Practical course in scanning electron microscopy

Fortgeschrittenen Praktikum

an der Technischen Universität München

Wintersemester 2017/2018

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Table of contents

1. Introduction 3

2. Formation of an electron beam 5

3. Lens aberrations 6

4. Interactions of electrons with matter 8

5. Transmission electron microscope (TEM) 10

6. Scanning electron microscope (SEM) 12

6.1 Depth of field 17

7. Detectors 18

7.1 Detection of secondary electrons 18

7.2 Detection of backscattered electrons 19

7.3 Detection of X-rays 20

8. Experiment 21

9. Evaluation of your work 22

10. References 23

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1. Introduction

Microscopes are used in many fields of science to probe beyond the limits of sight. The

human eye is able to distinguish two points as separate when the distance between them is

at least 0.2 mm. The resolution can be improved using magnifying lenses or whole systems

of these, i.e. optical microscopes. Unfortunately there exists a resolution limit for optical

microscopes based on the wavelength of light. The smallest distance d between two points

which can be resolved is given by the Rayleigh criterion:

𝑑 = 0.61 𝜆

𝑛 sin 𝛼

With:

𝜆: the wavelength of the light,

𝛼: the semi-angle of collection of the lens,

n: the refractive index of the viewing medium

The wavelength of visible light is about 400 nm for blue light and 720 nm for red light. The

resolution which can be reached is therefore about 200 nm equivalent to a magnification of

1000.

To improve resolution further, smaller wavelengths are needed. For doubling the resolution,

ultra violet light can be used. A further increase of the resolution requires electron beams.

In this practical course we are dealing with electron microscopy with a focus on scanning

electron microscopy.

Due to the wave-particle duality the wavelength λ of an electron beam can be calculated

with the well-known de-Broglie equation:

𝜆 = ℎ

𝑝 .

With:

p: the momentum

h: the Planck constant

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The wavelength depends on the electron momentum after acceleration in an electrostatic

field.

The momentum is:

𝑝 = √2𝑚 ∙ 𝑒 ∙ 𝑈 as 𝐸𝑘𝑖𝑛 = 𝑒𝑈 =𝑝2

2𝑚

With:

e: the elementary charge

U: the accelerating voltage.

This gives for the wavelength:

𝜆 = ℎ

√2𝑚 ∙ 𝑒 ∙ 𝑈 .

At high electron velocity (which is the case at high voltages) a relativistic correction is

needed:

𝜆 = ℎ

√2𝑚 ∙ 𝑒 ∙ 𝑈 (1 +𝑒𝑈

2𝑚0𝑐2)

.

With:

𝑚0: the rest mass of the electron,

c: the light velocity

The relativistic correction is necessary at voltages greater than above 80 kV. Typical voltages

used in scanning electron microscopes are between 1 kV and 30 kV. In this course the

student will operate such a microscope. In a transmission electron microscope higher

voltages of 100 kV to 300 kV are used.

With the above equation we can calculate that for an accelerating voltage of 100, 200,

300 kV we get a wavelength of 3.9, 2.7, 2,2 pm giving a 100 000 smaller wavelength than

light. Inserting into the Rayleigh criterion a resolution of down to 0.2 nm can be theoretically

reached with electron microscopy.

The aim of this course is to acquaint students with electron microscopy with a focus on

scanning electron microscopy. There are mainly two different types of electron microscopes:

the transmission electron microscope and the scanning electron microscope. The way these

two microscopes work is fundamentally different. First a short introduction to transmission

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electron microscopy is given followed by an introduction to scanning electron microscopy. In

the practical course the students will learn to operate a scanning electron microscope and to

interpret the images.

2. Formation of an electron beam

For creating an electron beam an electron source and an electrical potential for accelerating

the electrons are required. The source is a cathode producing electrons by either thermionic

emission or field emission. The electrons are accelerated by the electric field between the

cathode and the anode. Between the cathode and the anode a cylinder with an aperture,

the so called Wehnelt cylinder, is situated, see Fig.1. This cylinder is set on a negative

electrical potential shaping the electron beam to pass the aperture and being further

accelerated. The electrical field from the Wehnelt cylinder focuses the electrons into a

crossover, which is the virtual electron source for the lenses in the electron microscope

illumination system. The electron beam is scattered on gas molecules when the pressure is

not low enough and becomes wider in diameter. This reduces the imaging quality. The

needed pressure in the gun depends on the type of filament. For stabile operation of the

electron beam the vacuum should be better than 10-4 mbar.

