Hawkes P.W., Spence J.C.H. (Eds.) Science of Microscopy. V.1 and 2

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Chapter 3 Scanning Electron Microscopy 175

The backscattering coefﬁ cient of a single crystal depends sensitively

on the direction of the incident electrons related to the crystal lattice

(Reimer et al., 1971; Seiler, 1976). This dependence is caused by the

regular three-dimensional arrangement of the atoms in the lattice,

whose atomic density depends on the direction. The backscattering

coefﬁ cient is lower along directions of low atomic density, which

permits a fraction of the incident electrons to penetrate deeper than in

amorphous material before being scattered. Those electrons have a

reduced probability of returning to the specimen surface and leaving

the sample as BSE. The maximum relative variation of the backscatter-

ing coefﬁ cient is in the order of 5%.

2.2.3 Transmitted Electrons

When the thickness of a specimen approaches the electron range R or

becomes even smaller than R, an increasing fraction of beam electrons

is transmitted. Those transmitted electrons interact with the support,

thus generating non-specimen-speciﬁ c signals, which superimpose the

specimen-speciﬁ c signals. The spurious contribution of the support to

the signal, originating from the specimen, can be reduced signiﬁ cantly

by replacing the solid support by a very thin (about 5–15 nm thick)

amorphous carbon ﬁ lm. Such thin carbon ﬁ lms supported by a

metallic mesh grid are commonly used in TEM and STEM as electron-

transparent support for thin specimens. To improve the stability of the

5-nm-thick carbon ﬁ lm, the ﬁ lm is placed onto a holey thick carbon

ﬁ lm supported by a mesh grid. In contrast to a solid support, a 5-nm-

thick carbon ﬁ lm contributes only insigniﬁ cantly to the SE and BSE

signal (cf. Figure 3–19), thus particles deposited onto a thin support

ﬁ lm can be imaged in the normal manner using SE and BSE,

respectively.

In addition to the reduction of spurious signal, the transparent

support ﬁ lm enables use to be made of the transmitted electrons, which

carry information about the interior of the specimen (in some SEM the

specimen stage must be altered to make the transmitted electrons

accessible). As a result of electron–specimen interaction the transmit-

ted electrons can be unscattered or elastically or inelastically scattered

(cf. Figure 3–2). Due to their characteristic angular and energy distri-

bution, the transmitted electrons can be separated by placing suitable

detectors (preferentially combined with an electron spectrometer)

below the specimen. Frequently, a rather simple and inexpensive device

for observing an STEM image (Oho et al., 1986)—sometimes called

“poor man’s STEM in SEM detector”—is used. The transmitted elec-

trons are passing through an angle-limiting aperture, strike a tilted

gold-coated surface, and thus create a high SE and BSE signal, which

can then be collected by a conventional ET detector. The angle-limiting

aperture cuts off the transmitted, scattered electrons. In this case the

“poor man’s STEM in SEM detector” acquires those electrons, which

represent the bright-ﬁ eld signal. The “poor man’s STEM in SEM detec-

tor” just cuts the transmitted scattered electrons without making use

of their inherent information. Both the elastically and the inelastically

scattered electrons are signals, which very sensitively depend on the

176 R. Reichelt

mass thickness ρt if the specimen thickness t ≤ [Λ

/(Λ

+ Λ

)]

(Reichelt and Engel, 1984, 1985) (Figure 3–20) can be used, e.g., for mass

determination of biomolecules and assemblies thereof (Zeitler and

Bahr, 1962; Lamvik, 1977; Engel, 1978; Wall, 1979; Feja et al., 1997).

Although most of the mass determination studies were made with

dedicated STEM, high-resolution FESEM equipped with an efﬁ cient

Figure 3–19. SE and annular dark-ﬁ eld micrographs showing a particle on an ∼4-nm-thick amorphous

carbon ﬁ lm (CF) attached to a holey carbon ﬁ lm of ∼20 nm in thickness (HF), which is supported by

a Cu mesh grid (G). (a) SE micrograph recorded with a probe current of about 30 pA at 30 kV. A very

low probe current of ∼3 pA (pixeltime: 23 µs. i.e., ∼430 incident electrons/pixel) was used for simultane-

ously recording the SE micrograph (b) and the dark-ﬁ eld micrograph with scattered transmitted elec-

trons (annular dark-ﬁ eld mode) (c). The image intensity and the signal-to-noise ratio in (c) is much

higher than the intensity in (b) because the number of SE (almost only SE1 are generated) is signiﬁ -

cantly smaller than the number of the collected transmitted scattered electrons. No usable BSE signal

can be detected from the thick and thin carbon ﬁ lms. The scale bar corresponds to 20 µm.

