Deposition and Analysis of Thin Films
FB502
2018
ii
Contents
I Deposition methods 1
1 Magnetron sputtering 5
1.1 Sputtering principle . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Transport of sputtered atoms, gas rarefaction . . . . . . . . . 7
1.3 Planar magnetron . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Magnetic field configuration . . . . . . . . . . . . . . . . . . . 9
1.5 Reactive magnetron sputtering . . . . . . . . . . . . . . . . . 11
1.6 Practical aspects of magnetron sputtering . . . . . . . . . . . 12
1.7 Example of a deposition process . . . . . . . . . . . . . . . . 12
2 Vacuum evaporation 15
2.1 Vacuum evaporation principle . . . . . . . . . . . . . . . . . . 15
2.2 Evaporation sources . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Example of evaporation system . . . . . . . . . . . . . . . . . 17
3 Plasma enhanced CVD 21
3.1 The characteristics of the PECVD process . . . . . . . . . . . 23
3.1.1 Plasma parameters . . . . . . . . . . . . . . . . . . . . 24
3.1.2 Glow discharge . . . . . . . . . . . . . . . . . . . . . . 27
II Analysis methods 33
4 Scanning Electron Microscopy 35
4.1 The advantages of SEM in comparison with optical microscope 35
4.2 SEM construction . . . . . . . . . . . . . . . . . . . . . . . . 36
iii
iv CONTENTS
4.2.1 Gun . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.2 Vacuum system . . . . . . . . . . . . . . . . . . . . . . 38
4.2.3 Electromagnetic lenses and scanning coils . . . . . . . 38
4.2.4 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.5 Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.6 Scanning electron microscope Mira 3 – parameters . . 40
4.3 Sample preparation for SEM . . . . . . . . . . . . . . . . . . 41
4.3.1 Suitable samples . . . . . . . . . . . . . . . . . . . . . 41
4.3.2 Magnetic samples . . . . . . . . . . . . . . . . . . . . . 41
4.3.3 Non-conductive samples . . . . . . . . . . . . . . . . . 42
4.4 SEM signals, their detection and use . . . . . . . . . . . . . . 42
4.4.1 Secondary electrons (SE) . . . . . . . . . . . . . . . . 42
4.4.2 Backscattered electrons (BSE) . . . . . . . . . . . . . 43
4.4.3 X-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.5 Examples of a thin layer analysis by means of SEM . . . . . . 45
4.5.1 How to obtain sharp photos with good resolution? . . 45
4.5.2 How to discover the chemical homogeneity of the sample?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.5.3 The thickness of the layers and the cross section of the
sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.5.4 The information obtained by X-ray analysis . . . . . . 49
5 Atomic Force Microscopy 55
5.1 Atomic force microscopy principle . . . . . . . . . . . . . . . 55
5.1.1 Piezoelectric control of x,y and z movements . . . . . 56
5.1.2 Cantilevers . . . . . . . . . . . . . . . . . . . . . . . . 56
5.1.3 Cantilever deflection detection method . . . . . . . . . 57
5.1.4 Feedback control . . . . . . . . . . . . . . . . . . . . . 57
5.1.5 Basic AFM modes . . . . . . . . . . . . . . . . . . . . 59
6 X-Ray Diffraction 69
6.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . 69
6.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . 70
CONTENTS v
6.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.4 Practical aspects of X-ray diffraction . . . . . . . . . . . . . . 72
6.5 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7 X-Ray Photoelectron Spectroscopy 75
7.1 Basic principles . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.2 Surface sensitivity . . . . . . . . . . . . . . . . . . . . . . . . 77
7.3 Primary structures in XPS . . . . . . . . . . . . . . . . . . . 78
7.4 Chemical shift . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7.5 Spin-orbit splitting . . . . . . . . . . . . . . . . . . . . . . . . 80
7.6 Surface charging . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.7 Analysis features . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.7.1 Imaging & mapping . . . . . . . . . . . . . . . . . . . 81
7.7.2 Depth profiling . . . . . . . . . . . . . . . . . . . . . . 82
7.7.3 Angle resolved XPS (AR-XPS) . . . . . . . . . . . . . 83
7.8 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . 84
7.8.1 Vacuum system . . . . . . . . . . . . . . . . . . . . . . 84
7.8.2 X-ray source . . . . . . . . . . . . . . . . . . . . . . . 84
7.8.3 Electron energy analyser . . . . . . . . . . . . . . . . . 85
7.8.4 Sample handling . . . . . . . . . . . . . . . . . . . . . 86
8 Raman Spectroscopy 87
8.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . 87
8.2 Experimental setup and data acquisition . . . . . . . . . . . . 88
9 Surface Energy Analysis 93
9.1 Surface Tension and Surface Free Energy . . . . . . . . . . . 94
9.2 Young´s Equation . . . . . . . . . . . . . . . . . . . . . . . . 96
9.3 Models for determination of interfacial tension . . . . . . . . 97
9.4 Surface Free Energy Evaluation . . . . . . . . . . . . . . . . . 99
9.4.1 Zisman plot . . . . . . . . . . . . . . . . . . . . . . . . 99
9.4.2 Equation of State . . . . . . . . . . . . . . . . . . . . . 100
9.4.3 Fowkes Theory . . . . . . . . . . . . . . . . . . . . . . 101
vi CONTENTS
10 Instrumented indentation techniques 107
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
10.2 Load-displacement curve . . . . . . . . . . . . . . . . . . . . . 108
10.3 Analysis of load-displacement curve . . . . . . . . . . . . . . . 109
10.4 Elastic-plastic contact . . . . . . . . . . . . . . . . . . . . . . 112
10.5 Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
10.5.1 Hardness models . . . . . . . . . . . . . . . . . . . . . 113
10.5.2 The influence of the substrate on measured hardness . 116
10.6 Elastic modulus . . . . . . . . . . . . . . . . . . . . . . . . . . 116
10.7 Fracture toughness . . . . . . . . . . . . . . . . . . . . . . . . 117
10.8 Ratios of H/E and H3/E2 . . . . . . . . . . . . . . . . . . . . 119
10.9 Fischerscope measuring device . . . . . . . . . . . . . . . . . 119
10.9.1 Parameters and calibration . . . . . . . . . . . . . . . 119
10.9.2 WIN-HCU software . . . . . . . . . . . . . . . . . . . 121
11 Ellipsometry and spectrophotometry 123
11.1 Polarization of light and optical quantities . . . . . . . . . . . 123
11.2 Thin film systems . . . . . . . . . . . . . . . . . . . . . . . . . 128
11.3 Universal dispersion models . . . . . . . . . . . . . . . . . . . 130
11.4 Spectroscopic ellipsomety . . . . . . . . . . . . . . . . . . . . 130
11.5 Spectrophotometry . . . . . . . . . . . . . . . . . . . . . . . . 131
11.6 FTIR - Fourier Transform InfraRed . . . . . . . . . . . . . . . 132
Preface
The presented text is intended for the same-named course for postgraduate
students of Plasma Physics. The chapters consist of a brief presentation of
the physical background, fundamental properties, strengths and weaknesses
of different deposition and analysis methods and techniques available at the
Department of Physical Electronics at the Faculty of Science of the Masaryk
University.
vii
viii CONTENTS
Part I
Deposition methods
1
3
Thin film deposition process can be generally described as happening in
three consecutive steps [1]:
1. Creation of gaseous phase of the deposited material. Several
different ways of gaseous phase generation can be utilized, such as
evaporation, sputtering or applying of chemical gases and vapours.
2. Vapour transport from source to substrate. Atoms, atomic clusters
or molecules of the deposited material can be transported either
in ballistic mode (mutual collisions and collisions with background gas
atoms can be neglected) and/or in diffusion/thermal mode (collisions
during the transport can not be neglected). Crossover between these
modes is not sharp and the transport mode may not be easily distin-
guished.
3. Film growth on the substrate. This step accounts for the growth
process of the film from the first nucleation to a continuous film. The
composition and microstructure of the film can be affected by impinging
ion bombardment of the growing film during the deposition.
The deposition methods are usually divided into two branches depending
on the specific way of obtaining the gaseous phase of the deposited material
from the source. These two branches are PVD (Physical Vapour Deposition)
methods and CVD (Chemical Vapour Deposition) methods.
PVD methods are atomistic in nature. The coating is deposited from individual
atoms or their small clusters and the reactions take place on the
substrate.
PVD methods:
• vacuum evaporation — deposited material is placed in a vacuum chamber
and resistively heated until evaporation occurs
• sputtering — deposited material is sputtered from a target by energetic
ions supplied by an electric discharge
• pulsed laser deposition — deposited material is evaporated using high
power laser beam
• electron beam deposition — deposited material is evaporated using
energetic electron beam
• cathode arc deposition — material of the cathode is evaporated by
high-current low-voltage arc discharge
CVD methods are characterized by chemical reactions of molecules in the
volume as well as on the substrate surface. The temperatures needed for
4
activation of chemical reactions are often in the range of 800 – 1000 ◦C.
CVD methods:
• atmospheric pressure CVD — chemical vapour depositions at high
pressures and generally high temperatures
• atomic layer epitaxy/deposition — continual deposition of crystalline
monolayers from gas precursor(s) copying the crystalline structure of
the substrate or previous layer
• plasma enhanced CVD — CVD, where the energy needed for chemical
reactions is supplied by a discharge, temperatures can be closer to
ambient level
Chapter 1
Magnetron sputtering
Mgr. Pavel Souˇcek, Ph.D.
1.1 Sputtering principle
The basic physical principle of sputtering is knocking out of atoms from a
cathode (also called target) by incident energetic particles [2]. The sputter
yield Y is defined as the ratio of the number of particles ejected from the
cathode (target) to the number of incident bombarding particles:
Y =
number of ejected particles
number of incident particles
(1.1)
Sputtering can result from bombardment with a variety of incident species.
The most commonly used are inert gas ions (e.g. Ar+), but use of other
species such as neutrals, electrons or photons is possible.
The sputtering process consists of kinetic collisions — first between the
incident energetic particle and one or a few atoms of the target, and then
subsequent collisions between the atoms of the target (so called collision
cascades). The kinetic energy and the momentum of the incident particle
are redistributed to the target atoms. If, during the last interaction, the
momentum direction is oriented in an outward direction from the surface of
the target and enough energy is supplied to the atom to break the bonds
with other atoms, sputtering occurs (see Fig. 1.1).
Depending on the kinetic energy of the incident particle, different physical
results can occur [3]:
• Low energy (0 eV < E < 20 – 50 eV) This regime is known as subthreshold
regime. The energy of incident particles is too low to sputter
the target. For a long time, it was observed that sputtering seemed to
have a threshold of ∼ 40 eV for most materials, below which no sputtering
occurred. This was due to dramatic fall-off in the sputtering
5
6 CHAPTER 1. MAGNETRON SPUTTERING
Figure 1.1: Principle of sputtering.
yield as the incident particle energy decreases. Experimentally a low
intensity sputtering was observed in dense plasma such as ECR. The
sputtering yield is very low — in the order of 10−6.
• Moderate energy (50 eV < E < 1000 eV) This range is also called the
knock-on sputtering regime. It covers most of the practical applications
in PVD. The incident particle impacts a target atom, which recoils
and strikes one or more atoms, which recoil and the process continues.
The sequence of collisions will differ greatly for each incoming particle
because each particle will hit in a different place with regard to the
specific position of surrounding atoms. The sputter yield depends
strongly on the incident particle mass (more exactly on the ratio of
incident particle mass to the target atom mass) and the kinetic energy,
as well as on the target orientation. The target temperature does not
play a crucial effect in the sputtering yield as long as it is not close to
the melting temperature of the target material [4,5].
• High energy (1 keV < E < 50 keV) The incident particle causes a dense
cascade of secondary particles (target atoms) after the initial impact.
Within this cascade volume, all of the bonds between the particles are
broken and the region can be treated with statistical mechanics.
• Very high energy (E > 50 keV) At these energies, the incident particle
penetrates deep into the target many atomic layers before causing
a significant number of collisions and is effectively implanted into the
bulk of the target. The volume of the material affected by the collisions
lies deep in the target and only a few if any target atoms are sputtered.
1.2. TRANSPORT OF SPUTTERED ATOMS, GAS RAREFACTION 7
The sputtering yields of materials of interest can be found in tables [6],
papers dealing with similar elements (such as carbon [7]) or can be simulated
for example by the SRIM/TRIM program [8] based Monte Carlo simulation
method.
Since the basic principle of magnetron sputtering is the momentum and energy
transfer between the incident particle and the target atoms, the particular
species used are of great importance. The first reason is that the binding
energy of the target atoms differers for different target atoms species. A
general trend of higher sputtering yields for materials with low binding energies
and a correlation between low binding energy and low melting point
materials is observed [3]. The second reason is that the momentum transfer
efficiency corresponds to the ratio of mass of the incident particle and
the mass of the target atom mincident/Mtarget. Therefore the momentum
transport is most efficient for incident and target atoms of the same species
(self-sputtering), whereas it is inefficient (hence the sputtering yield is low)
if the incident and the target atoms are strongly mismatched in the atomic
mass. Self-sputtering mode can be employed in DC sputtering [9,10] and is
of major concern in HiPIMS discharges [11].
1.2 Transport of sputtered atoms, gas rarefaction
The type of sputtered atoms transport is governed by the configuration of the
sputtering device and the working pressure, particularly by the comparison
of the target-to-substrate distance and the mean free path of the sputtered
particle [12,13].
If the pressure is low enough, the sputtered particle does not undergo significant
number of collisions, if any. Thus it arrives at the deposition surface
with near the original kinetic energy. This transport mode is called ballistic
transport. Films deposited in this transport mode are generally small
grained and dense, they also often have good adhesion to the substrate and
show compressive stress. Ballistic transport is also directional, this can be
utilized with directional filtering. Ballistic deposition is preferred for industrial
applications [3].
At higher pressures the sputtered atom undergoes a significant number of
collisions and quickly looses its initial kinetic energy. This mode is known
as diffusive or thermal transport. The sputtered atoms progressively loose
energy and get cooler while the background gas is heated. Thermalized
deposition can lead to significantly different films compared with ballistic
depositions. The main reason is that the incident sputtered atoms arrive on
the deposition surface with virtually no kinetic energy [14]. Films prepared
by thermalized depositions show similar features to those prepared by evap-
8 CHAPTER 1. MAGNETRON SPUTTERING
oration — in both the grain size and the stress. Compared with the ballistic
depositions the grain size is generally larger and the stress is more tensile.
The temperature of the background gas can increase quite significantly especially
in the volume in the vicinity of the target. As hot gas atoms leave
the volume in the vicinity of the target faster than cooler gas atoms arrive
from further away, local gas rarefaction can occur. This phenomenon can
be quite significant and can decrease the original gas density down to as
low as 15 % of the original value [15]. Gas rarefaction can be an important
factor in scaling issues — high rate sputtering may have similar characteristics
to low pressure sputtering, while low sputtering yield processes at
moderate pressures can be significantly different as the sputtering power is
scaled up and the effective gas density is reduced. Gas rarefaction can also
be modelled by Monte Carlo method [16, 17]. Gas rarefaction does significantly
influence especially HiPIMS discharges, where high power is delivered
in a short time [18]. It can lead to draining of charge carriers and switch
to a DCMS-like regime [19] and to changes in transport processes during
deposition [20].
1.3 Planar magnetron
The aforementioned basic sputtering principle in section 1.1 is valid regardless
of the presence or absence of a magnetic field at the sputtered cathode.
This sputtering design consisting only of an anode and a cathode without
the presence of any magnetic field is the so called diode sputtering and is
limited by low deposition rate, low ionization efficiency in the plasma and
strong substrate heating [3].
Magnetron sputtering enhances diode sputtering by adding a magnetic field
parallel to the cathode surface [21]. The magnets are arranged in a way
that one pole of the magnet is in the centre of the cathode and the other
pole is composed of magnets arranged on the outer edge of the target. The
Lorentz force, given by the cross product of the electric and magnetic field
F = eE × B, is used to trap the electrons in the vicinity of the target. In
the case of magnetron sputtering E is perpendicular to the target surface
and applying B tangentially to the surface gives rise to electron velocity
parallel to the target surface (so called E × B drift). The electrons undergo
a cycloidal motion along the orbit path and can ionize the gas on a longer
trajectory.
