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).

材料分析Part B-4-3 TEM影像的對比機構 – 3/3 TEM和STEM高分辨影像

TEM和STEM高分辨影像

目前許多200KV以上的TEM都具有優於0.2奈米的儀器解析度。所以在TEM機況調整非常良好和搭配適當的試片條件下，TEM倍率超過100KX後，可看到晶體的晶格影像，這類TEM影像一般稱為高分辨影像，影像對比機構為相對比。這裡的相和前面提到的相不同，前面提到的相都是材料學的相，指的是一均勻組成的固態物質。相對比的相指的是電磁波相位的相。將電子束視為電子波，通過試片後，透射電子束和繞射電子束到成像面的路徑不同，產生波程差，造成相位差，彼此互相干涉(interfere)的結果是，同相位的波干涉產生建設性的干涉，形成亮點；反相位的波干涉產生破壞性的干涉形成暗點，最後形成一組明暗點重複交錯排列的影像，稱之為高分辨(HRTEM)影像。HRTEM影像是分析材料界面和奈米級界面反應的理想分析技術，尤其是對有磊晶關係的材料系統的界面更理想。圖B-33是一典型的例子，用分子束磊晶(MBE)法在6H碳化矽單晶基板長上一層鈦磊晶層，高溫反應後，在界面生出碳化鈦和矽化鈦二層新相。

Most of current TEM operated at 200 KV or higher has instrument resolution better than 0.2 nm. When the TEM is well aligned and a suitable crystal is obtained, lattice images are visible as TEM magnification is over 100 KX. We usually call this kind of images to be high resolution TEM (HRTEM) images. The contrast mechanism of HRTEM images is phase contrast. The “phase” is different from those phases mentioned in previous paragraphs, which mean homogenous solid matters. Here, the “phase” in “phase contrast” is the phase of electromagnetic waves. Electron beams are treated be electron waves. The transmitted beam and diffracted beams travel along different path to reach the first image plane after exiting the specimen. This results in phase shifts between the transmitted beam and diffracted beams. They interfere with each other at the first image plane, and bright spots appear at where constructive interference occurs, while dark spots appear at where destructive interference does. An image of an array of spots is formed, and we call this kind of image to be a high resolution TEM (HRTEM) image. HRTEM imaging is an idea analytic technique to explore the interface structure and interfacial reaction in nano scale, especially for material systems with epitaxial relationship. Fig.B-33 shows a typical example, the HRTEM image shows an interface structure of high temperature annealed Ti/6H-SiC with two interfacial reactants, TiC and Ti₅Si₃. 

圖B-33. 6H-SiC\TiC\Ti₅Si₃\Ti的HRTEM影像。

HRTEM影像是電子波的干涉影像，是為相干(coherent)影像。影像中的黑點和白點，和晶體內的原子位置並非唯一對應，會隨試片厚度變化與TEM欠焦值變化而改變，如圖B-34所示。現代的TEM都配備CCD數位影像機，可做即時性的傅立葉轉換，判斷當下的聚焦條件。最正確的拍攝聚焦條件為謝爾策欠焦(Scherzer defocus)，此時黑點代表原子位置。過多的欠焦值會造成HRTEM影像產生偏移的現象[1]，此時晶格影像仍然清晰可見，但是偏離其正確的位置。半導體業界經常使用Si/SiO₂/poly HRTEM影像量測閘極氧化層(GOX)的厚度，過多的離焦值會造成矽基板的矽原子延伸入二氧化矽層內，導致最後量測的閘極二氧化矽層厚度變小。

HRTEM images are images of interference of electron waves, is a kind of coherent image. The corresponding relationship between black and white spots with atoms is not unique, it changes with specimen thickness and TEM defocus values, as shown in Fig. B-34. Now, almost all TEM used are equipped with CCD digital cameras, live fast Fourier transfer (FFT) is available to judge the defocus condition. The optimum defocus condition for HRTEM images is Scherzer defocus, black spots in these HRTEM images are corresponding to atom positions. If too large defocus is used, image delocalization occurs, and features in the image displace from their true positions [1]. HRTEM images of Si/SiO₂/poly are often used to measure the thickness of the gate oxide in semiconductor industry. The measured thickness of gate oxide (GOX) will be thinner than its true value when delocalization exists in the HRTEM image.

圖B-34.鋁在[1 1 0]晶軸方向的HRTEM影像模擬地圖，TEM操作電壓= 800 KV。(Ref: M. A. O'Keefe, in Image Calculation Techniques, handout for ASU Winter School (1993)).

