固體表面與界面翻譯

1、固體的表面與界面期末考試作業(yè) 姓名： 劉繼瓊 學(xué)號： 200907120002翻譯章節(jié)：第三章翻譯頁碼：32-42Chapter 3Electron spectroscopy電子能譜Introduction3.1引言If we want to learn something about a system, a general experimental approach is a scattering technique: we shoot some particles in a well-prepared state on the target and look at particles co

2、ming out of the target (which do not have to be the same). In surface science the most basic questions we want to solve with this approach are for example: Is the surface clean? Which elements are on the surface? And in which chemical compound? What is the exact geometric structure of the surface?如果

3、我們想要了解一個(gè)系統(tǒng)，通常的實(shí)驗(yàn)方法是采用散射技術(shù)：我們向靶發(fā)射一些處于特 定狀態(tài)的粒子，觀察它們從靶出射的情況(各個(gè)粒子出射情況不同)，在表面科學(xué)中我們想 通過這種方法解決的最基本的問題有:表面是否清潔？哪種元素處在表面？以及它們的化學(xué) 組成？表面的精確的幾何結(jié)構(gòu)是什么樣的？The most common particles to scatter from surfaces are electrons, ions, atoms and photons both as probe and response particles. An important issue is the surface

4、 sensitivity of an experiment. In general, it is high if we choose particles which have a small mean free path in the solid because this means that the detected particles must originate near the surface. The opposite is true, for example, when the scattering of light by the surface is investigated(r

5、eflectivity and change of polarization). The photons will penetrate relatively deeply into the crystal. The amount of photons scattering at or near the surface be very small. Hence, light scattering is not a good tool to study surfaces. In some cases we can increase the surface sensitivity by choosi

6、ng an experimental set-up where we use a very grazing angle of incidence or emission. In this way the particles travel a long way close to the surface, even if their mean free path is relatively long.從表面上散射出來的最常見的粒子是電子，離子，原子和聲子，它們即作為探測粒子又 作為反應(yīng)粒子。一個(gè)重要的因素是實(shí)驗(yàn)的表面靈敏度。通常，如果當(dāng)我們選擇的微粒在固體 中有一個(gè)小的平均自由程時(shí)表面靈敏度很高，

7、因?yàn)檫@就意味著探測粒子必須在表面附近產(chǎn) 生。反之亦然，例如，研究表面光的散射(折射率和偏振變化)。光子將相對較深的深入固 體。在表面及其表面附近散射的光子數(shù)量就會很少。因此，光子散射不適宜用來研究表面性 能。有時(shí)候，我們可以選擇合適的入射角和出射角來提高表面靈敏度。這樣，及時(shí)粒子的平 均自由程很長，它們也會在表面附近運(yùn)動很長的一段距離。surface sensitivity-表面靈敏度mean free path-平均自由程Very many surface science techniques are based on electrons as a probe. Electrons have

8、 very useful properties: they are, at certain energies, very surface sensitive. Electrons in this energy range carry also enough momentum to explore the whole surface Brilloin zone of a material(in contrast to light), they also carry a spin and they are easy to generate and to handle. The extensive

9、use of electrons in surface sciences justifies a lecture explaining the physics of electron-solid in some more detail. Along with this, we will start to learn about some electron-based analytical techniques.很多表面科學(xué)技術(shù)都是基于電子作為探針進(jìn)行探測的。電子有非常有用的性質(zhì):他們在一 定的能量范圍內(nèi)有很高的表面敏感度。這些能量范圍內(nèi)的電子有足夠的動能來探測材料的整 個(gè)布里淵區(qū)表面(不同于光

10、子)，它們伴隨自旋并且容易產(chǎn)生和操控。電子在表面科學(xué)中的 廣泛的運(yùn)用更詳細(xì)的證明了一篇報(bào)告中所解釋的電子固體。同時(shí)，我們將開始學(xué)習(xí)一些基于 電子的分析技術(shù)。Brilloin zone-布里淵區(qū)A technique which is of particular interest in this lecture is Electron Energy Loss Spectroscopy (EELS) where a beam of monochromatic electrons is scattered from the surface. A sketch of this experiment i