Fig. 1.2 depicts a typical magnetron configuration with magnets confining
electrons into an annular closed path, which gives rise to an annulus of
intensive plasma region. This results in an uneven erosion of the target
material — a typical ”racetrack” is formed (see Fig. 1.3). The edge of the
1.4. MAGNETIC FIELD CONFIGURATION 9
Figure 1.2: A typical configuration for magnetron sputtering [22].
racetrack is given by the local magnetic field array where E and B fields are
nearly parallel and hence E × B ≈ 0. The cross-field confinement here is
minimal and the electrons escape the region without causing localized dense
ionization.
The design of planar source enables sputtering of magnetic as well as nonmagnetic
materials [23]. For the planar basic design the target material
utilization is rather poor ∼ 25 – 35 % in the standard two pole magnetic
configuration, but can be enhanced to ∼ 45 – 60 % in some special configurations
[24]. Other designs like cylindrical cathodes with movable magnets
are often used with material utilization > 80 % [25].
1.4 Magnetic field configuration
Balanced magnetic field configuration of magnetron sputtering was developed
in early 1970s [26,27]. In this configuration the electrons are trapped
in the vicinity of the target and the ionization efficiency is dramatically
increased compared with diode sputtering. This results in a much denser
plasma that can be sustained at lower pressure (∼ 10−1 Pa compared to
∼ 100 Pa) at lower voltage (∼ 500 V compared to ∼ 2 – 3 kV) than in
diode sputtering. The plasma region expands several tens of millimetres
from the cathode (typically ∼ 60 mm) [28]. If the substrate is within this
region during the deposition, ion flux on the substrate will be present. This
additional energy can alter the structure and properties of the final film.
If the substrate is outside of this region, it will be in a low ion concentration
area. Typically the saturated ion current on the substrate in this case
is < 1 mA/cm2, which is generally too low value to significantly alter the
film properties. The energy of impinging ions can be increased by applying
10 CHAPTER 1. MAGNETRON SPUTTERING
Figure 1.3: Racetrack formed throughout the target life. a) top view b) side
view
higher substrate bias value. Nevertheless, too high value of the bias can lead
to an increased stress in the film and/or to creation of defects. A higher ion
flux at a lower substrate bias is generally preferred.
In the late 1980s [29] an unbalanced configuration for magnetron sputtering
was developed. This configuration makes reaching higher ion currents on the
substrate (> 2 mA/cm2) possible. Here, even at lower negative substrate
bias < 100V, the impinging ion energy is sufficient to alter the parameters of
the growing film. There are essentially two ways to alter the magnetic field,
either to strengthen the central pole or the outer pole. The so-called type 1
unbalanced magnetron has stronger central pole compared to the outer pole.
In this case the magnetic field lines which do not close in on themselves are
directed to the chamber walls. This design is not commonly used due to low
ion currents to the substrate. Type 2 unbalanced magnetron on the other
hand utilizes stronger outer pole on the edge of the target. Using this design
some of the magnetic field lines are directed towards the substrate. Some
secondary electrons are drawn along these lines and as a result the plasma
is less closely bound to the target and is allowed to flow onto the substrate.
Consequently high ion currents can be extracted from the plasma without
the need of external biasing of the substrate. The comparison of a balanced,
type 1 unbalanced and type 2 unbalanced magnetic field configurations is
schematically sketched in Fig. 1.4.
1.5. REACTIVE MAGNETRON SPUTTERING 11
Figure 1.4: Comparison of a balanced, type 1 unbalanced and type 2 unbalanced
magnetic field configurations.
1.5 Reactive magnetron sputtering
Reactive magnetron sputtering is a process where one of the coating species
enters the deposition chamber in a gas phase. Typically nitrides (when
introducing nitrogen) and oxides (when introducing oxygen) are synthesized
in this manner. Such process has several advantages:
• compounds can be formed from simple single element targets
• insulating compounds can be prepared from conductive targets
However, the versatility of this process is gained at the expense of increasing
the complexity of the deposition process itself [1].
Chemical reactions during reactive magnetron sputtering occur at the target,
at the substrate and at the chamber walls. The relationship between the
depositions process parameters and the reactive gas flow is generally very
nonlinear as the growing film acts as an additional getter pump for the
reactive gas. When the reactive gas floe is low, virtually all of the reactive
gas atoms are incorporated in the growing film. The cathode processes are
largely that of a simple Ar sputtering. The coatings are largely of the same
composition as the target itself.
As the number of reactive gas atoms adsorbed per one metal atom reaches
a ratio corresponding to stoichiometric film composition (e.g. ratio of 1:1
for TiN compound for sputtering of Ti target in N2/Ar gas mixture), there
is a sudden increase in the reactive gas partial pressure. This change in
the composition of the sputtering gas results in a pronounced change of the
processes on the cathode. A surface layer of the compound is formed on the
target. The process is shifted to the so called poisoned state. This change
of the target surface composition is also generally accompanied by changes
12 CHAPTER 1. MAGNETRON SPUTTERING
in the target voltage due to differences in the secondary electron coefficient
of the target.
In order to shift back from the poisoned mode to the metallic mode a significant
decrease of the reactive gas flow is required. The reactive gas flow
needs to be much lower than in the situation of the reverse transition from
metallic to the poisoned mode. This behaviour is called hysteresis.
1.6 Practical aspects of magnetron sputtering
Magnetron sputtering requires low pressure environment in order to reach
high enough mean free paths of the sputtered particles. The typical operating
pressure during the deposition is in the order of 10−1 to 100 Pa. The
base pressure of the deposition chamber is generally much lower in the order
of 10−4 to 10−6 Pa. Therefore, a combination of a turbomolecular pump
(previously diffusion pump) and a forepump is employed. The forepump
can be a rotary oil pump, however, an oil–free pump such as scroll or Roots
pump is generally preferred due to possible contamination of the apparatus
by oil vapour.
Magnetron sputtering is a very versatile deposition technique. Nearly any
solid material can be deposited onto any solid or powder substrate. However,
the specifics of the process must be chosen accordingly. Sputtering by
direct current (DC) is suitable for conductive e.g. metalic targets. If DC
power would be used with non-conductive targets, those would get charged
until an arc occurred. Therefore, a different power source has to be used.
Radiofrequency (RF) power sources at 13.56 MHz can be utilized for such
applications. Bi-polar pulsed DC power sources are also an option. Both
enable the negative charge to be drained from the target either during the
positive half-period in case of RF or during a short switching of the target
to positive potential in case of the bi-polar pulsed DC.
1.7 Example of a deposition process
A deposition generally consists of several steps. First, the target needs to
be cleaned by a discharge to eliminate any contaminants on the surface.
The substrate itself needs to be cleaned as well to remove any surface contaminants
such as the native oxide layer to promote the coating adhesion.
These two steps can be done in parallel if the target and the substrate are
separated by a shutter. Only then the deposition itself starts by setting the
desired depositions parameters such as target powers, substrate bias, pressure,
gas flows and temperature. If ceramic non-conductive targets are used,
the power must be gradually ramped to avoid target fracture due to thermal
1.7. EXAMPLE OF A DEPOSITION PROCESS 13
stress. After the desired deposition time, the power to the targets is cut and
the gas valves are closed. The substrates generally need to cool down under
vacuum. Then, the chamber may be evacuated and the deposited coating
can be unloaded.
14 CHAPTER 1. MAGNETRON SPUTTERING
Chapter 2
Vacuum evaporation
doc. Mgr. Pavel Slav´ıˇcek, Ph.D.
2.1 Vacuum evaporation principle
The deposition by the thermal evaporation method is simple and very convenient.
The basic physical principle of evaporation is heating the material.
Solid materials vaporize when heated to sufficiently high temperatures. The
dependence of the vapour pressure on the temperature for evaporated materials
is important for the deposition. The condensation of the vapour onto
a substrate yields thin solid films.
Thin films of carbon deposited by evaporation inside an electric bulb were
probably first observed by Edison in 1879 [30]. Vacuum deposition of
metallic thin films was not common until the 1920s. Optically transparent
vacuum-deposited anti-reflection (AR) coatings were patented by Macula
(Zeus Optical) in 1935. [32].
A typical configuration for vacuum evaporation is shown in Fig. 2.1. Vacuum
deposition normally requires vacuum better than 10−2 Pa in order to
have a long mean free path between collisions. At this pressure there is still
a large amount of concurrent impingement on the substrate by potentially
undesirable residual gases that can contaminate the film. If film contamination
is a problem, a high or ultra-high vacuum environment can be used
to produce a film with the desired purity. Typical pumping system is a
combination of rotary vane pump + diffusion pump or dry pump (scroll,
multi-stage roots,..) + turbomolecular pump.
Some examples of the materials used for evaporation is shown in Tab. 2.1.
Many elements evaporate, but many such as chromium (Cr), cadmium (Cd),
magnesium (Mg), arsenic (As), and carbon (C) sublime, and many others
such as antimony (Sb), selenium (Se), and titanium (Ti), are on the borderline
between evaporation and sublimation [32]. Evaporation of alloys is
problematic. The constituents of alloys and mixtures vaporize in a ratio
15
16 CHAPTER 2. VACUUM EVAPORATION
VACUUM CHAMBER
SUBSTRATE HOLDER
SUBSTRATE
BOAT
BOAT HOLDER
Figure 2.1: Deposition system configuration.
that is proportional to their vapour pressure. The high vapour pressure
constituent vaporizes more rapidly than the low vapour pressure material.
Table 2.1: Examples of the materials for evaporation: M – molecular weight,
d – density, Tm – melting temperature, Te – temperature at which the
deposition rate at 10 cm from a 1 cm2 source will be 2.5 nm/s [31].
Element Symbol M d [g cm−3] Tm [K] Te [K]
Aluminium Al 27.0 2.70 930 1460
Chromium Cr 52.0 7.20 3700 1700
Copper Cu 63.5 8.92 1356 1580
Gold Au 197.0 19.3 1336 1670
Silver Ag 107.9 10.5 1230 1330
Iron Fe 55.8 7.86 1810 1770
Nickel Ni 58.7 8.90 1730 1810
2.2 Evaporation sources
Thermal evaporation requires that the surface and generally a large volume
of material be heated to a temperature at which there is an appreciable
vapour pressure. The most common way of heating materials that vaporize
is by contact with a hot surface that is heated by passing a current through
2.3. EXAMPLE OF EVAPORATION SYSTEM 17
a material (resistively heated). Direct and indirect heating are used. Evaporation
sources must contain molten liquid without extensive reaction and the
molten liquid must be prevented from falling from the heated surface. This
is accomplished either by using a container such as a crucible or by having
a wetted surface. The heated surface can be in the form of a wire, boat,
basket, crucible etc. Wetting is desirable to obtain good thermal contact
between the hot surface and the material being vaporized. Wetted sources
are also useful for depositing downward and sideways.
Typical resistive heater materials for direct heating are W, Ta, Mo, C. These
elements have a low vapour pressure at high temperature. Resistive heating
is typically by low voltage and very high current (up to several hundreds of
amperes) power supplies.
Example of various tungsten boats are depicted in Fig. 2.2. Tungsten
spirals and basket are shown in Fig. 2.3. Molybdenum boats with covers
are illustrated in Fig. 2.4.
Evaporation sources degradation can occur with time. This can be due to
reaction of the evaporation material with the heated surface. When there
is reaction between the molten source material and the heater material, the
vaporization should be done rapidly. For example, palladium, platinum,
iron, and titanium should be evaporated rapidly from tungsten heaters [32].
Solution to this problem can be used indirect heating. In this case crucibles
of quartz, graphite, alumina, beryllia and zirconia are used with tungsten
basket heater. Example of carbon, alumina and quartz crucibles are shown
in Fig. 2.5.
2.3 Example of evaporation system
Home-made evaporation system is used in our laboratories, see Fig. 2.6.
This device is assembled from standard vacuum components and few homemade
parts. This system has sphere vacuum chamber with inner diameter
of about 75 cm. The device is equipped with two holders for evaporation
sources. Maximal current for evaporation is 400 A.
The system is equipped with a turbomolecular pump backed by a dry scroll
pump and with a system of manually operated valves. The ultimate base
pressure is about 2×10−4 Pa. Pressure is measured by Pirani manometer
and ionization manometer with cold cathode. Layer thickness is measured
during deposition by crystal sensor. The thickness of the deposited layers
may be from 5 nm up-to several µm. This device can evaporate metals (Al,
Au, Ag, Cr, Cu, Fe, Ni,...) and some alloys and compounds (NiCr, SiO,
cryolite, MgF2, ITO,...).
18 CHAPTER 2. VACUUM EVAPORATION
Figure 2.2: Tungsten boats.
Figure 2.3: Tungsten spirals and basket.
2.3. EXAMPLE OF EVAPORATION SYSTEM 19
Figure 2.4: Molybdenum boats with covers.
Figure 2.5: Crucibles: carbon, ceramic and quartz.
20 CHAPTER 2. VACUUM EVAPORATION
Figure 2.6: Evaporation system.
Chapter 3
Plasma enhanced CVD
doc. RNDr. Vilma Burˇs´ıkov´a, Ph.D.
Plasma Enhanced Chemical Vapor Deposition (PECVD) is an important
deposition method for the fabrication of thin films with very wide range of
properties and potential applications. The first commercial application of
PECVD originated for semiconductor technology in the 1960s. The PECVD
technique has rapidly evolved and expanded and it is now used in many industries
for many different applications. PECVD forms a kind of connecting
area between physical and chemical deposition. The technique uses electrical
energy to generate a glow discharge (plasma). The electrical energy is
supplied to a neutral gas mixture causing formation of charge carriers. In
PECVD techniques, there are various ways to supply energy to a neutral
gas for plasma generation:
• Direct Current (DC) - DC electric fields are less frequently employed
due to charging effects in case of electrically nonconducting substrates.
• Radio-frequency (RF) - RF electric fields are most commonly used to
generate and sustain a plasma in a low-pressure environment for technical
applications. Most commonly, a frequency of 13.56 MHz is used
for plasma deposition, since this is the common standard in research
and industry in order to avoid interference with telecommunication
applications.
• Microwave (MW) - In the MW range electrons are accelerated and
collisions are induced less efficiently as in the RF range due to the
higher frequency. For this reason, the ignition of a MW plasma is
more difficult and depends strongly on the pressure and the gas composition.
(2.45 GHz was determined as the standard frequency for
MW discharges.)
• Electron Cyclotron Resonance (ECR) - In order to overcome the above
described problem of MW, often a magnetic field is additionally ap-
21
22 CHAPTER 3. PLASMA ENHANCED CVD
plied, forcing the electrons on helicon pathways. This concept is referred
to as an electron cyclotron resonance (ECR) source.
• Dual frequency discharges (MW/RF, DC/RF, LF (low frequency)/RF)
DF: For DF discharges, consisting of a MW discharge
simultaneously superimposed by a RF signal, high deposition rates are
reported [35] combined with the formation of a high voltage sheath.
Dual DC/RF and LF/RF plasma systems show the advantage of a
more flexible control of the ion current density and the ion kinetic
energy.
The RF PECVD technologies are most commonly applied and for this reason
they will be discussed more in detail. The RF PECVD techniques are further
divided into two categories. The RF plasma may be capacitively (CCP) or
inductively (ICP) coupled into the plasma according to the arrangement of
electrodes used to generate the discharge. Inductive coupling is realized by a
planar or a helical coil, mostly by external coupling through a dielectric wall
or window rather than directly in the plasma zone. A time-variant magnetic
field is induced by the RF powered coil, leading to electron acceleration. ICP
is favorable if a high ion density and low ion bombardment of the adjacent
walls is desired. Nevertheless, for most plasma processes, including deposition
and etching, capacitive coupling is of advantage. Here, electrodes are
arranged in parallel plate configuration. In the simplest case there is a bottom
powered electrode and the grounded walls create the second electrode,
as it is shown in Fig. 3.1.
Atmospheric pressure systems are also available however they are less common
as high pressure plasmas are more difficult to sustain. Moreover, it
is difficult to prepare homogeneous films using atmospheric pressure glow
discharges. Nevertheless, recently the application of atmospheric pressure
deposition methods has increasing tendency mainly because of the economic
point of view.
The plasma most commonly used for PECVD is a non-isothermic plasma
(glow discharge) that is excited in the gas in the presence of a high-frequency
electric field at low pressure [33]. In a high-frequency electric field, the gas is
partially ionized to electrons and ions. Electrons that are much lighter than
other plasma components are therefore quickly accelerated to high energy
level that corresponds to a value of 5000 K. As the electrons are very light,
they do not greatly contribute to the overall plasma temperature. On the
other hand, ions with their high mass and therefore considerable inertia are
unable to respond to the rapidly changing direction of the electric field. As
a result, the temperature of the ions is considerably lower than the electron
temperature and the overall plasma temperature is also lower. For this
temperature difference (electrons and ions), plasma is called non-isothermic.
