Interaction of an electron beam with a

5.4.1 Interaction of an electron beam with a

Figure 5.18 Construction of the Ewald reflecting sphere .

solid

When an electron beam is incident on a solid specimen

a number of interactions take place which generate use- ful structural information. Figure 5.20 illustrates these interactions schematically. Some of the incident beam is back-scattered and some penetrates the sample. If the specimen is thin enough a significant amount is transmitted, with some electrons elastically scattered without loss of energy and some inelastically scattered. Interaction with the atoms in the specimen leads to the ejection of low-energy electrons and the creation of X-ray photons and Auger electrons, all of which can

be used to characterize the material. The two inelastic scattering mechanisms important in chemical analysis are (1) excitation of the electron gas plasmon scattering, and (2) single-electron scat-

Figure 5.19 Principle of the power method . tering. In plasmon scattering the fast electron excites

a ripple in the plasma of free electrons in the solid. The energy of this ‘plasmon’ depends only on the vol-

and the Bragg law is satisfied; the line joining the ume concentration of free electrons n in the solid and origin to the operating reciprocal lattice spot is usually

2 /m ] D [ne 1/2 . Typically E p , the energy referred to as the g-vector. It will be evident that at

given by E p

loss suffered by the fast electron is ³15 eV and the any one setting of the crystal, few, if any, points will

scattering intensity/unit solid angle has an angular half- touch the sphere of reflection. This is the condition

E DE p / 2E 0 , where E 0 is the incident for a stationary single crystal and a monochromatic

E is therefore ³10 4 radian. The energy beam of X-rays, when the Bragg law is not obeyed except by chance. To ensure that the Bragg law is satisfied the crystal has to be rotated in the beam, since

this corresponds to a rotation of the reciprocal lattice about the origin when each point must pass through the reflection surface. The corresponding reflecting plane reflects twice per revolution.

To illustrate this feature let us re-examine the pow- der method. In the powder specimen, the number of crystals is sufficiently large that all possible orienta- tions are present and in terms of the reciprocal lattice construction we may suppose that the reciprocal lat- tice is rotated about the origin in all possible direc- tions. The locus of any one lattice point during such

a rotation is, of course, a sphere. This locus-sphere will intersect the sphere of reflection in a small cir- cle about the axis of the incident beam as shown in Figure 5.19, and any line joining the centre of the

Figure 5.20 Scattering of incident electrons by thin foil. reflection sphere to a point on this small circle is a pos-

With a bulk specimen the transmitted, elastic and inelastic sible direction for a diffraction maximum. This small

scattered beams are absorbed .

The characterization of materials 143 of the plasmon is converted very quickly into atom

vibrations (heat) and the mean-free path for plasmon excitation is small, ³50–150 nm. With single-electron scattering energy may be transferred to single elec-

trons (rather than to the large number ³10 5 involved

in plasmon excitation) by the incident fast electrons. Lightly-bound valency electrons may be ejected, and these electrons can be used to form secondary images in SEM; a very large number of electrons with ener- gies up to ³50 eV are ejected when a high-energy electron beam strikes a solid. The useful collisions are those where the single electron is bound. There is a minimum energy required to remove the single elec- tron, i.e. ionization, but provided the fast electron gives the bound electron more than this minimum amount, it can give the bound electron any amount of energy, up to its own energy (e.g. 1 0 0 keV). Thus, instead of the single-electron excitation process turning up in the energy loss spectrum of the fast electron as a peak, as happens with plasmon excitation, it turns up as an edge. Typically, the mean free path for inner shell ion- ization is several micrometres and the energy loss can

be several keV. The angular half-width of scattering is given by E/2E 0 . Since the energy loss E can vary from ³10 eV to tens of keV the angle can vary upwards from 10 4 radian (see Figure 5.36).

A plasmon, once excited, decays to give heat, which is not at all useful. In contrast, an atom which has had an electron removed from it decays in one of two ways, both of which turn out to be very useful in chemical analysis leading to the creation of X-rays and Auger electrons. The first step is the same for both cases. An electron from outer shell, which therefore has more energy than the removed electron, drops down to fill the hole left by the removal of the bound electron. Its extra energy, E, equal to the difference in energy between the two levels involved and therefore abso- lutely characteristic of the atom, must be dissipated. This may happen in two ways: (1) by the creation

ference E. For electron transitions of interest, E, (2) by transferring the energy to a neighbouring elec-

tron, which is then ejected from the atom. This is an ‘Auger’ electron. Its energy when detected will depend on the original energy difference E minus the binding energy of the ejected electron. Thus the energy of the Auger electron depends on three atomic levels rather than two as for emitted photons. The energies of the Auger electrons are sufficiently low that they escape from within only about 5 nm of the surface. This is therefore a surface analysis technique. The ratio of photon–Auger yield is called the fluorescence ratio ω, and depends on the atom and the shells involved. For

the K-shell, ω is given by ω K D X K /⊲A K C X K ⊳ , where

X K and A K are, respectively, the number of X-ray pho- tons and Auger electrons emitted. A K is independent

of atomic number Z, and X K is proportional to Z 4 so that ω K Z 4 /⊲a C Z 4 ⊳ , where a D 1.12 ð 10 6 . Light ele-

ments and outer shells (L-lines) have lower yields; for

K -series transitions ω K varies from a few per cent for carbon up to ½90% for gold.