Now that we've considered some methods for controlling and analyzing electron beams. These beams can be used in a variety of ways to examine surfaces and interfaces. Let's consider the physics of electron-surface interactions. The material presented and figures used are drawn from references [2] and [3].

8. Electron-Surface Interactions

 

At absolute zero, the electronic structure of metals is such that the allowed electron energy states within the metallic atoms are occupied up to a maximum energy called the Fermi energy, E_F. For temperatures above absolute zero, electrons are excited to higher energy available energy levels with some probability of occupancy related to the temperature. The energy difference between the Fermi level and zero potential energy is the work function, F. We are primarily interested in the ways in which electrons outside the surface interact with the allowed electron energy states at the surface. Usually this involves modifying the electron density, revealing pertinent information concerning the nature of the surface.

When an electron beam with a range of energies bombards a surface, a variety of processes take place. Many of these processes lead to the emission of electrons from the surface called secondary electrons. Figure 18 shows one type of system that is used to study secondary electrons.

 

Figure 18. A secondary electron emission apparatus is shown schematically. [Figure 14.3 in reference 2]

 

The electron gun in the figure emits electrons at a known rate and energy that are directed to the sample surface. The energy of the electrons may be anything from a few eV to several keV. The electrons that are scattered by the sample (primary electrons) as well as those that are knocked out of the sample (secondary electrons) are detected by a spherical collector surface. A voltage is applied to retarding grids to determine the energy distribution of the secondary electrons. The results of a typical experiment carried out with this kind of equipment are shown in Figure 19. If the retarding potential is the same as that of the surface, then all emitted electrons will pass through the grid. As the retarding potential becomes increasingly negative with respect to the surface, electrons with energies lower than the potential difference between the sample surface and the grids are repelled. The current drops to zero when the energy is that of the primary electrons.

 

Figure 19. A secondary electron emission from a surface bombarded by electrons of energy E_P. Part (a) shows the collector current versus the retarding potential. Part (b) shows the derivative of the current with respect to energy versus the retarding potential. [Figure 14.4 in reference 2]

 

Plotting the derivative of the current with respect to the energy as in part (b) of the figure provides more information. The sharp peak at V_P is due to the elastically scattered primary electrons. The behavior of these electrons is similar to that of the specular reflection of light from a mirror or X-rays from a periodic lattice (Bragg reflection). These electrons are diffracted according to Bragg's law and may be used to study crystal structure.

At energies just below that of the primary peak are some features due to primary electrons that have lost energy due to interactions with other electrons, either in the surface or of some adsorbed species on the surface. These inelastically scattered electrons represent specific energy loss processes. In the case of clean surfaces, no adsorbants, the peaks represent electron-plasmon interactions. A plasmon is a collective effect within the solid, which may be viewed as a distribution of positive ions and electrons. The system is completely described in terms of charge density distributions. Suppose there is a displacement of electrons in one direction. This results in a local excess of positive charge (where the ions are viewed as frozen in their positions). The displaced electrons are then attracted to the positive ions, but overshoot them. An oscillation is thus setup. These plasmon excitations require energies on the order of 10 eV. In the study of the inelastically scattered electrons, one generally observes the effects of both surface and bulk plasmon interactions. Through a classical calculation, one can show that the bulk plasmon frequency is

(22)

w_P = (4pn₀)^1/2

Therefore, the frequency (and thus, the energy) depends only on the free electron density. The surface plasmon frequency is related to the bulk plasmon frequency as

(23)

w_SP = w_P(2)^-1/2

These plasmon excitations give rise to features in the inelastic loss region of the secondary electron distribution at energies equal to the primary energy minus the plasmon energy.

The large, broad peak at low energies is due to the secondary electrons, ejected in interactions with the primary beam. No electrons will be emitted when the primary energy is less than the work function. As the primary energy is increased, the secondary electrons emitted increases until the primary energy reaches into the 100 eV range, then the number slowly decreases with increasing primary energy. The reason for the decrease is that the primary electrons penetrate deeper into the solid; and the secondary electrons are less likely to escape. Figure 20 shows that the probability of escape from the sample without inelastic scattering is dependent on the energy of the electrons and varies by metallic element.

 

Figure 20. The inelastic electron mean free path (escape depth) is plotted versus initial kinetic energy. [Figure 14.9 in reference 2]

 

For many materials, the number of secondary electrons emitted for each incident electron is often greater then one. This fact is used in the most common detector for low level electron (or ion) fluxes. Figure 21 schematically shows a secondary electron multiplier.