In order to be able to image the nanostructure of the sample the electron beam needs to be

further shaped. As the electrons are negatively charged, this is done using electrostatic and

magnetic fields. In a transmission electron microscope higher magnification is reached

(analogous to the optical microscope lenses) lenses which are electromagnets (often

arranged in a quadrupole). In a scanning electron microscope the lenses are used to form a

focused e- beam. The lenses are not used for imaging. The image quality suffers in both

types of microscopes from lens aberration. In the following the three most relevant lens

aberrations are described.

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Fig.1: Schematic view of a thermionic electron gun. A high voltage is applied between the cathode and the

anode. The electrical potential of the Wehnelt cylinder shapes the electron beam. The electrical field from the

Wehnelt cylinder focuses the electrons into a crossover, which is the virtual electron source for the lenses in

the electron microscope illumination system. [4]

3. Lens aberrations

As in optical microscopes the resolution of the image is limited by aberrations and therefore

the theoretically possible resolution of 0.2 nm is hard to reach in practice. Some

shortcomings of the lenses can be corrected, others can be at least minimized. A summary of

the three most important defects is given in the following:

Chromatic aberration:

The refractive index of a lens always has a small wavelength dependence with different

wavelengths having different focal lengths. This effect is called chromatic aberration (Fig. 2).

The wavelength of the incident electron beam varies due to the thermal Boltzmann energy

distribution. These differences can be neglected. Therefore chromatic aberration does not

play an essential role in a scanning electron microscope. In a transmission microscope,

where the electrons pass through a thick foil (the sample) chromatic aberration can play a

role.

Fig.2: Lens with chromatic aberration: Different colors, i.e. different wavelength have different foci. [5]

Astigmatism:

Astigmatism (Fig. 3) occurs if the focal lengths are different for perpendicular planes of the

incident beam. This defect originates from limitations in manufacturing perfectly cylindrically

symmetric pole pieces or/and due to not perfectly centered beam- limiter- apertures. It can

also originate from external electrical field. Fortunately astigmatism can be easily corrected

using stigmators. These are octupoles which create a compensating electric field. It is

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necessary to correct the image for astigmatism before taking images with an electron

microscope.

Fig.3: Lens with astigmatism. [6]

Spherical aberration:

Spherical aberration (Fig. 4) is a lens defect focusing off-axis rays differently than on-axis rays.

This lens defect cannot be corrected. It can be only minimized by centering the lenses and by

limiting off axis beam rays by apertures.

Fig.4: Lens with spherical aberration and with focal length F. Off axis beam are focused at different focal

lengths f1, f2, f3. [5]

These limitations of lenses described above are the most relevant ones for electron

microscopy.

4. Interaction of electrons with matter

An electron beam incident on matter interacts in several ways. Electrons can be elastically

and inelastically scattered in forward and backward directions. They can be absorbed or they

can induce X-ray emission. Scattering in the forward direction is used in transmission

electron microscopes and scattering in the backward direction is used in scanning electron

microscopes.

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Fig 5: showing an overview of the different signals being used in modern electron microscopes. The direction

shown for each signal does not always represent the physical direction. [7]

Fig.6: Above image gives an idea about the signal depth of the different signals. [5]

Electron scattering can be divided into elastic and inelastic scattering. A collision is called

elastic if there is no energy loss or the energy loss is negligible compared to the incident

energy and only the flight direction of the electrons is changed. Inelastic scattering means

the electrons lose energy. The scattering of an electron at an atomic nucleus is elastic if the

energy loss in this scattering event is small (<1 eV) compared to the primary beam energy

which is of the order of 30-100 keV.

Scattering events in which the incident electrons loose energy and change the flight

direction are inelastic. All interactions between the incident electrons and core electrons of

sample atoms are inelastic. Secondary electrons, auger electrons, cathodoluminescence,

characteristic X-rays are a result from inelastic interactions.