020406080100

0.8

unscattered

scattered

t [nm]

0.6

Fraction of electrons

0.4

0.2

Figure 3–20. Fraction of transmitted electrons scattered into an angular range

of 25–300 mrad for carbon (ρ = 2 g cm

−3

; solid line) and protein (ρ = 1.35 g cm

−3

;

dashed line). Parameters: E

= 30 keV, α

= 10 mrad. The graphs show an

increasing fraction of scattered and a decreasing fraction of unscattered elec-

trons with increasing thickness. (Calculation according to Krzyzanek and

Reichelt, 2003.)

Chapter 3 Scanning Electron Microscopy 177

annular dark-ﬁ eld detector capable of single-electron counting

and MHz counting rates would allow for such quantitative studies

(Reichelt et al., 1988; Krzyzanek and Reichelt, 2003; Krzyzanek et al.,

2004).

Another important application of STEM imaging is the measure-

ment of the physical probe size of the SEM using a thin carbon ﬁ lm

(thickness below 10 nm, preferably containing nanoparticles of gold

or gold-palladium for better contrast). In this case the broadening

of the electron beam in the ﬁ lm is negligible and so the resolution

of the STEM image is equal to the probe diameter. The image resolu-

tion can be determined either by analysis of the diffractogram

(power spectrum) of the STEM micrograph (Frank et al., 1970;

Reimer, 1985; Joy, 2002) or by cross-correlation function analysis

(Frank, 1980) of the phase noise in the bright-ﬁ eld STEM image of

the carbon ﬁ lm. The latter directly yields the probe diameter of the

SEM (Joy, 2002).

Combining the SE and BSE detectors above as well as the bright-ﬁ eld

and dark-ﬁ eld detectors below the specimen, its surface as well as its

internal structure can be observed simultaneously in the SEM.

2.2.4 Cathodoluminescence

Cathodoluminescence (CL) is the emission of light generated by the

electron bombardment of semiconductors and insulators (Muir and

Grant, 1974; cf. Figure 3–14). Those materials have an electronic band

structure characterized by a ﬁ lled valence band and an empty conduc-

tion band separated by an energy gap ∆E

= E

− E

. Electrons from the

valence band can interact inelastically with a beam electron and can be

excited to an unoccupied state in the conduction band. The excess

energy of the excited electron will be lost by a cascade of nonradiative

phonon and electron excitations. Most of the recombination processes of

excited electrons with holes in the valence band are nonradiative pro-

cesses, which elevate the sample temperature. There are different radia-

tive processes, which take place in inorganic materials, semiconductors,

and organic molecules.

In inorganic materials intrinsic and extrinsic transitions can take

place. The intrinsic emission is due to direct recombination of electron

hole pairs. Extrinsic emission is caused by the recombination of trapped

electrons and holes at the donor and acceptor level, respectively. The

trapping increases the probability of recombination. The extrinsically

emitted photons have a lower energy than intrinsically emitted

photons.

In semiconductors the radiative recombination can be due to the

direct collision of an electron with a hole with the emission of a phonon.

Depending on the nature of the band structure of the material, the

recombination can be either direct or indirect. In the latter case the

recombination must occur by simultaneous emission of a photon.

Indirect recombination is less likely than direct recombination. If

the material contains impurities, the process of recombination via

impurity level becomes important. The modiﬁ cation of CL efﬁ ciency

as a function of the purity and the perfection of the material is the

most important aspect of the use of this method in scanning electron

178 R. Reichelt

microscopy. It is because of such modiﬁ cations that a contrast is

generated (for details see, e.g., Holt and Yacobi, 1989; Yacobi, 1990).

It was shown in some cases that the sensitivity of CL analyses can be

at least 10

times higher than that obtainable by X-ray microanalysis,

i.e., an impurity concentration as low as 10

−3

(Holt and Saba,

1985).

In organic materials the excitation is inside an individual molecule.