相對於HRTEM影像，HRSTEM影像是用聚焦的電子束掃描試片而得，是為不相干(noncoherent)影像。影像中的白點恆為晶體的原子位置，白點的亮度隨該晶格點的平均原子序增大而增強，如圖B-35所示，InGaN層最亮，GaN次之，AlGaN最暗。

Instead of formation by the interference of electron waves, HRSTEM images are formed by focused electron beams and are non-coherent images. White spots in HRSTEM images are atom positions in the crystal. The intensity of white spots increases with the average of atomic number of the corresponding lattice points, as shown in Fig. B-35, l InGaN layers have the highest intensity, then GaN layers, and AlGaN layers have the lowest intensity. 

圖B-35. GaN1\AlGaN\GaN2\InGaN量子阱結構的HRSTEM影像。極軸方向= [1 1 -2 0]。

1] David B. Williams and C. Barry Carter, “Transmission Electron Microscopy, Microscopy”, 2nd edition, Plenum Press, New York (2009)

材料分析Part B-4-3 TEM影像的對比機構 – 2/3 TEM&STEM DF影像

TEM DF影像

TEM暗場像中的影像對比機構只有一個：繞射對比，因為TEM暗場像通常只用單一的繞射電子束成像。這類影像目前常用的有三大類型。

The only image contrast mechanism in TEM dark-field (DF) images is diffraction contrast, since TEM DF images usually use only single diffraction beam to form images. There are three kinds of DF images frequently used today.

第一類型暗場像用於分析晶體缺陷，影像中暗色背景區域和亮色特徵物屬同一晶粒。圖B-29(b)顯示一典型例子，差排造成晶體局部晶格扭曲，使該區域的繞射條件和晶粒其他地方略微不同，形成明暗對比。在明場像中，差排以暗色呈現，而在中央暗場像中，差排以亮色呈現，而且更清晰。此類型TEM暗場像，必須先將待分析的晶體傾轉至某些特定的雙束條件(two beam conditions)。

The first type of dark field images is used to analyze crystal defects in crystals. Bright features and dark background are in the same crystal. Fig. B-29(b) shows one typical example. Lattices around dislocations are distorted locally and cause corresponding diffraction conditions to be different from other regions of the crystal. Dislocations are black in BF images and white in CDF images. CDF images always reveal more detail structure of dislocations than BF ones do. The selected crystal has to be tilted to some specified two beam conditions for this type of DF images. 

圖B-29. 差排TEM影像。(a)明場像；(b)中央暗場像。

第二類型暗場像如圖B-30所示，用於分析奈米多晶材料，影像中暗的晶粒和亮的晶粒屬同一晶相材質，但是晶粒的方向不同，對應的繞射狀態不同。當晶粒尺寸比試片厚度小數倍時，由於重疊的問題，在明場像中，很難看清單一晶粒的輪廓。選用一小部分繞射點形成中央暗場像，雖然只能看到部分晶粒，但可以量測晶粒的大小。這一類型的暗場像如果採用空錐影像(hollow cone)技術攝取，則對於適當的多晶材料系統，可以一次同時將同組{h k l}，例如: {2 0 0}, {1 1 1}, {2 2 0}等，的所有繞射電子束拍攝在同一張暗場像中。

The second type of dark field images is used to analyze nano polycrystal materials. Bright and dark grains are same phase with different diffraction condition due to different orientation related to the incident beam. Crystals are overlapped and hard to be distinguishable in the BF images when their grain size is much smaller than the thickness of the specimen, as shown in Fig.B-30. Only parts of grains are in bright contrast when a few of diffracted beams are selected to form the CDF image, while their size can be measured easily. If hollow cone image is used for this kind of analysis, a special family of {h k l}, such as {2 0 0}, {1 1 1}, {2 2 0}, …etc., diffraction beams can be imaged simultaneously in single DF image for some polycrystal materials. 

圖B-30. 奈米多晶材料的TEM影像。左上角是明場像；左下角是選區繞射圖案，圖中黃色圓圈代表物鏡光圈；其他四張為中央暗場像。

第三類型暗場像如圖B-31(c)所示，用於相鑑定，影像中亮色特徵物和暗色區域為不同相的晶體。圖B-31(b)明場像用圖B-31(a)的選區繞射圖案中大黃色圓圈內的電子束成像，包括透射電子束、316不鏽鋼的繞射電子束、M₂₃C₆析出物的繞射電子束。而圖B-31(c)中央暗場像只用單一M₂₃C₆析出物的繞射電子束成像。

The third type of dark field images is used for phase identification. The bright features and dark background are not same phase. Fig.B-31(b) is a BF image using a large objective aperture indicated in Fig.B-31(a) to include the transmitted beam and diffracted beams from the matrix of 316 stainless steel and M₂₃C₆ precipitates to form the image. Fig.B-31(c) is a CDF image using a small objective aperture indicated in Fig.B-31(a) to include one diffracted beam of M₂₃C₆ precipitates to form the image.