Considering the electron beam as a wave we can separate the scattered electrons into

coherently and incoherently scattered electrons. Elastically scattered electrons in forward

direction are usually coherent. Inelastically scattered electrons are incoherent. The incident

beam can be assumed to be coherent, that means the incident electron waves are in phase

with each and have a fixed wavelength given by the acceleration voltage. Coherently

scattered electrons are those remaining in phase. The intensity of elastic coherent scattering

is highest at relatively low angles (1 -10°) in the forward direction.

5. Transmission electron microscope (TEM)

The elastic, coherent scattering of electrons in forward direction is used in transmission

electron microscopy. The electron beam passes through a thin sample and the transmitted

electrons are detected. This is analogous to an optical microscope where the light passes

through the sample and produces the image, see Fig. 7. By changing of the current in an

electromagnetic lens its focal length is changed resulting in different magnifications. The

switching of lenses as in an optical microscope to get different magnifications is therefore

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not required.

As the wavelength of the electron beam is of the order of the distance between two atomic

planes the specimen acts as a diffraction grating. Therefore a diffraction pattern or an image

of the specimen can be recorded.

Depending on the adjustment of the lenses the diffraction pattern or the image of the

sample can be observed. By observing the diffraction pattern the crystallinity and crystal

orientation of the sample can be investigated. By observing the image the microstructure of

the sample can be studied. The dominating contrast in TEM is the diffraction contrast, i.e.

the contrast arising due to different crystallographic orientations.

Fig. 7 shows schematically a light and transmission electron microscope. One can easily see

the similarity between a light and a transmission electron microscope. Fig. 8 shows a

scanning electron microscope. By comparing the set-up of a transmission electron

microscope and a scanning electron microscope it is clear that a scanning electron

microscope works fundamentally different from the way a transmission electron microscope

works.

In a classical transmission electron microscope the electron beam is parallel. When the

electron beam is focused and is scanned point by point through the samples the microscope

is a scanning transmission electron microscope.

Fig.7: Overview of an optical microscope and a transmission electron microscope. [8]

Fig.8: Overview of a scanning electron microscope. [9]

6. Scanning electron microscope (SEM)

In a SEM the incident beam is not transmitted through the sample but the surface is scanned

point by point by a focused electron beam. The focused electron beam is shaped by

electromagnetic lenses. The image observed is not a direct image given by the incident

electrons like in a TEM (by transmitting the sample), it is an image which results from the

interaction between the incident beam and the sample surface. When the incident electron

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beam hits the sample secondary and backscattered electrons are produced. Backscattered

electrons are electrons which were backscattered at the sample’s atoms and secondary

electrons are electrons which were ejected from the atom shell by the incident electron

beam. The image on the computer screen shows at each point the number of electrons

which are counted in the detector, encoded in brightness, produced at the corresponding

scanned point on the sample by the electron beam. The electron beam is deflected by

electric fields to scan the sample surface point by point. By detecting the signal resulting

from the interaction between the electrons and the sample surface the image is obtained

point by point. Different magnifications are obtained by changing the current in the

deflection coils. By decreasing the scanned area while keeping the number of scanned points

constant a higher magnification is reached. Note that higher magnifications are obtained by

scanning smaller areas of the sample and not by higher magnification through

electromagnetic lenses. This is totally different comparing to the above explained TEM. For

imaging in a SEM the signals from backscattered and secondary electrons can be used.

The probability of a scattering event taking place is given by the cross section σ. The larger

the cross section the more likely scattering occurs. The total cross section σ is the sum of the

cross sections for elastic collision events σel and inelastic events σin.

The three most important signals in a SEM are secondary electrons, backscattered electrons

and X-ray emission. All these three signals will be used in this practical training.

The image can be formed either by detecting the backscattered electrons (BSE) or by

detecting the secondary electrons (SE) or a combination of them.

Backscattered electrons are electrons which were at least once elastically scattered at the

sample’s atoms. The probability of an elastic event is given by the cross section for elastic

scattering σel. σel depends on the incident electron energy σel~1

𝐸02 . The elastic cross section

decreases with increasing energy. Therefore at high acceleration voltages elastic scattering is

infrequent and hence electrons are penetrating deeper into the sample. The elastic cross

section also depends on the atomic number of the analyzed sample and is proportional:

σel~Z2. With increasing Z the incident electrons are more frequently scattered. With

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increasing Z the scattering angle also increases so at higher Z the incident electrons have a

smaller penetration depth and a larger exit width, compare Fig. 9.