High energy electrons collide with gas molecules, dissociate them and form
3.1. THE CHARACTERISTICS OF THE PECVD PROCESS 23
isothermal non-isothermal
Discharge spark glow discharge
Frequency 1 MHz 50 kHz-13.56 MHz,
2.45 GHz (microwave)
Power MW kW
Flow rate 0 mg/s
El. concentration 1014/cm3 109 − 1012/cm3
Pressure 100 Torr ∼ atm. <2 Torr
El. temp. [K] 104 104
Ion temp. [K] 104 4x102
Table 3.1: Comparison of properties of isothermal and non-isothermal
plasma [33].
a chemical reaction mixture. In Tab. 3.1 the characteristics of isothermal
(spark) and non-isothermal (glow) discharges are compared.
3.1 The characteristics of the PECVD process
PECVD has several advantages over conventional thermal CVD techniques.
In particular, it is the low plasma temperature. This makes possible to
apply the technique to substrates with relatively low melting temperatures,
such as aluminum or organic polymers. The low deposition temperature is
advantageous also for some types of steel materials which may undergo phase
transformation at higher temperatures. In Tab. 3.2 the typical deposition
temperatures for CVD and PECVD are compared. Another advantage is
that the effect of different thermal expansion coefficients of the substrate
and the layer is suppressed due to the lower temperature. The deposition
rate is higher for PECVD. Uniformity of prepared layers is also high. The
low pressures under which the layers are formed lead to the formation of
amorphous or very pure crystalline structures. Further advantage of the
PECVD is that it allows control of the plasma-chemical interactions in a
wide range resulting in wide variation of film composition, microstructure
and properties. Tailoring the energetic interactions between the plasma
and the coated material surface, it is possible to prepare hard inorganic
materials as well as soft polymer-like materials. The method enables to
almost continuously vary the coating characteristics.
The disadvantages of PECVD are as follows: It is very difficult to create
absolutely clean layers. This problem is mainly related to the low pressure
and diffusion of gases from the environment into the apparatus as well as the
release of impurities from the substrate. Sometimes, these impurities may
24 CHAPTER 3. PLASMA ENHANCED CVD
Deposition temperature [◦C]
Material Thermal CVD PECVD
Epitaxial silicon 1000-1250 750
Polysilicon 650 200-400
Silicon nitride 900 300
Silicon dioxide 800-1100 300
Titanium carbide 900-1100 500
Titanium nitride 900-1100 500
Tungsten carbide 1000 325-525
Table 3.2: Comparison of typical deposition temperatures for thermal CVD
and PECVD [33]
be desirable and lead to improvements in some properties, sometimes they
may cause a substantial problem. Another disadvantage is the compressive
stress which arise in the deposited layers due to ion bomardement. This
is especially important for thicker layers where the compressive stress may
cause film delamination and cracking until the film is completely peeled. The
ion bombardment may also affect or damage the surface of the substrate,
especially at an ion energy higher than 20 eV. To prepare uniform samples,
the plasma above them must be very homogeneous. However, this problem
is also related to the construction of the apparatus.
3.1.1 Plasma parameters
To ensure high quality and reproducibility of a given plasma deposition process,
a lot of plasma parameters must be controlled. That include external
parameters such as working pressure p, gas flow Qg, discharge excitation
frequency f, applied power p, as well as internal plasma parameters, such as
the electron (plasma) density, ne, the electron energy distribution function,
fe(E) (EEDF), electrical potentials, and fluxes of different species toward
the surfaces exposed to plasma. Gas-phase chemical processes are largely
responsible for the chemical composition of the films deposited, along with
plasma - surface interactions and substrate surface conditions, which are
responsible for film microstructure and surface morphology [34,35,43]. The
following variables are considered the main plasma parameters, i.e. their
values characterize more or less accurately the plasma state.
Discharge excitation frequency
Depending on the value of the excitation frequency, f, discharges produced
in the laboratories can be separated into direct current discharges if f = 0,
and alternating discharges for any other value of the frequency. In case
of alternating discharges the electrons and the ions oscillate in plasma at
3.1. THE CHARACTERISTICS OF THE PECVD PROCESS 25
characteristic frequencies, namely electron plasma frequency, fpe, and ion
plasma frequency, fpi, respectively. The operation of the alternating mode
depends on the excitation frequency f relative to the two values of plasma
frequencies fpe and fpi. Radio frequency (RF) discharges correspond to a
value of plasma frequency that satisfies the relation fpi < f < fpe [34,35,39].
Plasma density
The abundance of species is quantified by their corresponding densities:
density of electrons, ne, positive ions, n+
i , negative ions, n−
i , and neutrals,
ng.
Ionization degree
The ionization degree Xiz is the ratio of the ion population to population
of neutrals and ions:
Xiz =
ni
ng + ni
(3.1)
Plasmas are considered fully ionized when it is of the order of 1, while weakly
ionized gases exhibit degrees lower than 10−3 [34].
Plasma temperature
Generally, temperatures of electrons, Te, ions, Ti, and neutrals, Tg, are not
identical, unless at thermodynamic equilibrium conditions in case of thermal
plasma, where these temperatures are approximately equal. In case of nonisothermal
plasma the relation between these temperatures is [33,34]:
Te Ti ≥ Tg (3.2)
Plasma potential
Because of their low mass, the velocity of the electrons is higher than the
velocity of the ions. At the initial time of discharge ignition, the flow of
electrons on a wall is much larger than that of the ions. Because of this, the
plasma acquires a residual positive charge due to the excess of positive ions,
the plasma potential, Vp(t). The plasma potential is the highest potential
of the system and it is taken often as a reference potential (i.e. all the other
potentials are expressed with respect to Vp). [34,43].
Floating potential
The floating potential Vf is the mean potential which develops on an electrically
isolated object immersed in plasma. It develops due to the fact that
the surface of the electrically isolated object is charged negatively because of
the larger mobility of electrons. The charge of the object will be stabilized
at a floating potential when the balance between electronic and ionic flux is
reached [34,35,39,43].
Applied RF potential
The applied RF potential Vappl(t) is measured at the exit of the power supply
before the blocking capacitor (Fig. 3.1).
26 CHAPTER 3. PLASMA ENHANCED CVD
Figure 3.1: Scheme of the chosen reactor geometry for asymmetrical capacitively
coupled RF discharge (on the left) ; Driving voltage, Vrf (dashed line
on the right), and plasma potential, Vp (solid line on the right.) [39,43]
Potential on powered electrode
The potential on the powered electrode Vrf (t) is the potential on the RF
electrode (Fig. 3.1) and it oscillates around the bias potential.
Negative self-bias potential
Most RF discharges are asymmetrical at low pressures, even if the area of
parallel plate electrodes is the same because the RF current is confined not
only by the electrodes, but also by the walls of the deposition chamber.
The dc voltage between the plasma and the powered electrode is larger than
that of between the plasma and the grounded electrode. A negative selfbias
voltage, Vbias, is created on the powered electrode. Fig. 3.1 on the left
shows the geometry of apparatus used to acquire capacitive RF discharges.
On the right the idealized time dependent plasma potential Vp(t) together
with driving voltage Vrf (t) is illustrated [43].
During the first half period of the positive cycle, the electrons are attracted
to the cathode, causing an accumulation of the negative charge due to the
existence of the blocking capacitor. In the negative half period a similar
phenomenon but in opposite direction occurs for ions. After a few periods,
equilibrium is reached between the electron and ion currents and the voltage
at the cathode stabilizes at Vbias. The value of this voltage depends on the
ratio of the areas between the grounded and powered electrode. This ratio
is given by the following relationship:
Vbias = 1 −
Ag
Arf
n
. ¯Vp, (3.3)
where Ag is the area of the grounded anode, Arf is the area of powered
cathode, ¯Vp is the average plasma potential and n is a constant depending
on the pressure. It can be shown that the ratio of the voltages on powered
and grounded electrodes
¯Vrf
¯Vg
is proportional to the ratio of the grounded
3.1. THE CHARACTERISTICS OF THE PECVD PROCESS 27
electrode area and the powered electrode area
Ag
Arf
[34,40]:
¯Vrf
¯Vg
≈
Ag
Arf
q
q ≤ 2.5 (3.4)
3.1.2 Glow discharge
In Fig. 3.1 the schema of the apparatus with capacitive configuration of
electrodes is shown. The application of potential difference between the
electrodes causes collisions between electrons and molecules in the gas. If
the generated potential difference is high enough, electron sources such as
ionization and secondary electron emission from the cathode increase the
electron population so much, that charge carriers are multiplied through an
avalanche process and the discharge becomes ignited. The electrons emitted
from the cathode by the bombardment of the accelerated ions arrive in the
plasma, and give rise to excitation and ionization collisions with the gas
atoms. The ionization collisions create new ion-electron pairs. The ions
are again accelerated towards the cathode, giving rise to new electrons.
The electrons can again produce ionization collisions, creating new electronion
pairs. The above described processes make the glow discharge a selfsustaining
plasma.
Plasma sheaths
Charged particles are lost by recombination or by diffusion to the electrodes
and to the reactor wall. Because of the higher mobility of the electrons
compared to the ions, the electron loss at the electrodes and wall is larger
than the ion loss. Subsequently, the electrodes will be charged negatively
with respect to the plasma. In front of both electrodes an electric field is
formed between the plasma and the electrode, in which the electrons are
repelled and the ions are accelerated towards the electrode. These positive
space charge regions are called the sheaths [38]. In Fig. 3.2 the plot of
potential profile along the x axis is illustrated. The role of plasma sheaths in
material processing is critical [35]. The materials to be treated are placed in
the boundary regions of plasmas. Therefore, ion bombardment in sputtering
targets, deposition of atoms, ion etching and ion implantation are controlled
by the shape and the potential drop in the sheaths. Several models of plasma
sheaths have been developed. Eq. 3.5 provides the sheath potential, Φ, and
ion and electron densities in a collisionless sheath [34]:
d2
dx2 Φ =
enx
ε0
exp
eΦ
kTs
− 1 −
eΦ
ξ
− 1
2
(3.5)
where nx is the electron or ion density at the sheath edge, Te is the electron
temperature, e is the elementary charge (1.602x10−19 C), k is the Boltzmann
28 CHAPTER 3. PLASMA ENHANCED CVD
Figure 3.2: Scheme of the plasma generated in a capacitive configuration.
The electric field associated to the sheaths promotes ion bombardment onto
the electrodes [41].
3.1. THE CHARACTERISTICS OF THE PECVD PROCESS 29
Figure 3.3: The Paschen curves for several different gases
constant (1.38x10−23 J/K), and ξ is the initial ion energy. Usually, sheath
thickness can be estimated by using the high-voltage approaches of matrix
sheath or Child Law sheath. These approximations point to thicknesses
between 10 and 100 times the Debye length, while smaller values as pressure
increases are observed in collisional sheaths [34,40,41].
Breakdown voltage The breakdown voltage, Vb, is the voltage which is
necessary for the discharge to be self-sustained. It is a function of the
product of the pressure p and the distance d between the electrodes, p.d.
The plotted curve in Fig.3.3 Vb(p.d) is called the Paschen curve, and shows
a minimum at intermediate values of p.d. For too low or too high values of
p.d the discharge will not ignite.
Debye length The electron Debye length, λDe , is the characteristic length
scale in a plasma. The Debye length is defined by the following relations [37]:
λDe =
ε0kTe
en0
(3.6)
It is the distance scale in plasmas over which potential gradients vanish.
Φ(x) = Φ0 exp −
abs(x)
λDe
(3.7)
For low-pressure plasmas, λDe ∼ 0.1 mm. Te, ne, and are fundamental
parameters in plasmas. Along with plasma potential, their values are of
30 CHAPTER 3. PLASMA ENHANCED CVD
great utility in the discussion of glow discharge properties. The parameter
restricts sheath dimensions and fulfills the relation:
λDe =
υTe
ωpe
(3.8)
where is the electron thermal velocity and is the electron plasma frequency:
ωpe =
e2n0
ε0m
(3.9)
with m being the electron mass. It can be considered the fundamental
characteristic frequency of the plasma,ωp , since vibrational amplitude of
ions, ωpi , is neglected as a consequence of infinite ion mass assumption:
ωp = ω2
pe + ω2
pi ≈ ωpe (3.10)
This frequency has a clear physical meaning. The electron cloud in plasma
oscillates with respect to the ion cloud at this natural frequency, when both
clouds are displaced as response of an external perturbation. This is a
mechanism to keep the electric quasineutrality in plasmas.
Ion energies
Various approaches to quantitative description of the effect of ion bombardment
on the the quality of films prepared by PECVD have been taken [35].
Martinu et al [36] proposed that there exist critical ion energies (Ei)c and
critical ion to neutral flux ratios ( Φi
Φn
)c, which can be associated with transitions
in the evolution of the film microstructure and properties. According
to their research, the energy EP delivered to the growing film per deposited
particle can be adjusted to the same level by combining low and high (Ei)c
and ( Φi
Φn
)c values. It was suggested that good-quality (dense, hard, chemically
stable, low-stress) films are obtained under conditions of low (10-50
eV) or intermediate (about 100 eV) ion energies, sufficient for densification
(Ei ∼ (Ei)c), but using high Φi. This reduces microstructural damage and
gas entrapment yielding low values of stress. High fluxes are highly advantageous,
especially when one aims at achieving high deposition rates (higher
than 10 nm/s).
Plasma gas-phase reactions and plasma-surface interactions
Plasma gas-phase chemical reactions are largely responsible for the chemical
composition of the deposited films along with plasma-surface interactions
and substrate surface conditions, which control the film microstructure and
surface morphology. During deposition, the bulk plasma parameters generally
control the rate at which chemically active precursor species (molecular
fragments free radicals) and energetic species (electrons, ions, photons) are
created. Even for relatively simple gas mixtures involving two or three gases,
several dozens of plasma reactions are taking place and many new species
3.1. THE CHARACTERISTICS OF THE PECVD PROCESS 31
are created [35]. Optimization of the PECVD processes involves identification
of plasma parameters prospective for the formation of large densities
of free radicals that diffuse toward the substrate surface, as well as to high
concentrations of ions. The processes leading to the deposition of thin films
in the plasma environment include reactions in the gas phase, transport toward
the surface involving specific energetic considerations, and reactions
at the surface, giving rise to film formation and microstructural evolution,
providing specific film functional properties. In Tab. 3.3 examples of the
basic reactions in active plasma environment are given [35].
32 CHAPTER 3. PLASMA ENHANCED CVD
Reaction General equation Example
Reactions with electrons
Ionization e + A → A+ + 2e e + N2 → N2
+
+ 2e
Excitation e + A → A∗ + e e + O2 → O2
∗
+ e
Dissociation e + AB → e + A + B e + SiH4 → e + SiH3 + H
Dissociative ion-
ization
e + AB → 2e + A+ + B e + TiCl4 → 2e + TiCl3
+
+ Cl
Dissociative
attachment
e + AB → A + B e + SiCl4 → Cl + SiCl3
Three-body
recombination
e + A+ + B → A + B e + H+ + CH4 → H + CH4
Radiative recom-
bination
e + A+ → A + hν e + Ar+ → Ar + hν
Reactions between heavy species
Charge A+ + B → A + B N2
+
(fast) + N2(slow) →
exchange N2(fast) + N2
+
(slow)
Penning ioniza-
tion
A∗ + B → A + B+ + e He∗ + O2 → He + O2
+
+ e
Ionization by in-
terchange
A+ + BC → AB+ + C N+ + O2 → NO+ + O
Combination A + B → AB 2SiH3 → Si2H6
AB + CD → AC + BD SiH2 + O2 → SiO + H2O
Heterogeneous interactions (with surfaces)
Adsorption Rg + S → RS CH2 + S → (CH2)S
Metastable deex-
citation
A∗ + S → A + S N2
∗
+ S → N2 + S
Sputtering A+ + BS → A + B Ar+ + HS → Ar + H
Secondary electron
emission
A+ + S → S + e O+ + S → S + e
Table 3.3: Basic reactions in active plasma environments R: radical; S:
surface; g: gas [35].
Part II
Analysis methods
33
Chapter 4
Scanning Electron
Microscopy
Mgr. Jana Jurmanov´a, Ph.D.