11、s given in Fig.3.1在這個(gè)報(bào)告中特別提到的一種技術(shù)是電子能量損失能譜法，該技術(shù)采用的是從表面散射出 的一束單色電子，實(shí)驗(yàn)示意圖如圖3.1所示byFig3.1: An EELS experiment. The momentum transfer parallel to the surface is determined the electron energy and the scattering geometry.圖3.1： 一個(gè)能量損失能譜法的實(shí)驗(yàn)。平行于表面?zhèn)鬟f的能量有電子能量和幾何外形共同 決定。Why electrons: The mean free path3.2為什么

12、用電子：平均自由程One of the main reasons to use electrons in surface science is the mean free path of electrons in matter. This mean free path is determined by collisions:用電子作為表面科學(xué)的研究的一個(gè)主要原因是電子的平均自由程。這個(gè)平均自由程可有電 子間的相互碰撞計(jì)算出來：CE 、k人(Ekin)= v(Ekin凡=T,(3.1)Where v is the velocity and T is the collision time. In

13、the Drude model T is the mean time between two scattering events. In a quasiparticle-picture T is given by the imaginary part of the self-energy, i.e. by the life time of the quasi-particle. We are interested in energies of electrons between a few eV and many hundred eV. The mean free part of the el

14、ectrons in this regime is plotted in Fig.3.2. The dashed curve shows a calculation of the mean free path independent of the material and the points are measured data from many elemental solids. The data points scatter more or less around the calculation. The curve is therefore often called a univers

15、al curve. The reason for this universality is that the inelastic scattering of electrons in this energy range is mostly involving excitations of conduction electrons, which have more or less the same density in all elements. Note that at lower energies other scattering mechanisms will be important,

16、like the scattering with phonons.其中，v是電子的速度，T是碰撞時(shí)間。在德魯特模型中，T是兩次散射間隔的平均 時(shí)間。在準(zhǔn)粒子圖像中，T由其自身能量的虛部得出，也就是準(zhǔn)粒子的壽命。我們主要研 究的是能量在幾電子伏到幾百電子伏之間的粒子。在此能量范圍內(nèi)的電子的平均自由程如圖 3.2所示。虛線表示平均自由程的計(jì)算值與材料無關(guān)，其中的點(diǎn)代表多組物質(zhì)的測量值。散 射點(diǎn)大致分布在計(jì)算值附近。這條曲線通常被稱萬有曲線。這條曲線具有普適性的原因是在 此能級范圍的電子在發(fā)生非彈性散射時(shí)大多包含了傳導(dǎo)電子的激發(fā)，而其被激發(fā)電子的密度 在所有元素中是相同的。應(yīng)當(dāng)注意的是，在低能級中其

17、他的散射機(jī)制將很重要，比如聲子的 散射。Drude model德魯特模型quasiparticle-picture 準(zhǔn)粒子universal curve 萬用曲線conduction electrons 傳導(dǎo)電子curve is calculation. After Ref. 13.:圖3.2：固體中電子的平均自由程。點(diǎn)代表測量值，虛線代表理論值。參考【13】)點(diǎn) uHd $4 ueoE AlO A AuA BeT CThe mean free path curve has a broad (note the log-log scale) minimum around a kinetic0en

18、ergy of about 70 eV. There it is less than 10 A . This means that if we observe an electron with this kinetic energy which has left the solid without suffering a scattering event it must originate from the first few layers. How do we know that the electrons has not been scattering inelastically? For

19、tunately, the energy loss associated with a scattering from the valence electrons is rather large (as we shall see below). Therefore it is relatively easy to distinguish between inelastically scattering and non-scattered electrons.平均自由程曲線在動能約為70電子伏時(shí)取最小值(兩坐標(biāo)軸均為對數(shù)尺度)。這個(gè)最小 值小于10艾。這就意味著如果我們觀察的電子沒有經(jīng)過散射，動

20、能為此最小值，那么它一 定產(chǎn)生于最外幾層。我們?nèi)绾沃离娮記]有經(jīng)過非彈性散射呢？幸運(yùn)的是，由價(jià)電子散射引 起的能量損失很大(見下文)。因此，很容易判斷電子是經(jīng)過非彈性散射的還是未經(jīng)過散射 的。3.3: electron sources and analysers3.3：電子源和分析器One big advantage of using electrons is that they are relatively easy to produce. The most common way is electron emission from a hot filament. A filament is