Electrons go from a ground state to a singlet state at least two states

above. Then the deexcitation to the ground state is radiationless up to

the singlet state directly above the ground level and from this state the

deexcitation can be either radiationless or radiative with decay times

larger than 10

−7

s (ﬂ uorescence). The CL spectra depend on the chemical

structure of the molecule (DeMets et al., 1974; DeMets, 1975). Cathodo-

luminescence of organic matter also can be caused by selective staining

with luminescent molecules (ﬂ uorochromes). Typical ﬂ uorochromes

are, e.g., ﬂ uoresceine, ﬂ uoresceine isothiocyanate (FITC), and acridine

orange.

Independent on the material the light generated by CL inside the

specimen has to pass the surface according to the Snell law (Bröcker

et al., 1977). The critical angle θ

of total internal reﬂ ection is given as

sin θ

= n

/n (2.35)

where n

= 1 (vacuum) and n is the refractive index of the specimen

(1 < n < 5). As shown by Eq. (2.35) the fraction of emitted light is signiﬁ -

cantly reduced by total internal reﬂ ection for n > 2 (semiconductors).

2.2.5 X-Rays

The X-ray spectrum is considered to be that part of the electromagnetic

spectrum that covers the wavelengths λ

from approximately 0.01 to

10 nm. The energy of X-rays is given as

= hν = hc/λ

(2.36)

where h = 6.6256 × 10

−34

Js is Planck’s constant, c = 2.99793 × 10

m/s is

the speed of light, and ν is the frequency of X-rays. The X-rays are

generated by deceleration of electrons (X-ray continuum or brems-

strahlung) or by electron transition from a ﬁ lled higher state to a

vacancy in a lower electron shell (characteristic X-ray lines) (Figure

3–21).

The X-ray continuum is made up of a continuous distribution of

intensity as a function of energy whereas the characteristic spectrum

represents a series of peaks of variable intensity at discrete element-

speciﬁ c energies. As the electron energy increases the intensity of the

continuous spectrum also increases and the maximum of the distribu-

tion is shifted toward higher energies. The general appearance of the

continuous spectrum is independent of the atomic number of the speci-

men, however, the absolute intensity values are dependent on the

atomic number. The maximum possible energy E

is given by the elec-

tron energy E

, which corresponds to instantaneous stopping of an

electron at a single collision (Duane-Hunt limit). According to Kramers

Chapter 3 Scanning Electron Microscopy 179

(1923) the intensity of the continuous spectrum I

emitted in an energy

interval with the width dE

is given as

)dE

= kZ(E

− E

)/E

⋅ dE

(2.37)

k represents the Kramers constant, which varies slightly with the

atomic number (Reimer, 1985). A detailed treatment of the continuous

X-ray emission is given by Stephenson (1957).

The characteristic X-ray spectrum consisting of peaks at discrete

energies is superimposed on the continuous X-ray spectrum (cf. Figure

3–21). Their positions are independent of the energy of the incident

electrons. The peaks occur only if the corresponding atomic energy

level is excited. The generation of characteristic X-rays consists of three

different steps. First, a beam electron interacts with an inner shell

electron of an atom and ejects this inner shell electron leaving that

atom in an excited state, i.e., with a vacancy on the electron shell.

Second, subsequently the excited atom relaxes to the ground state by

transition of an electron from an outer to an inner shell vacancy. The

energy difference ∆E

between the involved shells is characteristic for

the atomic number. Third, this element-speciﬁ c energy difference is

expressed either by the emission of an electron of an outer shell with

a characteristic energy (Auger electron) or by the emission of a char-

acteristic X-ray with energy E

= ∆E

. The fraction of characteristic X-

rays emitted when an electron transition occurs is given by the

ﬂ uorescence yield ω. This quantity increases with the atomic number

and depends on the inner electron shell involved (Figure 3–22). The

complement, 1 − ω represents the Auger electron yield, which gives the

corresponding fraction of Auger electrons produced. The ﬂ uorescence

yield for the different shells and subshells can be calculated (for details

see Bambynek et al., 1972).

Characteristic

X-ray spectrum

X-ray

continuum

Intensity

Figure 3–21. Schematic representation of the X-ray spectrum emitted from a

specimen bombarded with fast electrons.