The scanning electron microscope (SEM) was invented in 1942, the first
commercial models were constructed in 1965 by the Oatley Laboratory at
Cambridge University in the UK. In Brno scanning electron microscopes are
produced by three companies: Tescan, Thermo Fisher (formerly FEI) and
Delong Instruments. Every third electron microscope in the world is made
in Brno.
The SEM is used for observation and analysis of specimen surfaces. When
the specimen is irradiated with a fine electron beam (called an electron
probe) different signals are emitted from the specimen’s surface and from a
small depth under the surface. The electron beam is scanned by scanning
coils over the surface of the specimen and an image is obtained from the
entire field of view on the sample surface.
4.1 The advantages of SEM in comparison with
optical microscope
• The electron microscope has a better resolution then optical. The resolution
is determined by the wavelength of used particles - for photons
it is about 200 nm, while for electrons it is about 1 nm (in dependence
on the accelerating voltage and adjustment of the whole imaging system).
The resolution determines the possible image magnification.
• The electron microscope has a larger depth of field (depth of focus),
about several millimeters or more (in dependence on the numerical
aperture of objective).
• The electron microscope uses more types of signals in comparison to
35
36 CHAPTER 4. SCANNING ELECTRON MICROSCOPY
the optical microscope (secondary electrons, backscattered electrons,
Auger electrons, cathodoluminescence, X-ray signals etc.).
4.2 SEM construction
In this part will be briefly describe the construction of important parts of the
electron microscope. Many more details can be found in [44], [45], [46], [47]
and [48], in Czech [49] and [56].
The block diagram of the microscope can be seen in Fig. 4.1.
Figure 4.1: The set-up of a scanning electron microscope – taken from [53]
4.2.1 Gun
The electron gun produces the electron beam. More types of the guns exist,
most often with thermionic emision (TE), field-emission (FE) and Shottkyemission
(SE). The construction of these guns is schematically drawn in
Fig. 4.2.
FE and SE are the most often used guns. The field emision gun has smaller
electron source size (5 - 10 nm versus 15 - 20 nm), energy spread (0.3 eV versus
0.7∼1 eV) and lower lifetime (several years versus 1 to 2 years) in comparison
with Shottky emission gun. The Shottky emission gun has smaller current
fluctuation (< 1 % versus > 10 %).
4.2. SEM CONSTRUCTION 37
+
+
+
-
-
Bias
power
supply
Filament heating power supply
Accelerating voltage
power supply
Accelerating
electrode
Wehnelt
electrode
Emitter
Emitter
Emitter
Real
Crossower
= Source
(15μm)
+
-
Extracting
electrode
+
+
-
-
Extracting
voltage
power
supply
Extracting
voltage
power
supply
Supresing
voltage
power
supply
Flashing power supply
Accelerating voltage
power supply
Accelerating
electrode
Virtual
Source
(10 nm)
+
++
+
-
-
-
Heating
power supply
Accelerating voltage
power supply
Accelerating
electrode
Extracting
electrode
Virtual
Source
(20 nm)
Construction of the TE gun
Construction of the FE gun Construction of the SE gun
Supresor
Energy diagram
Figure 4.2: Construction of thermionic emision (TE), field-emission (FE)
and Shottky-emission (SE) guns and the energy diagram of emissions from
the metal to vacuum
38 CHAPTER 4. SCANNING ELECTRON MICROSCOPY
4.2.2 Vacuum system
The inside of the electron optical system and the specimen chamber must be
kept at high vacuum of 10−3 to 10−4 Pa. These components are evacuated by
a turbomolecular pump backed by an oil-free pump (diffusion pump, scroll).
FE or SE guns need ultrahigh vacuum and a sputter ion pump is used.
4.2.3 Electromagnetic lenses and scanning coils
The electron optical system for a SEM consists of four lenses – condenser
lens, second condenser lens, objective lens, stigmators (see Fig. 4.1). The
lenses are constructed based on the magnetic, the electromagnetic or the
electrostatic principle. The focal length of lenses and the size of the beam
spot can be changed by changing the current flowing through the coils.
Condenser lens – the adjustment of the excitation of this lens provides
for changing of the electron beam diameter and the beam current.
Objective lens – is used for focusing, it determines the final diameter of
electron beam.
Stigmators – lenses without spherical symmetry (quadrupole, octopole)
reduce astigmatism of the beam.
Scanning coils – move the electron beam over the sample. High scanning
speed is used to observe the field of view, lower speeds are used for image
acquisition.
4.2.4 Detectors
The detectors process the signals generated in the sample by the electron
beam. Usually we use a secondary electron detector, a backscattered electron
detector and X-ray detectors.
The Everhart-Thornley detector is most often used for the detecting of
electrons emitted from the specimen. The construction is shown in Fig. 4.3.
The electrons from the specimen are attracted to the detector and hit the
scintilator to create a light signal. This light is directed to a photo-multiplier
tube throught a light guide. Then, the light is converted to electrons, and
these electrons are amplified as a electric signal.
This detector is appropriate as the secondary electrons detector (with the
positive voltage on the collector before the scintilator) or as the backscattered
electrons detector (without the positive voltage on the collector and
over the specimen). For the backscattered electrons, another detector constructions
are also possible.
4.2. SEM CONSTRUCTION 39
Figure 4.3: Construction of Everhart-Thorneley detector for secondary
electrons – picture is published in http://www.technoorg.hu/news-and-
events/articles/high-resolution-scanning-electron-microscopy-1
The X-ray detectors have usually two possible constructions - EDX
(energy-dispersive X-ray spectroscopy) with SDD (silicon drift detector) detector
and WDX (wave-dispersive X-ray spectroscopy) with the gas proportional
counter type.
The EDX analyzer analyzes the characteristic X-ray spectra by measuring
the energies of the X-rays. The X-rays emitted from the specimen enter the
semiconductor detector, electron-hole pairs are generated whose quantities
correspond to the X-ray energy. The X-ray analysis of all the elements from
boron to uranium are made simultaneously. The EDX detector is shown
in Fig. 4.4, more information about Oxford Instruments EDX detector is
in [52].
Figure 4.4: Construction of EDX detector and EDX spectrum
Inside the WDX spectrometer, crystals of specific lattice spacing are used
to diffract the characteristic X-rays from the sample onto the detector (see
Fig. 4.5). The wavelength of the X-rays diffracted into the detector may be
selected by varying the position of the analysing crystal with respect to the
sample, according to the Bragg’s law
nλ = 2d sin θ, (4.1)
40 CHAPTER 4. SCANNING ELECTRON MICROSCOPY
where n is an integer referring to the order of the reflection; λ is the wavelength
of the characteristic X-ray; d is the lattice spacing of the diffracting
material; and θ is the angle between the X-ray and the diffractor’s surface.
A constructive interference and high intensity diffracted signal occurs only
when this condition is met and therefore interference from peaks from other
elements in the sample is inherently reduced. However, X-rays from only one
element at a time may be measured by the spectrometer and the position
of the crystal must be changed to tune the WDX to another element.
Specimen
Electron
Beam
R
Johansson geometry
bent to radius 2R and
ground to radius R
X-ray
detector
Rowland
circle
Figure 4.5: Construction of WDX detector and comparison of EDX and
WDX spectra
4.2.5 Stage
The stage moves with the sample. The image sharpening is done by moving
the stage in the vertical direction. The stage can be moved in x,y (horizontal
plane) axes and in z-axis, can be rotated around z-axis and can be tilted
around z-axis.
4.2.6 Scanning electron microscope Mira 3 – parameters
MIRA3 is a high performance SEM system which features a high brightness
Schottky emitter for achieving high resolution and low-noise imaging. Its
excellent resolution at high beam currents has proven to be especially advantageous
for EDX, WDX. The MIRA3 configurations include GM chamber
sizes with optimised geometry capable of both low and high vacuum opera-
tions.
Key features
• High brightness Schottky emitter for high-resolution/high
current/low-noise imaging - resolution: 1 nm at 30 kV.
• Unique Wide Field Optics design with a proprietary Intermediate Lens
(IML) offering a variety of working and displaying modes, for enhanced
field of view or depth of focus, etc.
4.3. SAMPLE PREPARATION FOR SEM 41
• Excellent imaging at short working distances with the powerful InBeam
detector.
• All MIRA3 chambers provide superior specimen handling using a 5axis
fully motorized compucentric stage and have ideal geometry for
EDX.
• Investigation of non-conductive samples in variable pressure modes.
4.3 Sample preparation for SEM
SEM does not generally need a too sophisticated sample preparation. The
sample will be glued to an imaging stub with a carbon adhesive tape and
then inserted into the stage and screwed in.
• The sample has to be dust free.
• The sample has to be oil and water free.
• The operator wears dust-free latex gloves to work with samples and for
inside the chamber - there is a risk of contamination of the chamber
with fat and sweat from the fingers.
• For the observing of small particles (powders, nanopowders), the particles
have to adhere securely to the specimen holder (new carbon
tape) or fill the cavity in the holder. The sample must be blown over
by a photo balloon before insertion into the chamber to remove any
non-adherent powder and dust.
4.3.1 Suitable samples
Suitable sample is dust free, oil and water free and conductive. Such sample
will be microscoped and analysed easily.
4.3.2 Magnetic samples
Microscope without immersion objective, such as MIRA 3, allows the observation
of magnetic sample. The operator has to be carefull with such sample
in small working distance, and, especially, with the magnetic powders not
to contaminate the microscope chamber and objective.
42 CHAPTER 4. SCANNING ELECTRON MICROSCOPY
Figure 4.6: Electron mirror - image created by SE detector on the left, image
obtained by BSE detector on the right
4.3.3 Non-conductive samples
The non conductive sample will be charged under the electron beam. This
way we obtain an electron mirror (see Fig. 4.6) – the mirroring of the chamber
on the electron layer over the sample and we will not obtain the photo
of the sample surface.
A non conductive sample has to be observed carefully (low voltage, low
beam density, image acquisition mode) or it has to be coated. We use
the sputter/carbon coater Q150R ES [51] for sputtering with noble metals
(Au, Au/Pd) and for carbon coating. The usual thickness of the conductive
coating is 10 or 20 nm. The use of low-vacuum mode is appropriate for non
conductive samples, whose surface cannot be coated.
4.4 SEM signals, their detection and use
The signals generated by the electron beam in the sample are schematically
depicted in Fig 4.7.
The size of interaction volume is dependent on the accelerating voltage and
on the chemical composition of the sample. The often detected signals are
described hereunder.
4.4.1 Secondary electrons (SE)
SE have low energy (below 50eV) and are created near the surface of the
specimen (about 5 nm). Topographic sensitivity and high spatial resolution
make them the frequent choice for micrographic images that are sensitive
4.4. SEM SIGNALS, THEIR DETECTION AND USE 43
Figure 4.7: Interaction volume
Figure 4.8: Thin delaminated carbon layer on silicon wafer. On the left: SE image,
the detector is in the chamber under an angle to sample. On the right: SE image,
the detector is in the beam axis above the sample
to the tilting of the sample and to the position of the used detectors - see
Fig 4.8.
4.4.2 Backscattered electrons (BSE)
BSEs are more energetic than secondary electrons so they are able to escape
from larger depth in the sample (dependent on the sample chemical composition
and the electron beam energy). They carry information about the
sample chemical composition (the brightness is proportional to the atomic
number), but they are not as much topographic and have lower spatial resolution
compared to secondary electrons - see Fig 4.9.
4.4.3 X-rays
X-rays are generated by elastic and inelastic electron scattering on sample
nuclei. Generation of continuous spectrum of radiation (Bremsstrahlung) is
44 CHAPTER 4. SCANNING ELECTRON MICROSCOPY
Figure 4.9: Thin partially delaminated carbon layer on silicon wafer. On the
left: SE image with topographical contrast. On the right: BSE image without
topographical contrast but with elemental contrast
Figure 4.10: The classification of spectral lines. Concrete values for almost all
elements see http://www.med.harvard.edu/jpnm/physics/refs/xrayemis.html
4.5. EXAMPLES OF A THIN LAYER ANALYSIS BY MEANS OF SEM45
Figure 4.11: The resolution and depth mode - different depth of focus
the result of elastic scattering, while the consequence of inelastic scattering
is generation of characteristic lines typical for individual elements. The Xray
generation depth is larger than that of SE or BSE and depends on the
chemical composition of the sample. The used acceleration voltage has to
be 1.5 to 2 times higher than the voltage needed to generate the required
element line to ensure adequate excitation. The classification of spectral
lines is in Fig. 4.10.
4.5 Examples of a thin layer analysis by means of
SEM
This section describes how to get the most information about a sample
composed of thin layers. The theory described above will be illustrated on
specific examples.
4.5.1 How to obtain sharp photos with good resolution?
First we have to select the suitable working distance, accelerating voltage
and imaging mode - resolution or depth. If we choose a smaller working
distance, we will achieve greater magnification (and resolution) of the image,
but less depth of field. In this case, we use the resolution mode — our
microscope has the highest resolution at 30kV accelerating voltage. If we
choose a larger working distance, we do not achieve such a high resolution,
however the image has a greater depth of field, especially in the depth mode
- see Fig 4.11. We use wide field mode for overviews.
Then it is necessary to adjust the microscope as best as is possible — to
realise the gun centering, column centering, to set the working distance and
the stigmators.
46 CHAPTER 4. SCANNING ELECTRON MICROSCOPY
Figure 4.12: On the left: The thin carbon layer (37 nm) is transparent for secondary
electrons accelerated by 4 kV accelerating voltage. On the right: The layer
is chemically homogeneous, the bright surface on the left image is charged.
The accelerating voltage determines the final appearance of the image — how
bright will be the edge effect (significant lightening edges of the sample), and
whether the thin layers for the different types of electrons will be transparent
– see Fig. 4.12.
4.5.2 How to discover the chemical homogeneity of the sam-
ple?
Backscattered electrons and X-rays provide information about the chemical
composition of samples. Thus, for the first analysis the BSE detector is
used. This detector distinguishes light elements from heavy ones, but can
not determine specific elements included in the sample — it is necessary
to perform EDX analysis. If the sample includes only elements with very
close proton numbers in the sample, the shades of grey associated with
these elements are difficult to distinguish and the sample looks chemically
homogeneous – see Fig 4.13 and Fig 4.14.
4.5.3 The thickness of the layers and the cross section of the
sample
The sample thickness can be determined by the means of imaging of a delaminated
part of the layer suitably positioned against the lens of the microscope,
or by imaging of the cross-section of the sample. The thickness of
the delaminated layer is shown in Fig 4.15, the cross-section of the sample
shown in Fig 4.16.
4.5. EXAMPLES OF A THIN LAYER ANALYSIS BY MEANS OF SEM47
Figure 4.13: Carbon residue on steel mesh – the BSE detector shows the chemical
contrast between mesh material and carbon clusters, but does not specify the exact
chemical composition of the mesh.
Figure 4.14: The crystals of teluroxide between silver little branches on silicon
wafer - the contrast between silicon (atomic number 14) and heavy elements is visible,
the contrast between tellurium (atomic number 52) and silver (atomic number
47) is very small.
48 CHAPTER 4. SCANNING ELECTRON MICROSCOPY
Figure 4.15: The thickness of a delaminated layer - SE and BSE images of this
sample are Fig 4.8 and Fig 4.9
Figure 4.16: Sample cross-section. Layers are: silicon substrate, aluminum layer
(thickness 180 nm), tungsten layer (thickness 135 nm), aluminum layer (thickness
145 nm), tungsten layer (thickness 120 nm). The topography of the cross section is
visible in SE, BSE image separates the layers of lighter and heavier elements. For
the specific determination of the elements of the different layers an X-ray analysis
is required.
4.5. EXAMPLES OF A THIN LAYER ANALYSIS BY MEANS OF SEM49
Figure 4.17: The map sum spectra of sample in Fig 4.8 measured at 4 kV (red)
and 15 kV (yellow) – which results are correct?
4.5.4 The information obtained by X-ray analysis
X-ray spectroscopy can exactly determine the chemical composition of the
sample — elements from boron to uranium can be measured. The results
can be represented as a spectrum (chemical composition at a given location),
a map (artificial colours for detected elements) or linescan (graph of the
concentration of the elements on the position along the selected line).
The operator needs to choose the correct accelerating voltage to have one
and a half to two times the electron’s excitation energy to correctly determine
the element. However,with increasing energy of the electron, the depth
of penetration increases. If multiple thin layers are analysed, misinterpretations
may occur by choosing to high acceleration voltage.
