x10^-9 torr。一般電子顯微鏡，例如TEM，的工作腔真空度為1x10^-6 torr，在此真空狀態下，約100秒的時間，樣品表面就蓋滿5奈米厚的碳原子；5分鐘以後，表面分析所需要的訊號就完全無法逸出。

The vacuum of working chamber of surface analyzer must be ultra-high vacuum, i.e. < 1x10^-9 torr. Electron microscopes, for example TEM, the vacuum of their working chambers is around 1x10^-6 torr. It takes only about 100s to deposit 5 nm thick carbon atoms on the top surface of the sample under such vacuum condition. After 5 minutes, all signals used for surface analysis are not able to escape from the sample. 

C-1-1 歐傑電子能譜儀(AES)

在超高真空的環境下，利用一能量1 ~ 10 KeV的電子束激發試片表面，造成表面原子發射Auger電子，藉由量測Auger電子的特性動能，可研判試片表面元素的種類、含量、和化態(Chemical state)。Auger電子的產生機構如圖C-2所示，一K軌域的電子被入射的高能電子撞擊出成為二次電子，在K軌域留下一空缺；下一瞬間，某一L₁軌域的電子躍下填補此K軌域空缺，放出一(E_K – E_L1) 能量的X-射線；此X-射線逸出過程恰好撞擊到另一L_2,3軌域的電子，L_2,3軌域的電子吸收此X-射線能量，轉化為動能，脫離原子的束縛。經過此連續機構而逸出原子的電子被命名為歐傑電子，紀念1924年發現該電子的法國科學家皮爾歐傑(Pierre Auger)。

An electron beam of 1 to 10 KeV is used to excite Auger electrons from a specimen surface in an ultra-high vacuum environment. Kinds of elements, their concentration, and chemical bonding state can be obtained by analyzing the characteristics of kinetic energy of Auger electrons. The mechanism of Auger electron generation is shown schematically in Fig. C-2. An electron in the K shell is knocked out to be a secondary electron by a high energy incident electron, and a vacancy is left in the K shell. An electron in the L₁ shell jumps into the K shell vacancy and emits an X-ray with an energy of E_K – E_L1. The emitted X-ray hit an electron in L_2,3 shell before escaping out of the atom. The L_2,3 shell electron absorbs the X-ray and transfers the radiation energy to kinetic energy, then escapes from the atom. The electron generated by these continuous mechanisms is named Auger electron in memory of Dr. Pierre Auger, a French physicist discovered this sort of electron in 1924. 

圖C-2 歐傑電子產生程序的示意圖。(a)高能電子撞擊K軌域電子；(b)某一個L軌域的電子躍下填補K軌域的空缺，多餘的能量以X-射線的方式釋出，並射向L軌域另一個電子；(c) L軌域電子吸收X-射線的能量，轉化為動能，逸出原子。

歐傑電子的能量約為50 ~ 2000 eV，屬低能量範圍，所以對輕元素較靈敏。歐傑的原始能譜(raw spectrum)有很高的背景值和很小的峰背比(P/B)，傳統上很少人直接使用原始能譜，而是使用微分能譜(differential spectrum)。典型的歐傑微分能譜中，背景訊號被拉成近乎水平線，如圖C-3所示，各元素能峰則相對放大，其能量解析度約為7 eV，比原始能譜稍差。AES微分能譜中，元素的能峰有許多特性微細結構。這些特性微細結構源自於(1)主量子軌域含有不同能量的的副軌域，例如：L軌域有2s, 2p；M軌域有3s, 3p, 3d等。(2)電子軌域的自旋角動量(spin angular momentum)和軌道角動量(orbit angular momentum)，例如：3p^1/2, 3p^3/2；  3d^1/2, 3d^3/2, 3d^5/2，利用這些特性微細結構，可以分辨元素的化態。新世代的歐傑能譜儀增加訊號偵測器的個數，提升P/B值，因此愈來愈多AES能譜直接用原始能譜。

The energy of Auger electrons falls in the range of 50 ~ 2000 eV. They are sensitive to light elements due to their low energy electrons. The background of AES raw spectra is high, and peak-to-background ratio (P/B) is small. So traditionally, differential spectra were usually used instead of raw spectra. A typical AES differential spectrum with nearly horizontal background is shown in Fig. C-3, peaks for elements are enlarged with an energy resolution about 7 eV, a little degrade from their original spectra. There are many fine structures, resulting from (1) there are sub-orbitals for each principle quantum orbital, such as 2s and 2p for L shell, 3s, 3p, 3d for M shell, (2) spin angular momentum and orbit angular momentum for shells, such as 3p^1/2, 3p^3/2, 3d^1/2, 3d^3/2, 3d^5/2 , …etc., in these AES differential spectra. Chemical bonding state can be characterized from these fine structures. More detectors are built in new generation Auger spectroscopes. This improves the P/B of raw AES spectra, and raw AES spectra are used more and more now.

