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

Подождите немного. Документ загружается.

Chapter 4 Analytical Electron Microscopy 305

therefore parallel detectors were developed in the late 1980s (Krivanek

et al., 1987) to record a portion of the spectrum of 1024 energy channels.

For this early technology, the slit is replaced by a series of multipole

lenses (three quadrupoles) to focus and magnify the spectrum (Figure

4–28). These optical elements change the prism dispersion (from about

1.8 µm/eV at 100 keV) to up to 1 mm/eV at the detector plane (Krivanek

et al., 1987). Incident electrons are converted to photons using a scintil-

lator material (e.g., YAG) and a photodiode array (with 1024 channels)

is used as the recording system with acquisition times as short as 25 ms.

Recent commercial spectrometers have more complex optics (better

focusing capability and aberration correction of the magniﬁ cation

lenses), new scintillator materials with improved transfer function,

and improved transfer of the generated light between the scintillator

and detector. Fast-readout two-dimensional arrays (now about 100 ×

1200 pixels) allow acquisition of more than 100 spectra per second in

commercial systems (the ENFINA spectrometer from Gatan). Noncom-

mercial systems have achieved the same readout performance and

used optical lenses to transfer the signal generated in the scintillator

to two-dimensional (2D) detectors (Tencé, 2002).

For the acquisition of energy-ﬁ ltered images using postcolumn ﬁ lters,

a series of multipole lenses (Figure 4–29) is used to transform the spec-

trum at the slit plane back to an image (or diffraction pattern) at the

detector plane and to correct the image distortions and aberration. This

“transformation” is possible because both the in-column ﬁ lter and the

postcolumn prism are electron optical components that produce, at the

dispersion plane, spectra that contain information on the object that

Figure 4–28. Schematic diagram of the parallel EELS spectrometer. (Adapted

from Krivanek et al., 1987.)

306 G. Botton

enters the spectrometer. The slit allows selection of the electrons with

the energy loss of interest, which is subsequently used to form an

image at the detector plane. As for the in-column ﬁ lters, both images

and diffraction patterns can be obtained in the detector plane of post-

column ﬁ lters depending on whether an image or diffraction pattern

is projected at the entrance plane of the spectrometer. Worth mention-

ing is the use of ﬁ lters to remove inelastically scattered electrons from

diffraction patterns (Figure 4–30) of thick samples to enhance the vis-

ibility of the dynamic structure in the convergent beam disks and to

retrieve quantitative information on structure factors (Saunders, 2003).

Further details of the optical function, aberration of the spectrometers,

and ﬁ lters have been described extensively (Rose and Krahl, 1995;

Krivanek et al., 1991a, 1995a; Egerton, 1996).

Figure 4–29. (a) Postcolumn imaging ﬁ lter (Gatan Imaging Filter GIF);

schematic diagram of the electron optics components and detection system

(top diagram). (Adapted from Krivanek, Gubbens et al., 1991a.) (b) Actual

spectrometer [Gatan’s GIF 2000 series spectrometer (Tridiem model)] and

components (bottom diagram). (Courtesy of M. Kundman, Gatan.) (See color

plate.)

Chapter 4 Analytical Electron Microscopy 307

Alignments in postcolumn ﬁ lters are carried out using automated

routines tuning the multipole lenses functions so as to minimize dis-

tortions, aberrations, and the uniformity of the energy within the ﬁ eld

of view so that every point in an image corresponds to the same energy

loss (the isochromaticity). The detection of images in postcolumn ﬁ lters

can only be carried out using scintillators and CCD cameras.

From a practical point of view, in-column energy ﬁ lters offer the

advantage that energy-ﬁ ltered images can be directly observed on

the microscope viewing screen while the postcolumn ﬁ lters offer the

advantage of being added to a microscope column as a optional attach-

ment. As various implementations and models of in-column and post-

columns exist, a detailed comparison of the two ﬁ ltering techniques

should be carried out cautiously based on the type of application of

interest and thus the speciﬁ c relevant parameters for that application.

2.4.2 New Developments: Monochromators

Based on the interest in energy loss near edge structures and for the

purpose of increasing the temporal coherence terms of the imaging

transfer function, the energy spread of the electron energy source must

be decreased. One approach is to use electron guns with narrower

energy distribution (e.g., see Table 4–1 in Section 2.1). This approach is

limited to about 0.3 eV energy distribution with cold FEG as measured

at the FWHM of the energy distribution. For cold FEG, the distribution

is nonsymmetrical due to the nature of the tunneling process, which

follows a Fowler–Nordheim distribution. Although this energy width

allows the acquisition of good quality energy loss spectra where the

intrinsic broadening of the features is in the order of 0.3 eV or greater,

there are cases when spectra obtained with electrons having a nar-

rower energy distribution is of interest (Terauchi et al., 1999; Egerton,

a) b)

Figure 4–30. Energy-ﬁ ltered electron diffraction pattern of Si (110) orientation. (a) Pattern recorded

by selecting only the electrons that have lost no energy (Zero-loss ﬁ ltering) and (b) pattern recorded

without energy ﬁ ltering.

