材料分析Part B-1 原子力顯微鏡(AFM)

SPM(scanning probe microscope)是一群研究樣品表面性質(形態、磁性、電性、…….等等)的顯微鏡的總稱。在SPM族群中被應用最廣的是STM(scanning tunneling microscope)和AFM(atomic force microscope)，分析層次可從微米級至原子級。

Scanning probe microscope(SPM) is a terminology for a group of probing microscopes exploring properties, including morphology, magnetism, electric of top surfaces of materials. Scanning tunneling microscope(STM) and atomic force microscope(AFM) are the two most used. Their resolutions fall in the range of micrometer to atomic scale. 

STM於1981年由IBM公司的Dr. Gerd Binning和Dr. Heinrich Rohrer共同發明。1986年兩人和Dr. Ernst Ruska(TEM發明人)共享諾貝爾物理獎。STM乃藉由探針尖端和試片的穿隧電流的變化，產生STM影像。STM的解析度可達0.1奈米，高解析STM通常必須在真空之中操作，樣品必須是導體。

STM was developed by IBM Dr. Gerd Binning and Dr. Heinrich Rohrer in 1981. They received Nobel Prize in Physics in 1986. STM images are formed by recording the variation of current which tunneled from the probe tip to the specimen surface during scanning. The resolution of STM can reach 0.1 nm. Usually, it is better to perform the scanning in an isolated vacuum chamber and use a conductive specimen to get resolution of atomic scale. 

AFM則是藉由探針尖端和樣品表面的原子吸力或斥力的作用，使懸桿彎曲或偏折進而導致背面“鏡子”偏轉雷射光束到達PSPD的不同位置，電腦接收並分析4片光偵測器光訊號的變化，產生AFM 影像，如圖B-2所示。AFM 分析通常在空氣中進行，試片可以是非導體樣品，成為目前最方便，而且使用最廣泛的SPM。AFM有三種基本操作模式：接觸模式、不接觸模式、中間模式，對應的探針和試片位置如圖B-3所示。

AFM images are formed by using a position sensitive photodetector (PSPD) senses the variation of the laser beam which reflects from the back of the tip, as shown in Fig. B-1. AFM experiments are performed in air, and the specimen is not necessary to be conductive. This convenience makes AFM be the most popular in SPM family. There are three operation modes for AFM: contact mode, noncontact mode, and tapping mode, corresponding distance between tips and specimens are shown in Fig. B-2.

圖B-4展示一典型的AFM應用，光碟片記錄溝槽輪廓量測。圖B-4(a)局部CD的AFM俯視圖，圖B-4(b) (a)的3D立體圖，圖B-4(c) (a)中紅線位置的溝槽輪廓線。

Fig. B-4 displays a typical application of AFM, measurement of CD profiles. Fig. B-4(a) is a top view of part of CD, (b) is a 3D view of (a), and (c) is the profile of the position marked by the red line in (a).

圖B-2. AFM基本結構示意圖。

圖B-3. AFM操作模式原子間作用力(F)和原子間距(d)的關係圖。

圖B-4. AFM典型應用。(a)局部CD的俯視圖；(b)同一區域的3D圖；(c) (a)中紅線位置的輪廓線。

材料分析 Part B: 顯微鏡影像分析技術

對應材料分析儀器的功能分類，所得到的訊息也分為三大類：影像、能譜、繞射圖案，本節先介紹影像。影像的主要功能是顯示分析物的形貌(morphology)和大小(dimension)。提供最高解析度的顯微鏡是TEM，目前台灣TEM分析需求量最大的用戶是半導體業界，在半導體業界的TEM分析中約百分之九十是影像分析。

Typical, data of materials analysis are summed up into three groups: images, spectra, and patterns. We will introduce images in this paragraph, and others later. Images offer information of morphology and dimension of materials analyzed. For microscopes family, TEM has the best resolution for routine analysis. Semiconductor is the number one TEM user in Taiwan. More than 90% TEM analyses are image analysis in semiconductor industry.