21、heated by passing a current through it. To help the thermally excited electrons out of the metal one additionally puts an anode in front of the filament. The electron beam is focused by placing a so-called Wehnelt cylinder between the anode and filament. The Wehnet cylinder is at a negative potentia

22、l with respect to the filament. The basic principle is shown in Fig 3.3. the simple filament has two disadvantages when one eventually wants to produce a monochromatic beam of electrons. The first is that the voltage drop over the length of the filament (0.5 V) is also reflected in the kinetic energ

23、y of the electrons. The second is the thermal broadening due to high temperature needed to emit the electrons. A better design for emitting monochromatic electrons is an indirectly heated crystal which has a low work function.使用電子的一個(gè)巨大的優(yōu)點(diǎn)是電子的獲得相對容易。最常用的一種方法是通過熱燈絲發(fā)射 電子。燈絲被流過它的電流加熱。為了 “幫助”熱的受激電子從金屬中發(fā)射

24、出來，可以在燈 絲前放一個(gè)陽極，電子束在陽極和燈絲間的經(jīng)柵極匯聚。經(jīng)柵極相對于燈絲為負(fù)電勢?；?原理如圖3.3所示。當(dāng)最終所要得到的是單色電子束時(shí)，這種簡易燈絲有兩個(gè)缺點(diǎn)。第一個(gè) 缺點(diǎn)是當(dāng)電勢降落超過0.5V會同樣影響電子動能。第二個(gè)缺點(diǎn)是高溫引起的熱膨脹需要發(fā) 射電子。發(fā)射單色電子的一個(gè)更好的設(shè)計(jì)方法是間接加熱有低的電子逸出功的晶體。Wehnelt cylinder anodefilament Figure 3.3： An electron gun /圖3.3：電子槍Electrons can be detected using an electron multiplier, usuall

25、y a so-called channeltron. Such a device is essentially a glass tub with a resistive coating on the inside. A high voltage is applied between the front and the end. An electron which enters the channeltron will be accelectrated to the wall where it kicks out more electrons. In this way an electron a

26、valanche is created which eventually lead to a measurable current pulse.電子可以通過電子倍增器被檢測到，通常稱為電子增倍器。這個(gè)裝置本質(zhì)上是一個(gè)內(nèi)部 涂有電阻層的玻璃槽。給槽的前后加高電壓，電子進(jìn)入增倍器后就會被加速，撞擊槽壁，從 而產(chǎn)生更多的電子。這樣，電子雪崩就產(chǎn)生了，并且最終引起一個(gè)可測量的電流脈沖。Electron monochromators are needed both for creating a mono-energetic probe-beam and for analyzing the energy

27、distribution of scattered or emitted electrons. Electrostatic monochromators are the most common choice. Actual designs represent a trade-off between the need for high count rates and high angular/energy resolution. The so called cylindrical mirror analyser (CMA) is mostly used for checking the chem

28、ical composition of the surface. It consists of two co-axial cylinders in front of the sample. The inner cylinder is held at a positive potential and the outer cylinder at a negative potential. Only the electrons with the right energy can pass through this set-up and are detected at the end. The cou

29、nt rates are high but the resolution (both in energy and angle) is poor. A hemispherical analyser is often used for applications where higher resolution is needed. It consists of two con-centric hemispheres held a different potentials. The electrons enter and leave through slits. Again, only the ele

30、ctrons with the right kinetic energy, the so-called pass energy Ep can pass the analyser. An electrostatic lens-system can be placed in front of the hemispheres in order to focus the electrons into the analyser and to change the angular acceptance. Such an analyser is shown in Fig. 3.4.具有單一能量得探測光束由電

31、子單色儀來產(chǎn)生，用來分析散射電子和出射電子的能量分 布。最常見的是靜電單色儀。實(shí)際的設(shè)計(jì)中是以高的計(jì)數(shù)率和大的角度/能量分辨率作為交 換的。圓柱形鏡像分析儀主要用來效驗(yàn)表面的化學(xué)成分。樣品前有兩個(gè)同軸的圓桶，內(nèi)圓桶 為正極，外圓桶為負(fù)極。只有指定動能的電子才能穿過裝置并且最終被檢測到。計(jì)數(shù)率大是 分辨率（能量和角度）就低。當(dāng)需要高分辨率時(shí)使用半球形分析儀。它包含兩個(gè)同心半球作 為兩個(gè)電極。電子通過狹縫進(jìn)出儀器。只有具有適當(dāng)?shù)膭幽蹺p的電子才能通過儀器。為了 使電子聚焦進(jìn)入分析器并改變接受角，可以在半球前面放一個(gè)靜電透鏡系統(tǒng)。In the EELS experiment mentioned ab