Spectrum and map
For example — a thin (about 40nm) carbon layer on a silicon wafer – see
Fig. 4.8 and Fig. 4.9 — will be analysed. The first analysis was performed
with an accelerating voltage of 15 kV in order to find all the expected elements
and possible impurities. Silicon, carbon and oxygen were detected
(argon is included in the deposition atmosphere). The characteristic energy
for carbon, oxygen and silicon are 0.277 keV C-Kα1, 0.5249 keV O-Kα1 and
1.73998 keV Si-Kα1 (moreover Kα2 and Kβ1). At an accelerating voltage
of 15 kV, the penetration depth into the silicon is much greater than the
thickness of the layer — see Fig 4.18. The ratio between silicon and carbon
concentration is therefore totally incorrect. The results obtained by the 4 kV
analysis (2 times energy Si-Kα1) are more accurate.
The maps measured using these accelerating voltages are shown in Fig 4.19,
Fig 4.20 and Fig 4.21. Obviously, using lower accelerating voltage leads to
better results.
Linescan
50 CHAPTER 4. SCANNING ELECTRON MICROSCOPY
Figure 4.18: The Casino (monte CArlo SImulation of electroN trajectory in sOlids)
simulates recorded signals (X-rays and backscattered electrons) in a scanning electron
microscope for 4kV and 15kV accelerating voltages. The X-ray resolution and
the signal depth are very diferent for these voltages.
Figure 4.19: Comparison of the maps for 15 kV (on the left) and 4 kV (on the
right) - part one. See Fig. 4.8 for the topology of the sample.
4.5. EXAMPLES OF A THIN LAYER ANALYSIS BY MEANS OF SEM51
Figure 4.20: Comparison of the maps for 15 kV (on the left) and 4 kV (on the
right) - part two. See Fig. 4.8 for the topology of the sample.
52 CHAPTER 4. SCANNING ELECTRON MICROSCOPY
Figure 4.21: Comparison of the maps for 15 kV (on the left) and 4 kV (on the
right) - part three. See Fig. 4.8 for the topology of the sample.
Figure 4.22: The simulations obtained by the CASINO software are shown on
the left side . The spectrum of sample shown on the right side on Fig. 4.16 was
measured perpendicularly to the sample surface at the beam voltage of 4 kV. The
accelerating voltage used for the measurement is the lower limit for the detection
of tungsten. Electrons penetrate through one layer.
4.5. EXAMPLES OF A THIN LAYER ANALYSIS BY MEANS OF SEM53
Figure 4.23: The simulations obtained by the CASINO software are shown on
the left side . The spectrum of sample shown on the right side on Fig. 4.16 was
measured perpendicularly to the sample surface at the beam voltage of 8 kV. The
accelerating voltage used for the measurement is twice the lower limit for the detection
of tungsten. Electrons penetrate two layers, the spectrum must be interpreted
with this in mind.
Figure 4.24: The simulations obtained by the CASINO software are shown on
the left side . The spectrum of sample shown on the right side on Fig. 4.16 was
measured perpendicularly to the sample surface at the beam voltage of 10 kV.
Electrons penetrate through three layers.
Figure 4.25: The simulations obtained by the CASINO software are shown on
the left side . The spectrum of sample shown on the right side on Fig. 4.16 was
measured perpendicularly to the sample surface at the beam voltage of 15 kV.
Electrons penetrate through four layers.
54 CHAPTER 4. SCANNING ELECTRON MICROSCOPY
Figure 4.26: The simulations obtained by the CASINO software are shown on
the left side . The spectrum of sample shown on the right side on Fig. 4.16 was
measured perpendicularly to the sample surface at the beam voltage of 20 kV.
Electrons penetrate through four layers.
Figure 4.27: The linescan of the sample shown in Fig. 4.16 were measured via the
sample cross-section. The interpretation of the linescan results needs to factor in
the acceleration voltage (15 kV as in Fig. 4.25.
Linescan is a very useful tool when the sample changes the element concentration
in the chosen direction. A linescan across the layers of the sample
shown in Fig. 4.16 are plotted in Fig. 4.27. The result depends on the choice
of the appropriate accelerating voltage. The accelerating voltage must be
sufficient to determine all the elements, but the spatial region from which the
X-ray signals are generated must be less than the thickness of the individual
analysed layers.
Chapter 5
Atomic Force Microscopy
doc. RNDr. Vilma Burˇs´ıkov´a, Ph.D.
5.1 Atomic force microscopy principle
The atomic force microscope (AFM) was invented in 1986 by Binning et
al [59]. From that time the AFM equipments have undergone a large development.
Recently, the AFM is an invaluable technique not only to acquire
high-resolution topographical images, but also to map certain physical properties
of specimens, such as their mechanical, electrical, magnetic or chemical
properties. The AFM technique has the advantage that it can image
both conducting and non-conducting samples, including polymers, ceramics,
composites, glass and biological samples. With the recent AFM devices,
the topography and structure of a surface can be studied either in air or in
fluid. That means, that using this imaging technique, it is possible to map
sample surfaces under natural conditions (in ambient air or water) without
the samples being placed under destructive artificial conditions, such
as drying, coating with metal, placing into vacuum conditions or freezing.
AFM enables not only imaging, but also touching the tested objects and
manipulating with them at the nanoscale.
The development of three technical improvements were necessary for the
invention and for the further development of atomic force microscopes:
• development of piezoelectric materials (piezoscanners)
• micromachining of cantilevers (MEMS technology)
• cantilever deflection measurement techniques
55
56 CHAPTER 5. ATOMIC FORCE MICROSCOPY
5.1.1 Piezoelectric control of x,y and z movements
The piezoelectric ceramic material expands or contracts depending on the
polarity of the voltage applied on them. The piezoscanner is constructed
by combining independently piezoelectrodes for x, y and z direction. The
piezoscanner is able to manipulate the tip or the sample with extreme precision.
The scan range is established by setting the minimum and the maximum
voltage and the position is established by offsetting the voltages on
the piezoceramic. The scan orientation is changed by changing the phase
between the signales. The relationship between the piezo-movement and
piezovoltage is not linear and due to that fact the piezoscanner behaves differently
when it contracts compared to its expansion. This causes hysteresis
and differences between the forward and backward scan directions.
5.1.2 Cantilevers
In order to acquire images with excellent resolution it is necessary to have
cantilevers with sharp tips, high displacement and high force sensitivity.
Recently, the cantilevers are prepared using MEMS fabrication [61]. The
following formula shows the relationships between the force F acting on the
cantilever, and its displacement ∆z at the place, where the tip is mounted
(see Fig.5.1) :
∆z = w(L) =
FL3
3EI
, (5.1)
where w(x) is the displacement of the centre axis as a function along the
cantilever, L is the cantilever length E is the cantilevers Young’s modulus
and I is the moment of inertia.
The moment of inertia can be expressed as:
I =
bh3
12
, (5.2)
where b is the cantilever width and h is its thickness.
For the deflection angle (see Fig.5.2 ) at the end of the cantilever it is possible
to calculate :
θ =
dw(L)
dx
=
FL2
2EI
, (5.3)
Both the cantilever deflection at the end as well as the slope at the end of
the cantilever are proportional to the force applied to the tip. Therefore the
cantilever spring constant k can be expressed as follows:
k =
3EI
L3
=
Ebh3
4L3
. (5.4)
5.1. ATOMIC FORCE MICROSCOPY PRINCIPLE 57
Figure 5.1: Schematic of the AFM cantilever [61].
Figure 5.2: Schema of the cantilever deflection [61].
5.1.3 Cantilever deflection detection method
Recently, most of the AFMs use a laser beam to detect the cantilever deflection.
The laser shines onto the back of the cantilever, which is coated with
a reflecting film (for example gold), and the angle of the reflected beam is
measured using a four-quadrant laser diode. The deflection and the torsion
of the cantilever can be measured on the basis of the total amount of the
laser light, that hits on the four quadrants (see Fig. 5.3) :
Vertical deflection =(A1 + A2) − (B1 + B2)
Horizontal deflection (torsion)=(A1 + B1) − (A2 + B2).
Because the cantilever deflection is proportional to the force acting on the
cantilever (and it is proportional to the tip displacement) we can use the
deflection angle change as a measure of the tip displacement.
5.1.4 Feedback control
The feedback control is necessary in order to maintain a fixed relationship
(force, displacement, etc.) between the tip and the scanned surface. The
feedback control enables to keep the forces between the tip and the surface
58 CHAPTER 5. ATOMIC FORCE MICROSCOPY
Figure 5.3: Cantilever deflection readout [61].
at user defined setpoint level. For example in case of the contact mode,
when the control signal (in the case of the contact mode this is the cantilever
deflection) is above the setpoint. When the deflection is less than
the specified setpoint, the feedback loop will expand the piezo to move the
tip closer to the sample. Although signal processing varies according to the
image mode used (contact mode, tapping mode, etc.), the feedback loop
always performs essentially the same function. The feedback system used
to control tip-sample interactions and render images must be optimized for
each new sample. This is accomplished by adjusting various gains in the
SPM`s feedback circuit.
In the AFM, the feedback control device takes an input from the force
sensor and compares the signal to a set-point value. The resulting signal is
the error signal, which is sent through a feedback controller. The output of
the feedback controller then drives the z piezoelectric ceramic. The most
common implementation of a feedback loop in AFM is via proportional,
integral and derivative (PID) controller. The PID controller takes the error
signal and processes it as follows [62]:
Z(t) = P (s(t) − sset) + I
t
0
(s(t − τ) − sset) dτ + D
d
dt
(s(t − τ) − sset) ,
(5.5)
where Z(t) is the response signal, s(t) is the signal from the measured interaction,
sset is the signal, what was set, (s(t) − sset) is the error signal and
P,I, and D have the following meaning:
• P is the proportional term describing the immediate response to the
difference between the setpoint and the measured signal. It allow the
probe to follow smaller, high frequency features on a surface.
5.1. ATOMIC FORCE MICROSCOPY PRINCIPLE 59
• I is the integral term and it helps the system to reach the setpoint
value if the present interaction signal value is only slightly shifted
from the required value (in that case the P term would react too
slowly). Moreover, the I term smooths the response to noise due to
its averaging nature. The integral term facilitates the probe moving
over larger surface features.
• D is the derivative term and it describes the response to te change in
the error.
When the PID parameters are optimized, the error signal image will be
minimal. As a rule of thumb: the higher the feedback gains, the faster
the feedback loop can react to changes in topography while scanning [61].
Therefore, ideally one would set the gains as high as possible. However,
since the AFM is not infinitely fast in responding to the output of the PID
controller, one can only increase the feedback gains to a certain value. This
also limits the maximum achievable scan speed. Establishing where this
point is requires practice and some intuition.
5.1.5 Basic AFM modes
The principle of atomic force microscopy is based on detection of interaction
forces between the probe and the force field associated with a studied material
surface. The simplest model describing the interaction between two
atoms is the Lennard-Jones (LJ) potential (see Fig. 5.4) It can be described
by the formula
U(r) = 4ε
σ
r
12
−
σ
r
6
= ε
rm
r
12
− 2
rm
r
6
, (5.6)
where ε is the measure of the interaction strength (it corresponds to the
depth of the potential well), σ is the interatomic distance, where the potential
is zero and rm is the distance at which the potential reaches its
minimum.
According to the Fig. 5.5, there are three basic regions of interaction between
the probe and surface:
• free space
• attractive region
• repulsive region
Attractive forces near the surface are caused by a nanolayer of contamination
that is present on all surfaces in ambient air. The contamination is typically
60 CHAPTER 5. ATOMIC FORCE MICROSCOPY
Figure 5.4: Lennard-Jones potential.
Figure 5.5: Lennard-Jones potential. Illustrations of the contact, semicontact
and non-contact mode.
5.1. ATOMIC FORCE MICROSCOPY PRINCIPLE 61
an aerosol composed of water vapor and hydrocarbons. The amount of
contamination depends on the environment in which the microscope is being
operated. Repulsive forces increase as the probe begins to ‘contact’ the
surface. The repulsive forces in the AFM tend to cause the cantilever to
bend up. There are two primary methods for establishing the forces between
a probe and a sample when an AFM is operated. In contact mode the
deflection of the cantilever is measured, and in vibrating mode the changes
in frequency and/or amplitude are used to measure the force interaction. As
a rule of thumb, the forces between the probe and surface are greater with
contact modes than with vibrating modes.
Contact mode
In Contact mode, the cantilever deflection during the scanning reflects repulsive
force acting upon the tip, which is related to the cantilever deflection
value x under Hooke’s law: F = -kx. Here k is the cantilever spring constant,
which usually vary from 0.01 to several N/m. The main disadvantages
of Contact Mode are, that soft samples can be destroyed by the scratching
because the probe scanning tip is in direct contact with the surface. As a
result the acquired topography of the sample may become distorted. The
possible existence of substantial capillary forces imposed by a liquid adsorption
layer can decrease the resolution. There are two different possibilities
to scan the surface in Contact mode [63]:
• Contact Height Mode - The scanner of the microscope maintains fixed
end of cantilever on the constant height value. Therefore the deflection
of the cantilever reflects topography of sample under investigation
(Fig. 5.6). The main advantage of Constant Height mode is the high
scanning speed, which is restricted only by resonant frequency of the
cantilever. The disadvantage of this mode is that the scanned samples
must be sufficiently smooth.
• Constant Force Mode - The deflection of the cantilever is maintained
by the feedback circuitry on the preset value. So the vertical displacement
of the scanner under scanning reflects topography of sample
under investigation (Fig. 5.7). The main advantage of Constant
Force mode is the possibility to measure with high resolution simultaneously
with topography some other characteristics, such the friction
forces, spreading resistance etc. The disadvantage of the Constant
force mode is that the speed of scanning is restricted by the response
time of feedback system.
62 CHAPTER 5. ATOMIC FORCE MICROSCOPY
Figure 5.6: Constant Height Mode [63].
Figure 5.7: Constant Force Mode [63].
5.1. ATOMIC FORCE MICROSCOPY PRINCIPLE 63
Figure 5.8: Semicontact Mode - tip landing [63].
Semicontact Mode
The dynamic AFM mode is often also called tapping, semicontact or intermittent
contact mode. In case of this mode, the cantilever is excited at a
fixed frequency f that is below the free resonance frequency fo. Far away
from the surface, the cantilever oscillates with amplitude of Ao (see Fig. 5.8).
When the cantilever gets closer to the surface, the resonance curve shifts,
but the cantilever is still excited with frequency f.
When the oscillating cantilever approaches the surface, the amplitude of the
oscillation decreases (see Fig. 5.9). This decrease in amplitude can be used
as the feedback parameter for AFM imaging, similarly like the cantilever
deflection in contact mode. However, there is a difference, in the semicontact
mode, decreasing the setpoint value increases the force on the sample on
contrary to contact mode, where decreasing the setpoint decreases the force
on the sample. The resonance behavior of the cantilever is shown in Fig. 5.10.
The black curve in Fig. 5.10 B represents the situation far away from the
surface and the red curve in Fig. 5.10 B represents the situation close to the
surface. When the cantilever gets close to the surface, an additional restoring
force acts on the cantilever (the tip sample interaction pushes the cantilever
back), and this manifests itself as an increase in the spring constant, which
manifests itself in a shift of the cantilever resonance frequency to higher
values [61].
Using the change in amplitude as a feedback parameter is called operating
the AFM in amplitude modulation (AM) mode. In case of the frequency
64 CHAPTER 5. ATOMIC FORCE MICROSCOPY
Figure 5.9: Semicontact Mode - scanning [63].
Figure 5.10: Amplitude dependence on the tip-sample distance in semicontact
mode [61].
5.1. ATOMIC FORCE MICROSCOPY PRINCIPLE 65
modulated (FM) mode the feedback parameter is the frequency. The amplitude
modulation mode is the most common way to operate the AFM.
Cantilever for semicontact mode are stiffer than cantilever for contact mode
to allow for a higher resonance frequency. Typical values for k are 40N/m
and fo 300-400kHz.