影像之所以能判別分析物的形貌與大小，主要在於光源通過試片時會產生散射、繞射、反射等交互作用，同劑量密度的光源經過不同材質或同材質但不同晶向，經歷不同程度的散射、繞射、反射，最後到達影像偵測器的像素時劑量不同。在黑白影像中，劑量高的像素呈亮區，劑量低的像素則呈暗區，這種影像中的明暗變化稱之為對比(contrast)。

When homogenous beams pass through the specimen, interactions, such as scattering, diffraction, and reflection, of light with the specimen occurs, the final dose reach the image detector vary from pixels to pixels. In black and white images, they show bright in high dose pixels and dark in low dose pixels. This change in intensity is named contrast.

對比是影像的第一要素。影像因為有對比才能區別不同材質或不同晶向的晶粒。在不同種類，尤其是不同光源，的顯微鏡中，影像對比機構不同。例如，同材質但不同粗糙度(roughness)的樣品表面，例如圖10(a)，在光學顯微鏡影像中，如圖10(b)所示，平滑區是亮區；而在SEM二次電子影像，如圖10(c)所示，粗糙區是亮區。工程師必須先瞭解影像的對比機構，才能從影像中正確解讀試片內的結構。

Contrast is the most important factor of an image. It is the contrast that can tell the difference in materials and crystals of different orientation. The mechanism of image contrast is different for different type of microscope, especially with different light source. For example, a specimen of single phase has two part of surfaces, smooth and rough, as shown in Fig. 9(a). The smooth region will be bright in an optical microscope image, as shown in Fig. 9(b), but will be dark in a SEM SE image, Fig. 9(c). An engineer can read the structure of the analyzed material from images when he/she understand the mechanism of the image contrast, otherwise those images are just black and white images.

影像第二項要素是解析度，隨著影像倍率提高，通常解析度也會跟著提高。但是到達儀器的解析度極限之後，倍率的提高只會犧牲影像視野，不會繼續提升解析度。影像第三項要素是訊雜比(S/N)，訊雜比必須高過某值後，影像才會有一定的視覺品質。通常訊號強度必須超過影像偵測器飽和強度的一半，才有較佳的訊雜比。

The second factor for image is resolution. The resolution power of a microscope usually increases with the magnification until it reach the resolution limit of the microscope. Further increase in magnification does not raise resolution power, while reduces the view only. The third factor for images is signal-to-noise ratio (S/N). An image looks quality only when its S/N is over certain value. Usually, the maximum intensity of an image has to be higher than the half of saturated intensity of the detector, then the S/N reaches a satisfied value.

圖B-1. 試片表面形貌與對應顯微鏡影像的示意圖。(a)試片表面形貌；(b)光學顯微鏡影像，(c)SEM二次電子影像。。

高能電子與試片的交互作用(Interaction of High Energy Electrons with the Specimen)

由於待測樣品(材料或組件)的顯微結構不是肉眼或簡單的放大鏡/光學顯微鏡(OM)可觀察的，因此這些顯微結構對於人類的眼睛來說相當於一個「黑箱」。我們必須藉由一些比材料顯微結構尺寸上小許多的高能粒子(離子、電子、光子等)撞擊樣品，交互作用後產生一些可偵測訊號，然後用適當的偵測器 “看”這些材料顯微結構，如圖7所示。

The details of those structure are too small to be observed by either a magnified lens or an optical microscope, thus they are black boxes for human being eyes. To see them, we have to use some tiny and high energy particles, such as ions, electrons, and photons, to knock them, and acquire signals generated from the interactions by suitable detectors, as stated in Fig. 7.

圖7. 用高能粒子或光子做材料分析示意圖。

以高能電子束為例。當高能電子入射試片後，撞擊原子後產生反射電子、二次電子、歐傑電子、特性X…等諸多訊號，如圖8所示。唯有那些逸出試片並進入偵測器的訊號才是有效的訊號，其他在試片內被吸收(absorbed)的訊號和逸出試片但沒進入偵測器的訊號都是無效的訊號。從塊材(bulk)試片的角度來看，以上諸多訊號中，X光的穿透力最強，所以訊號來自最深層到表面都有，同時範圍也最廣闊(空間解析度最差)；反射電子能量最大，穿透力小於X光，但大於其他電子訊號；二次電子來自100奈米內的淺層區域；歐傑電子來自10奈米內的表面層，如圖9所示。

Let’s consider high energy electron beam only, many kinds of signals, such as backscattered electrons (BE), secondary electrons (SE), Auger electrons, and characteristic X-ray, are induced when high energy electrons strike a specimen and hit electrons in atoms, as shown in Fig. 8. Signals are effective signals only when they escape out of the specimen and enter the detector, those absorbed in the specimen or not entering the detector are ineffective signals. In a bulk specimen, X-ray comes out from the deepest and widest regions due to its powerful ability in penetration. Backscattered electrons have the highest energy among all electron signals, so does its penetration. Secondary electrons can be emitted from regions less than 100 nm in thickness. Auger electrons escape only from surface regions less than 10 nm below the top surface, as shown in Fig. 9.