Altogether the elastic cross section can be written as σel~𝑍2

𝐸02 ∙

1

sin2 𝜃/2 . In consequence this

allows to gain some information about the composition of the sample. If a sample consists of

two different phases with different Z, then the high Z material will appear brighter in the BSE

image than the low Z material as more electrons are scattered in the high Z material

compared to the low Z material. This contrast is called Z-contrast.

Fig. 9: shows the dependence between the interaction volume of the electron beam (EB) and the acceleration

voltage and the material atomic number Z. [10]

The second signal used for taking images are the secondary electrons. The secondary

electrons are orbit electrons ejected by incident electrons or by already backscattered

electrons. The production of secondary electrons is an inelastic scattering event, i.e. the

incident electrons are losing energy and changing their direction. The cross section for the

production for SE is increasing with decreasing energy of the incident electrons and depends

not on Z.

Secondary electrons have low energies. By definition all electrons with energies below 50 eV

are called secondary electrons. Because of the low energy only secondary electrons

produced close to the surface at depths below 50 nm can exit the sample and can be

detected. As the secondary electron signal originates only from depths up to 50 nm its

intensity mostly depends on the topography of the sample surface giving a high quality

image of the surface structure. When a surface is tilted towards the incident electron beam

the volume from which secondary electrons can exit the sample is larger giving more signal,

i.e. the tilted surface appears brighter, see Fig. 10. This is also the case at edges and needles,

which appear brighter in the image. SE images appear like illuminated from the side because

normally the SE detector is placed at a large angle and acts like a “light source”, giving a

good topography contrast and making the images intuitive. To interpret SE images correctly

it is important to know from which side the SE detector “looks” on the sample.

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Fig. 10: SE production as a function of the incident angle of the beam electrons (EB). [10]

When analyzing the images, it is important to remember that incident electrons can undergo

several elastic and inelastic collisions before reaching the surface and being detected.

Therefore electrons will not have discrete energies but rather an energy distribution as

shown in Fig. 11. All electrons with an energy >50 eV are called backscattered by definition

because they were at least once elastically backscattered. Electrons with energy E close to

the primary incident energy E0 were backscattered exactly once. Electrons with an energy

between 50 eV and the primary energy (50 eV < E < E0) underwent inelastic scattering events

in addition to backscattering.

Fig. 11: Energy distribution of the BSE and SE leaving the sample surface. [10]

A very important signal used in a SEM is the characteristic X-ray emission which allows

obtaining some information about the chemical composition of the sample. To characterize

the chemical composition of the sample X-ray spectroscopy is used. This method is based on

an interaction between the incident electrons and the sample’s atoms: the characteristic X-

ray emission. An incident electron can eject an electron from an inner atomic shell; say K, L

or M leaving a vacancy in this shell. This vacancy is then filled by an outer shell electron and

X-rays are emitted with an energy equivalent to the energy difference between the higher

and lower energy state, see Fig. 12. The expression “characteristic X-ray emission” originates

from the fact that the energy of the X-ray radiation is characteristic for each chemical

element: This enables the identification of the chemical composition of the sample. The

energy depends on the atomic number Z given by the Moseley law:

𝐸 = [𝐶1(𝑍 − 𝐶2)]2

with E the energy of the X-rays, Z the atomic number and C1, C2 constants.

The emitted X-rays are named after the chemical element and the electron transition

between the two atomic shells. For example the transition from the L to the K shell in Cu is

called Cu-Kα. From M to K it is called Cu-Kβ. The roman capital marks the shell from which

the electron was ejected, the greek character gives the shell distance between the higher

energetic shell and the lower energetic shell (α for a transition from the next higher shell,

β from the second higher shell). In X-ray spectroscopy the spectroscopic lines from the K, L

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and M shells are most often used. The Kα and Kβ lines are very useful as their intensities are

high. Fig. 12 shows a typical X-ray spectroscopy spectrum.

There are two kinds of the X-ray spectroscopy depending on the spectrometers used. If the

spectrometer measures the wavelength of the X-ray radiation it is called wavelength

dispersive spectrometry WDX. If the energy is measured it is called energy dispersive X-rays

analysis EDX. In this course EDX will be used.