308 G. Botton

2003; Lazar et al., 2003; Mitterbauer et al., 2003). This can be achieved

with gun monochromators and improvements in microscope stability

and spectrometer resolution (Barfels et al., 2002). Improvements in

energy resolution to 0.1 eV have been obtained in recent commercial

instruments based on various approaches (Figure 4–31). Three types

of monochromators have recently been developed commercially based

on the Wien spectrometer (Tiemeijer et al., 2001), the double focusing

Wien spectrometer (Tanaka et al., 2002), and the omega-type ﬁ lter

(Uhlemann and Haider, 2002). The effect of monochromation on the

energy distribution of the incident electrons is shown in Figure 4–32

and on spectra in Figure 4–33.

2.5 Sample Preparation Requirements

Although the quality of the microscope and of the vacuum are key

elements of good AEM work, sample preparation and cleanliness are

certainly factors affecting the quality of the data. To avoid sample

contamination buildup under the electron beam, plasma cleaning of

the samples with dedicated systems prior to insertion into the TEM

column has become a routine practice. This technique gently burns off

all hydrocarbons built up on the surface of the sample so that diffusion

of the species during analysis in the TEM is no longer possible. An

alternative to this approach is to gently heat the samples prior to inser-

tion on the TEM with a halogen lamp in vacuum (it is possible to build

such a system with off-the-shelf vacuum components) at temperatures

of about 70–80°C. Although this technique does not replace the plasma

cleaning approach, it is a solution for samples that might be sensitive

Figure 4–31. Various implementations of monochromators in commercially available instruments.

Left: The FEI monochromator, single Wien ﬁ lter. (Courtesy of P. Tiemeijer, FEI Company.) Center: The

JEOL monochromator double-Wien ﬁ lter. (Courtesy of JEOL Ltd.) Right: The lectrostatic omega ﬁ lter

implemented in the Libra Zeiss microscope. (Courtesy of M. Haider, CEOS GmbH.) (See color plate.)

Chapter 4 Analytical Electron Microscopy 309

to the reactive gases used in the plasma process and often solves

contamination problems due to the sample. Samples permitting,

alternatives are also low-energy milling (a few hundred electronvolt

ions) prior to sample insertion (with regular mills or dedicated low-

energy systems). Cooling samples in a dedicated cryogenic analytical

holder in the TEM also reduces the contamination buildup during

Figure 4–32. Zero-loss peaks

obtained with a monochromator

switched on using a Schottky FEG

source (with stabilized electronics);

the same instrument with the

monochromator switched off and

with a cold-ﬁ eld emission source

(VG-STEM).

Figure 4–33. Effects of a monochro-

mator on the visibility of peaks of

the Ti L

edge in CaTiO

. Clearly

resolved are the small triplet states

in front of the ﬁ rst strong peak.

310 G. Botton

analysis but at the expense of increased drift rate during very long

analyses.

Removal of the amorphized layer produced by ion milling has become

an increasingly common approach as ever thinner samples are used to

achieve the ultimate spatial resolution in analysis. A combination of

mechanical polishing and low-energy milling has proved excellent for

obtaining very clean samples and minimal amorphous damage. Several

manufacturers offer these new approaches to improve the quality of

the samples. Often these methods make the difference between suc-

cessful work, major scientiﬁ c breakthrough, and plain disaster!

2.6 New Developments in Electron Optics

In recent years, there have been signiﬁ cant developments in electron

optics that have led to a new generation of instruments with much ﬁ ner

probe-forming capabilities making use of aberration correctors (Section

2.1 and this volume, Chapter 2). Although there is emerging literature

making use of these capabilities, particularly with EELS systems (Varela

et al., 2004; Arslan et al., 2005), results on EDXS are very limited at this

moment in the open literature (e.g., Watanabe and Williams, 2005b;

Watanabe et al., 2005). The main advantage of the aberration corrector

of the probe-forming lens for AEM purposes is not the ability to form

smaller probes (although a positive advantage) but rather the signiﬁ -

cant increase in electron beam current for a given spot size (see Figure

4–15). It is exp ec ted t hat the l au nc h of com me rc ial in st r ument s eq uippe d

with such correctors will result in a dramatic improvement in the

analytical performance of new AEMs. There will be new limitations,

however, facing the users as electron beam damage will undoubtedly

be the ultimate barrier in the analysis of most interesting materials.