圖8. 高能電子/光子和原子交互作用，產生訊號示意圖。

圖9. 塊材試片中被高能電子激發後產生的訊號和深度示意圖。

典型常用的材料分析儀器(Typical Materials Analysis Instruments)

分析儀器的硬體結構主要基本元件有三：光源、試片承載台、和訊號偵測器。電子顯微鏡需要真空環境，所以增加一真空系統，包含柱體、幫浦、真空計。現代常用的材料分析儀器幾乎都用個人電腦控制，所以又加上電子控制系統。電腦操控技術的進步日新月異，大幅改善儀器操作方式，舊型的SEM純用手移動試片位置，現在的SEM只要用滑鼠在螢幕的即時影像上，點在某一位置，該位置即自動移到螢幕中心。

The basic configuration of analytical instruments is consisted of three major parts: source, sample loader, and signal detectors. Electron microscopes need a vacuum environment, so a vacuum system, including column, pumps, and vacuum gauges, has to be added. Almost all current materials analytical instruments are controlled by PCs now, thus a set of electronic control system is added. The method of operating new model instrument has become much easy by means of PC control. Take the SEM for example, it moved the specimen to any feature to the screen center manually. For new types of SEM, once an interested feature is double clicked by a mouse by the operator, it moves to the screen center automatically.   

從功能來分，典型常用的材料分析儀器可分為三大類，如圖6所示:

顯微鏡 – 提供材料顯微結構的放大影像。有

AFM, FIB, SEM, STM, TEM, Thermal wave imaging, X-ray 影像儀等。

能譜儀/質譜儀 – 提供試片特定區域組成元素的訊息。有

AES , EDS, EPMA, ESCA(XPS), EELS, FTIR, Raman, RBS, SIMS, TXRF, WDS, XRF等。

繞射儀 – 提供試片特定區域晶體結構的訊息。

TEM/Diff, XRD等。

Typical materials analysis instruments are divided into three groups by their function, as shown in Fig. 6. They are:

Microscopes – offering images of high magnification and high resolution, such as:

AFM, FIB, SEM, STM, TEM, Thermal wave imaging, X-ray imaging systems, et al.

Spectroscopes – offering composition information of an interested region, such as:

AES , EDS, EPMA, ESCA(XPS), EELS, FTIR, Raman, RBS, SIMS, TXRF, WDS, XRF, et al.

Diffractometers – offering crystallography information of a sample or an interested region, such as:

TEM/Diff, XRD, et al.

圖6. 典型常用材料分析儀器的功能性分類與提通的訊息。

依光源和訊號類別的組合，則典型常用的材料分析儀器可分類如表1中的歸類。

Typical materials analysis instruments can also be divided into groups by types of sources and signals, as shown in table 1.

表1. 光源和訊號類別分類典型常用的材料分析儀器。

材料分析的程序(Steps of Materials Analysis)-2/2

儀器分析

試片進入儀器後，儀器光源系統要做調機，使光源-目標物-偵測器落在光軸上。尤其是穿透式電子顯微鏡(TEM)的電子光源系統，從電子鎗經試片到偵測器之間的所有電磁透鏡都要仔細調整一番，務使電子束的球面像差和散光缺陷降至最低，同時降低系統背景訊號值。

Instrument alignment to make beam-specimen-detector along the optical axis is a very important step in the analysis process. Pre-analysis alignment is extremely critical in transmitted electron microscopes (TEM), After being extracted from the emitter, the electron beam goes through several sets of magnetic lenses, hits the specimen, pass through sets of magnetics lenses, then enters the detector. The electron beam has to be aligned along the optical axis as close as possible to minimize the effect of spherical aberration and astigmatism, so does the system background.

