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

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Chapter 4 Analytical Electron Microscopy 285

The emission current density J for thermal sources is related to the

material and the operation temperature T and follows the Richardson’s

law

J = AT

exp(−φ/KT) (2)

where A is a constant of the material (the Richardson constant given

in units of A/cm

), and φ is the workfunction. The ﬁ eld emission

current is related to the tunneling process and thus to the electric ﬁ eld

at the tip. For Schottky emission, the workfunction is effectively reduced

by a factor ∆φ due to the strong electric ﬁ eld applied to the tip and

becomes

φφφφ πε

eff

=− =−∆ eeE4

where E is the electric ﬁ eld (in

the order of 10

V/m) , ε

is the vacuum permittivity, and e is the electron

charge. This reduction of the workfunction arises from the well-

established Schottky effect (e.g., Solymar and Walsh, 2004) that effec-

tively increases the emission current by a factor exp(∆φ/kT) (Egerton,

2005) due to the negative term in the exponential factor in Richardson’s

law [Eq. (2)]. The temperature of the source will affect the temporal

coherence of the source and the energy spread of the electrons due to

thermal energy. The source size and the angular spread α will affect

the spatial coherence. Considering the source size, the temperature of

the source, the vacuum requirements, and the brightness, the sources

can be compared (Table 4–3).

It is possible to comment on the merits of the various electron sources

for AEM. The high brightness of the cold FEG makes it the ideal tool

for analytical work requiring a small probe. Minimal source demagni-

ﬁ cation is required as the source size is in the order of 10 nm although

the ultimate probe size and shape will depend on electron optical

considerations related to aberration of the probe forming optics (see

below). An additional advantage of the cold FEG is the low energy

Table 4 –3. Comparison of sources.

Schottky

emission Thermal FEG Cold FEG

Thermionic Thermionic FEG (ZrO on W (100) (W single

Characteristic W hairpin LaB

W crystal) orientation crystal)

f (eV) 4.5 2.7 2.8 4.5 4.5

(A/m

) ª10

ª10

–10

ª10

a (rad) ª10

-2

ª10

-2

ª10

-3

ª10

-3

–10

-4

ª10

-4

d (mm)

ª50 ª10 ª0.02–0.03 ª0.01–0.1 ª0.01

Brightness [A/(m

sr)]

ª10

–10

ª10

–10

Temperatu re (K) 2700 1800 1800 1600 300

Energy spread (eV) 1–3

0.6–2

0.6–1.5

0.6–0.8 0.3

Vacuum (Pa) 10

-2

-4

-7

-8

Speciﬁ c values depend on the exact tip conﬁ guration.

The brightness values are given for 100-keV electrons and scale linearly with accelerating voltage. The reduced

brightness is given by B/V (where V is the accelerating voltage in volts).

The energy spread is dependent on the operation condition of the gun (the bias of the Wehnelt, ﬁ lament heating

current, or the extraction voltage of the Schottky FEG).

286 G. Botton

spread of the electron source allowing, in principle, detailed analysis

of the energy loss near-edge structures in EELS spectra. Although the

ultimate brightness of the Schottky sources is lower by about one order

of magnitude, the practicalities of the less stringent vacuum and demon-

strated reliability have made the Schottky guns very common within

the AEM ﬁ eld. Worth mentioning is the fact that the total current might

be a more important parameter for some AEM analysis techniques

such as energy-ﬁ ltered imaging when a large ﬁ eld of view needs to be

illuminated (with enough current per individual pixel in a map). In

that case, the thermionic emission sources (LaB

in particular) provide

very large total currents. New research is in progress to develop alter-

nate even brighter sources by exploiting low workfunction materials,

carbon nanotube electronic properties (Fransen et al., 2005), and semi-

conductor p–n junctions.