3 Fundamentals

3.1 Fundamental Processes of Elastic and Inelastic Scattering

The interaction of primary electrons with electrons and nuclei in the

solid results in various scattering processes and the generation of

signals that can be detected in different analysis tools such as the TEM,

the scanning electron microscopes, or surface analysis instruments. We

can subdivide these processes into elastic and inelastic based on the

energy changes of the primary incident electrons following the scat-

tering event. Elastic scattering causes no detectable change in the

energy of the primary electrons within the resolution of the measure-

ment system typically available in the TEM. These processes do not

give rise to “analytical” signals in the strict sense of the term but are

nevertheless very relevant to the understanding of signal generation,

imaging, and all discussions on spatial resolution as they signiﬁ cantly

affect the angular distribution of the incident electrons, their propaga-

tion in the solid, and consequently the spatial spread of these electrons

as they travel through the sample. Elastic scattering is at the basis of

contrast mechanisms in TEM and STEM imaging and can directly

Chapter 4 Analytical Electron Microscopy 311

affect the interpretation of energy-ﬁ ltered images. Furthermore, the

powerful technique of Z-contrast imaging (see Chapter 2, this volume)

is based on signals generated by electrons elastically scattered at high

angles. The technique is commonly used in combination with analyti-

cal measurements using EELS or X-ray microanalysis and provides

indirect information on changes in average atomic number within the

area illuminated by the electron beam. Although traditionally this is

not considered an analytical technique, this imaging method com-

bined with spectroscopic measurements such as EDXS and EELS pro-

vides the most powerful ability to analyze materials with the highest

spatial resolution.

Inelastic processes are the key to all analytical measurements as they

directly and indirectly give rise to the signals detected. Figure 4–34

summarizes the various energy loss processes generating the excita-

tion and the subsequent signal generation processes by deexcitation.

Analysis techniques focus, on the one hand, on the detection of the

primary event of energy loss where excitation of single electrons from

strongly bound core energy levels (inner-shell ionization) and weakly

bound electrons (from the valence band) occurs. These excitations

cause transitions of electrons from the deep bound states to levels just

above the Fermi energy and the continuum. Energy losses for the

primary electrons can also occur through collective excitation of weakly

bound valence electrons in the solid behaving as an electron gas

(known as plasmon excitations) (Figure 4–34) or from defect states

within the gap of a material. In the case of EELS, the energy losses of

the primary electrons range from a few electronvolts to tens of elec-

Figure 4–34. Various processes of inelastic scattering events from core levels,

valence states, and defect states. Inelastic processes via collective excitation of

valence electrons is also possible. Measurement of the energy losses of the

primary electrons is possible with EELS. The deexcitation processes give rise

to X-ray and Auger signals.

312 G. Botton

tronvolts (typically up to 50–60 eV) in the case of single electron valence

excitation and plasmon losses while core losses range from a few tens

of electronvolts (typically down to 30 eV) up to a few kiloelectronvolts

for the core losses with signiﬁ cant overlap between these regions.

Other processes of inelastic scattering leading to detectable signals in

the spectra include the excitation of quasi-free single electrons (also

known as Compton scattering) and losses due to radiative phenomena

(Cerenkov effect).

On the other hand, secondary processes give rise to other signals

(Figure 4–3) used in analytical techniques. The deexcitation process

leads to the generation of photons detected with EDXS or Auger elec-

trons with related characteristic energies.

3.2 Elastic Cross Sections

As discussed above, some theoretical background on elastic scatter-

ing is useful to understand electron propagation in the sample and the

related contributions on inelastic signal generation. A good under-

standing of elastic scattering is particularly useful to simulate electron

trajectories and to estimate the electron beam broadening and thus the

spatial resolution in analytical measurements. We will follow the

description given in detail by Reimer (1995) and Egerton (1996) using

the terminology adopted by R.F. Egerton.

The differential elastic cross section dσ/dΩ representing the proba-

bility of scattering per unit solid angle dΩ is given by

Ω

(6)

where the amplitude of the scattering factor f is directly proportional

to the Fourier transform of the potential of the atom. Various models

and approximations of the potential can be used. In its simplest form,

the potential considers the unscreened electrostatic Coulomb potential

of type

()

πε

(7)

for a free atom yielding the Rutherford cross section

σγ

Ω

(8)

where a

is the Bohr radius, γ is the relativistic factor [γ

= (1 − v

)

−1

q = 2k

sin (θ/2) represents the amplitude of the scattering vector q

shown in Figure 4–35, h

= γm

v represents the momentum of the

incident electron, q is the scattering vector deﬁ ned in Figure 4–35, and

is the momentum given to the nucleus.