180 R. Reichelt

Moseley studied the line spectra in detail and found that the general

appearance of the X-ray spectrum is the same for all elements. The

energy of a characteristic X-ray line depends on the atomic shells

involved in the transition resulting in the emission of this line. The X-

ray lines can be classiﬁ ed in series according to the shell where the

ionization took place, e.g., K-, L-, M-shell, etc. The quantum energies of

a series are given by Moseley’s law

= A(Z − B)

(2.38)

where A and B are parameters that depend on the series to which the

line belongs. The characteristic X-ray energy E

is denoted by symbols

that identify the transition that produced it. The ﬁ rst letter, e.g., K, L,

identiﬁ es the original excited level, whereas the second letter, e.g., α,

β, designates the type of transition occurring. For example, K

denotes

the excitation energy between the K- and L-shell, whereas K

denotes

the excitation energy between the K- and M-shell. Transitions between

subshells are designated by a number, e.g., a transition from the sub-

shell L

III

to K is denoted as K

α1

and from the subshell L

to K is denoted

as K

α2

, respectively. The transition from the subshell L

to K is forbid-

den. The characteristic X-ray energies and X-ray atomic energy levels

for the K-, L-, and M-shells are listed in tables (Bearden, 1967a,b). For-

tunately, the atomic energy levels are not strongly inﬂ uenced by the

type and strength of the chemical bonds. However, chemical effects on

X-ray emission are observed for transitions from the valence electron

states, which are involved in chemical bonds. In such cases the narrow

lines show changes of their shape and their position (energy shift

<1 eV) as well (Baun, 1969).

0.7

K-shell

Fluorescence yield ω

1 - ω

L-shell

M-shell

0.6

0.5

0.4

0.3

0.2

0.1

0.4

0.3

0.5

0.6

0.7

0.8

0.9

1.0

020

Atomic number

40 60 80 100

Figure 3–22. Dependence of the X-ray ﬂ uorescence yield ω and its comple-

ment (1 − ω) of the K-, L-, and M-shell from the atomic number. The comple-

ment (1 − ω) corresponds to the Auger electron yield.

Chapter 3 Scanning Electron Microscopy 181

2.2.6 Auger Electrons

As mentioned in Section 2.2.5, when an excited atom relaxes to the

ground state by transition of an electron from an outer to an inner shell

the energy difference ∆E

between the involved shells can be expressed

by the emission of an electron of an outer shell with a characteristic

energy E

. The emission is due to the Auger effect (Burhop, 1952;

Åberg and Howart, 1982) and the emitted electron is designated as an

Auger electron (AE). Its energy E

is given by

= ∆E

− E

ionr

(2.39)

where the term E

ionr

contains the ionization energy of the AE emitting

outer shell and also considers relaxation effects. The shape and the

position of the AE peaks are inﬂ uenced by the type and strength of

the chemical bonds (Madden, 1981). The AE peaks have an energy

width of a few electronvolts and are superimposed on the low-energy

range of the BSE spectrum up to energies of about 2.5 keV (Figure 3–12).

The identiﬁ cation of the AE peaks on the BSE background (Bishop,

1984) can be improved by differentiation of the electron energy

spectrum.

The Auger electrons are generated within the excitation volume

(Figure 3–14). Due to their low energies only AE with a short pathway

to the specimen surface can escape. However, energy losses caused by

inelastic scattering on the pathway to the surface remove AE from the

AE peaks. The decrease of the AE peak is proportional to exp(−x/Λ

where x denotes the length of the path inside the specimen and Λ

the mean free path of the AE. Depending on their energy and the

atomic number of the specimen the mean free path Λ

can have values

in the range of about 0.4 nm to a few nanometers (Palmberg, 1973; Seah

and Dench, 1979). If AEs are inelastically scattered on their path to the

surface, then they cannot be identiﬁ ed as an AE in the BSE background.

Therefore, only atoms within a depth of about Λ

can contribute to

the AE peaks. Since Auger electrons yield information on element

concentrations very near the surface, the specimen must be in an ultra-

high vacuum environment and special sample preparations are

required (e.g., ion sputtering in situ, cleavage in situ) to obtain clean

surfaces.

Because the AE yield of the K-shell 1 − ω

is much larger than ω

for

light elements (cf. Figure 3–22) AE spectroscopy is advantageous for

elements with atomic number Z = 4(ω

= 4.5 × 10

−4

) up to Z ∼ 30(ω

4.8 × 10

−1

) (Bauer and Telieps, 1988). Similar to SE, which are also

emitted only from a very thin surface layer, the AE can be generated

directly by the beam electrons and by BSE within a larger circular

area around the beam impact point (cf. Figure 3–14). Like the SE

yield, which increases with increasing angle of incidence θ according

to δ(θ) = δ

/cos θ [cf. Eq. (2.31)], the integral AE peak intensity is

proportional to 1/cos θ (Bishop and Riviere, 1969; Kirschner, 1976;

Reimer, 1985).