圖C-3 典型AES能譜。(a)原始能譜；(b)微分能譜。。

目前常用的歐傑電子能譜儀有二：球扇電子能量分析器(SSA)和筒鏡能量分析器(CMA)，其基本結構示意圖分別如圖C-4和(圖C-5所示。在歐傑電子能譜儀內加裝離子鎗，用一定的速率濺射試片表面，每間隔一定的時間再以電子束做歐傑電子分析，可對樣品做縱深分析，甚至成像3D成份映像。由於在Z方向的解析度高(可達1 nm)，使得歐傑電子非常適用於多層薄膜結構的分析。一般使用氬離子(Ar⁺)做為入射離子源，調整氬離子的入射量、入射角度、濺射間隔時間、和入射能量，可以控制剝離表層原子的速率，調整縱深分析的解析度。總濺射時間，視試片的總厚度決定。縱深分析時，在注入氬離子階段，分析室的真空度不得超過1 x 10^-6 torr。

There two main types of AES, spherical sector analyzer (SSA) and cylindrical mirror analyzer (CMA), their basic configurations are schematically shown in Fig. C-4 and Fig. C-5 respectively. When an ion gun is included, the specimen can be sputtered in a controlled rate, a depth profile of composition as well as 3D mapping of the specimen can thus be obtained. The AES is a good analytical technique for multilayer materials system due to its good resolution in z direction. Generally, Ar⁺ source is used for the ion gun. The sputtering rate can be controlled by modulating Ar⁺ dose, incident angle, energy, and sputtering time, the resolution of the depth profile can thus be regulated. The total sputtering time for a depth profile depends on the total specimen thickness. The vacuum must be controlled to be better than 1 x 10^-6 torr during Ar⁺ sputtering.

圖C-4 球扇電子能量分析器(SSA)型歐傑電子能譜儀基本結構示意圖。

圖C-5 筒鏡能量分析器(CMA)型歐傑電子能譜儀基本結構示意圖。

材料分析Part C 微區成份分析簡介

前面提過，材料的性質由組成元素、晶體結構、和顯微結構決定。在B篇章節內介紹一些常用的微奈米影像分析，用於分析材料與元件的顯微結構。本篇將簡介一些常用的微區成份分析技術，包含AES，XPS，SIMS等表面分析儀，和能量散佈能譜儀(EDS)，以及電子能量損失能譜儀(EELS)。

We mentioned that properties of a material depend on its composition, crystal structure, and microstructure. Some image analysis techniques for nano materials and nano devices had been discussed in paragraph B. This paragraph will discuss some routinely used techniques for composition analyses, including AES, XPS, SIMS, EDS, and EELS.

許多材料的研發過程中，會經過熱處理的過程，某些新相會在熱處理過程中產生。這些新相的成份和晶體結構通常需要經過材料分析技術的鑑定，此時成份分析就不可避免的要進行。半導體元件是經過設計的結構，在嚴謹控制的製程條件下，一層一層長上去的。所以正常狀況下，從影像就可以知道半導體元件各層的組成，通常無需進行成份分析。唯有在某些新製程或新配方的研發階段，以及異常點的分析，才需要進行成份分析。半導體元件材料分析有一個特殊的領域叫做逆向工程分析，說白一點就是偷看別人的產品設計。逆向工程的材料分析時，由於結構不是自家的，所以影像分析和成份分析都需要。

Heat treatment is usually used in R&D of many new materials, some new phases are formed during the heating process. The composition and crystal structure of these new phases needs to be identified by techniques of materials analysis. Composition analyses are necessary in this field. On the other way, semiconductor devices are designed and manufactured by carefully controlled processes. The composition of each layer is known from images, and composition analysis is usually not necessary. In semiconductor industry, composition analysis is only wanted in R&D of new recipes and in failure analysis. One special field in materials analysis for semiconductors is reverse engineering. It is to spy on other’s products honestly. Because the target is unknown, composition analysis as well as image analysis are required.

