固体表面与界面翻译

《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：32-42

Chapter 3

Electron spectroscopy

电子能谱

3.1 Introduction

3.1 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 coming 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 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(reflectivity 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 choosing 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，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 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 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 is 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

Fig3.1: An EELS experiment. The momentum transfer parallel to the surface is determined by 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。

3.2 Why electrons: The mean free path

3.2 为什么用电子：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：

,)(）（ττλm k

E v E kin kin == (3.1)

Where v is the velocity and τ is the collision time. In the Drude model τ is the mean time between two scattering events. In a quasiparticle-picture τ 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 electrons 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 universal 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, like the scattering with phonons.

其中，v 是电子的速度，τ 是碰撞时间。在德鲁特模型中，τ 是两次散射间隔的平均时间。在准粒子图像中，τ 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

Figure 3.2: The mean free part of electrons in solid. The dots are measurements the dashed 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】

The mean free path curve has a broad (note the log-log scale) minimum around a kinetic

energy of about 70 eV. There it is less than 100

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? Fortunately, 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 analysers

3.3：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 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 potential 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 energy 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。

Figure 3.3：An electron gun

图3.3：电子枪

Electrons can be detected using an electron multiplier, usually 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 avalanche 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 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 chemical 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 count 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 electrons 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。

Figure 3.4: A hemispherical electron analyser with a lens system

图3.4：一个带有镜头的半球形电子分析仪

In the EELS experiment mentioned above 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

3.4 Electrons in solids: elastic and inelastic scattering

3.4 固体中的电子：弹性和非弹性散射

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

0E E s = （3.2）

Where

E 0 is the energy of the incoming electrons and E s that of the scattered electrons. The momentum parallel to the surface is also conserved apart from a surface reciprocal lattice

vector →g

其中，E

0 为入射电子的能量，E s 为散射电子的能量。平行于表面的动量守恒，表面

倒格失为→g

→

→→+=g k k s 0|||| (3.3)

The crystal itself provides perpendicular momentum such 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 function

3.4.1 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 light →

E vector 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→

E 表示沿x 方向传播的平面波。 e t kx i )

(0ω-→→E =E , (3.4)

With λπN k 2=

and ik n N += (3.5)

Between the complex index of refraction N and the dielectric function

εwe have the

Maxwell relation

光的折射率N 和介电常数ε之间满足麦克斯韦关系式 i r i N εεε+== (3.6)

The description of the optical properties in terms of N and

ε is completely equivalent. The two part of N and ε are not independent but can be transformed into each other the Kramers-Kronig relations

用N 和ε 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。

'022''')(2)()(ωω

ωωεωπεωεd i r ?∞-+

∞= （3.7） and '')()'(2)(022ωω

ωεωεπω

ωεd r r i ?∞

-∞-= （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 ε 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ε的两个部分。

The absorption of light in matter is given by Lambert ’s law

光在物质中的吸收通过兰伯特定律得出

x e I I α-=0 and λπκα4= （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

))(1()(ωεω-∞?p （3.10）

This probability is exactly 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 excitations 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—克朗尼希关系

kinetic energies 动能

3.4.2 Phonons

3.4.2 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 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 has to be considered at low energy.

声子的能量很小（通常小于100 eV）但矢量→

q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

3.4.3 Excitons

3.4.3 激子

Consider the case that an electron is excited from a bound state to a previously unoccupied state. In a metal, the scattering 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 function

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。

|

|),(2

R r e R r V Coul --=ε （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 bound. 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 surface 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。

bound state 束缚态

Coulomb potential 库仑电势

hydrogen atom 类氢原子

conduction bound 导带

3.4.4 Interband transitions

3.4.4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 Fermi 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 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 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 ?.

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κ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 ? 增强。

electron-hole pairs 电子空穴对

critical points 临界点

unoccupied bands 空态

3.4.5 Bulk and surface plasmons

3.4.5等离子体的内部和表面

In the Drude model of metals, the dielectric function is

在特鲁特模型中,金属的介电常数为

22-1）（ω

ωωεP =, (3.12) where ωP is the so-called plasma frequency

这里，ωP 就是所谓的等离子体的频率，

02

2

εωm ne P = (4.13) ωP 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 excitations are called plasmons

ωp 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。

Figure 4.5: A simple picture for a plasma

oscillation

Figure 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. 3.4 as

等离子体频率对金属光学性能而言十分重要。把公式3.4写作

(3.14)

We can distinguish between two cases: if ω < ωP then ? 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 permit propagating solutions of the electric field.

我们可以分两种情况来讨论: 如果ω < ωP 则? 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 simpl e metals, there is a good agreement with the calculated plasma frequency ωP , or plasmon energy ? ωP , and the experimental values.

对于简单金属，计算出的ωP 或等离子体能量? ωP 与实验值吻合的很好。

There is also a plasmon mode which is localized at a metal surface and decays exponentially towards both metal and vacuum. It can be described as a longitudinal wave

这里还有一种等离子体振子，它们局域在金属表面，在金属中和真空中都以指数衰减，他可以被描述为一列纵波。

（3.15）

Fig. 3.6 shows the field and charge distribution for such a mode.