圖B-31. 316不鏽鋼基材與M₂₃C₆析出物的TEM影像。(a)選區繞射圖案；(b)明場像(使用如大黃色圓圈所示的物鏡光圈)；(c)中央暗場像(使用如小黃色圓圈所示的物鏡光圈)。

STEM ADF和HAADF影像

如前一章節圖B-27所示，在STEM影像模式時，當相機長度減小後，環狀影像偵測器排除透射電子束的訊號，所形成的影像為STEM暗場像。當環狀影像偵測器的內收集角在0.3 ~ 1.0度之間時，STEM暗場像的對比機構以繞射對比為主，在1.0 ~ 2.0度之間時，原子序對比的比例逐漸提高，這些STEM暗場像稱為環狀暗場(ADF)像。當環狀影像偵測器的內收集角大於2.0度後，繞射電子束的訊號非常微弱，收集到的訊號幾乎都是被彈性散到高角度的入射電子，這些STEM暗場像稱為高角度環狀暗場(HAADF)像，此時影像對比機構為原子序對比。這些STEM暗場像特徵的變化如圖B-32所示。

As shown in Fig.B-27 in the last paragraph, the annual detector will exclude the transmitted beam when small cameral lengths are used. These STEM images are then dark field type. Diffraction contrast dominates in these STEM DF images when the corresponding inner collection angles fall in the range of 0.3 ~ 1.0 degrees, but weight of atomic number contrast increases gradually when the inner collection angle is larger than 1.0 degree and smaller than 2.0 degree. We call STEM DF images in this range to be ADF images. When the inner collection angle is larger than 2.0 degree, the contribution of the diffraction beams can be neglected, electrons scattered elastically to high angles are signals to form these images, and we call these images HAADF images. The image contrast mechanism in HAADF images is atomic number contrast only. Characteristics of these images are shown in Fig.B-32. 

圖B-32. 半導體元件的STEM影像。(a)對應的TEM明場像；(b)STEM明場像；(c)STEM ADF像；(d)STEM HAADF像。

材料分析Part B-4-3 TEM影像的對比機構 - 1/3 TEM BF影像

TEM影像本質上屬科學與工程類的影像，影像內容的主要重點是有沒有包含工程需要的訊息。要充分萃取影像內的訊息，必須先瞭解影像的成像對比機構，然後才能解讀無誤。例如3月25日發布的一文中，圖B-1所示，同樣的樣品表面在OM和SEM的影像中明暗對比恰好相反，如果用OM影像的觀念解釋SEM影像必定誤判樣品表面狀態。以下針對前一章節(B-4-2)談論到的幾種影像，簡單敘述其影像的成像對比機構。

TEM images are essentially images of science and engineering, the information inside images is the key point of these images. It is necessary to understand the mechanism of imaging to fully and correctly extract information form an TEM image. For example, the corresponding brightness of the sample shown in Fig. B-1 in the text issued at March 25 reversed in OM and SEM image. If we use the contrast mechanism of OM to explain the SEM image, we will misjudge the condition of the sample surface. Below, I will discuss the mechanism of imaging for types of images mentioned in the last section (B-4-2).

TEM BF影像

TEM明場像中的影像對比機構有二個: 原子序對比和繞射對比。以下用圖B-28說明。圖B-28(a) 和圖B-28(b)中是一半導體元件中的MOS(metal-oxide-silicon)結構，從下往上依序為矽基板，金屬矽化物，氧化層，多晶矽+襯墊(氮化矽+氧化矽)，氮化矽覆蓋層。在氮化矽覆蓋層上方為氧化矽介電層。

(1) 原子序對比：

黑白的TEM明場像中有效原子序愈大(或密度愈大)的相，顏色愈暗。因為原子序愈大的原子將入射電子散射到高角度的能力愈強。物鏡光圈置入後，通過原子序大的的區域的電子被擋掉的比例愈大，最後成像的電子劑量就愈少，因此影像呈暗色。由圖B-28(a)的灰階顯示各相的密度排列順序為金屬矽化物 > 矽 ~ 氮化矽 > 氧化矽。

(2) 繞射對比：

只存在於晶體相，非晶質相沒有繞射對比。所以圖B-28(a)和圖B-28(b)中，矽基板，金屬矽化物，和多晶矽三相本身的明暗度會有明顯變化。矽基板是單晶，所以在閘極下方較暗的半圓形代表應力場的存在，使該環帶區域的晶格方向和其他區域略有不同，因此和入射電子束的夾角不同，形成繞射對比。金屬矽化物和多晶矽是多晶相，每一晶粒和入射電子的夾角不同，自然產生繞射對比。氮化矽和氧化矽都是非晶質，沒有規則性的晶格，相內各處的電子束繞射情況都一樣，所以整個相的明暗度均勻，而且不會隨試片的傾轉而有所變化。所有晶體在試片傾轉過程中，其明暗度都一直在改變，因為晶格面和入射電子束的夾角一直在變動，繞射情況也一直在更改。

There are two kinds of image contrast mechanisms in TEM BF images, atomic number contrast (z-contrast) and diffraction contrast. Let me illustrate them by means of Fig. B-28. The feature in Fig. B-28(a) & (b) are MOS(metal-oxide-silicon) structure of semiconductor devices. They are constituted of Si substrate, metal silicide, oxide layer, poly, spacer (nitride and oxide), and capped nitride. Above capped nitride is a silicon dioxide dielectric layer.

