固体表面与界面翻译

1、固体的表面与界面期末考试作业 姓名： 刘继琼 学号： 200907120002翻译章节：第三章翻译页码：32-42Chapter 3Electron spectroscopy电子能谱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、我们想要了解一个系统，通常的实验方法是采用散射技术：我们向靶发射一些处于特 定状态的粒子，观察它们从靶出射的情况(各个粒子出射情况不同)，在表面科学中我们想 通过这种方法解决的最基本的问题有:表面是否清洁？哪种元素处在表面？以及它们的化学 组成？表面的精确的几何结构是什么样的？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.从表面上散射出来的最常见的粒子是电子，离子，原子和声子，它们即作为探测粒子又 作为反应粒子。一个重要的因素是实验的表面灵敏度。通常，如果当我们选择的微粒在固体 中有一个小的平均自由程时表面灵敏度很高，

7、因为这就意味着探测粒子必须在表面附近产 生。反之亦然，例如，研究表面光的散射(折射率和偏振变化)。光子将相对较深的深入固 体。在表面及其表面附近散射的光子数量就会很少。因此，光子散射不适宜用来研究表面性 能。有时候，我们可以选择合适的入射角和出射角来提高表面灵敏度。这样，及时粒子的平 均自由程很长，它们也会在表面附近运动很长的一段距离。surface sensitivity-表面灵敏度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.很多表面科学技术都是基于电子作为探针进行探测的。电子有非常有用的性质:他们在一 定的能量范围内有很高的表面敏感度。这些能量范围内的电子有足够的动能来探测材料的整 个布里渊区表面(不同于光

10、子)，它们伴随自旋并且容易产生和操控。电子在表面科学中的 广泛的运用更详细的证明了一篇报告中所解释的电子固体。同时，我们将开始学习一些基于 电子的分析技术。Brilloin zone-布里渊区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在这个报告中特别提到的一种技术是电子能量损失能谱法，该技术采用的是从表面散射出 的一束单色电子，实验示意图如图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.图3.1： 一个能量损失能谱法的实验。平行于表面传递的能量有电子能量和几何外形共同 决定。Why electrons: The mean free path3.2为什么

12、用电子：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:用电子作为表面科学的研究的一个主要原因是电子的平均自由程。这个平均自由程可有电 子间的相互碰撞计算出来：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是电子的速度，T是碰撞时间。在德鲁特模型中，T是两次散射间隔的平均 时间。在准粒子图像中，T由其自身能量的虚部得出，也就是准粒子的寿命。我们主要研 究的是能量在几电子伏到几百电子伏之间的粒子。在此能量范围内的电子的平均自由程如图 3.2所示。虚线表示平均自由程的计算值与材料无关，其中的点代表多组物质的测量值。散 射点大致分布在计算值附近。这条曲线通常被称万有曲线。这条曲线具有普适性的原因是在 此能级范围的电子在发生非弹性散射时大多包含了传导电子的激发，而其被激发电子的密度 在所有元素中是相同的。应当注意的是，在低能级中其

17、他的散射机制将很重要，比如声子的 散射。Drude model德鲁特模型quasiparticle-picture 准粒子universal curve 万用曲线conduction electrons 传导电子curve is calculation. After Ref. 13.:图3.2：固体中电子的平均自由程。点代表测量值，虚线代表理论值。参考【13】)点 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.平均自由程曲线在动能约为70电子伏时取最小值(两坐标轴均为对数尺度)。这个最小 值小于10艾。这就意味着如果我们观察的电子没有经过散射，动

20、能为此最小值，那么它一 定产生于最外几层。我们如何知道电子没有经过非弹性散射呢？幸运的是，由价电子散射引 起的能量损失很大(见下文)。因此，很容易判断电子是经过非弹性散射的还是未经过散射 的。3.3: electron sources and analysers3.3：电子源和分析器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.使用电子的一个巨大的优点是电子的获得相对容易。最常用的一种方法是通过热灯丝发射 电子。灯丝被流过它的电流加热。为了 “帮助”热的受激电子从金属中发射