32、ove two electron monochromators are needed: one to produce a monochromatic beam and one to analyse the scattered electrons. In a typical apparatus one of these monochromators is moveable in order to change the scattering geometry and the momentum transfer (see Fig.9.3).在電子能量損失譜的實(shí)驗(yàn)中，要用到上述兩種電子單色儀：一個(gè)用來

33、產(chǎn)生單色光束，一個(gè) 用來單子束，一個(gè)用來分析散射電子。在標(biāo)準(zhǔn)儀器中一個(gè)單色儀可以移動改變散射的幾何條 件和動量傳遞。(如圖9.3)Electron monochromator 電子單色儀Wehnet cylinder 經(jīng)柵極electron multiplier 電子倍增器cylindrical mirror analyser (CMA)圓柱形鏡像分析儀electrostatic lens-system 靜電透鏡系統(tǒng)momentum transfer 動量傳遞Electrons in solids: elastic and inelastic scattering3.4固體中的電子：彈性和非彈

34、性散射Let us now consider the interaction of electrons with solid in some more detail. First consider the scattering of an electron beam from the surface of the solid.現(xiàn)在我們來更詳細(xì)的考慮電子和固體的相互作用。首先考慮從電子表面散射的電子束。In an elastic scattering event the energy is (by definition) conserved, i.e.在彈性散射中能量守恒Es = E0(3.2)

35、Where 0 is the energy of the incoming electrons and s that of the scattered electrons.The momentum parallel to the surface is also conserved apart from a surface reciprocal latticeTgvector其中，E0為入射電子的能量，Es為散射電子的能量。平行于表面的動量守恒，表面T倒格失為g(3.3)k|s = k|0The crystal itself provides perpendicular momentum suc

36、h that (3.2) and (3.3) can be fulfilled simultaneously. Observing the elastically scattered electrons provides information about the surface reciprocal lattice and the surface geometry. The technique concerned with this called LEED and will be discussed later.晶體自身產(chǎn)生正交動量使(3.2)和(3.3)式同時(shí)滿足。通過對彈性散射電子的觀察

37、可以 得到表面倒格子和表面幾何信息。涉及的低能電子衍射技術(shù)將在后文討論。Here we are more interested in the inelastic scattering since it determines the mean free path of the electrons and hence the surface sensitivity.這里我們更感興趣的是非彈性散射，因?yàn)樗鼪Q定了電子的平均自由程，進(jìn)而反映了表面的 靈敏度。reciprocal lattice 倒格子inelastic scattering 非彈性散射3.4.1 The dielectric funct

38、ion3.4.1介電函數(shù)The dielectric function is a very useful concept because it describes the macroscopic absorption of both light and charged particles in solids and, at the same time, has a microscopic interpretation. Let us remind ourselves about some fundamental optical equations. Let the lightT .B vect

39、or be described by a plane wave which propagates in the x direction.介電函數(shù)是一個(gè)非常有用的概念，因?yàn)樗枋隽斯腆w中光和帶電粒子的宏觀吸收，并做出 了微觀解釋。讓我們回憶一些光學(xué)基本公式。向量T表示沿x方向傳播的平面波。亙=亙0 e i(kx-wt)WithandN = n + ik (3.5)Between the complex index of refraction N and the dielectric function 8 we have theMaxwell relation光的折射率N和介電常數(shù)8之間滿足麥克斯

40、韋關(guān)系式N = 8 = %；8 + 18.(3.6)The description of the optical properties in terms of N and 8 is completely equivalent. The two part of N and 8 are not independent but can be transformed into each other theKramers-Kronig relations用N和8描述的光學(xué)性質(zhì)是完全等價(jià)的，它們的兩個(gè)部分不是獨(dú)立的，可以通過克拉茂克朗尼希關(guān)系相互轉(zhuǎn)換。8 ()= 8(8)+。竺心切，2 02 2（3.7）