Recent developments in scanning Auger microscopy and AE spec-

troscopy are described by Jacka (2001).

182 R. Reichelt

2.2.7 Others

The incident electron beam bombards the specimen with electrons

thereby introducing a negative electric charge. A certain amount of

negative electric charge is leaving the specimen as secondary (I

backscattered (I

BSE

) and Auger electrons (I

). To avoid an accumulation

of charges a specimen current I

must ﬂ ow from the specimen to the

ground. The conservation equation for the electric charge is

= I

+ I

BSE

+ I

(2.40)

where I

is the probe current. The specimen current changes the sign

when I

+ I

BSE

+ I

> I

. Because I

+ I

BSE

>> I

this means basically

that δ + η > 1 (cf. Figure 3–16). I

depends on the angle of beam inci-

dence θ and the electron energy E

as expected from δ(θ, E

) and η(θ,

) (Reimer, 1985). The resolution of specimen current images is com-

parable to that of BSE images. One advantage of the specimen current

mode is that the contrast is independent on the detector position. A

critical review of this mode was published by Newbury (1976).

The electron–specimen interaction also generates acoustic waves. The

frequencies of these waves depend on the imaging conditions of the

SEM and the specimen studied. They cover a range from low sound up

to very high ultrasound frequencies. The electron acoustic mode, usually

denoted as scanning electron acoustic micro scopy (SEAM), was intro-

duced by Brandis and Rosencwaig (1980) and Cargill (1980). SEAM uses

a periodic beam modulation or short electron beam pulses that allow for

analysis of the SEAM frequency response (Balk and Kultscher, 1984;

Balk, 1986; Kultscher and Balk, 1986). The SEAM was reviewed by Balk

(1989) and applications of this method in semiconductor research

(Balk, 1989) and for the investigation of magnetic structures were

shown (Balk et al., 1984).

2.3 Contrast Formation and Resolution

Since the image formation is due to the image signal ﬂ uctuation ∆S

from one point to another point, the contrast C is designated as in

television to be

C = (S − S

)/S = ∆S/S (2.41)

is the average value of the signal and S represents the signal of the

considered point (S > S

, i.e., C is always positive). The signal ﬂ uctua-

tion may be caused by local differences in the specimen topography,

composition, lattice orientation, surface potential, magnetic or electric

domains, and electrical conductivity. The minimum contrast is obtained

if S = S

, whereas the maximum contrast is obtained for S

= 0. This

is the case, e.g., when the signal S from a feature is surrounded by a

background with S

= 0. The contrast will be visible if C exceeds the

threshold value of about 5 × 10

−2

According to the point-resolution criterion two image points sepa-

rated by some horizontal distance (i.e., within the x–y plane perpen-

dicular to the optical axis) are resolved when the minimum intensity

Chapter 3 Scanning Electron Microscopy 183

between them is 75% or less of the maximum intensity. The point reso-

lution therefore corresponds to the minimum distance of two object

points, those superimposed image intensity distributions drop to 75%

of their maximum intensity between them. Due to the inherent noise

of each signal of the SEM characterized by its signal-to-noise ratio

(SNR) the drop to 75% of the maximum intensity will not be reliably

deﬁ ned at the minimum distance. Consequently, at low SNR two image

points can be resolved only if their distance is larger than the minimum

distance reliably deﬁ ned for noiseless signals.

As opposed to the light or transmission electron microscope the

resolution of the SEM cannot be deﬁ ned by Rayleigh’s criterion. The

resolution obtained in the SEM image depends in a complex manner

on the electron beam diameter, the electron energy, the electron–

specimen interaction, the selected signal, the detection, as well as the

electronic ampliﬁ cation and electronic processing. An object “point”

corresponds to the size of a small local excitation volume (cf. Figures

3–13 and 3–14) designated as the spatial detection limit from which a

sufﬁ cient signal can be obtained. Obviously, the point resolution cannot

be less than the spatial detection limit. It becomes clear from Figure

3–14 that the spatial resolution of an SEM is different for each signal

since the size of the signal emitting volume as well as the signal inten-

sity depends on the type of signal selected.