鑑定週期表上的元素，可經由原子質量，或者經由原子內電子特定的鍵結能階，如圖C-1。因此，分析組成元素的儀器分成二大類型：質譜儀和能譜儀。對於固態材料分析領域，成份分析儀器以能譜儀居多，如EDS、EELS、AES、XPS、…等等，而SIMS則是固態材料分析領域，唯一比較常用的質譜儀。

We can identify elements in the periodic table by their mass or the characteristic bonding energy of electrons in atoms. Thus, spectroscopes are divided into two groups: mass spectroscopes and energy spectroscopes. For solid state materials, most spectroscopes are energy type, such as EDS, EELS, AES, XPS, … etc., SIMS is the only one mass spectroscope routinely used. 

圖C-1 週期表內元素的鑑定。

材料分析Part B-4-4 TEM明場像中常見的共同特徵影像 – 2/2 弗瑞斯聶爾條與莫瑞條紋

弗瑞斯聶爾條紋(Fresnel fringes)

顯微鏡影像一般都在正聚焦(in-focus)條件下拍攝，唯獨TEM明場像試在欠焦(under focus)條件下拍攝，旨在補償一些球面像差，同時使邊界位置或界面更清楚，更容易辨識。如圖B-39明場像所示，圖B-39(a)是正聚焦影像，圖B-39(b)欠焦影像，而圖B-39(c)則是過焦影像。相比之下，可以看出圖B-39(a)中物體的邊界沒有圖B-39(b)中的清晰明確，欠焦的TEM明場像沿物體輪廓邊緣多出一白線，使物體的輪廓邊緣更清晰，過焦的影像則在物體輪廓邊緣多出一條黑線。這些白線和黑線都叫弗瑞斯聶爾條紋。

Images taken by microscopes are usually photographed at in-focus condition, except TEM BF images. TEM BF images are usually photographed at under focus conditions, which can compensate some spherical aberration and highlight positions of boundaries or interfaces. Fig. B-39 shows images taken at in-focus, under focus, and over focus respectively. Apparently, the boundaries in the image in Fig. B-39(b) are more clearly than that in Fig.B-39(a). Those while lines along boundaries in under focus TEM BF images make boundaries more definitely. There are black lines along the boundaries when TEM images are photographed at over focus conditions. Both white and black lines are Fresnel fringes。

圖B-39弗瑞斯聶爾條紋(Fresnel fringes)。(a)正聚焦，Δf = 0 nm；(b)欠焦，Δf = -200 nm；(c) 過焦，Δf = +200 nm。[1]

在大多數狀況下，適當欠焦的明場像強調出邊界的位置，是一般TEM工程師拍攝TEM明場像的慣用條件。但是有時候這一層很薄的白色層次會造成顯微結構上的誤解。在半導體業界，弗瑞斯聶爾條紋最普遍被工程師誤認為矽原生氧化層，有時候連製程上的專家都會陷入此種迷惘。圖B-40展現此典型的例子，第一層多晶矽和第二層多晶矽之間的弗瑞斯聶爾條紋被誤判為矽原生氧化層，導致TEM顯微結構分析和該元件的電性不符。

Generally, the boundaries of phases are highlighted by a suitable under focus which is used for almost all TEM engineers to take TEM BF images. However, these white lines can be mistaken to be thin layers in the microstructure sometimes. Fresnel fringes are easy to be confused with Si native oxide layers for process engineers, even some process experts were puzzled, in semiconductor industry. Fig. B-40 shows a typical case, the Fresnel fringe between poly 1 and poly 2 was mis-judged to be a Si native oxide layer. This mistake resulted in a contradictory between the microstructure and the resistance measured.