無論是影像還是成分訊號，訊號收集的強度在未超過偵測器的飽和極限值之前，在允許的條件下應盡量足夠，以提升訊號的訊雜比(S/N)。

It is always better to acquire enough signals both images and spectra. The intensity of signals should be acquire to the level higher than half of the limit of the detector to give a good signal to noise ratio (S/N).

由於近代材料科學與工程的躍進，新型材料分析儀器的光源強度和訊號偵測效率，解析度與動態範圍(dynamic range)都大幅提升，使得訊號收集時間大幅縮短，而總訊號強度反而提升數倍。透過個人電腦的控制，所有的資料都數位化。因此分析的效率明顯的提升。以影像為例，不但免去暗房過程，連拍立得照片都不再使用，數位化影像資料在收集完成後幾分鐘內，即刻用光碟片或隨身碟(USB)儲存交付給客戶。

Because of the jump in materials science and engineering, the intensity of source and the efficiency, resolution, and dynamic range of detectors have been improved a lot. This improvement make the collection time shorter than it used to be. All data are digitized since all instruments are all controlled by personal computers (PCs). It make post analyses more efficient. All images can be stored in a CD or a USB directly without any darkroom work. 

資料解析與歸納

從儀器分析得到的資料是原始資料(raw data)，必須經過適當地解析後才能變成有用的資料(processed data)，例如: 晶粒大小量測，膜厚量測，成份計算…等等。

Without further process, those raw data just acquired from instrument do mean something. Information extracted from raw data after data process, such as grain size, thickness of thin films, composition, are really valuable.

將數組解析後的資料比對後，找出一些製程參數--顯微結構--性質的變化關係，是為歸納。

Induction means to find the relationship among the microstructure, process, and properties from analyzing data.

現在很多分析儀器的控制軟體，在攝取訊號後，都具有進一步處理資料的能力。

Today, many analytical instruments have built in software to process data to extract desired information after acquiring.

結論

集合解析和歸納的資料，參考之前性質測試的資料，再佐以分析者的學識，知識，和專業經驗，將此次分析的結果寫成一份報告。報告是一份檢測報告或是分析報告在於，是否能把此次分析的資料連結之前性質測試的資料，將材料顯微結構變化對材料性質變化的影響敘述清楚。

A final conclusion is drawn after carefully processing and analyzing data acquired combined with some acknowledge from the analyzer in the report. A report becomes much more valuable when information of materials, properties, and related processes is stated. 

材料分析的程序(Steps of Materials Analysis)-1/2

材料分析實驗的進行的主要步驟有取樣、試片製做、儀器分析、資料解析與歸納、結論等五項。進行分析之前最好先確認材料分析的目的，同時決定所需資料的類別(亦即決定儀器分析方式)，以免浪費時間與金錢。

There are five mains steps in the experiment of materials analysis, they are sampling, sample preparation, instrument analysis, data process and analysis, conclusion. It is better to make clear the objects of the analysis, and decide what kinds of information (i.e. to determine what kinds of analysis to be performed) to avoid wasting time and money.

取樣(Sampling)

正確的取樣是有效率材料分析的第一步驟。所謂「失之毫釐，差之千里」，如果第一個步驟就錯誤，接下來的材料分析，輕者浪費一些人力與物力的資源，重者得到錯誤的結論，而導致後續嚴重的投資損失。

Precise sampling is the first step for efficient materials analysis. It is very important for this step. It will waste time and resource when improper samples are taken. Even more, a big mistake in investment can be made from a conclusion made from this incorrect analysis.

樣品數要足夠，才有足夠可信度的資料；但是又不能太多，否則效率降低，成本增加。以鋁合金時效強化為例，其強度隨者熱處理時間增長，逐漸提升，到達峰值之後，再下降，如圖5所示。要瞭解顯微結構變化與強度變化的關係，最少要取A, B, C三點的樣品做分析，再加取D, E二點的樣品做分析，可更確認顯微結構變化和強度的關係，再多取樣品，則在有限的資源下就會形成浪費。

Confident data come from enough samples in an experiment. However, it will be inefficient if too many samples are included. Considering the example of precipitation hardening (aging strengthening) of Al alloys. After alloying, the alloy is annealed at an adequate temperate. The strength of the Al alloy increases with time, and gradually decreases after reaching its peak value, as shown in Fig.5. It needs at least three samples, A, B, C, to study the relationship between the strength and the microstructure. Two more samples, D&E, will give further results to make things more clear. More samples will result in wasting when resource is limit.

