Graef M. Introduction to conventional transmission electron microscopy

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228 The transmission electron microscope

phosphor screen is about 50 µm (the smallest detail that can be resolved on the

screen depends on the phosphor grain size). The apparent image brightness on the

viewing screen depends on the microscope acceleration voltage (a higher voltage

corresponds to a dimmer image) and on the thickness of the lead glass viewing

window.

3.11.3 Photographic emulsions

Photographic emulsions are perhaps the most commonly used electron detectors.

Although digital detection systems are becoming increasingly important, it is doubt-

ful that photographic ﬁlm will be replaced completely in the near future by purely

digital systems. In this section, we will describe brieﬂy how a photographic emul-

sion reacts to an incident electron and how one may extract quantitative information

from the exposed and developed negative.

When an incident electron beam with current density j

hits a photographic

emulsion, then the total exposure E is deﬁned as the product of current density

(also known as illuminance) and exposure time τ:

E = j

τ.

The energy of the absorbed electrons locally converts at least one and often more

than one silver halide grains into metallic silver. Those regions of the emulsion that

have been converted to metallic silver are then developed, which essentially means

that the entire halide grain is converted to metallic silver by a suitable reducing

agent (i.e. the developer). Grains that have not been exposed are then removed

by the ﬁxing or ﬁxation process, and the exposed regions appear as dark patches

on the transparent acetate support ﬁlm. For extensive details on the theory of the

photographic process we refer the interested reader to the book Fundamentals of

Photographic Theory by James and Higgins [JH68].

When the developed negative is illuminated by a light source of intensity I

fraction I (x, y) is transmitted, depending on the density of metallic silver at the

location (x, y). We deﬁne the photographic density D by

D(x, y) = log

I (x, y)

The ratio I /I

is known as the intensity transmittance of the negative. The pho-

tographic density can be measured by a densitometer or a scanner equipped with

a transparency adapter. Instead of using the actual intensity of the light source as

, it is often easier to use the scanned intensity from a region near the edge of

the negative (a region which was not exposed to electrons, but underwent the same

development and ﬁxation process as the exposed region).

3.11 Electron detectors 229

Optical Density D

fog

log E

max

slope = electron speed k

Fig. 3.44. Schematic representation of the Hurter–Drifﬁeld curve, relating optical density

D to the logarithm of the exposure E. The fog level represents the density of an unexposed

but developed region of the negative. The maximum density level is typically

around

D ≈ 3.

The relation between the density D and the exposure E is commonly represented

by a logarithmic plot of D versus log E, known as the Hurter–Drifﬁeld curve or the

characteristic curve. A schematic example of such a curve is shown in Fig. 3.44.

For exposure to light, such a curve properly describes the relation between E and

D. Up to a minimum exposure level, the ﬁlm density is constant and equal to a

small number, known as the fog level. Then the curve becomes linear with slope k,

the ﬁlm speed, sometimes known as the photographic contrast. Electron speeds for

modern emulsions are in the range 0.3–1.1

µm

per electron. For large exposures,

all halide grains are converted into metallic silver and the ﬁlm saturates at a limiting

density D

max

. The practical value of the saturation density is between D

max

= 2 and

3 for most applications, D = 3 indicating that only

1000

of the illuminated intensity

is transmitted through the negative. The precise shape of the characteristic curve

depends in a sensitive way on the experimental conditions during development

and ﬁxation (temperature, time, etc.), and it is not a trivial matter to extract reliable

intensity data from photographic negatives. For an extensive discussion of this topic

the reader is referred to the early work by Frieser, Klein, and Zeitler [FKZ59] and

the more recent approach to quantitative analysis of electron negatives by Campbell,

Cohen and King [CCK97]. Zeitler [Zei92] has shown that for electron exposures

at densities of less than 1.5 the relation between D and E is essentially linear.