An EDX spectrum (Fig. 12) contains not only characteristic X-ray radiation but also X-ray

radiation resulting from the deceleration of the electrons in the electrostatic potential of the

atoms. This is called Bremsstrahlung and is visible as background in the X-ray spectrum.

Fig.12: schematic view of the origin of characteristic X-ray radiation [11] (right). Example spectrum (left)[12].

6.1 Depth of field in SEM images

Besides the excellent resolution of SEM images the high depth of field of SEM images is a

further advantage.

The depth of field describes the depth ranges where the image is in focus. The depth of

focus D depends on the magnification M, d the resolution limit of the eye and α the angular

aperture of the objective lens for the ideal case of no lens defects and an electron beam with

no diameter.

𝐷 = 𝑑/𝑀𝛼

When taking into account the diameter of the beam db the depth of field is:

𝐷 =

𝑑𝑀 − 𝑑𝑏

𝛼

The high depth of field of SEM images results from the very small angle α as the electron

beam is focused. Because of the high depth of field of SEM images rough surfaces can be

imaged well giving a 3D impression of the topography.

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7. Detectors

7.1. Detection of secondary electrons

For the detection of secondary electrons an Everhart-Thornley detector (scintilator-

photomultiplier detector) is used. Usually it is mounted at an angle of about 45° from the

incident beam direction and has a collector mesh. Between the sample and the detector

collector mesh a potential (of about 50 V) is applied which sucks the low energetic secondary

electrons towards the detector. Due to this attractive potential the effective solid angle for

detection of secondary electrons is large as electrons originating from the far side of the

sample also reach the detector. After reaching the detector mesh the electrons are further

accelerated by an inner potential towards the scintillator where they generate light signals.

These light signals are then conducted through an optical fiber to the photomultiplier. In the

photomultiplier the light signal is converted in electrons and these electrons are multiplied.

This signal is used by the electronics to generate the image.

The Everhart-Thornley detector also detects backscattered electrons. As these electrons

have high energies the additional potential between the sample and the mesh hardly

influences them. Therefore only backscattered electrons exiting the sample towards the

detector can reach the detector. This results in a very small solid angle. Therefore when the

attractive potential is turned on the number of the detected BSE is negligible in comparison

to the number of detected SE.

Of course the Everhart-Thornley detector can be also used to record a BSE image. To prevent

secondary electrons reaching the detector an inverse potential of -50 V between the sample

and the mesh can be applied. In that case the signal originates only from backscattered

electrons, the secondary electrons are suppressed. As the solid angle for the detection of

backscattered electrons is small the BSE image is noisy.

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7.2. Detection of backscattered electrons

To get high quality BSE images usually different types of detectors are used. Typically a

semiconductor detector is used. A semiconductor detector is a diode biased reversed. The

basic module of a semiconductor diode is the junction between a n-doped semiconductor

and a p-doped semiconductor or a junction between a metal and a semiconductor. When

biasing in inverse direction such a diode a depletion layer is formed. When the electrons

reach the depletion layer they generate a number of electron-hole pairs which create a

current pulse. This current pulse is then amplified and measured.

BSE detectors are often located above the sample having a large opening to ensure a large

solid angle for the BSE detection. To enable small working distances usually the BSE detector

is mounted close below the end of the SEM column (pole piece). It is circular with a hole for

the incident electron beam. This position is called high take-off angle. At this position the Z-

contrast is excellent and the topography contrast is suppressed. Sometimes there is an

additional BSE detector at a smaller angle or the BSE detectors can be tilted to that angle in

order to get a better BSE topography contrast. This position is called low take -off angle. A

BSE detector usually is either a semiconductor detector or scintillator-photomultiplier

detector. A semiconductor BSE detector located at the high take-off position is often divided

into several segments. The signals from each segment can be add or subtracted. With this

the contrast can be influenced giving a better topography image or Z-contrast.