Once the electrons are accelerated by the anode stack to the high-

voltage potential of the TEM, the condensing optics demagniﬁ es (Figure

4–12) the source image in the plane of the sample. In this chapter we

will not describe the various aberrations and defects of lenses but refer

the reader to other chapters in this book. We remi nd the reader, however,

that all round electromagnetic lenses have positive spherical aberration

coefﬁ cients C

(in the order of C

= 0.5–1.0 mm for high-resolution micro-

scopes offering limited sample tilt and a small polepiece gap and

around C

= 1.5–3 mm for large tilt and large polepiece gaps). Electro-

magnetic lenses also suffer from chromatic aberrations C

in the order

of C

= 1–2 mm and that, just as in light optics, the wave nature of elec-

Figure 4–12. Schematic

diagram of a ﬁ eld emission

electron gun with gun anodes

(also called gun lens) and the

accelerating anodes (acceler-

ating the electrons up to

the accelerating voltage of

the TEM). The illumination

system consists of condenser

lenses (C

, C

) and the

objective lens (OL). See the

text for function details.

Chapter 4 Analytical Electron Microscopy 287

trons imposes a diffraction limit to the resolution as imposed by the

Rayleigh criterion. Given these imperfections of the lenses and wave

nature of electrons, the probe size at the specimen level d

is limited not

only by the demagniﬁ ed image source size d

but also by a combination

of the aberration of the illumination system (spherical and chromatic)

and the diffraction limit of the probe-forming aperture all added in

quadrature (Spence and Zuo, 1992; Reimer, 1984)

= d

+ d

(3)

where d

is the demagniﬁ ed source image, d

= 0.6λ/α is the diffraction

limit broadening, d

= 0.5 C

is the spherical aberration broadening,

= (∆E/E

α is the chromatic aberration contribution of the probe

forming lens, d

= 2α∆f is the defocus contribution to a small defocus

error where α is the convergence half-angle at the specimen determined

by the condenser C

aperture limiting the probe and ∆f is the defocus

of the probe forming lens. The size of the unaberrated probe source

image d

is related to the deﬁ nition of brightness that, as mentioned

above, is constant through the illumination system (from the gun to the

sample) and is determined as

dIB

(

)

2 πα

where I

is the beam

current. Calculations of the unaberrated source size therefore assume

that the current at the sample is known (or can be measured).

Equation (3) assumes incoherent illumination, i.e., all electrons at the

aperture are not in phase and every point within the aperture can be

considered as an independent source. Strictly speaking, this assump-

tion is not valid for high brightness ﬁ eld emission sources (and for

particular operating conditions of thermionic electron sources) and it

is necessary to deﬁ ne the conditions where incoherence in illumination

applies to determine the conditions of validity of Eq. (3) for the calcula-

tion of the probe size. Due to the various aberration terms in Eq. (3)

there is an optimum probe size as a function of the illuminating angle.

Plots for two microscope conﬁ gurations and sources are shown in

Figure 4–13 for a high-resolution microscope conﬁ guration—not dedi-

cated to analytical work but for designed optimum imaging resolution

(low tilt angle in the specimen area: ±20–24°)—and for a high-tilt ana-

lytical conﬁ guration (±35–40°). It is clear that the use of FEG allows

smaller probes. Based on the equations above and typical gun bright-

nesses for Schottky guns, it is possible to calculate the probe current

dependence with probe size, calculated based on the incoherent illu-

mination condition, for an FEG and an LaB

source (Figure 4–14). We

also demonstrate the effect of reducing the spherical aberrations in the

probe-forming lens using the recently developed correctors in a cold

FEG-scanning transmission electron microscope (STEM) operating at

100 kV based on the data reported in the literature (Dellby et al., 2001)

(Figure 4–15). For the latter case, Eq. (3) needs to be modiﬁ ed to account

for the limited residual aberrations (see Chapter 2, this volume; Dellby

et al., 2001).

As discussed above, the coherence of the source is a key concept that

needs to be considered for high-brightness ﬁ eld emission sources and

analytical microscopy. In conditions of coherent illumination all elec-

trons can be considered to be emitted by a single point source and all

288 G. Botton

Figure 4–13. Variation of the electron

probe size for analytical TEM work as a

function of the illumination aperture

convergence for instruments equipped

with different electron sources and

lenses.

Figure 4–14. Variation of the electron

beam current with electron probe size

for two instruments equipped with a

thermionic source and Schottky FEG.

Figure 4–15. Variation of the probe current as

a function of probe size for a conventional cold

ﬁ eld emission source dedicated scanning trans-

mission electron microscope and an aberration

corrected cold-FEG microscope. (From Dellby

the Japanese Microscopy Society.)