It is possible to deﬁne and measure the point spread function for an electron

negative. It can be shown (e.g. [Zei92]) that the radially symmetric PSF T (r)is

given by

T (r) =

2π x





, (3.86)

where K

is a modiﬁed Bessel function and x

is a decay length, which depends on

the electron energy. The corresponding modulation transfer function T (q)isgiven

230 The transmission electron microscope

by the Fourier transform:

T (q) =

1 + q

. (3.87)

This function has no zero-crossings and can, therefore, be deconvolved from the

recorded transmittance. In practice, such a deconvolution will be performed nu-

merically, which means that the negative must be digitized, either by means of

a densitometer, or by regular scanning using a transparency adapter. Whichever

digitization method is used, the reader should be aware that the scanning device

itself may impose its own modulation transfer function on the digitized image. For

densitometers such an instrumental MTF is well understood and can be determined

easily. For ﬂat-bed scanners on the other hand, the MTF depends on the details of

the illumination and also on the discreteness of the detector array, typically a diode

array.

3.11.4 Digital detectors

Charge-coupled device detectors, commonly known as CCD detectors, have been

around since 1970, when Boyle and Smith proposed the ﬁrst charge-coupled semi-

conductor device [BS70]. While there have been many advances in the performance

of CCD detectors since their invention, the basic operational principles have not

changed signiﬁcantly. A silicon substrate (Fig. 3.45a) is lightly doped with about

acceptor atoms cm

−3

so that it acts as a p-type semiconductor. A thin (100

nm) silicon dioxide layer is deposited on top of the substrate, followed by a metal

gate. When a positive voltage is applied to the gate the majority carriers, holes in

the case of a p-type semiconductor, are repelled from the area underneath the gate

SiO

Metal gate

p-type Si

depletion

region

shift all

elements

Active detector

area

read-out

circuitry

extra column

(a) (b) (c)

Fig. 3.45. (a) Schematic representation of the structure of a single element of a CCD device;

(b) all elements of a 4 × 4 detector array are exposed to incident light; (c) the array is ﬁrst

shifted one element to the right, and then the elements of the vertical column are shifted

into the read-out circuitry. Then the array is shifted again, until all elements have passed

through the read-out circuitry.

3.11 Electron detectors 231

and a depletion layer is formed. The bias voltage therefore creates a potential well,

the depth of which is determined by the bias voltage, the thickness of the oxide

layer and the size of the metal contact [BL80]. This potential well can subsequently

be ﬁlled with minority carriers (electrons), which will form a thin layer close to

the oxide. As the number of electrons increases, the depletion region shrinks, until

a maximum number of electrons has been accumulated. At this point the potential

well is saturated and can accept no additional electrons.

When an array of CCD elements is exposed to light, the potential wells will be

ﬁlled with electrons, and the number of electrons in each well will be proportional

to the incident light intensity for that particular well. Once the exposure has been

completed, the charge in each CCD element must be determined. This is accom-

plished by a clever combination of voltage changes applied to neighboring detector

elements. For a detailed discussion of this mechanism as well as a description of

other CCD geometries we refer to [BL80] or [HM79]. All the charges accumulated

along a line of CCD elements are simultaneously shifted one element sideways

(Fig. 3.45b), and the ﬁnal column is shifted down towards the read-out circuitry

which measures the total charge in each individual element (Fig. 3.45c). When all

elements have been read, the CCD device is ready for the next exposure.

Scientiﬁc CCD detectors are typically square detectors, with element sizes in the

range of 10–25

µm on the side. For TEM imaging, the beam electrons are ﬁrst con-

verted into photons in a phosphor or YAG (yttrium aluminum garnet) scintillator.

Subsequently, the photons hit the active area of the CCD elements and generate

electrons that ﬁll the potential wells in the depleted regions of the p-type semicon-

ductor. The scintillator is coupled to the CCD detector array through a ﬁber-optic

coupling, or is directly cemented onto the array. To reduce electronic noise, CCD de-

tectors are cooled down to the range −30 to −50

◦

C using Peltier cooling elements.