Electrostatic force microscopy modes
The electrostatic force AFM modes are based on the detection of tip-sample
electrostatic forces. They include Electrostatic force microscopy (EFM),
Kelvin probe force microscopy (KPFM) and probing of local dielectric properties
in various configurations including Maxwell stress microscopy and
others. These modes were introduced for mapping the variations of electrostatic
force, measurements of local surface potential and dielectric permittivity
[64]. Electrostatic force microscopy (EFM) is a type of dynamic
atomic force microscopy where the electrostatic force between the sample
and the conductive tip is probed. This force arises due to the attraction or
repulsion of separated charges. It is a long-range force and can be detected
100 nm or more from the sample [60]. In case of the two-pass EFM technique
the conductive tip scans the surface to get the topography map. Then, the
tip is distanced from the sample surface and records the offsets of the phase
signal of the interactions with the gradient of electrical forces present on
the surface at the same frequency that in case of scanning. In case of the
single-pass EFM technique the conductive tip detects simultaneously the
mechanical and electrostatic interactions at different frequencies [64]. This
approach requires a use of several lock-in amplifiers in the detection system.
Magnetic force microscopy modes
In case of magnetic force microscopy (MFM) it is possible to map the space
distribution of some parameters characterizing magnetic probe-sample interaction,
such the interaction force, amplitude of vibrating magnetic probe
and the like. This is a two pass technique. In the first pass (see Fig. 5.11)
the topography map is acquired in Contact or Semicontact mode. In the
second pass the magnetic tip is lifted from the surface (Fig. 5.12) to a certain
height from the surface. The tip-sample separation during second pass
scanning kept constant. This tip-sample separation must be large enough to
eliminate the Van der Waals forces in order to affect the cantilever only by
long-range magnetic force. Both the height-image and the magnetic image
are obtained simultaneously with this method [63].
The MFM modes may be divided into to categories: DC MFM and AC
MFM.
66 CHAPTER 5. ATOMIC FORCE MICROSCOPY
Figure 5.11: Magnetic mode microscopy - topography mapping [63].
Figure 5.12: Magnetic mode microscopy - magnetic force scanning in DC
MFM mode [63].
5.1. ATOMIC FORCE MICROSCOPY PRINCIPLE 67
Figure 5.13: Magnetic mode microscopy - magnetic force scanning in AC
MFM mode [63].
In case of the DC MFM during second pass the deflection (DFL) of a nonvibrating
cantilever is detected. In the AC MFM during second pass the
cantilever resonance oscillations are used to detect the magnetic force data
(just as in the semicontact mode)(Fig. 5.13).
Force - distance curves
Using the AFM tip it is possible to record force-distance (FD) curves similarly
as in case of nanoindentation. The plot of cantilever deflection is
obtained as a function of sample position along the z-axis (see Fig. 5.14).
68 CHAPTER 5. ATOMIC FORCE MICROSCOPY
Figure 5.14: Measurement of force - distance curves [63].
Chapter 6
X-Ray Diffraction
Mgr. Pavel Souˇcek, Ph.D.
X-ray diffraction is a widely used non-destructive method of analysis of at
least partly crystalline samples. X-ray diffraction is used for identification of
the present crystalline phase and for its subsequent quantitative analysis —
evaluation of the crystallite size, the lattice parameter, preferential growth
orientation and the crystallite strain.
6.1 Theoretical background
In 1912 Max von Laue discovered that crystalline material acts as a threedimensional
grating for X-rays. If we consider that monochromatic X-ray
radiation is incident on a polycrystalline material and that all the grains
are small and all grain growth orientations are present, only those grains
for which the the Bragg diffraction rule is fulfilled will lead to constructive
interference of the radiation [57]. A sketch illustrating the Bragg rule is
shown in Fig. 6.1.
For the cubic lattice the Bragg diffraction rule can be simply written as
2d sin θ = λ h2 + k2 + l2, (6.1)
where h, k and l are the Laue indices that are calculated by multiplying the
Miller indices h0, k0 and l0 by an integer n corresponding to the diffraction
order. The diffraction intensity is determined by the structure factor of the
unit cell. For different structure types of the unit cell certain Laue indices
can be found that provide for zero intensity diffractions. These are the socalled
forbidden diffractions. In conditions corresponding to the forbidden
diffractions the waves refracted by different planes cancel out. Certain rules
for allowed diffractions exist [58]:
• simple lattice — all diffractions are allowed
69
70 CHAPTER 6. X-RAY DIFFRACTION
Figure 6.1: A sketch illustrating the Bragg rule. Taken from [65].
• face centred lattice — diffractions with the same parity Laue indices
are allowed
• base centred lattice — diffractions with even h + k + l are allowed
• diamond lattice — diffractions with odd Laue indices or diffractions
with even Laue indices whose sum is divisible by 4 are allowed
The knowledge of these rules complemented by the knowledge of present
elements allows one to identify the present lattice.
6.2 Experimental setup
The simplest geometry used for XRD measurements is the so called focussing
Bragg-Brentano geometry. This geometry is sketched in Fig. 6.2. Here, the
incident angle ω is defined between the X-ray source and the sample. The
diffraction angle 2θ is defined between the incident beam and the detector
and the incident angle ω is always 1/2 of the 2θ angle. The diffraction vector
(vector that bisects the angle between the incident and scattered beam) is
always normal to the sample surface.
The X-rays are produced by a sealed tube or a rotating anode. Both work
on a principle of X-ray generation by striking of an anode (copper in our
case) with an electron beam from a heated tungsten filament. Copper Kα
line is used for the measurement.
The X-rays from the source go through X-ray optics in a divergent ray towards
the sample. There the diffraction occurs and the X-rays are scattered
in a sphere around the sample in the so called Debye diffraction cone. A
6.3. DATA ANALYSIS 71
Figure 6.2: A sketch of the Bragg-Brentano geometry. Taken from [66].
certain part of this cone intersects the detector after going through more
optics. The signal on the detector consists of the record of photon intensity
versus the 2θ angle.
6.3 Data analysis
The diffraction pattern is a fingerprint of the diffracting material. Based
on the diffraction peak position, its width and its relative intensity in the
diffraction pattern the present phase can be positively matched to a database
pattern. Databases can consist of either measured data like the Powder
Diffraction File (PDF) of of calculated data such as the Crystallography
Open Database.
The lattice parameter can be calculated directly from the Bragg diffraction
rule, whereas the simplest way of calculation of the crystallite size comes
from using the Scherrer equation [67]. The Scherrer equation can be written
as
τ =
Kλ
β cos θ
, (6.2)
where K is the dimensionless shape factor (0.94 for round grains), λ is the
X-ray wavelength, β is the full width at half maximum of the diffraction
peak and θ is the Bragg diffraction angle. The Scherrer equation presents
the simplest case, where the total peak broadening is attributed only to
the grain size and the strain is neglected. This approach is sufficient for
powder samples, whereas care needs to be taken for thin films. The grain
strain can be estimated either by different treatment of the measured data
(Williamson-Hall analysis) or by measurements in special geometry.
72 CHAPTER 6. X-RAY DIFFRACTION
Figure 6.3: SmartLab Guidance — main screen.
6.4 Practical aspects of X-ray diffraction
XRD is a powerful fast non-destructive method of crystalline sample analysis.
Minimum preparation of the sample is needed, however, some experience
is needed to understand the acquired data. First source of confusion comes
from the nature of the X-ray radiation. The Kα line is a doublet of Kα1 and
Kα2 lines. Their separation is especially visible for diffractions at higher 2θ
angles. Moreover diffractions caused by Kβ and Wα lines can be visible.
Their intensity can be reduced by using a nickel filter in the path of the
signal from the sample to the detector. However, these lines can be present
in the measured pattern. Secondly, knowledge of the present elements is
immensely useful for the identification of the present phase. The diffraction
pattern of the substrate must be also taken into consideration.
6.5 Measurement
The practical measurements will utilize Rigaku Smartlab X-ray diffractometer
with copper sealed-tube X-ray source. The device is controlled via SmartLab
Guidance software. The main screen is sown in Fig. 6.3. The left-hand
panel (no. 1) shows the steps in the currently selected recipe or macro, panel
no 2. is for selecting macros, the central panel 3 shows the detector output,
i.e. the measurement data and the right-hand panel 4 shows the current
state of the machine.
Any measurement generally consists of 3 steps:
6.5. MEASUREMENT 73
Figure 6.4: SmartLab Guidance — measurement macro.
1. optics calibration
2. sample positioning calibration
3. measurement.
Example of such a measurement is shown in Fig. 6.4. A macro for XRD
measurement in the Bragg-Brentano configuration was selected in panel 5
and its parts is shown in panel 6. The first two steps are the calibration —
the optical path is calibrated in step 1 and the used detector is calibrated in
step 2. The measured sample is introduced into the measurement chamber
after step 2 and is aligned with the X-ray beam in step 3. The measurement
itself is step 4.
The measurement is set-up by clicking on the yellow highlighted measurement
step. A popup window appears as is show in Fig. 6.5. Here the
measurement can be configured for any specified sample. The most relevant
fields are the Start and Stop angles and the Speed of the measurement
in degrees per minute. The longer the measurement, the lower the noise.
However, this relation is not linear but a square root one. Therefore, if
you want to reduce the noise twice, you need to set the measurement four
times as long and the measurements can become very time consuming. The
measurement is started by clicking on the execute button.
When the measurement is finished, the measured peaks can then be indexed
according to the aforementioned rules and the crystallite size and the lattice
parameter can be calculated as well. An example of measured data of cubic
TiC can be seen in Fig. 6.6.
74 CHAPTER 6. X-RAY DIFFRACTION
Figure 6.5: SmartLab Guidance — measurement setup.
Figure 6.6: X-ray diffractogram of TiC.
Chapter 7
X-Ray Photoelectron
Spectroscopy
RNDr. Monika Stupavsk´a, PhD.
X-ray photoelectron spectroscopy (XPS) is a surface analytical technique
that has become into an essential tool for material characterization. XPS is
at present a widely utilized method of studying the qualitative and quantitative
composition of surfaces of materials and represents a unique combination
of surface sensitivity and chemical specificity as well as relatively
straightforward means of quantification.
7.1 Basic principles
In XPS, the sample is irradiated with low energy X-rays hν (controlled), in
order to provoke the photoelectric effect (Fig. 7.1). As a result, emission
of photoelectrons is observed. Kinetic energies of these electrons can be
described most simply by the photoelectric equation:
hν = Eb + Ek, (7.1)
where, Eb is the binding energy (unknown variable) and Ek is the photoelectron
kinetic energy (measured by XPS Spectrometer). The equation will
calculate the energy needed to get an electron out from the surface of the
solid. Knowing Ek and hν, the Eb can be calculated.
Each element produces a characteristic set of XPS peaks at characteristic
binding energy values that directly identify each element on the surface,
therefore photoemission spectra can serve as fingerprints of the respective
elements. Almost all elements except for hydrogen and helium can be identified
via measuring the binding energy of its core electron. Furthermore,
binding energy of core electron is very sensitive to the chemical environment
of element. The same atom is bonded to the different chemical species, leading
to the change in the binding energy of its core electron. The variation
75
76 CHAPTER 7. X-RAY PHOTOELECTRON SPECTROSCOPY
Figure 7.1: Principle of photoelectron emission [68].
of binding energy results in the shift of the corresponding XPS peak. This
effect is termed as chemical shift, which can be applied to studying the
chemical state of element on the surface. Therefore, XPS is also known as
electron spectroscopy for chemical analysis (ESCA).
XPS is used not only to identify the elements but also to quantify the chemical
composition. The number of detected electrons in each of the characteristic
peaks is directly related to the amount of the element within the
irradiated volume. The atomic concentration of an element, Ci, can be
expressed as:
Ci =
Ii/Si
i Ii/Si
, (7.2)
where Ii is the peak intensity for element i , and Si is the sensitivity factor
for the peak i.
The ejection of an electron from an inner shell (Fig. 7.2A-B) creates an
unstable electronically excited state with a core hole in that shell. This
excited state can decay via two distinct de-excitation routes:
• Auger decay
The core hole is filled by an electron from an outer shell and the excess
energy is transferred to another outer shell electron, which is emitted
(Fig. 7.2C). The process involves three electrons: the electron knocked
out in the initial photoionization event, the electron that decays to fill
the inner shell vacancy, and the emitted electron from the outer shell
(Auger electron). Auger transitions are labelled for the orbital shells
involved in the transitions. For example, in a KLL transition the
electron that leaves behind the initial core hole is from the K shell (1s
7.2. SURFACE SENSITIVITY 77
Figure 7.2: Schematic of (A-B) photoionization, (C) Auger decay, (D) X-Ray
fluorescence
state), while the other two electrons come from the L shell (2s or 2p
levels).
• X-ray emission process or X-ray fluorescence
The core hole is filled by an electron from an outer shell with simultaneous
emission of a photon with energy equal to the difference in
binding energy of the two levels involved in the electron transition
(Fig. 7.2D)
X-ray fluorescence and Auger electron emission are competitive processes,
the branching ratio of which is governed by the respective decay crosssections.
Generally, elements with low atomic number prefer the nonradiative
decay.
7.2 Surface sensitivity
All electron spectroscopies are highly surface sensitive, due to the strong
interaction of electrons with matter. X-rays penetrate a few micrometers
into the sample surface, and photoelectrons are generated throughout the
irradiated volume. The XPS experiments are mainly concerned with the
78 CHAPTER 7. X-RAY PHOTOELECTRON SPECTROSCOPY
Figure 7.3: Parameters affecting XPS information depth [69,70].
intensity of emitted photoelectrons that have suffered no energy losses, e.g.
electrons can travel without undergoing inelastic scattering events. Those
photoelectrons produced close to the surface will be able to escape in to the
vacuum of the spectrometer without colliding with something on the way
out. Quantity describing the average distance that an electron can travel
through the material without suffering energy losses by inelastic scattering,
is the inelastic mean free path λe, which is defined as the average distance
that an electron of given kinetic energy Ekin travels between two successive
inelastic collisions (Fig. 7.3). The sampling depth of the XPS experiment is
often defined as 3λe, which means that 95% of the photoemission intensity
comes from the corresponding region below the surface. So the sampling
depth (3λe) for XPS under these conditions is 3-10 nm. Those electrons
produced deeper down will lose energy before reaching the surface, thus
contributing to the background of the measured spectrum.
7.3 Primary structures in XPS
A typical XPS spectrum is obtained at a given photon energy by recording
the number of photoelectrons as a function of the kinetic energy and can
be plotted as a function of the binding energy. This spectrum, often called
survey spectrum or wide scan, allows a complete elemental analysis. Fig.
7.4 represents the survey spectra of plasma treated polylactic acid surface.
As can be seen, spectrum displays a series of signals correspond to carbon,
oxygen and nitrogen. Survey scans give qualitative information about
atoms/molecules present in the sampling depth. The relative intensities of
the different photoelectron peaks reflect both the surface atomic abundance
and the probability of photoemission from a given energy level. After having
identified the elemental composition, it is then possible to acquire detailed
”high resolution” scan of any single energy level. An example of detailed
7.4. CHEMICAL SHIFT 79
Figure 7.4: Wide scan and high resolution C1s scan of plasma treated polylactic
acid surface [71].
scan relevant to the C 1s region, selected from a previous investigation, is
shown in Fig. 7.4 on the right. High resolution scans show the subtle shifts in
energy of photoelectrons originating from different chemical environments.
7.4 Chemical shift
Binding energies of a given element are not fixed values because the exact
value of Eb reflects the chemical environment of the surrounding atoms and
that energy shifts may occur when inequivalent atoms of the same elemental
species are present (Fig. 7.5A). These energy shifts are called chemical
shifts. Variations in the elemental binding energies arise from differences
in the chemical potential and polarizability of compounds. The chemical
shift range for any element is quite small, typically less than 10 eV. Usually
species of a higher positive oxidation state are shifted towards higher binding
energy due to the extra coulombic interaction between the emitted electron
and the ion core (Fig. 7.5B). The core level C1s peak of a polyethylene
terephthalate in Fig. 7.5A shows a clear shift in binding energy, related
with differences in the chemical environment of the carbon. Based on these
shifts, it is possible to determine 4 carbon chemical bonds: C-C/C-H at
284.8 eV, C-O at 286.5 eV and COO at 288.9 eV. The values of the binding
energy shifts can often be used to determine oxidation states and the nature
of the chemical bond formed by the atoms, although the shifts are normally
quite small, and often peak fitting routines need to be used because they
overlap in binding. This ability to discriminate between different oxidation
states and chemical environments is one of the major strengths of the XPS
technique.
80 CHAPTER 7. X-RAY PHOTOELECTRON SPECTROSCOPY
Figure 7.5: (A) Chemical shifts of C1s core level peak of polyethylene terephthalate,
(B) A plot of the chemical shift in the C1s binding energy in different
carbon - containing compounds [72].