24、出来，可以在灯 丝前放一个阳极，电子束在阳极和灯丝间的经栅极汇聚。经栅极相对于灯丝为负电势。基本 原理如图3.3所示。当最终所要得到的是单色电子束时，这种简易灯丝有两个缺点。第一个 缺点是当电势降落超过0.5V会同样影响电子动能。第二个缺点是高温引起的热膨胀需要发 射电子。发射单色电子的一个更好的设计方法是间接加热有低的电子逸出功的晶体。Wehnelt cylinder anodefilament Figure 3.3： An electron gun /图3.3：电子枪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.电子可以通过电子倍增器被检测到，通常称为电子增倍器。这个装置本质上是一个内部 涂有电阻层的玻璃槽。给槽的前后加高电压，电子进入增倍器后就会被加速，撞击槽壁，从 而产生更多的电子。这样，电子雪崩就产生了，并且最终引起一个可测量的电流脉冲。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.具有单一能量得探测光束由电

31、子单色仪来产生，用来分析散射电子和出射电子的能量分 布。最常见的是静电单色仪。实际的设计中是以高的计数率和大的角度/能量分辨率作为交 换的。圆柱形镜像分析仪主要用来效验表面的化学成分。样品前有两个同轴的圆桶，内圆桶 为正极，外圆桶为负极。只有指定动能的电子才能穿过装置并且最终被检测到。计数率大是 分辨率（能量和角度）就低。当需要高分辨率时使用半球形分析仪。它包含两个同心半球作 为两个电极。电子通过狭缝进出仪器。只有具有适当的动能Ep的电子才能通过仪器。为了 使电子聚焦进入分析器并改变接受角，可以在半球前面放一个静电透镜系统。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).在电子能量损失谱的实验中，要用到上述两种电子单色仪：一个用来

33、产生单色光束，一个 用来单子束，一个用来分析散射电子。在标准仪器中一个单色仪可以移动改变散射的几何条 件和动量传递。(如图9.3)Electron monochromator 电子单色仪Wehnet cylinder 经栅极electron multiplier 电子倍增器cylindrical mirror analyser (CMA)圆柱形镜像分析仪electrostatic lens-system 静电透镜系统momentum transfer 动量传递Electrons in solids: elastic and inelastic scattering3.4固体中的电子：弹性和非弹

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.现在我们来更详细的考虑电子和固体的相互作用。首先考虑从电子表面散射的电子束。In an elastic scattering event the energy is (by definition) conserved, i.e.在弹性散射中能量守恒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为入射电子的能量，Es为散射电子的能量。平行于表面的动量守恒，表面T倒格失为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.晶体自身产生正交动量使(3.2)和(3.3)式同时满足。通过对弹性散射电子的观察

37、可以 得到表面倒格子和表面几何信息。涉及的低能电子衍射技术将在后文讨论。Here we are more interested in the inelastic scattering since it determines the mean free path of the electrons and hence the surface sensitivity.这里我们更感兴趣的是非弹性散射，因为它决定了电子的平均自由程，进而反映了表面的 灵敏度。reciprocal lattice 倒格子inelastic scattering 非弹性散射3.4.1 The dielectric funct

38、ion3.4.1介电函数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.介电函数是一个非常有用的概念，因为它描述了固体中光和带电粒子的宏观吸收，并做出 了微观解释。让我们回忆一些光学基本公式。向量T表示沿x方向传播的平面波。亘=亘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和介电常数8之间满足麦克斯

40、韦关系式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描述的光学性质是完全等价的，它们的两个部分不是独立的，可以通过克拉茂克朗尼希关系相互转换。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，从技术上讲，如果我们必须