The dominant sources of noise are in the scintillator electron–photon conversion

and the detector photon–electron conversion processes.

Modern CCD detectors can have as many as 4096 × 4096 detector elements, and

each element has a dynamic range of 12, 14, or 16 bits. A single image from such

a detector will occupy 32 megabytes (33 554 432 bytes) of memory or disk space.

File compression algorithms may be used to reduce the ﬁle size, but care must be

taken to use only lossless compression algorithms when raw image data is stored.

†

Image analysis should only be performed on raw image data, not on data that has

been stored using a lossy compression algorithm.

The imaging characteristics of a CCD detector are well described using the MTF

formalism introduced in Section 3.11.1.2. For a rather complete description of the

†

Lossless image compression is typically available in the tagged image ﬁle format, or tiff -format. Lossy image

compression algorithms are used for the Joint Photographic Experts Group format, or jpeg-format.

232 The transmission electron microscope

1.0

0.8

0.6

0.4

0.2

0.0

0.0 0.1 0.2 0.3 0.4 0.5

Frequency (1/pixels)

MTF (PSF)

ideal MTF for

square pixel detector

Gatan 679

slow-scan

CCD at 120 kV

inverse MTF

normalized PSF

Pixels (for PSF)

0 1020304050

Fig. 3.46. Modulation transfer function for a 1 K × 1 K Gatan 679 slow-scan CCD camera

with a 120 kV incident electron beam

[Zuo96]. The inverse of the MTF (MTF

max

/MTF) is

also shown, along with the ideal MTF for a signal lined up with one of the rows or columns

of a square detector array. The bottom curve is the normalized point spread function T (r)

versus distance measured in pixels (scale on top).

imaging characteristics of CCD cameras we refer the interested reader to de Ruijter

[dR95] and Zuo [Zuo96]. In this section, we will only state the most important facts.

The MTF of a CCD camera is similar in form to that of a photographic negative.

Zuo [Zuo96] has modeled slow-scan CCD cameras with different scintillators at

different microscope acceleration voltages using the following MTF:

T (q) =

1 + αq

1 + βq

+ c, (3.88)

where the ﬁrst two terms model the head and tail part of the point spread function

and c is a constant. Figure 3.46 shows an example MTF for a Gatan model 679

slow-scan CCD camera operated at 120 kV. The camera has 1024 × 1024 pixels

with a dynamic range of 12 bits, a YAG scintillator, and Peltier cooling to −30

◦

The ﬁtting coefﬁcients are a = 0.3293, α = 3328.8, b = 0.46423, β = 13.511,

and c = 0.147 94

†

[Zuo96]. The frequency range goes from zero to the Nyquist

frequency q

; in other words, the frequency axis is labeled in units of the sampling

rate.

†

The reader should note that these are approximate parameters; at zero frequency, the MTF should be equal to

unity, or a + b + c = 1, and for the case shown we have a + b + c = 0.941 47.

Exercises 233

The corresponding point spread function consists of two modiﬁed Bessel func-

tions K

plus a delta-function (the Fourier transform of the constant c):

T (r) =

2πα



√



2πβ



√



+ cδ(r), (3.89)

which is a sharply peaked function with a slowly decaying tail. For the ﬁtting pa-

rameters introduced above, 85% of the area under the PSF falls within the ﬁrst

six pixels, while 99% falls within the ﬁrst 30 pixels. This indicates that an in-

cident electron has an 85% probability to be detected inside a circle with radius

six pixels centered on the point of impact on the scintillator. The main conse-

quence of the point spread function is that the highest spatial frequencies are

suppressed with respect to the low spatial frequencies, and this in turn causes

sharp features in the image to be smoothed. The inverse MTF, also shown in

Fig. 3.46, can be used to deconvolve the PSF from the image. Care must be

taken that the various operations in equation (3.84) are performed in the proper

order.