7.5 Spin-orbit splitting
The photoemission process is inherently a many-electron event. All of the
other electrons in the system must readjust their positions and energy since
they are no longer in their ground electronic states. Splitting of core level
peaks can occur when the system has unpaired electrons in the valance
levels. The energy of a level varies according to the total angular momentum,
j = l+s. States with l > 0 can have two possible j values: j = 1− 1
2, 1+ 1
2 for
l = 1(p), or j = 2− 1
2 , or j = 2+ 1
2 for l = 2(d), etc. In the XPS spectra this
results in pairs of peaks with relatively close values of the binding energy
as well as intensity as illustrated in the Fig. 7.6A which shows a doublet of
Palladium. The intensity ratio of the two spin-orbit components is dictated
by the ratio of the respective multiplicities: which determines the relative
probability of transition to the two states upon photoionization. Generally,
in the photoemission spectrum from a given subshell the core level sub-peak
with maximum j is detected at lower binding energy. Obviously, no spinorbit
splitting occurs in the photoemission from s core levels. The theoretical
peaks area ratio is based on the degeneracy of each spin state of the doublet.
In the case of energy levels having quantum number l = 1, as in the case
of the 2p1/2/2p3/2 doublet, the peaks area ratio is 1/2, while in the case of
the 3d3/2/3d5/2 doublet the peak area ratio is 2/3 and, in the case of the
4f7/2/4f5/2 doublet, the peak area ratio is 3/4 (Fig. 7.6B).
7.6. SURFACE CHARGING 81
Figure 7.6: (A) Spin - orbit coupling leads to a splitting of the 3d photoemission
line of palladium into a doublet [73], (B) Table listing spin-orbit
split components and intensity ratios for different subshell
7.6 Surface charging
Many sample specimens have electrically insulating properties that would
affect the XPS binding energy measurements. These samples can exhibit
charging. This problem arises since photoelectrons emitted from the sample
are not replaced by electrons from the ground due to poor conductivity.
For nonconducting surface, electrons cannot return to the surface easily and
are lost faster than they return. After a steady state is reached, a positive
charge develops due to deficiency in electron density. Photoelectrons from
the analyte would thus be ejected with a decreased kinetic energy (higher
binding energy) along with broadening of the peak full width half maximum.
Measurements of binding energy for these systems involve flooding of the
sample surface with low energy secondary electrons to neutralize the charge.
7.7 Analysis features
7.7.1 Imaging & mapping
XPS can also be used to image the surface of a sample. This is useful
in understanding at the distribution of chemistries across a surface or for
finding the limits of contamination. There are two approaches for obtaining
XPS images: mapping (serial acquisition) or parallel imaging (parallel
acquisition).
Serial acquisition of images is based on a two-dimensional, rectangular array
of small-area XPS analyses. This method enables measurements of the
82 CHAPTER 7. X-RAY PHOTOELECTRON SPECTROSCOPY
Figure 7.7: XPS map of oxygen distribution on the surface of treated
polystyrene [74].
distribution of elements or chemical states (Fig. 7.7). The ultimate spatial
resolution in the image is determined by the size of the smallest analysis
area an is ∼ 15 µm for ESCALAB 250Xi. Serial acquisition is generally
slower than parallel acquisition but can collect a range of energies at each
pixel compared to collecting only a single energy for parallel acquisition.
Parallel acquisition of photoelectron images simultaneously images the entire
field of view. The spatial resolution of parallel imaging depends on the
spherical aberrations of the lens. This method of imaging is fast and produces
the best possible imaging resolution. Fig. 7.8 illustrates the combined
use of parallel imaging, high energy resolution, excellent sensitivity and optimum
charge compensation. It shows high resolution chemical state images
from a sample consisting of carbon fibres on a polyethylene terephthalate
(PET) substrate. This is a particularly challenging sample for XPS imaging
studies because the substrate is an insulator while the fibres have some
conductivity. Moreover, the sample is not flat, contributing further to the
dangers of differential surface charging [75].
7.7.2 Depth profiling
Depth profiling uses an ion beam to etch layers of the surface or surface
contamination, revealing subsurface information. The surface is etched by
rastering an Ar ion beam over a square of the sample. After the etch cycle,
the Ar beam is blanked and another set of spectra is recorded. This sequence
of etching and spectrum acquisition is repeated until profiling has proceeded
7.7. ANALYSIS FEATURES 83
Figure 7.8: (A) C1s image of the carbon fibers on the PET substrate, (B)
color overlay image showing two chemical states of carbon [75].
to the required depth and provides quantitative information. The damaged
part of the surface can be a few nanometers thick depending on the surface
material, the density and energy of the argon ions [75]. The results for the
Al2O3 film on the Si wafer are plotted in Fig. 7.9. Concentrations for Al,
O, C, and Si were quantified as a function of sputtering time. For Al2O3
on the Si, the Al concentration decays to zero at a sputtering time of 270 s.
The O concentration decays to zero later than the Al concentration because
of the SiOx interlayer [76].
7.7.3 Angle resolved XPS (AR-XPS)
Using angle resolved XPS it is possible to characterize ultra-thin films without
sputtering. Unlike depth profiling with ion sputtering, AR-XPS is capable
of non-destructive analysis of areas deep down to the escape depth
of photoelectrons. From Beer-Lambert equation, it is clear that the depth
of analysis is dependent on the angle of electron emission. This technique
varies the emission angle at which the electrons are collected, thereby enabling
electron detection from different depths. This is usually undertaken
by tilting the sample with respect to the analyzer. AR-XPS provides information
about the thickness and composition of films and can be applied
to films that are too thin to be analyzed by conventional depth profiling
techniques.
84 CHAPTER 7. X-RAY PHOTOELECTRON SPECTROSCOPY
Figure 7.9: XPS depth profiles for the Al2O3 film deposited on the Si wafer
[76].
7.8 Experimental set-up
7.8.1 Vacuum system
The sample analysis is conducted in a vacuum chamber, under the best
vacuum conditions achievable, typically ∼ 10−10 mbar. XPS is a surface
sensitive method. Impurities can play a major role in the observed spectra
and most of the effort that goes into the sample handling directly involves
this problem. The first criterion then is that a good vacuum is needed
to maintain the integrity of the surface. In general, 10−6 mbar would be
sufficient to allow the photoelectron to reach the detector without suffering
collisions with other gas molecules. On the other hand, 10−9 mbar is required
to keep an active surface clean for more than several minutes [77]. Even in
the case of a vacuum of 10−9 mbar, typically carbon peaks are found as a
result of surface contamination. Therefore, often the sample is cleaned by a
slight sputtering.
7.8.2 X-ray source
In XPS instruments, X-rays are generated by bombarding a metallic anode
with high-energy electrons. The energy of the emitted X-rays depends on the
anode material and beam intensity depends on the electron current striking
the anode and its energy. Electrons are emitted from a bright source, such as
LaB6, and focused onto a water-cooled, aluminum anode. A small portion
of the bombarding electrons cause vacancies in inner electron shell of the
7.8. EXPERIMENTAL SET-UP 85
target atoms and electrons from higher levels fall to fill the vacancies with
the simultaneous emission of X-ray photons. If the electrons fall from the L
shell to the K shell, then the X-ray is designated Kα1; if it is produced by an
L2 shell to K shell transition it is designed Kα2. In case of aluminum, the Al
Kα X-ray line consists of doublet with the Kα1 (at 1486.70 eV) having twice
the intensity of the Kα2 (at 1486.27 eV). In addition to the characteristic
Kα1, 2 lines, there are other features in the X-ray emitted. There is a Kβ
line as well as satellite lines arising from doubly ionized atoms [78–80]. The
wavelength of X-ray must be restricted precisely in order to remove the
satellites (associated X-rays of different energies, which are less intense than
the primary, and preferred, X-ray) from the Al Kα X-ray line. This ensures
that the energy imparted to photoelectrons will be precise. Therefore some
of the X-rays emitted from the anode are intercepted by the crystal and a
monochromated beam of X-rays is focused onto the sample. The size of the
X-ray spot at the sample is equal to the size of the electron beam spot on
the anode. Therefore the analysis area can be controlled by controlling the
electron beam spot size.
7.8.3 Electron energy analyser
Electrons ejected from the surface enter the input lens, which focuses the
electrons and retards their energy for better resolution. A lens system focuses
the electron beam into a hemispherical analyser. This analyser consists
of two plates carrying a potential, so that only electrons with a small range
of energy differences reach the exit. Finally, an electron detector analyses
the electrons (Fig. 7.10A). Hemispherical analyser disperses electrons inside
two hemispheres with applied voltages V1 and V2 (V2 > V1), and the
dispersion depends on these voltages and on the kinetic energy of the photoelectrons.
It means that the hemispherical analyser behaves like an energy
filter.
Potential of mean path through analyser is:
V0 =
V1R1 + V2R2
2R0
(7.3)
The figure 7.10B shows schematically how this happens. An electron of
kinetic energy eV = V0 will travel through a circular orbit through hemispheres
at radius R0. Since R0, R1 and R2 are fixed, in principle changing
V1 and V2 will allow scanning of electron kinetic energy following mean path
through hemispheres. Once the electron is focused to the back of the analyser,
it is counted by a channeltron detector.
86 CHAPTER 7. X-RAY PHOTOELECTRON SPECTROSCOPY
Figure 7.10: (A) Schematic diagram of the major components of XPS, (B)
Path of photoelectrons in a concentric hemispherical analyser [81].
7.8.4 Sample handling
Samples that can be analysed by XPS are all solids ranging from films, powders
to frozen liquids including inorganic compounds, metal alloys, semiconductors,
polymers, elements, glasses, ceramics, papers, inks, woods, plant
parts, bio-materials and many others. In majority of XPS applications,
sample preparation and mounting are not critical. Typically, the sample is
mechanically attached to the specimen holder, and analysis is begun with
the sample in as-received condition. Additional sample preparation is discouraged
in many cases because any preparation might modify the surface
composition. Argon etching is a long-established method for in-situ sample
cleaning. It can be highly effective at removing thin oxide layers of
contamination but also can leave significant damage.
Chapter 8
Raman Spectroscopy
Mgr. Pavel Souˇcek, Ph.D.
Raman spectroscopy is a light-scattering based method for investigation of
the molecules on the surface of the studied material. It is based on the
change in the polarizability of the molecules due to their interaction with
the incident monochromatic light beam [82]. These observed specific energy
transitions arise from specific molecular vibrations. When the energies of
the transitions are plotted as a spectrum, they can provide a “molecular fingerprint”
of the molecule. Raman spectroscopy is a complementary method
to the infrared spectroscopy, where the observed signal arises from a change
in the dipole moment of a molecule. Often molecules that are infra-red
inactive are not Raman active and vice versa.
8.1 Theoretical background
When light is scattered in matter, it can be scattered elastically or inelastically.
The incident light interacts with the molecule and distorts the electron
cloud which forms a virtual state. This state is unstable and the photon is
re-radiated very fast. Most photons are scattered elastically, i.e. they undergo
the so called Rayleigh scattering, where the excited electron in the
molecule falls onto the same level it has been excited from, and their energy
and hence also their wavelength is the same as of the incident photons.
Raman spectroscopy uses the approximately 0.00000001 – 0.000001 % of
photons that are scattered inelastically and undergo the so called Raman
scattering [83]. Both these processes are shown in Fig. 8.1. Raman scattering
can be further divided to Stokes and anti-Stokes scattering. In Stokes
scattering part of the energy from the photon is transmitted to the molecule
and it is excited from the ground level to a higher vibrational level. The
scattered photon therefore has lower energy and a higher wavelength than
the incident photon. In anti-Stokes scattering the energy is transmitted the
other way. The molecule that is originally in a higher vibrational level is
87
88 CHAPTER 8. RAMAN SPECTROSCOPY
Figure 8.1: Scattering of light in matter. Taken from [83].
de-excited into the ground level. The scattered photon therefore has higher
energy and shorter wavelength than the incident one. As low number of
molecules is excited into a higher vibrational level at room temperature, the
anti-Stokes scattering is less likely to occur than the Stokes scattering by
several orders of magnitude.
8.2 Experimental setup and data acquisition
A typical Raman spectroscopy system is composed of one or several lasers
with an optical path focussed on a sample holder. The optical signal is then
directed to a grating splitting the signal to its spectral components. These
are gathered by a CCD detector [84].
The actual system used in this laboratory is the Horiba LabRam HR Evolution
shown in Fig. 8.2. The system is equipped with 3 lasers — 325 nm
UV, 532 nm VIS and 785 nm IR. Each laser has certain advantages as well
as disadvantages and sometimes it is necessary to measure a sample with
more than one laser. The system is in a confocal configuration meaning that
the laser goes through a confocal objective lens with a very shallow depth
of field to the sample as well as back from the sample towards the gratings
and the detector. The system is equipped with two gratings in the device
itself — 600 mm−1 and 1800 mm−1. A third grating of 1200 mm−1 can be
swapped manually with the 1800 mm−1 grating. The signal is collected by
a CCD detector cooled to -60 degrees centigrade to reduce the signal noise.
The Raman spectrometer is controlled via LabSpec 6 software. The main
screen of the software os shown in Fig. 8.3. The device settings are done
in the righthand bar (highlighted as no. 1 in Fig. 8.3), whereas the direct
device control is done by the top icon row (highlighted as no. 2 in Fig. 8.3).
First the laser needs to be chosen in the righthand bar in the instrument
setup panel. The appropriate Range needs to be set as well — Visible range
for 532 nm and 785 nm lasers and UV range for the 325 nm laser. The
appropriate objective needs to be set with regards to the used laser and the
8.2. EXPERIMENTAL SETUP AND DATA ACQUISITION 89
Figure 8.2: Horiba LabRam HR Evolution
Figure 8.3: LabSpec6 — main screen
90 CHAPTER 8. RAMAN SPECTROSCOPY
Figure 8.4: LabSpec6 — sample focussing
sample. The lens 10x, 50x and 100x objectives are suitable for the 532 nm
and 785 nm lasers, while the mirror xCG 74x objective needs to be used for
the 325 nm laser.
Before the first measurement of the day or in any new laser-objective combination
the calibration of the device needs to be performed due to sensitivity
of the device to to external parameters such as the temperature. The calibration
is done on a Si sample due to very simple Raman spectra of silicon.
The silicon reference sample is put on the sample holder and the software is
switched to the Video tab as is shown in Fig. 8.4. The sample is focussed
by moving it up and down. The first rough focussing is done by a rotating
slider on either side of the sample holder. Fine adjustments are done by a
joystick connected to the spectrometer. Once the sample is focussed, the
calibration can be performed. The easiest calibration — autocalibration —
can be done for the 532 nm visible laser. This can be done by clicking oh the
red AC sign on the bottom of the screen (see Fig. 8.5). Then select Current
Auto Calibration to perform the calibration in the currently selected setup.
The calibration is done in two steps - first the Rayleigh-scattered signal is
set to 0 cm−1 and then the Stokes first order scatter peak of Si is set to
520.7 cm−1. This way we have 2 points and the output of the CCD can be
linearised. The AC sigh turns green after successful autocalibration.
The measurement of the investigated sample can be done after the device is
calibrated. The measurement range and length need to be set up now in the
Acquisition parameters tab as is shown in Fig. 8.6 — box 5. The example
range of 800 – 2000 cm−1 is suitable for the measurement of first order D
and G peaks of carbon. After the appropriate measurement range is set it
8.2. EXPERIMENTAL SETUP AND DATA ACQUISITION 91
Figure 8.5: LabSpec6 — autocalibration
is advisable to use the real time display (RTD) highlighted by no 6. This
makes short repeated measurements that are continually refreshed on the
screen. These short measurements make it possible to judge the time needed
for the full measurement (note that the maximum detector count is cca. 64
000). This can then be started by the Start measurement button (no. 7).
If some damage to the sample after the measurement is observed, the time
of the measurement needs to be shortened and/or an neutral-density (ND)
filter needs to be applied.
The data analysis of different samples greatly varies and reaches form comparison
of the measured spectra with a database to identify the peaks and
therefore to identify the sample material to fitting of the peaks an calculation
of different material parameters like evaluation of the bonding hybridization
of carbon.
92 CHAPTER 8. RAMAN SPECTROSCOPY
Figure 8.6: LabSpec6 — measurement
Chapter 9
Surface Energy Analysis
doc. RNDr. Vilma Burˇs´ıkov´a, Ph.D.