Chapter 4 Analytical Electron Microscopy 289

are in phase in the illuminating aperture and on the electron wavefront

at the sample. This condition implies that interference effects between

electrons can occur. A detailed discussion on coherence and sources

can be found in Spence and Zuo (1992) and we summarize the key

elements of coherence relevant to the discussion on the probe size for

the purpose of discussing the ultimate limits of the instrumentation.

Following the concepts developed in classical optics, it is necessary to

consider the transverse coherence width X

concept related to the width

of the electron beam in the plane of the condensor aperture X

λ/(2πθ

) = f

λ/(πd

) where θ

is the angular width of the probe of size

(i.e., not the convergence angle) as subtended at the condensor aper-

ture (Figure 4–16). This angle can be determined geometrically given

a probe size d

and focal length f

of the probe-forming lens. Source

points in the aperture plane closer than X

can interfere as in a slit

experiment with coherent light. This transverse coherence term must

be compared with the diameter of the probe-forming aperture D

determine if the illumination is coherent or not. If X

<< D

, the aper-

ture is incoherently illuminated and all points in the illumination

aperture can be considered as emitting independently. Still, for a given

aperture of convergence angle α incoherently ﬁ lled, the coherence

width will be X

= λ/(2πα). Object points at the sample separated by a

distance smaller that X

will be illuminated coherently and will give

rise to interference effects.

In the other extreme, if X

> D

, the aperture is coherently ﬁ lled and

the electron wavefront illuminating the sample will be in phase. For

example, for the smallest probe in an FEG (say 0.2 nm), a C

aperture

of 5 µm would be coherently ﬁ lled. At 200 keV, for a LaB

emitter and

a probe size of about 3 nm, one would need an aperture of 0.5 µm for

the coherence criterion to be fulﬁ lled. By changing the illumination

conditions (demagniﬁ cation of the source and reducing the accelerat-

ing voltage) and the condenser aperture, the coherence illumination

condition could be achieved even for thermionic sources as demon-

strated by Dowell and Goodman (1973).

In coherent illumination conditions, the terms contributing to the

determination of the probe size cannot be added incoherently as inde-

Figure 4–16. Factors entering

the description of the source

coherence for illumination of

samples. (Adapted from Spence and

Zuo, 1992.)

290 G. Botton

pendent contributions [as done in Eq. (3)] and detailed calculations

based on the incident electron wavefunction and the transfer function

of the objective lens must be carried out. It has been demonstrated that

with the judicious choice of defocus of the probe forming lens, sub-

Ångstrom electron probes can be obtained even without aberration

correctors (Nellist and Pennycook, 1998) to improve imaging resolution

albeit with very small currents and tails to the intensity distribution

containing up to 50% of the beam current. Such beams, although rele-

vant for optimal imaging resolution, are therefore not suitable for ana-

lytical work. Optimum probe sizes (Mory et al., 1987) for analytical work

are achieved with convergence α

and defocus ∆f conditions deter-

mined by α

= 1.27 C

−1/4

1/4

and ∆f = −0.75 C

1/2

. In these optimal

conditions, the probe size containing 80% of the intensity is d

(80%)

0.4 C

1/4

3/4

. For aberration corrected instruments these terms need to be

revised to correctly treat the contributions of the residual aberrations

as discussed in Dellby et al. (2001) and in Chapter 2 (this volume).

2.2 Electron Optic Conﬁ guration

In the discussion so far we have made abstraction of the technical

aspects necessary to achieve the demagniﬁ cation of the source required

for small probe analysis and the need to provide, with the same system,

illumination at the sample for conventional imaging and energy-

ﬁ ltered microscopy. Modern instruments capable of conventional TEM

and STEM are based on the double condensing optic system (C

+ C

)

with the addition of a supplementary weaker condenser lens C

(called

“condenser minilens” or “minicondenser”) and a strong magnetic ﬁ eld

before the sample (i.e., a preﬁ eld) generated by an objective lens (OL)

composed of two parts: an upper lens and a lower lens surrounding

the sample (Figure 4–17). “Parallel” illumination at the sample plane

is achieved by a combination of C

and C

yielding, at the focal point

of the objective lens, a convergent beam that is then made parallel by

the strong upper objective lens ﬁ eld (Figure 4–17a). A small probe

required for analytical work or for STEM imaging and analysis in

STEM mode is obtained by effectively optically switching the C

off

(using various schemes depending of the exact location of the C

lens)

and by making use of the strong OL preﬁ eld (of the upper objective

lens) to achieve large convergence angles and large source demagniﬁ -

cation (Figure 4–17b). Practically speaking, this mode of operation is

called the nanoprobe or energy-dispersive spectrometry (EDS) mode.