41、and8.()=竺M8 -8 *)d ， 兀（3.8）Note that technically spoken one quantity has to be known over the whole frequency spectrum if we wish to obtain the other. In similar ways both part of N or 8 can be obtained from just measuring the normal-incidence reflectivity over a large spectral range.注意，從技術(shù)上講，如果我們必須

42、首先得到全光譜下的一個(gè)量，才能得到另一個(gè)量。同樣 的道理，我們可以通過測量大范圍內(nèi)正常入射的光的反射率得到N或8的兩個(gè)部分。The absorption of light in matter is given by Lamberts law光在物質(zhì)中的吸收通過蘭伯特定律得出（3.9）The probability p for the electrons to suffer an inelastic scattering event is given by電子收到非彈性散射的幾率由下式得出/ 、 z - 1、（3.10）P(W)8p) 8()This probability is exactly

43、 what we are concerned with here. When looking at the mean free path, there seems to be a scattering probability which is very high for electrons with kinetic energies around 70 eV.幾率使我們最關(guān)心的問題，當(dāng)考慮平均自由程時(shí)會發(fā)現(xiàn)，電子動能在70 eV附近時(shí)散射幾率 最大。In the following subsections we go quickly through the elementary excitat

44、ions which are important contributions to the dielectric function, ordered by energy. These excitations provide a detailed microscopic picture for the dielectric function.在接下來的章節(jié)中，我們將按能量的高低順序來迅速了解那些對介電函數(shù)有貢獻(xiàn)的元激 發(fā)。這些激發(fā)為我們提供了介電函數(shù)的微觀圖像。charged particles 帶電粒子plane wave 平面波Kramers-Kronig relations克拉茂一克朗尼希

45、關(guān)系kinetic energies 動能Phonons3.4.2聲子On its way through the solid and the surface the electrons can be scattered inelastically by absorbing or creating phonons.電子在通過固體內(nèi)部和表面時(shí)，可以通過吸收和產(chǎn)生光子的形式發(fā)生非彈性散射。The phonon energies are small (usually less than 100 eV) but the q vector can be large. The phonon losses

46、one observes in an EELS spectrum can be used to map the dispersion of the surface phonons or to learn something about the adsorbates by measuring their vibrational frequencies. We will come back to this in later lecture. In our context here, phonon scattering is not very important because it only ha

47、s to be considered at low energy.聲子的能量很小(通常小于100 eV)但矢量? 可以很大。在電子能量損失光譜中觀察 聲子的損耗可以得到表面聲子的散布情況或者通過測量它們的振動頻率來研究吸附物。在這 里，聲子散射并不重要因?yàn)樗挥性诘湍芰肯虏判枰紤]。vibrational frequencies振動頻率Excitons3.4.3激子Consider the case that an electron is excited from a bound state to a previously unoccupied state. In a metal, the s

48、cattering is so strong that the electron and the hole will have very little interaction. In a semiconductor, however, electron and hole can remain loosely bound to form a so-called exciton. This exciton has a spectrum like a hydrogen atom but the Coulomb potential is screened by the dielectric funct

49、ion考慮一個(gè)電子從束縛態(tài)被激發(fā)到未占據(jù)態(tài)的情況。在金屬中，散射很強(qiáng)，電子和空穴交互 作用將很弱。但在半導(dǎo)體中，電子和空穴可以被弱的束縛從而形成激子。激子有類氫原子光 譜，但庫侖電勢被介電常數(shù)屏蔽了。e2Vcoulr，R)(3.11)The energy levels of this “hydrogen atom” lie just below the conduction band in an insulator or semiconductor. Ionizing the exciton means exciting the electron into the conduction bou

50、nd. The exciton is not bound to a particular site: the hole and the electron have some finite probability to hop to an adjacent site. This probability broadens the excitonic energy levels into bands.在絕緣體和半導(dǎo)體中這種類氫原子的能級處在導(dǎo)帶之下.激子電離就是把電子激發(fā)到導(dǎo)帶. 激子沒有被束縛在特定的位置:空穴和電子可能躍遷到鄰近位置.這種可能性是機(jī)子的能帶擴(kuò) 展至波帶.At the surfac