The important “quality parameters” such as spatial resolution, astig-

matism, and SNR of SEM images, as well as drift and other instabilities

that occur during imaging, can be determined most reliably and objec-

tively by Fourier analysis of the recorded micrographs (Frank et al.,

1970; Reimer, 1985). Recently, a program SMART (Scanning Micro-

scope Analysis and Resolution Testing) became freely available, which

allows the SEM resolution and the imaging performance to be mea-

sured in an automated manner (Joy, 2002). It should be mentioned in

the context of resolution that the ultimate resolution of an SEM speci-

ﬁ ed by the manufacturers is determined by imaging a test sample (gold

or gold–palladium-coated substrate with a low atomic number).

However, such samples are quite atypical compared to those usually

investigated, thus the resolution determined in this way is not properly

representative of the routine performance of the SEM. At present, con-

ventional SEMs using a heated tungsten or lanthanum hexaboride

emitter as the electron source have a speciﬁ ed resolution in the range

of 3–5 nm at an acceleration voltage of 30 kV.

2.3.1 Topographic Contrast

Presumably the SEM is most frequently used to visualize the topo-

graphy of three-dimensional objects. The specimen topography gives

rise to a marked topographic contrast obtained in secondary and back-

scattered images. This contrast has a complex origin and is formed in

SE images by the following mechanisms:

1. Dependence of the SE yield δ on the angle of incidence θ of the

electron beam at the local surface element [cf. Eq. (2.31)]. The tilt angle

of the local surface elements is given by the topography of the sample.

184 R. Reichelt

2. Dependence of the detected signal on the angular orientation of

the local surface element related to the ET detector (see Section 2.1.3).

SE generated “behind” local elevations, in holes, in ﬁ ssures, or in cavi-

ties reach the ET detector incomplete. This causes a more or less pro-

nounced shadow contrast (cf. Figure 3–7a).

3. Increase of the SE signal when diffusely scattered electrons pass

through an increased surface area. This is the case at edges or at pro-

truding surface features, which are smaller than the excitation volume.

Electron diffusion leads to overbrightening of edges and small surface

protrusions in the micrograph and is known as an edge effect.

4. Charging artifacts with objects of low electric conductivity.

Contributions (1) to (3) are illustrated by SE micrographs of different

specimens shown in Figures 3–23a and 3–24a as well as schematically

by proﬁ les of the topography and the related SE signals in Figure 3–25.

In these ﬁ gures the direction to the ET detector is indicated. The ball

in Figure 3–23a shows a contrast, which is mainly due to the varying

angle θ of beam incidence across the ball [cf. (1) above] and the angular

orientation of the local surface elements related to the ETD [cf. (2)

above]. The collection efﬁ ciency of the ETD is signiﬁ cantly higher for

surface elements facing the detector than for those on the back (shadow

region). Whereas the intensity of emitted secondary electrons of the

ball reveals radial symmetry, the effect of detection geometry causes

the nonradial symmetric image intensity distribution of the ball (cf.

Figure 3–25a–c). The rim of the ball is bright in the SE image because

of the enhanced SE emission due to an incidence angle θ ≈ 90° and the

effect of diffusely scattered electrons passing through an increased

surface area [cf. (3) above]. The radius of the ball is larger than the

electron range R (cf. Figure 3–14) therefore the latter effect occurs just

near the rim of the ball. If the mean radius of ball-like particles becomes

comparable or smaller than the electron range, diffusely scattered elec-

trons generate more SE over the whole particle surface, thus the SE

emission typically is distinctly enhanced (small particles are marked

by small arrowheads in Figures 3–23a and 3–24a). If the shadow con-

trast is visible in the image and the direction toward the ETD is known

then elevations and depressions clearly can be readily identiﬁ ed (cf.

Figure 3–23a). Another way to distinguish elevations and depressions

is to record and to analyze SE stereopairs.

The SE micrograph of large crystal-like particles (Figure 3–24a) basi-

cally shows the same contrast mechanisms as discussed above but with

a more complex structured sample than the ball. The individual ﬂ at

surface planes of the crystal-like particles occur with almost constant

brightness because of the constant angle of beam incidence and the

constant detection geometry (provided that there is no shadow effect

from other large particles). Some surface planes possess ﬁ ssures of

different size, which typically appear rather dark because just a minor

fraction of the generated SE can escape from inside the ﬁ ssures. In such

cases SE can be extracted either by a positively biased grid in front of

the specimen (Hindermann and Davis, 1974) or by a superimposed

magnetic ﬁ eld in which the SE follow spiral trajectories around the