42、首先得到全光谱下的一个量，才能得到另一个量。同样 的道理，我们可以通过测量大范围内正常入射的光的反射率得到N或8的两个部分。The absorption of light in matter is given by Lamberts law光在物质中的吸收通过兰伯特定律得出（3.9）The probability p for the electrons to suffer an inelastic scattering event is given by电子收到非弹性散射的几率由下式得出/ 、 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.几率使我们最关心的问题，当考虑平均自由程时会发现，电子动能在70 eV附近时散射几率 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.在接下来的章节中，我们将按能量的高低顺序来迅速了解那些对介电函数有贡献的元激 发。这些激发为我们提供了介电函数的微观图像。charged particles 带电粒子plane wave 平面波Kramers-Kronig relations克拉茂一克朗尼希

45、关系kinetic energies 动能Phonons3.4.2声子On its way through the solid and the surface the electrons can be scattered inelastically by absorbing or creating phonons.电子在通过固体内部和表面时，可以通过吸收和产生光子的形式发生非弹性散射。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.声子的能量很小(通常小于100 eV)但矢量? 可以很大。在电子能量损失光谱中观察 声子的损耗可以得到表面声子的散布情况或者通过测量它们的振动频率来研究吸附物。在这 里，声子散射并不重要因为它只有在低能量下才需要考虑。vibrational frequencies振动频率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考虑一个电子从束缚态被激发到未占据态的情况。在金属中，散射很强，电子和空穴交互 作用将很弱。但在半导体中，电子和空穴可以被弱的束缚从而形成激子。激子有类氢原子光 谱，但库仑电势被介电常数屏蔽了。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.在绝缘体和半导体中这种类氢原子的能级处在导带之下.激子电离就是把电子激发到导带. 激子没有被束缚在特定的位置:空穴和电子可能跃迁到邻近位置.这种可能性是机子的能带扩 展至波带.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.在固体表面，配位数的减少不仅改变了单个激子的库伦势能激子之间跃迁的矩阵元素。这 样的结果是产生表面激子的迁移和不同宽度。boun

52、d state 束缚态Coulomb potential 库仑电势hydrogen atom 类氢原子conduction bound 导带Interband transitions3.4.4带间转变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.另一种损失机制是电子空穴对的产生。在金属中，一个人很小的能量就能使电子从费米能 级以下正好跃迁到费米能级以上从而产生电子空穴对。电子空穴对的产生对各个能级的介电 函数都有贡献。对半

56、导体情况就不同了。它存在一个最小的电子空穴对的产生能量，即基态 间隙能。在半导体中，介电函数中的结构与间隙中的激发态类似。激子的能量略低于此。在 金属和半导体中，波带结构中所谓的临界点的存在都提高了介电函数的特征强度。临界点， 就好比是，被填充的波带与空波带在一个大的K空间区域是平行的。于是，此区域光跃迁就 具有相同的能量，使e增强。electron-hole pairs 电子空穴对critical points 临界点unoccupied bands 空态Bulk and surface plasmons3.4.5等离子体的内部和表面In the Drude model of metals,

57、 the dielectric function is在特鲁特模型中，金属的介电常数为S ()=1 - 3,(3.12)where % is the so-called plasma frequency这里，3诙是所谓的等离子体的频率，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有个简要的解释。它与电子气体对带正电离子的纵向共振类似(如图3.5)。这类激发被 称为等离子体。forplasmaoscillationFigure 4.5:A simple pictureFigure 4.5: A simple picture for a plasma oscillation图4.5:等离子振荡示意图The plasma frequency is very important for the optical properties of a metal. We write equ. 3.4as等离子体频率对金属光学

59、性能而言十分重要。把公式3.4写作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.我们可以分两种情况来讨论：如果w wp则e为负实数，式(3.14)只给出了阻尼振荡的 解。这意味着电场不能穿透金属，金属能反射一切光。当高于等离子频率时，电场能透过金 属传播。For simple metals, there is a good agreement with the calculated plasma frequency wp, or plasmon energy h wp, and the experimental values.对于简单金属:计算出的wp或等离子体能量h wp