图3.6 为此模式下的场和电荷分布

The planar component of the E field associated with this is continuos. but the perpendicular component is not. Just above and below the surface it is

与此相关的电场E 的平行分量是连续的，垂直分量不连续。刚好处在表面上和表面下的电场为

（3.16）

Now the D =? E field must be continuos. This gives us the condition for the existence of the surface plasmon

而电场D =? E 必须连续，这就给出了表面等离子体振子存在的条件

）＝－１（ｓｐ

ωε （3.17） And hence

因此

２／＝Ｐｓｐωω （3.18）

The energy loss of electrons due to plasmons and surface plasmons is illustrated in Fig. 3.7. It shows two energy distributions from an electron beam with approx. 2 keV kinetic energy which has been scattered from a surface of α-Ga. Distinct losses are visible which can be ascribed to bulk and surface plasmons. Note that the energy difference between these losses is in good agreement with equ. 3.18. The difference between the spectra is due to the experimental geometry. This will be picked up in the exercises.

由于等离子体振子和表面等离子体振子所引起的电子能量的损失如图3.7 所示。图示为

从镓表面散射的电子束在能量约为2eV 时的两种能量分布。由内部和表面等离子体引起的缺失是很明显的。注意到这些不同的缺失能量都满足公式（3.18）。光谱间的差异由实验中的几何形状引起的。它们将在实践中获得。

Figure 4.7: EELS spectra from the (010) surface of α-Ga. The surface and bulk plasmon losses can be identified. The difference between the spectra is due to the experimental geometry (to be discussed in the exercises ).

图4.7：镓表面（010）晶面的电子电子能量损失光谱。表面和内部的等离子体振子损失可以被识别出来。光谱的不同是由于实验中的几何条件不同引起的（在练习中将讨论）

The excitation of plasmons and surface plasmons is the major reason for the inelastic scattering of the electrons in the energy regime we are interested in. When looking again at the universal curve we can see that the mean free path is long for lower energies because it is not possible to excite the plasmons. Above the edge for plasmon creation the mean free path drops drastically. At high energies it goes up again because the cross section for the plasmon creation diminishes.

在我们研究的能量范围内，等离子体振子的激发和表面等离子体振子是两个引起电子非弹性散射的主要原因。再次观察曲线我们会发现，在能量较低时平均自由程大，这是因为不会产生等离子体振子的激发。在等离子体振子形成的边缘以上，平均自由程急剧减小。在能量较高时又回升，这是由于产生等离子体振子的横截面减小了。

Drude model 特鲁特模型

Plasmons 等离子体振子

3.4.6 Core levels

3.4.6 谱线中心能级

At much higher energies, several hundred eV or so, small structures in the dielectric function can be found which are due to the excitation of core electrons.

在能量很高时，大约几百eV左右，由于中心电子的激发而引起的介电常数的微小结构可以被观察到。

3.5 Concluding remarks

3.5 结束语

We have seen that the minimum in the electron mean free path in Fig. 3.2 is mainly determined by the excitations of plasmons. Below the edge for plasmon excitation, the most important loss mechanism is interband transitions. This raises the question about how universal the curve actually is. If we take, for example, a wide band semiconductor, then interband transitions below the gap energy will not be possible and this will increase the mean free path considerably.

从图3.2 看出,电子平均自由程的最小值主要是由等离子体振子的激发决定的。在等离子体振子激发之下，最主要的损失机制是带间转变。这就引发了一个问题，即这条曲线使用田间到底是怎样的。如果我们以宽频带半导体为例,那么在能隙以下将不可能发生带间转变,这将大大地增加平均自由程.

The fact that plasmon creation is the most important mechanism for inelastic scattering makes it clear why it is simple, in most cases, to distinguish elastically scattered (emitted) electrons from electrons which have been scattered by plasmons. The reason is that the plasma energies are rather large so that the loss peaks are far away from the elastic peak (see Fig. 3.7).

等离子体振子的产生是非弹性散射的重要机制,它使我们更容易辨别非弹性散射电子与等离子体振子散射电子.原因是等离子体能量大,所以能量损失峰远离弹性峰.(如图3.7)

The most common way to measure the mean free path of electrons in a material is to evaporate a thin film of the material on a substrate. Then the intensity of characteristic Auger transitions in the substrate is measured as a function of film thickness.

测量材料中电子平均自由程的通常方法是在基片上蒸发这种材料的薄膜。然后基片中特征俄歇转变的强度就可以通过薄膜的厚度被测量出来。

interband transition 带间转变

Auger transitions 俄歇转变

3.6 Further reading

3.6 延伸阅读

The basic principles of electron spectroscopy are discussed in most surface science books [3, 2, 1, 4]. A good section about analysers and electron optics can be found in [4]. The elementary excitations which contribute to the dielectric function are discussed nicely in [3]. The basic physics of the Drude model and the plasmons is discussed in [11]. Surface plasmons are described in [3].

电子能谱学的基本原理在大多数表面科学的书中都有介绍【3,2,1,4】。关于分析器和电

子光学的部分可以参见文献【4】。文献【3】中详细介绍了有关介电函数的基本激发类型。特鲁特模型和等离子体的基本物理性质参见【1】。表面等离子体参见文献【3】。