                                                                                  

圖5. 鋁合金時效強化熱處理實驗，樣品強度和熱處理時間關係示意圖。

試片製做

受限於材料分析儀器工作腔體的空間大小和光源與偵測器的特性，樣品必須先經過適當的處理後，變成符合該儀器尺寸和形貌的試片，才能置入材料分析儀器，進行材料分析。

Due to the space limitation and characteristics of instruments, most of samples have to be appropriately processed before being put into the working chamber for analysis.

對掃描式電子顯微鏡(SEM)來說，最基本的試片製做程序是先切割，部份試片包括平面型半導體元件試片，鍍導電金屬後即可進入SEM觀察分析，其餘大部分試片需要進一步鑲埋、研磨、拋光，適當地蝕刻後再鍍導電金屬。一般固態無機穿透式電子顯微鏡(TEM)的試片需雙面研磨拋光減薄至10微米以下，再用渦穴研磨機局部減薄至1微米左右，最後用離子削薄機(ion miller)削薄到100奈米以下的薄區。金屬試片可用雙面電解拋光法，簡單又快速．近代半導體元件試片則多用聚焦離子束(FIB)定點精準切割。要進入歐傑分析儀(AES)或X射線光電子分析儀(XPS/ESCA)的試片必須注意待分析區表面，不要被任何物品(尤其是金屬鑷子)碰觸到，以避免表面汙染。

Traditionally, the basic process for SEM samples is to cutting, mounting, grinding, polishing, etching, and coating, except for a few special types of samples. For almost all solid state inorganic TEM samples, they have to be thinned and polished from both sides to about 10 um thick, and then dimpled to about one micron meter, finially be ion milled down to 100 nm and/or less by Ar ions. Metal samples can be done by twin jet polish, easy and quick. Most of samples of modern semiconductor devices are prepared by focus ion beam (FIB) for the requirement of accurate specified positions. It needs to be very careful to handle samples to be analyzed by Auger or XPS(ESCA), any touch by metal tweezers on the surface will be a serious surface contamination. 

材料分析的角色與認知(Role of Materials Analysis)

材料分析是現代材料科學與工程的一環，在歐美日等工業先進國家的大公司中不可或缺的一部分，而且通常擁有高階人力，不過在以製造業為強項的華人科學工程世界，材料分析的角色被許多高階主管忽略，因為它不是直接生產獲利的單位；但是如果考慮因正確材料分析而省下的成本，材料分析是一賺錢的單位。一直到45奈米製程後，華人主導的半導體廠的工程高階主管才醒悟電子顯微鏡材料分析的重要性。

Materials analysis is one of subgroups of science and engineering of materials, it is an important unit with high level human resources in big manufacturing companies in developed countries in American, Europe, and Japan. it does catch same attention as the others two in industry companies run by Chinese, especially in Mainland China and Taiwan, due to MA does not make products which can be traded directly. The importance of MA by electron microscopes in saving money for R&D and production had been usually neglected by high level engineering managers in semiconductor companies coordinated by Chinese until the 45 nm node process.

專業博士執行TEM分析時，TEM試片內蘊含的有用訊息會被系統性地分析與收集，而非只是進行制式的資料收集，例如: (1)傾轉試片至正極軸(exact zone)方向，(2)拍攝一些不同倍率的影像，(3)攝取某一區域性的EDS能譜影像。試片中一些有用的材料相關訊息經常在這些制式的分析中浪費掉。

A Ph.D can carefully extract all useful data out of a specimen in a TEM analysis. Well trained operators are very skillful at operating TEM, but not familiar with all functions in a TEM and all related materials information inside the specimen. They only take high magnification BF images, HRTEM images at Si[110] zone, and some sets of EDS map as told. From time to time, some useful data beyond those images and elemental maps passed away from the fingers in these routine jobs.