STEM operation for these microscopes is achieved in exactly the same

electron-optical conﬁ guration. FEGs (cold and Schottky) have an addi-

tional electrostatic gun lens (Figure 4–12) leading to additional demag-

niﬁ cation of the source and more ﬂ exibility in the gun operation. The

strength of the C

lens determines the fraction of electrons (hence the

current) that will enter the C

aperture and the demagniﬁ cation of

the source. A strongly excited C

lens will give rise to larger demagni-

ﬁ cation and, conversely, a weakly excited C

lens will result in a smaller

demagniﬁ cation and more current entering the C

aperture. In this

ﬁ xed operation mode, changes in the convergence angle are achieved

Chapter 4 Analytical Electron Microscopy 291

by changing the physical aperture size (using a strip aperture contain-

ing four to eight apertures, including a top hat Pt aperture for analyti-

cal work—see Sections 2.3.6 and 7.2 on instrumental contributions in

EDXS analysis). Continuous change in convergence is achieved by

controlling the strength of the C

lens and OL preﬁ eld or/and addition

of a third condenser lens.

The electron optical conﬁ guration required for STEM imaging and

analysis is achieved, in a TEM-STEM instrument capable of both opera-

tion modes and, as discussed above, with the combination of the C

lens optically switched off and the subsequent focus of the nearly par-

allel beam into a small source image by the upper OL ﬁ eld. The scan-

ning operation of the beam over the sample is carried out by deﬂ ection

coils located before the specimen (optically before the upper objective

lens) so that the beam is shifted (but not tilted) on the specimen plane

(Figure 4–18). As the beam is rastered pixel by pixel over the area of

sample of interest, various signals (including analytical information)

can be recorded sequentially at each position to form images and ele-

mental maps based on analog or digital signals recorded synchro-

nously (e.g., bright-ﬁ eld, secondary electrons, backscattered electrons,

annular dark-ﬁ eld electrons, and EELS, EDXS, etc). Dedicated com-

mercial STEM instruments (offering no TEM operation mode) built by

the company Vacuum Generator in the 1980s and 1990s have tradition-

ally been equipped with cold FEG and, in the later models, operate

with a gun lens, two condenser lenses, and an asymmetric objective

lens (no imaging lenses are necessary). Their design is based on the

gun located at the “bottom” of the microscope column for stability

reasons with the detectors at the “top.” New commercial instruments

Figure 4–17. Electron optical

conﬁ guration of the illumina-

tion system of a double-objective

lens system. Conﬁ guration (a)

describes the formation of paral-

lel illumination while conﬁ gura-

tion (b) describes the conditions

needed to achieve a highly

convergent and small focused

electron beam.

292 G. Botton

developed based on the same approach and equipped with aberration

correctors are in development (Krivanek, 2005). Dedicated STEM

instruments based on the upper portion of a conventional TEM column

(but in this case without imaging lenses) are also available. These

instruments are designed for quick and simple operation particularly

popular for routine analysis in device fabrication environments.

As supplementary information, we should brieﬂ y note that the pro-

cesses of image formation and interpretation in STEM mode and TEM

mode are closely linked by the reciprocity theorem further discussed

in Chapter 2 (this volume) and earlier references (Cowley, 1986;

Humphreys, 1979). This principle links the electron source in STEM to

a detector point in the TEM image (pixel on a camera or negative plate)

and the detector in STEM to the source of electrons in TEM. Effectively,

the principle states that for identical optical components, sources, and

detectors, STEM and TEM images will show the same resolution, and

contrast. Given the respective strengths and weaknesses of these tech-

niques (related to the ﬁ eld of view, recording time, dose, sequential

recording, and analytical signals) the techniques should be considered

Figure 4–18. Electron optical conﬁ guration for STEM operation showing the

role of the deﬂ ection coils in shifting the electron beam over the sample

(without tilt of the beam) and the detection of signals on the dark-ﬁ eld STEM

detectors and bright-ﬁ eld or energy-loss spectrometer. (Adapted from Gross

et al., 1987.)