 

Figure 21. A secondary electron multiplier is based in the fact that for many metals, more than one electron will be emitted for every one that is incident. The electrons emitted from the first dynode accelerate toward the second, emitting even more secondaries, and so on. Gains of 1 - 100 million are easily achieved using this type of device. [Figure 14.10 in reference 2]

 

Returning now to the small peaks at intermediate energies in Figure 19. These are due to Auger electron processes. Auger Electron Spectroscopy (AES) is a popular and widely-used surface analysis technique. Some applications include film growth studies, elemental analysis, and component concentration depth-profile analysis. To understand the Auger process, consider Figure 22. An incident electron scatters off an atom in the sample and excites a core-level electron. These electrons lie at energies well below the conduction band. The excited electron may return to the lower energy state by one of two competing processes. In one process, the electron simply returns to the core level state and a photon is emitted carrying off the energy difference between the states. This is the process of X-ray fluoresence. The alternative process is the Auger de-excitation process in which the excited electron drops from a less tightly bound level, but in this case, the excess energy is carried away by another electron located in a less tightly bound level.

 

Figure 22. This energy diagram illustrates the processes that give rise to X-ray fluoresence or Auger electron emission via inner shell excitation of an atom by scattering of an incident, energetic electron. [Figure 14.11 in reference 2]

 

Since the emitted auger electron has a particular energy related to the possible energy levels of the ionized atom, measurement of the energy can lead to identification of the particular atom. This kind of chemical analysis is similar to that that might use the X-ray emissions with the exception that the Auger electron measurement is more sensitive to the surface.

The principal Auger electron energies of the elements are given versus atomic number in Figure 23. The various transitions within the KLL, LMM, and the MNN process branches result from different spin orientations in the final state of the atom. It is the strong Z-dependence makes the Auger technique so powerful.

 

Figure 23. The principal Auger electron energies are strongly dependent on the atomic number Z. The bold dots indicate the strongest transitions of each element. [Figure III.2 in reference 3]

 

Figure 24 shows a typical AES system. A widely-used energy analyzer for AES is the cylindrical mirror analyzer (CMA). Electrons entering from a directed entrance into a certain cone (with apex angle of 42^o 18.5') are focused by two concentric, cylindrical electrodes onto an image point where the detector is positioned. The electric field determining the pass energy is radially directed between the concentric electrodes. The bias voltage is adjusted to pass only a narrow range of kinetic energies.

 

Figure 24. A typical arrangement for AES is shown. Primary electrons are emitted by an electron gun, located on the central axis of a cylindrical mirror analyzer (CMA). A sputter ion gun may also be included in the system to perform depth profile analysis. [Figure III.2 in reference 3]

 

Figure 25 shows the Auger spectrum from a contaminated nickel surface. The curve in part (a) is the number of secondary electrons emitted versus electron kinetic energy. The primary electron beam is generally in the 3 to 5 keV range. Most AES systems run in derivative mode to improve the signal-to-noise ratio. To perform this differentiation, a small alternating voltage is applied to the outer cylinder. A lock-in amplifier is used to detect the in-phase signal from the electron multiplier. The derivative is some multiplier of the applied ac voltage. In the AES literature, Auger line energies are reported as the minimum in the derivative spectrum. Therefore, these energy lines do not coincide with the peaks in the n(E) versus E spectrum.

 

Figure 25. The Auger spectrum from a contaminated nickel surface is shown. Part (a) shows the number of electrons versus electron kinetic energy. Part (b) is the derivative of the curve in part (a). [Figure 14.13 in reference 2]

A great deal of information may be found in a plot such as in Figure 25b. First of all, the position along the energy axis provides qualitative information about the elements that are present at the surface of the sample. These energies are determined by the use of reference spectra from clean, high purity specimens of each element. The peak-to-peak height of a feature in the derivative plot is nearly proportional to the concentration of a given atomic species near the surface. This determination of concentration is OK, as long as one makes appropriate corrections for chemical effects and relative transition intensities. In same cases, it is even possible to determine chemical state information, especially if the transitions involve valence electron states.

To carry out depth profiling using AES, one must systemically remove the surface since Auger electrons have a mean escape depth on the order of 1 nm. Thus, many AES systems as the one in Figure 24 showed, include an ion sputter gun. The surface of the sample is slowly removed by bombarding it with ions. As the surface is etched away, the Auger spectra are repeatedly taken. Figure 26 shows an example of depth-profiling of an indium-tin oxide film on a glass substrate. The peak-to-peak height of the derivative feature is plotted versus sputtering time. The depth below the original surface is directly proportional to the sputtering time.

 

Figure 26. An Auger depth profile is shown for an In-Sn-O film on a glass substrate. [Figure 14.15 in reference 2]

To continue to the next section, click here.
To return to the main page, click here.

If you have any questions, please e-mail webmaster@siu.edu.