This ﬁ rst approximation of the unscreened electrostatic Coulomb

potential satisfactorily describes scattering for light atoms, for large

scattering angles and high incident electron energy (typical of TEM).

The model, however, needs reﬁ nements for elements of high atomic

number, for small scattering angles, and low incident energies (in low

Chapter 4 Analytical Electron Microscopy 313

voltage SEM, for example) due to a singularity in the cross sections at

θ = 0 arising from neglect of the screening. The Rutherford model can

be subsequently reﬁ ned by incorporating an exponential screening

factor used in the Wentzel atomic model

()

=−

(

)

πε

exp

(9)

where r

is the screening radius that can be estimated by r

= a

−1/3

This potential and the screening radius lead to a Lenz model of dif-

ferential cross section

σγ γ

θθ

Ω













≈

()

−

441

(10)

where θ

is the characteristic elastic scattering angle representing the

width of the angular distribution of elastic scattering.

The total scattering cross section is obtained by integrating Eq. (10)

over all scattering angles

πθθ

πγ

∫

Ω

sin

(11)

A more accurate model of the potential considering electron spin and

relativistic effects leads to the Mott cross section applicable to a large

range of atomic numbers, low voltages, and low scattering angles.

Based on the elastic cross sections and the number of atoms per unit

volume n

we can deﬁ ne a quantity called the elastic mean free path

= (σ

)

−1

(12)

which represents the mean distance between elastic scattering events

in a solid assumed, for simplicity, to be amorphous.

In crystals, the elastic scattering must account for diffraction effects

and the treatment of the electron distribution in the solid follows the

diffraction theory developed elsewhere in this volume. With the deve-

lopment of Z-contrast imaging as one of the tools available in the ana-

lytical electron microscope and use of this technique with electron

probes of diameter smaller than the unit cell, the characteristics of

electron beam propagation in the sample become important. Detailed

calculations with the multislice technique have shown that when a

Figure 4–35. Diagram for an

elastic scattering process.

314 G. Botton

small probe is positioned on an atomic column, electrons are chan-

neled along the column for samples of thicknesses up to a few nano-

meters. When the beam is positioned in between the columns it strongly

disperses and broadens while propagating in the sample (Dwyer &

Etheridge, 2003) (Figure 4–36). This effect is probe size dependent with

the channeling conditions being more relaxed with “larger” probes of

0.2 nm. Calculations show that the electron intensity builds up in the

adjacent columns as the electron beam propagates (Figure 4–36b). The

effect is demonstrated in other calculations (Voyles and Muller, 2004;

Mobus and Nufer, 2003) showing that the beam can channel on an

adjacent column and give rise to a signal even if not nominally on the

initial position (Figures 4–36b, 4–37b). Although these effects are not

part of the traditional AEM literature, they are becoming increasingly

relevant when the very smallest probes produced by aberration-

corrected instruments are used to achieve the ultimate spatial resolu-

tion in very thin samples (Section 5.1).

3.3 Inelastic Scattering Cross Sections

Before describing the cross sections of various inelastic processes, it is

useful to review the concept of the total inelastic cross sections so that

a comparison of elastic and inelastic scattering distributions can be

made. The total inelastic cross section is also relevant to understand

the process of energy losses that slow down the electrons in thin foils

or in bulk samples. This concept is useful in the modeling of electron

propagation in samples using Monte Carlo methods.

The differential inelastic cross section can be calculated by

σγ

Ω

=−

(

)

[]





















(13)

where γ, a

, and r

are as described in Section 3.2. As the scattering

vector q is energy loss dependent (Section 3.4), it is approximated for

the purpose of the evaluation of the total cross sections by

≈ k

(θ

+ θ

) (14)

where k

= 2π/λ = γm

v/h

is the magnitude of incident wavevector, θ is

the scattering angle, and θ

= E

–

/(γm

) is the characteristic scattering

angle corresponding to the mean energy loss E

–

As pointed out in Egerton (1996), the ﬁ rst term of the expression of

the total inelastic cross section [Eq. (13)] is similar to the Rutherford

elastic cross section with a second term being described by the inelastic

form factor.

Substitution of the scattering vector by the scattering angle leads to

the angular dependence of total inelastic scattering (Colliex & Mory,

1984)

σγ

θθ

θθθ

Ω

()

−

()













(15)

where θ

= (k

)

−1

is related to the elastic scattering distribution deﬁ ned

in Section 3.2. As demonstrated in Figure 4–38, the expressions for the