Chapter 4 Analytical Electron Microscopy 293

as complementary and not competitive (Cowley, 1986). Practically, this

implies that materials analysis, and AEM in particular, should involve

all possible optimized techniques and instrumentation both for TEM

and STEM approaches. As demonstrated in the case of EELS analysis,

energy-ﬁ ltered imaging carried out in the TEM mode is highly comple-

mentary to the scanning EELS imaging method with both approaches

offering advantages and presenting limitations (Section 6).

2.3 EDXS Detector Systems

2.3.1 The EDXS Detector

In AEM experiments, photons are emitted in the sample following

ionization of atoms by the primary incident electrons and subsequent

deexcitation process. The energy of these photons is in the X-ray part

of the electromagnetic spectrum (a few hundred electronvolts to a few

tens of kiloelectronvolts) and we therefore refer to them as X-rays. In

the analytical TEM, the most common and effective tool for the detec-

tion of X-rays is the energy-dispersive detector that is attached to the

microscope column (refer to Figures 4–2 and 4–19) with the active

component detecting the X-rays located as close as possible to the

sample. Alternative approaches to detect X-ray signals with wavelength

dispersive detectors have been attempted in prototype systems but

have not been commercially implemented due to low efﬁ ciency (serial

analysis of X-rays energies) and compatibility with the geometry of the

microscope column (solid angle, vacuum etc.). The key component of

the energy-dispersive X-ray detector is a semiconductor material (Si or

Ge) that absorbs incident photons by generating electron hole (e–h)

Figure 4–19. Schemat-

ics of a commercial

EDXS detector showing

the detector front, the

Dewar system to cool

the detector, and various

components that are

interfaced in the elec-

tron microscope. (Cour-

tesy of N. Rowlands,

Oxford Instruments.)

(See color plate.)

294 G. Botton

pairs through photoelectric effect. When this process occurs in an

electric ﬁ eld, a current pulse is generated and subsequently measured

by low-noise electronic components. Detectors based on Si are more

commonly used in AEM because of the lower cost than Ge-based

detectors (described below). Due to the fact that very high purity Si

crystals are not available, Li additions in Si are used to compensate for

residual impurity dopants that would create undesirable recombina-

tion sites for electronhole pairs and uncharacteristic current related to

the existence of impurity-generated acceptor levels (thus holes in the

valence band). The Li role in the so-called Si(Li) detectors is therefore

to effectively create an intrinsic semiconductor region where e–h pairs

generated by the incident photons produce a current ﬂ ow that can be

measured. Incident photons generate e–h pairs at the rate of 1 pair/

3.8 eV. The number of e–h pairs generated in the “active layer” of the

detector is thus proportional to the incident photon energy (which is,

in turn, related to the energy level involved in the transitions following

ionization of the atom by the incident electron beam). For Ge detectors,

high-purity crystals can be obtained and Li additions are not

necessary.

The electric ﬁ eld in the detector necessary to cause the current ﬂ ow

is generated by metallic contacts (Au) (Figure 4–20) on the front and

back surfaces of the crystals (typically 3 mm thick) and the application

of a bias (0.5–1 kV) between the front and back of the detector with

electrons traveling to the positive electrode and holes to the negative

electrode. Some loss of charges occurs, however, in proximity of the

contacts due to recombination in the charges near the metallic contact

(about 200 nm in width). These regions are typically referred to as

“dead-layers” in the literature as they do not contribute to the genera-

tion of signal and transfer of charge. The thickness of the crystal is

normally large enough to convert all the photons to e–h pairs but for

Figure 4–20. Diagram of

an EDXS detector demon-

strating the various ele-

ments of the detector

contacts, the dead layer,

and the preampliﬁ er.

(Adapted from Woldseth,

1973.)