51、e of a solid, the reduce coordination changes both the Coulomb potential for a single excition and the hopping matrix elements between the excitons. This results in a so-called surface exciton which is shifted and has a different width.在固體表面，配位數(shù)的減少不僅改變了單個(gè)激子的庫倫勢能激子之間躍遷的矩陣元素。這 樣的結(jié)果是產(chǎn)生表面激子的遷移和不同寬度。boun

52、d state 束縛態(tài)Coulomb potential 庫侖電勢hydrogen atom 類氫原子conduction bound 導(dǎo)帶Interband transitions3.4.4帶間轉(zhuǎn)變Another loss mechanism is the creation of electron-hole pairs. In a metal electron-hole pairs can be created with infinitely small energies by lifting an electron from an energy level just below the F

53、ermi energy to a level just above. Electron-hole creation does thus contribute to the dielectric function at all energies. For a semiconductor the situation is different. There is a smallest energy for electron-hole pair creation, the energy of the fundamental gap. In semiconductors, a structure in

54、the dielectric function can be found which corresponds to excitations over the gap. At slightly lower energy, the excitons are found. For both, metals and semiconductors so-called critical points in the band structure give rise to strong features in the dielectric function. A critical point is, for

55、example, a situation where the occupied bands and unoccupied bands are parallel in a larger region of k-space. Then the optical transitions from the region all have the same energy and contribute strongly to e.另一種損失機(jī)制是電子空穴對的產(chǎn)生。在金屬中，一個(gè)人很小的能量就能使電子從費(fèi)米能 級以下正好躍遷到費(fèi)米能級以上從而產(chǎn)生電子空穴對。電子空穴對的產(chǎn)生對各個(gè)能級的介電 函數(shù)都有貢獻(xiàn)。對半

56、導(dǎo)體情況就不同了。它存在一個(gè)最小的電子空穴對的產(chǎn)生能量，即基態(tài) 間隙能。在半導(dǎo)體中，介電函數(shù)中的結(jié)構(gòu)與間隙中的激發(fā)態(tài)類似。激子的能量略低于此。在 金屬和半導(dǎo)體中，波帶結(jié)構(gòu)中所謂的臨界點(diǎn)的存在都提高了介電函數(shù)的特征強(qiáng)度。臨界點(diǎn)， 就好比是，被填充的波帶與空波帶在一個(gè)大的K空間區(qū)域是平行的。于是，此區(qū)域光躍遷就 具有相同的能量，使e增強(qiáng)。electron-hole pairs 電子空穴對critical points 臨界點(diǎn)unoccupied bands 空態(tài)Bulk and surface plasmons3.4.5等離子體的內(nèi)部和表面In the Drude model of metals,

57、 the dielectric function is在特魯特模型中，金屬的介電常數(shù)為S ()=1 - 3,(3.12)where % is the so-called plasma frequency這里，3詼?zhǔn)撬^的等離子體的頻率，ne2唯=(4.13)Pms03p has a simple interpretation. It corresponds to a longitudinal collective vibration of the electron gas against the positively charged ions (see Fig. 3.5). These exc

58、itations are called plasmons3 p有個(gè)簡要的解釋。它與電子氣體對帶正電離子的縱向共振類似(如圖3.5)。這類激發(fā)被 稱為等離子體。forplasmaoscillationFigure 4.5:A simple pictureFigure 4.5: A simple picture for a plasma oscillation圖4.5:等離子振蕩示意圖The plasma frequency is very important for the optical properties of a metal. We write equ. 3.4as等離子體頻率對金屬光學(xué)

59、性能而言十分重要。把公式3.4寫作IO !-E.(3.14)We can distinguish between two cases: if w w p then e is real and negative and ( 3.14) gives only exponentially damped solutions. This means that an electric field can not penetrate a metal, the metal is reflecting all the light. Above the plasma frequency (3.14) does p

60、ermit propagating solutions of the electric field.我們可以分兩種情況來討論：如果w wp則e為負(fù)實(shí)數(shù)，式(3.14)只給出了阻尼振蕩的 解。這意味著電場不能穿透金屬，金屬能反射一切光。當(dāng)高于等離子頻率時(shí)，電場能透過金 屬傳播。For simple metals, there is a good agreement with the calculated plasma frequency wp, or plasmon energy h wp, and the experimental values.對于簡單金屬:計(jì)算出的wp或等離子體能量h wp