圖B-40弗瑞斯聶爾條紋造成第一層多晶矽和第二層多晶矽之間有原生氧化層的誤判。[1]

莫瑞條紋(Moirè fringes)

在TEM試片厚度內，電子束前進的路徑如果通過二個晶粒，而這二個晶粒有某種晶向關係的時候，就有可能產生莫瑞條紋。圖B-41內的示意圖解說產生莫瑞條紋的二種主要型式[2]：(1)上下二個晶體不同相，但是某一組晶格面互相平行，而且晶格面間距大小很接近；(2)上下二個晶體同相，同組晶格面相對旋轉一個小角度。第一類型的條紋走向和原來的晶格面平行，間距則為晶格面間距的數倍到數十倍，視二組晶格面間距的差而定。第二類型的條紋走向和原來二組晶格面的伯格向量差垂直，間距約為晶格面間距除以旋轉角度(徑度)。圖B-42顯示氮化鎵柱狀晶重疊產生的第二類型莫瑞條紋。

Moirè fringes are possible to be observed when the incident electron beam passes through two crystals with a special relationship in crystal orientation. Fig. B-41 explains how Moirè fringes are formed schematically [2]. For the first type, two crystal are different phase, (h₁ k₁ l₁) and (h₂ k₂ l₂) are crystal planes parallel to each other and the difference in d-spacings is small. For the second type, two crystals are same phase, the (h_i k_i l_i) crystal planes of one crystal rotates a small angle related to the same (h_i k_i l_i) crystal planes of the other crystal. The direction of Moirè fringes of the first type run parallel to the (h k l) planes and their spacing is about several to more than ten times of the d-spacing of (h k l) planes. Fig. B-42 shows a second type of Moirè fringes of GaN columnar crystals.

圖B-41莫瑞條紋的形成的機構。(a)電子束與試片關係示意圖；(b)第一類型莫瑞條紋產生機構的示意圖；(c)第二類型莫瑞條紋產生機構的示意圖。[2]

圖B-42氮化鎵柱狀晶重疊產生的莫瑞條紋。

參考文獻

1] 鮑忠興和劉思謙，近代電子顯微鏡實務，第二版，滄海書局，台中 (2012)。

2] Practical Electron Microscopy in Materials Science, edited by J. W. Edington, Van Nostrand Reinhold Company (1976).

材料分析Part B-4-4 TEM明場像中常見的共同特徵影像 – 1/2 厚度條紋與彎曲條紋

本章節所要討論的特徵影像並非試片本身待分析的結構，但是卻經常出現各種TEM試片。不是每個TEM試片都會有這些特徵影像，但是經常有些TEM試片會出現一或二種下列提到的特徵影像。

What are going to discuss in this paragraph are some feature images which are not characteristic structures in the specimen but observed in many TEM specimens from time to time. It is not for all TEM specimen to have these feature images, however sometimes some TEM specimens have one or two of them 

厚度條紋(thickness fringes)

此種特徵條紋如圖B-36所示，黑白相間的條紋和試片的邊緣平行，條紋的間距會因繞射狀態而改變。此類條紋在機械研磨的TEM試片的邊緣經常看到，目前半導體元件的TEM都是用FIB製備，試片厚度大致均勻，所以很少看到此類條紋，但是當TEM試片剛好切在某些特殊的位置時，仍可以看到厚度條紋。厚度條紋形成的原因類似牛頓環的原理，在一玻璃材質的契形試片邊緣，當試片厚度等於四分之一波長，四分之三波長…等位置，入射光波從試片上表面和下表面個別反射的波剛好反相，二者干涉後呈暗線；在試片厚度等於二分之一波長，一個波長…等位置，從試片上表面和下表面各別反射的波剛好同相，二者干涉後呈亮線。在晶體TEM試片中，除了入射電子波的波長外，繞射狀態也會影響條紋間距。

Typical thickness is shown in Fig. 36, alternative black and white fringes run parallel to the specimen edge, and their spacings vary with diffraction conditions. This kind of fringes is common in TEM specimens prepared by mechanical grinding and polishing. They are hardly to be observe in the field of semiconductor industry since all TEM samples are prepared by FIB and their thicknesses are nearly constant through the specimen. However, thickness fringes can still be visible when TEM specimens are cut from some special positions. The principle of forming thickness fringes is similar to that of Newton’s rings. When light incidents a wedge specimen made of glass, dark lines are observed at positions of specimen thickness equaling to 1/4 λ, 3/4 λ, .., etc., where the phases of the reflected waves from top surface and bottom surface are reverse. White lines are observed at positions of specimen thickness equaling to 2/4 λ, λ, .., etc., where the phases of the reflected waves from top surface and bottom surface are in phase. For crystalline TEM specimen, the spacing of thickness fringes is affected by both the wavelength and the diffraction condition. 