材料科學與工程三大領域(Three Fields in Science and Engineering of Materials)

材料科學與工程三大領域(Three Fields in Science and Engineering of Materials)

一般來說，材料科學與工程大致劃分為三大領域：材料研發與設計、材料製造、材料測試與分析(圖4)。材料研發與設計者根據市面需求開發新材料的配方與製程﹔材料製造者則依據前者開發出來的配方與製程將材料的產能大量化生產﹔材料測試與分析者則分別在研發過程，測試與分析實驗過程中的產品，提供材料性質與微結構訊息，協助研發者調整實驗的方向，和量產中，抽測產品，分析不合格產品的微結構，提供製程參數的微調的依據。

Generally, science and engineering of materials can be divided into three subgroups: R&D and design, manufacture, test and analysis. People of R&D and design develop new materials and new processes to meet requirements emerged. People of manufacturing make these new materials into mass production or use these new processes to improve the yield in production. People of test and analysis either help R&D people to test and analyze the microstructure of new materials and find the relationship between process and the microstructure of materials or analyze the microstructure of defect products in production line.

圖4. 材料科學與工程的三大領域：材料研發與設計、材料製造、材料測試與分析。

材料分析的目的

    如圖A-1- 4.1所示，材料的基本性質由主要成份的元素決定，經由添加少量和微量元素調整材料性質，再透過熱處裡加工進一步調整材料性質。以精密陶瓷(fine ceramics)為例。研發新材料時，首先根據材料性質要求，選定主成份的元素種類，再添加數種少量和微量的元素，均勻混合之後，壓錠成形先行鍛燒，再用不同的溫度燒結(sintering)。每一添加元素的添加量(x)和燒結溫度(T)的變化都可形成一份矩陣，再加上燒結時間(t)的變化，總實驗條件至少達n1 x n2 x n3個，假設 n1 = n2 = n3 = 5，需要燒結的樣品最少需要125個樣品才可以系統性完成第一階段的性質評估。這樣的作法是依靠大量的實驗室數據堆積出結果，而且只知其然而不知其所以然。

    The basic properties of the material are basically determined by its major composition, and tuned by minor and trace additives, and following heat treatment, as shown in Fig. A-1- 4.1. Let’s take fine ceramics to be an example of R&D in a new material. We chose one kind of the major composition according to the requirements of demands in material properties, then minor elements, and finally trace elements. Those homogeneously mixed powder are then pressed to discs to be put into furnaces for calcination and following sintering. If there are five doses of one minor element, five sintering temperatures, and five sintering time for each sintering temperature in this experiment. Then there are 125 conditions totally in this experiment. It takes a lot of resource to finish this experiment. We may get some samples meeting requirements, but we do not know why from this type of experiment.

    換一個實驗方向，如果先調配二種少量元素添加量的配方，即n1= 2，樣品數降至50個。然後再從性質測試曲線挑出5 ~ 6個樣品做材料分析，從其顯微結構的特徵，推演和歸納出少量元素添加量，燒結溫度，和燒結時間對材料顯微結構變化的影響。再將材料顯微結構和材料性質的關聯性推導出來，就容易推導出下一階段的配方，燒結溫度和燒結時間調整方向。

    Let’s do another way. If only two different doses for the minor element are used, the amount of samples drop to 50 from 125. Then 5 to 6 samples are picked up to do MA after property test. We can deduce effects of addition, sintering temperature, and sintering time on the microstructure. After understanding the relationship between the microstructure and properties, we are then able to decide the tuning direction for the amounts of minor element, sintering temperature and sintering time.

    透過對材料的顯微結構、組成元素、和結晶結構的分析，充分瞭解原料、製程、和材料性質的對應關係，確立調製原料和製程調整的方向，減少錯誤嘗試的時間，達到縮短研發時間和減少資源浪費，這就是材料分析主要的目的。更重要的是，當材料分析結果分門別類整理成一資料庫後，成為下一世代材料開發的重要資產。

    We can fully understand the relationship among properties, process, and raw materials through studying the microstructure, composition/composition distribution, and crystal structure of the processed materials. The direction of process tuning can be focused after MA. MA work can save huge of resources, including time, in R&D. It is more important that results of MA can be organized to be valuable database for related materials of next generation.

圖A-1- 4.1. 影響材料性質的參數。