The detective quantum efﬁciency, DQE, is in the range 0.5–0.7 for electron doses

between 100 and 1000 counts pixel

−1

. For explicit expressions for the frequency-

dependent DQE (DQE(µ, ν)) we refer to [dR95] and [Zuo96]. It can also be shown

from experimental measurements that the number of CCD well electrons is be-

tween 10 and 30 per incident beam electron, depending on the details of the

scintillator.

Exercises

3.1 Derive the paraxial radial trajectory equation (3.17).

3.2 Use the

lens.f90 program to determine an empirical relation between a and B

(for

Glaser’s bell-shaped ﬁeld) for which the lens

has the so-called

“telescopic property”,

i.e. the incident and exciting trajectories are both parallel to the optical axis, but at

a different distance from the axis. Such a lens would change the beam diameter of a

cylindrical beam.

3.3 Use the

lens.f90 program to create a conﬁguration consisting of two unequal lenses

which, for a given acceleration voltage, will produce an exit trajectory at half the

distance from the optical axis (i.e. r (z

) ≈ 0.5r(z

) and r



) = 0.0) and which has

zero total image rotation.

3.4 Derive the components of the lens transfer matrix (3.29).

3.5 Verify graphically that the image Q of the object point P will be magniﬁed when the

object is located at a distance shorter than the object focal length from the object focal

plane (see Fig. 3.9 and the discussion on page 160).

3.6 Draw ray diagrams similar to the one in Fig. 3.27(b) for the under-focus and over-focus

conditions of the second condensor lens.

234 The transmission electron microscope

3.7 Show that the barrier reduction due to the Schottky effect is given by equation (3.48)

on page 181.

3.8 Equation (3.77) was derived for HOLZ reﬂections with the incident beam along a

zone axis. If the incident beam is tilted slightly away from the zone axis, so that the

wave vector k

acquires the components L

and L

with respect to the vectors g

and

, what will be the resulting changes to equation (3.77)?

Getting started

4.1 Introduction

This chapter covers a wide range of topics, all of which are related to standard,

routine microscope operation. Microscope operation can be divided into three

levels: (1) operations common to all microscope models, regardless of manufac-

turer; (2) operations speciﬁc to a particular model; and (3) operations speciﬁc to

a particular laboratory or location. In this chapter, we will only deal with the ﬁrst

kind of operations.

For operations speciﬁc to a given microscope model, we refer the reader to

the microscope manual, which comes with every installation. Most manuals are

very detailed, with photographs of microscope components and the layout of the

console. In addition, routine procedures such as specimen exchange, photographic

plate exchange, switching between imaging modes (which buttons to press), and

so forth, are detailed in the microscope manual. For the beginning microscopist, it

is a good idea to keep this manual at hand throughout the ﬁrst series of microscope

sessions.

In addition, there may be special (local) rules for such things as:

specimen and specimen holder handling (where the gloves are, what kind of tweezers

should be used, how the specimen holder should be stored, etc.);

how to turn up the ﬁlament current (i.e. how much time should be left between subsequent

ﬁlament current

increments, should the acceleration voltage be left on between

users, etc.);

what type of log should one keep? Is there a general log for all micrographs, or does every

user keep a personal log? How does one sign up for microscope time?

in what state should the microscope be left for the next user (e.g. the minimum number of

unexposed plates to be left in the camera, the position of all apertures, the magniﬁcation

at which the microscope should be left, etc.).

Such rules are often written up in a laboratory manual, or verbally passed on to new

microscope users. Rather than attempt to cover every possible laboratory situation,

235

236 Getting started

for the remainder of this book we will assume that: (1) the reader has access

to a transmission electron microscope; (2) there is an experienced microscopist or

microscope technician in the laboratory who can be consulted when problems arise;

(3) the microscope manual is at hand; and (4) ample microscope time is available.

The microscope manual and additional local procedures make up what we shall call

the standard procedures manual. The reader is encouraged to become familiar with

all such procedures, and to follow them at all times. Whenever we use statements

such as “switch to diffraction mode” we will assume that the reader can ﬁnd out

from the standard procedures manual how to do that.