圖B-36 TEM明場像。機械研磨的矽試片，試片邊緣呈現厚度條紋。(a) [0 0 1]正極軸；(b) [4 0 0] 雙束條件。[1]

彎曲條紋(bend contour)

為了拍攝清晰的高分辨影像，TEM試片厚度常會減薄至50奈米以下，當試片本身的物理結構無法支撐它本身的重量時，在試片薄區就會產生局部性的彎曲。彎曲的晶體將造成入射電子束和同一族(h k l)晶面的夾角連續改變，如圖B-37(a)示意圖上半部所示，因此在同一晶體內，繞射狀態卻一直在改變，造成對應影像的強度也一直在改變，如示意圖B-37(a)示意圖下半部所示。圖B-37(b)為一金屬試片的彎曲條紋，圖B-37(c)是圖B-37(b)中紅色框區域的放大圖，圖中沿著紅線的影像強度變化和圖B-37(a)所示的明場影像強度與繞射狀態的變化吻合。圖B-37(c)中黑色帶狀區域相當於圖B-37(a)中間偏離參數(deviation parameter) s小於零的地帶，該地帶內明場像和暗場像的強度都降至最低。

To obtain clear HRTEM images, the thickness of the TEM specimen is usually reduced to be less than 50 nm. If the structure is not able to support its weight itself, the specimen bends locally. The bending results in that the angle between the incident electron beam and the same family (h k l) crystal planes varies from place to place, as shown schematically in Fig. B-37(a). The diffraction condition then changes correspondingly, so does the image intensity. It is a typical bend contour in a metal specimen in Fig. B-37(b), and Fig. B-37(c) is the magnified image of the area in the red rectangle in Fig. B-37(b). The variation of the image intensity along the red line across the black band meet the variation of BF image intensity as well as diffraction condition shown in Fig. B-37(a). The diffraction condition of the black band is thus in s < 0 conditions which has minimum BF and DF intensity.

圖B-37彎曲條紋。(a)彎曲的晶體和對應繞射狀態與影像強度變化的示意圖[2]；(b)金屬晶體內的彎曲條紋；(c) (b)中紅框區域的放大影像，紅色線條畫過區域的影像強度變化對應(a)中的繞射狀態與影像強度曲線。

彎曲條紋常見於延性的金屬材料試片，尤其是大於數十微米薄區的金屬TEM試片中。彎曲條紋的形狀和繞射狀態有關。圖B-38(a)整組彎曲條紋的形狀類似該晶體的[0 1 1]菊池線圖案，數條彎曲條紋的交會點是面心立方晶金屬正[0 1 1]極軸的位置，每一條彎曲條紋的帶狀區域內都對應一組雙束繞射條件。當脆性晶體材料的TEM試片中有薄又寬的區域時，也會產生彎曲條紋，如圖B-38(b)的右下方的矽單晶基板內。此時要拍攝良好的矽基板-氧化層-多晶矽HRTEM影像，必須傾轉試片，使彎曲條紋的交會點中心移到試片薄區又恰好位於某個MOS結構的正下方。

Bend contours are frequently observed in ductile materials, such as metals, especially when a metal TEM specimen with thin enough areas more than several ten micrometers wide. The shape of bend contour is closely related to the local diffraction condition. In Fig, B-38(a), the appearance of this set of contours looks like the [0 1 1] Kikuchi patterns of fcc crystals, the center of intersection of all bend contours is where the exact [0 1 1] zone axis of the fcc metal crystal locates, and the diffraction condition in each bend contour is two beam condition. Bend contours show up in brittle crystalline materials too when the specimen is thin and wide, as shown in Si substrate in Fig. B-28(b). If we want to take good HRTEM images of Si sub\oxide\poly Si, we have to tilt the specimen to make the center of the bend contours locate at a MOS structure where is thin enough for HRTEM images.

圖B-38彎曲條紋。(a)金屬試片[0 1 1]；(b) 矽基板[0 1 1]。

參考文獻

1] 鮑忠興和劉思謙，近代電子顯微鏡實務，第二版，滄海書局，台中 (2012)。

2] Practical Electron Microscopy in Materials Science, edited by J. W. Edington, p.113, Van Nostrand Reinhold Company, (1976).