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7.3. Detection of X-rays

A classical semiconductor detector for EDX is a silicon semiconductor crystal. As in the X-ray

spectroscopy the energy of photons is to be measured and these energies are in the order of

a few keV it is important to minimize the background signal. Therefore only crystals with a

high chemical purity and a low number of intrinsic crystal defects are used. To minimize

further the conductivity the EDX detector is cooled with liquid nitrogen. When a photon

reaches the depletion area it generates a number of electron-hole pairs which create a

current pulse. As the energy needed to create an electron-hole pair in Si is 3.8 eV the

number of created electron hole pairs by a photon is large. The energy of the electrical pulse

is equal to the energy of the incoming X-ray. The electrical pulses are sorted by height in a

multichannel analyzer which allows determining the X-ray energy giving the spectrum shown

in Fig. 10.

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8. Experiment

First get acquainted with the microscope: look into the vacuum chamber, try to identify the

different detectors, think about the geometry. You should use gloves.

Sample 1: Observation of a screw and a coil filament

Exercise 1: Try to take images in the SE mode and BSE mode

To take an image:

Check the cross over: if it is not in the middle of the axis move it there. Adjust brightness/contrast. Focus roughly your image. Recheck the cross over in the image Focus your image in a high magnification. When the sample is in focus click

Z <-> FWD to tell the microscope that the sample is focused Check whether there is astigmatism; if so try to correct the astigmatism by adjusting

the stigmator settings. Take your images in the SE mode. Switch to the BSE mode. Adjust contrast/brightness. Take some images.

Exercise 2: Record an EDX spectrum and identify the elements with the EDAX Genesis software

Start the program EDAX Genesis and collect the spectrum by clicking button “Collect”. Identify the peaks with Peak ID and consider whether the peak identification by the

program is correct. Identify all peaks.

Sample 2: “pyramid” W on Fe sample

Exercise 1: Take SE images of the sample and BSE images. How to make topography contrast with BSE? Make a topography contrast BSE image.

Exercise 2: Rotate with scan rotation and consider how to identify “Berge und Täler”

Sample 3: polished sample

Exercise 1: Take SE and BSE images.

What do you learn from this? What do you see?

Exercise 2: Take an EDX spectrum.

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Sample 4: unknown sample

Exercise 1: Take SE image and BSE (A+B), (A-B) and record an EDX spectrum.

Why are the images so different?

9. Evaluation

Sample 1:

Show your images.

Sample 2:

Explain the differences between a SE and BSE image and a topography BSE image. Explain how to see topography with the BSE detector.

Discuss how to identify rough surface. How do you see which part of the sample is higher.

Discuss the scan rotation and why you should be very careful when interpreting the images.

Sample 3:

Explain how to distinguish in a BSE image whether you see material contrast or something else. Evaluate the taken EDX spectra and identify the element/elements on the sample. Describe your procedure in identifying the peaks.

Sample 4:

Evaluate the taken EDX spectra and identify the element/elements on the sample.

Please add the taken images and EDX spectra to your evaluation.

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10. References:

[1] Peter Fritz Schmidt et al.: „Praxis der Rasterelektronenmikroskopie und

Mikrobereichsanalyse“, 1994, expert verlag, Renningen-Malmsheim

[2] Andrzej Barbacki: „Mikroskopia elektronowa“, 2007, Wydawnictwo Politechniki

Poznanskiej, Poznan

[3] David B. Williams, C. Barry Carter “Transmission Electron Microscopy part 1 basics”,

1996, Springer Science+Business Media, New York

Images references:

[4] https://lp.uni-goettingen.de/get/text/353

[5] wikipedia.de; wikipedia.org, wikipedia.pl

[6] https://www.onlinesehtests.de/astigmatismus/

[7] David B. Williams, C. Barry Carter “Transmission Electron Microscopy part 1 basics”, 1996,

Springer Science+Business Media, New York

[8] http://wiki.polymerservice-erseburg.de/index.php/Transmissionselektronenmikroskopie

[9] http://www.technoorg.hu/news-and-events/articles/high-resolution-scanning-electron-

microscopy-1/

[10] Peter Fritz Schmidt et al.: „Praxis der Rasterelektronenmikroskopie und

Mikrobereichsanalyse“, 1994, expert verlag, Renningen-Malmsheim

[11] http://geo-consulting.warnsloh.de/rfaxrf-allgemein/

[12] Andrzej Barbacki: „Mikroskopia elektronowa“, 2007, Wydawnictwo Politechniki

Poznanskiej, Poznan