What this chapter does deal with can then be summarized as follows:

startup and alignment procedures;

basic observation modes;

how to take “good” micrographs;

microscope calibration;

basic preparation to begin observations on a “new” material.

The last item includes thin-foil preparation as well as gathering crystallo-

graphic information concerning the material and producing

crystal information

package.

This chapter does not provide the reader with a detailed overview of all possi-

ble thin-foil preparation methods. Specimen preparation is simply too important

to be discussed in only one short chapter. Specimen preparation may take well

over 80% of the overall experimental effort; it is not unusual for a microscopist

to spend ﬁve or more times as much time on the specimen preparation part than

on the actual microscopy observations! With the advent of atomic resolution mi-

croscopes and advanced analytical instruments it has become clear that without

a clean, well-prepared foil there is little or no point in reserving time on a mi-

croscope. Conventional TEM techniques are perhaps a bit more forgiving about

the quality of the foil (e.g. foils which are useless for analytical measurements

may still be useful for conventional imaging), but it is always better to invest

time in preparing good foils, regardless of the observations subsequently carried

out on those foils. However, because of overall page limitations, this textbook

does not devote a proportional number of pages to specimen preparation. We re-

fer the reader to one of the following books for a detailed account of various

specimen preparation techniques: Specimen Preparation for Transmission Elec-

tron Microscopy of Materials (P. Goodhew, [Goo84]); the four volumes in the MRS

conference series Specimen Preparation for Transmission Electron Microscopy of

Material [BAM88, And90, ATB92, AW97]; and volume 5 of the original Edington

monographs on Practical Electron Microscopy in Materials Science (difﬁcult to

ﬁnd but an excellent source, [Edi76]).

4.2 The xtalinfo.f90 program 237

As stated in the Preface on page xiv, one of the main goals of this text is to

provide a good starting point for the microscopy student. The author has selected

four materials from which nearly all micrographs in this book have been obtained.

The materials will be discussed in Section 4.3 and are relatively easy to obtain.

Detailed specimen preparation instructions are included for these four materi-

als, so that the reader may prepare his/her own foils and then reproduce most

of the micrographs in the book. These four materials will also be used in later

chapters for a variety of theoretical and numerical computations of image con-

trast and diffraction features. While this approach limits the range of microstruc-

tural features and defects that are considered, the advantage is that the reader can

practice and compare his/her observations with the images in this book. After a

discussion of specimen preparation for the four study materials, Cu-15 at% Al,

Ti, GaAs, and BaTiO

, we conclude the chapter with a series of typical observa-

tions, both in image and diffraction modes. It will then be the primary goal of the

theoretical chapters to explain and model the various contrast features observed,

and to create a framework for the routine simulation of conventional TEM image

contrast.

4.2 The

xtalinfo.f90 program

Whenever one starts to work on a new material, it is useful to gather all the necessary

crystallographic information about this material. In addition, it is often useful to

calculate several relevant, usually low-index, zone axis diffraction patterns. We will

see in Chapter 5 that there are also a few quantities, such as the extinction distance,

which are useful for the interpretation of conventional TEM micrographs.

The program

xtalinfo.f90, available from the website, creates several pages of

PostScript output, listing the most relevant information about the crystal structure

in a form useful to the TEM operator. All of the entries on these pages can be

obtained readily from various public domain and commercial software packages,

but it is convenient to have everything available in one single program, formatted

in a consistent way. The input to the program is the basic crystallographic in-

formation (lattice parameters, space group, and asymmetric unit), the microscope

acceleration voltage and camera length; the output consists of crystallographic in-

formation, structure factor amplitudes, intensities, and extinction distances ranked

by family, stereographic projections for the three basic crystallographic directions

(both direct and reciprocal space projections), and computed electron diffraction

patterns for a series of low-index zone axes (drawn to the correct scale). The pro-

gram combines nearly all of the routines described in Chapters 1 and 2, and for

information on the individual modules we refer to the relevant sections in those

chapters.