(1) Atomic number contrast:

In black and white TEM images, phases with higher atomic number are darker because they elastically scatter more incident electrons to high angles. The inserted objective aperture blocks electrons scattered to high angles. Electrons finally reach the image detector are less for phases consisted of high atomic number elements. Thus, their corresponding images are dark. From the grey level, the density of these phases are metal silicide > Si ~ silicon nitride > silicon oxide.

(2) Diffraction contrast:

This mechanism exists in crystalline phases only not in amorphous phases. In Fig.B-28, the brightness of Si substrate, silicide, and poly vary from place to place. Si substrate is a single crystal, thus the light-dark half circle band under the gate indicates that there is a strain field which distorts the lattice locally and makes the diffraction condition different from other regions. Metal silicide and poly silicon are polycrystal, each crystal has its own diffraction condition and is different from other crystals of same composition. Both nitride and oxide are amorphous phases without any defined crystal lattice, thus the diffraction condition is same everywhere inside each phase, and each phase is monochromatic even the specimen being tilted. The brightness of a crystalline phase varies when the specimen is tilt because the angles between the incident beam and crystal planes change.

圖B-28. TEM明場像。(a)矽基板在任意晶向；(b)矽基板在[011]正極軸晶向。

圖28(a)的矽基板與金屬矽化物都和入射電子束成任意角度，所以通過的二相的入射電子主要匯流到透射電子束。金屬矽化物的有效原子序較大，對入射電子有較強的散射作用，因此等量的入射電子通過二相後，通過金屬矽化物的電子被散射到高角度的比例較大。當物鏡光圈置入後，散射到高角度的電子被物鏡光圈擋住，沒有貢獻到影像，也就是說，矽基板成像的電子劑量較多，所以矽基板的對應影像比金屬矽化物的影像亮。當傾轉矽基板使其[011]極軸和入射電子束平行時，通過矽基板的入射電子形成強烈的繞射，很大比例的電子分流到繞射電子束，被物鏡光圈擋住而沒有貢獻到影像，此時矽基板成像的電子劑量和金屬矽化物成像的電子劑量接近，形成的明場像就如圖28 (b)所示，矽基板和金屬矽化物明暗度幾乎相同，人類肉眼無法辨識。

In Fig.B-28(a), the orientations of the Si substrate and the metal silicide are arbitrary related to the incident beam, and most of electrons passing through the specimen converge to the transmitted beam. The effective atomic number of the metal silicide is larger than that of Si and has larger ability for elastically scattering. When same electron dose passes these two phases, the ratio of electrons scattered to high angles is higher for those going through the metal silicide. The inserted objective aperture blocks electron scattered to high angles. This makes the corresponding image of Si substrate has more electrons and shows bright contrast. Electrons passing Si substrate are in strong diffraction condition when the Si substrate is tilted to [011] zone axis. More than half of electrons are now divided into diffracted beams and are blocked by the objective aperture. The net electron dose for Si substrate and metal silicide is then almost same, and the corresponding images have same gray level, as shown in Fig.B-28(b). It is hard for human eyes to distinguish these two phases in this image. 

有的TEM教科書將原子序對比分成質量對比(mass contrast)和厚度對比(thickness contrast)。從電子散射的角度來說是同一件事，原子序的原子質量也大，對入射電子的散射能力較強，同一組成的試片隨著厚度增加，對入射電子的散射比例也增加。因此David B. Williams和C. Barry Carter在Transmission Electron Microscopy[1, 2]一書中將二者合併為一，稱為質厚度比(mass-thickness contrast)。

Some TEM textbooks used the terminology of mass contrast and thickness contrast instead of atomic number contrast. They are same if we consider the behavior of electron scattering, atoms with higher atomic number have larger mass and then larger ability for electron scattering, the probability for incident electrons being elastically scattered to high angles increases with the specimen thickness. David B. Williams and C. Barry Carter used mass-thickness contrast in their book, Transmission Electron Microscopy [1, 2].

References:

1] David B. Williams and C. Barry Carter “Transmission Electron Microscopy”, Plenum Press, New York (1996)

2] David B. Williams and C. Barry Carter, “Transmission Electron Microscopy, Microscopy”, 2nd edition, Plenum Press, New York (2009)