The determination of surface free energy of a solid is of a great importance
in a wide range of problems in applied science. Because of the difficulties to
measure directly the surface free energy of a solid phase, indirect approaches
have been used. Among the indirect methods used for estimation of the
surface free energy of the solids, the contact angle measurements are believed
to be the simplest.
The contact angle measurement could be easily performed by establishing
the tangent angle of a liquid drop with a solid surface. The contact angle
of a liquid drop on a solid surface is defined by the mechanical equilibrium
of the drop under the action of three interfacial tensions solid/vapour,
solid/liquid and liquid/vapour. The surface free energy of plasma treated
polymers can be easily examined by using contact angle measurement. The
method is suitable for surface characterization of various materials i.e. polymers
with or without adhesive treatment, protective coatings, materials with
biocompatible modification, natural materials (paper, textiles) etc. Thanks
to wide range of possible use becomes this method useful in chemical and
plasmachemical laboratories, in packaging techniques, chemical, automotive
industry etc.
The determination of the surface free energy of solids from contact angles
relies on a relation, which has been proposed by Young in 1805 [86] and the
equilibrium relation is known as Young`s equation. In the literature there is
wide range of different methods for surface free energy calculation which are
based on the Young`s relation [86]. There are various graphical or numerical
methods (Zisman Theory, Fowkes Theory, The Extended Fowkes Theory,
Wu Equation of State, Owens - Wendt - Raeble - Kaeble Theory, Lifshitz
& van der Waals - Lewis Acid - Base Theory etc.). One of the most often
used methods is the Owens-Wendt-Rable-Kaeble (OWRK) method [85].
93
94 CHAPTER 9. SURFACE ENERGY ANALYSIS
9.1 Surface Tension and Surface Free Energy
In case of liquid surfaces the term ‘surface tension’ and the term ‘surface
free energy’ are often interchanged. The term surface tension arose from
historical concept that the liquid has a ‘skin’ which can exert a force per
unit length. Generally, the surface tension γ can be defined as the reversible
work, W done in creating a unit surface area
W = γ∆A. (9.1)
Here ∆A is the newly created surface area. γ may be associated with units
of either Jm−2 (surface free energy) or Nm−1 (surface tension). These two
units are dimensionally equivalent.
The total Helmholtz free energy Ftot of the system may be written in the
following form
Ftot = NFa + AFsurf . (9.2)
Here Fa is the Helmholtz free energy per atom, N is the number of atoms
of the bulk material and Fsurf is the Helmholtz free energy per unit area of
the surface:
dFtot = −SdT − PdV + µdN + Fsurf dA → dFtot(T,V,N) = Fsurf dA. (9.3)
Here S is the entropy, P is the pressure and µ is the chemical potential. The
reversible work done in creating of unit area of surface is the Helmholtz free
energy for that area at constant temperature T and volume V
γ =
dFtot
dA T,V,N
(9.4)
From 9.3 and 9.4 follows:
γ = Fsurf . (9.5)
The surface tension equals the Helmoltz free energy for the surface, which
is generally termed the surface free energy.
In case of solid surfaces the interatomic/intermolecular forces are stronger
than in case of liquids, therefore the solid material is not able to rearrange
itself in order to minimise its energy. This results in another contribution
to the surface free energy, which is the contribution of the surface stress,
resulting from the work required to deform the surface. The relationship
between the surface tension, surface stress and surface free energy is too
complex to deal with here in detail [85].
9.1. SURFACE TENSION AND SURFACE FREE ENERGY 95
Figure 9.1: Schema of adhesion and cohesion [85].
The surface free energy of solids can be described as a measure of disruption
of chemical bonds that occurs when a new surface is created. Surfaces must
be energetically less favourable than the bulk of the material otherwise there
would be a driving force for creation of new surfaces. Cutting a piece of a
solid material in half (see Fig 9.1) breaking its bonds consumes energy. If
the cutting is done reversibly, then the energy W consumed by the cutting
process is equal to the energy of the two newly created surfaces 2γi. The
unit surface energy would be therefore half of the cohesion energy (see Fig
9.1) of the solid material.
Wc
2
= γi (9.6)
In practice it is true only for surfaces newly prepared in ultra-high vacuum
conditions. All surfaces are energetically unfavourable in that they have
a positive energy of formation. Due to positive energy of newly created
surface there are driving forces leading to creation of surface layers of natural
oxides or contaminations. Therefore clean surfaces in ultra-high vacuum
conditions have higher free energy, than oxidised or contamined surfaces.
Energy of adhesive bonds Wa is energy released at creation of adhesive
bonding between two different materials i and j. The energy of adhesion
can be also defined as the energy which is needed for the separation of two
different materials i and j.
Wa may be determined according to Dupr´e´ formula:
Wi + Wj = Wij + Wa, (9.7)
where Wi is the cohesion energy of the substance i, Wj is the cohesion
energy of the substance j and Wij is the energy of the solid-solid or solidliquid
interface. Direct measurements of surface free energy of solid surface
96 CHAPTER 9. SURFACE ENERGY ANALYSIS
Figure 9.2: Contact angle of a sessile drop (a) neglecting the spreading
pressure (b) accounting for spreading pressure. [101].
Wj and of the interfacial energy Wij are rather difficult, so the equation
in the above described form could not be used easily for determination of
energy of adhesion Wa.
9.2 Young´s Equation
If a drop of a liquid l is brought into contact with a flat horizontal solid
surface s in a gas atmosphere v, it can either spread over the surface or
assume the shape of a spherical segment from a flat lens up to an almost
complete ball. The most well known description of wetting state was derived
by Young in 1805. The Young´s equation describes the equilibrium of forces
between the surface tension at the three-phase boundary:
γsl − γsv = γlv cos Θ, (9.8)
where γsv is the solid-vapor interfacial free energy, γsl is the solid-liquid
interfacial free energy, and γlv is the liquid-vapor interfacial tension.
In Fig 9.2 a the wetting state by Young is illustrated: γsv is the solid-vapor
interfacial free energy, γsl is the solid-liquid interfacial free energy, and γlv is
the liquid-vapor interfacial tension. In Fig 9.2 b the wetting state accounting
for spreading pressure πe is illustrated.
If the contact angle is equal to 0o then the liquid will completely spread over
9.3. MODELS FOR DETERMINATION OF INTERFACIAL TENSION97
the surface of the solid phase. If the contact angle is equal to 180o, liquid
will not wet the solid surface. Generally, the solid surface is called wettable
if the contact angle of the liquid drop is less than 90o and is not wettable if
the contact angle is higher than 90o. The solid surfaces may be divided into
two groups, they may be hydrophilic (wettable with water) or hydrophobic
(not wettable with water). The first case concerns the high-energy surfaces
and the second case concerns the low-energy surfaces. High-energy surfaces
such as metal, oxide or ceramic surfaces should be completely wetted by
fluids. However, the complete wetting (Θ = 0o) may be obtained only in the
case of completely clean, highly polished surfaces and pure liquids in inert
gas atmospheres that are completely free of contaminants. Even a shorttime
contact with a gas atmosphere of less than 1% relative atmospheric
humidity substantially changes the surface properties of the high-energetic
materials [85].
On the basis of γsv, γsl and γlv the following thermodynamic quantities may
be defined:
Work of adhesion
Wa = γsv + γlv − γsl = γlv(cos Θ + 1) (9.9)
Spreading coefficient
πe = γsv − γlv − γsl = γlv(cos Θ − 1) (9.10)
Wetting energy
We = γsv − γsl = γlv cos Θ (9.11)
9.3 Models for determination of interfacial tension
According to Dupr`e (see Eq. 9.9) [86] the interfacial tension between two
phases i and j may be expressed as
γij = γi + γj − Wij (9.12)
Antonow [93] estimated the interfacial tension as a difference between the
surface tensions of the individual phases i and j:
γij = |γi − γj| (9.13)
This approach was found to be not sufficiently accurate.
98 CHAPTER 9. SURFACE ENERGY ANALYSIS
Good and Girifalco [98] used the Berthelot`s [91] rule to calculate the interfacial
tension. Berthelot suggested, that the free energy of adhesion (∆Ga
ij)
is equal to the geometric mean of free energies of cohesion of the separate
phases i and j ( ∆Gc
i and ∆Gc
j). According to this rule, the following
relationship applies to apolar substances:
∆Ga
ij = ∆Gc
i .∆Gc
j →
∆Ga
ij
∆Gc
i .∆Gc
j
= 1. (9.14)
In case of polar phases, the experimental results are often in conflict with
Eq. 9.14. In order to correct these discrepancies the interaction parameter
Φ was defined in the following way:
Φ =
∆Ga
ij
∆Gc
i .∆Gc
j
. (9.15)
The free energy of adhesion is the negative work of the adhesion and the
free energy of cohesion is the negative work of cohesion:
∆Ga
ij = −Wa
ij, ∆Gc
i = −Wc
i , ∆Gc
j = −Wc
j . (9.16)
Using the Dupr`e`s relationship Eq. 9.7, Eq. 9.6, Eq.9.15 and the geometric
combining rule, the following equation will be obtained:
∆Ga
ij = −Wa
ij = −2Φ
√
γi.γj. (9.17)
From Young`s equation 9.8 it is possible to obtain the relationship between
the equilibrium contact angle and the interaction parameter:
γij = γi + γj − 2Φ
√
γi.γj (9.18)
From the above relations follows:
cos Θ ∼= −1 + 2Φ
γi
γj
(9.19)
The interaction parametr Φ depends on the mutual properties of the liquid
and the solid surface:
Φ = 1 for so called regularinterfaces, i.e. systems for which the cohesive
forces of the two phases and the adhesive forces across the interface
are of the same type.
Φ < 1 the dominant forces within the separate phases are unlike, e.g.
London - van der Waals vs. metallic or ionic or dipolar.
Φ > 1 there are specific interactions between the molecules forming
the two phases.
9.4. SURFACE FREE ENERGY EVALUATION 99
Figure 9.3: Example of the use of Zisman model (there were used four
liquids: water, glycerol, ethylene glycol a methylene iodide). The value of
the calculated critical surface free energy for amorphous diamond-like carbon
was γc = 27.9 mJ
m2 [85].
9.4 Surface Free Energy Evaluation
9.4.1 Zisman plot
Zisman [87] noticed that a plot of cos Θ versus γl is often linear [1, 2, 3].
The Zisman method is based on the determination of the dependence of the
cos Θ on the total liquid tension
cos Θ = f(γl) (9.20)
With linear extrapolation (for cos Θ → 1) we can obtain the critical surface
energy γc. The dependence could be fitted by the following equation:
cos Θ = 1 + b(γc − γl), (9.21)
where b is a constant characteristic for the set of liquids used. Te value γc
characterises the type of molecules on the surface.
The relative inertness of surfaces can be evaluated by comparing the value
of γc of the surface. The theory becomes complex if nonpolar liquids are
used. However, the plot of cos Θ versus γl is not exactly linear. Neglect
of spreading pressure πe for Θ < 10o and the assumption that Φ = 1 are
not always valid. Surface energy varies widely with the functional groups
at the surface. For hydrophobic surfaces, free energy decreases in the order
−CH2 > −CH3 > −CF2− > −CF2H > −CF3. In table there are listed
100 CHAPTER 9. SURFACE ENERGY ANALYSIS
Group γc[mJ.m−2]
−CF3 6
−CF2− 18
−CH3 22
−CH2− 31-33
Table 9.1: Characteristic values of critical surface energy for several functional
groups [85].
the critical surface energy values for several highly hydrophobic functional
groups [85].
According to Girifalco and Good [98] (Eq. 9.19) cos Θ ∼= −1 + 2Φ γsv
γlv
the
dependence of cos Θ on 1
γlv
has to be linear. This suggests that if we plot
cos Θ against 1
γlv
. The intercept should be - 1 and the slope should be
equal to 2Φ
√
γsv.
9.4.2 Equation of State
One of the groups of models for surface free energy calculation is based on
the thermodynamic equation of states expressed in the form γsl = f(γlv, γsv),
where γsl depends only on γlv and γsv.
Ward and Neumann [90] proposed for low energetic surfaces the following
equation
γsl =
(γsv −
√
γlv)2
(1 − 0.015
√
γsvγlv
. (9.22)
Combining this equation with Young`s formula one cane obtain:
cos Θ =
(0.015γsv − 2)
√
γsv + γlv + γlv
γlv(0.015
√
γsvγlv − 1)
. (9.23)
The equation gives from known contact angle cos Θ the value of γsv. The
equation derived by Li a Neumann [99] was determined empirically by using
a large number of contact angle data:
γsl = γsv + γlv − 2
√
γsvγlve−0.0001247(γlv−γsv)2
. (9.24)
Combining Eq. 9.24 with Young`s equation yields
cos Θ = −1 + 2
γsv
γlv
e−0.0001247(γlv−γsv)2
. (9.25)
9.4. SURFACE FREE ENERGY EVALUATION 101
Kwok and Neuman proposed the following form of equation of states
γsl = γsv + γlv − 2
√
γsvγlv(1 − 0.0001057(γlv − γsv)2
), (9.26)
what in combination with Young`s equation gives
cos Θ = −1 + 2
γsv
γlv
(1 − 0.0001057(γlv − γsv)2
). (9.27)
Wu suggested for equation of state the following expression
γc =
γl(1 + cos Θ)2
4
. (9.28)
. where γc is function of interaction parameter and of the surface free energy.
Wu obtained from the dependence γc = f(γl) the maximum value of γc as
γs.
9.4.3 Fowkes Theory
Theory of Fowkes [88,89,95] forms a basis of all the surface free energy component
evaluations used today and the dispersion component of the total
surface energy is still calculated by using this approach. Fowkes considered
the surface free energy to be a measure of the attractive force between surface
layer and liquid phase and that these attractive forces and their contribution
to the free energy are additive. The intermolecular attractions, which cause
surface tension, arise from a variety of well-known intermolecular forces.
Most of these forces, such as metallic bonding and hydrogen bonding, are
a function of specific chemical nature. However, London dispersion forces
exist in all types of matters and always give an attractive force between adjacent
atoms or molecules, no matter how dissimilar their nature may be. The
London dispersion forces arise from the interaction of fluctuating electronic
dipoles with the induced dipoles in neighbouring atoms or molecules. The
effect of fluctuating dipoles cancels out, but not that of the induced dipoles.
These dispersion forces contribute to the cohesion in all substances and are
independent of other intermolecular forces, but their magnitude depends on
the type of material and density. Therefore, the γd term includes only the
London dispersion force contribution and Keesom and Debye force contributions
are included in the γp term. If only dispersion forces are considered,
than
γsl = γs + γl − 2 γd
s γd
l (9.29)
From Young-Dupr`e equation it is possible to obtain the work of adhesion
WA
102 CHAPTER 9. SURFACE ENERGY ANALYSIS
WA = γl(1 + cos Θ) = 2 γd
s γd
l (9.30)
If there are additional interactions Esl at the interface, the equation should
be written as:
WA = γl(1 + cos Θ) = Wd
A + Esl → Wd
A = 2 γd
s γd
l (9.31)
The work of adhesion was considered to be made up of independent additive
terms:
WA = Wd
A + Wp
A + Wh
A + Wi
A + Wab
A + ... (9.32)
Therefore the surface free energy was similarly considered to made up from
independent additive terms:
γ = γd
+ γp
+ γh
+ γi
+ γab
+ ... (9.33)
suffix d marks dispersion (London) interactions, suffix p means Keesom`s
interactions, h means hydrogen bonds, i means inductions (Debye) interactions
and ab means acid-base interactions.
Owens, Wendt, Rabel and Kaelble (OWRK) Theory
Owens, Wendt, Rabel and Kaelble [94] proposed the division of the total
surface energy of a solid or liquid in two components: dispersion force
component γd and polar component γp. The interaction energy of the non
-dispersive forces at the interface was quantified and included as geometric
mean of the non-dispersive components of solid and liquid. The equation
proposed was the extension of the equation proposed by Fowkes:
γsl = γs + γl − 2( γd
s γd
l + γp
s γp
l ) (9.34)
Combining this equation with Dupr`e`s formula the following term was ob-
tained
WA = γl(1 + cos Θ) = 2( γd
s γd
l + γp
s γp
l ) (9.35)
Dalal [97] developed a method for the best-fit solution of simultaneous equations,
which are obtained when more than two testing liquids are used. Least
squares method is used to solve the over-determined systems of equations
in the following form:
(1 + cos Θ)
2
γl
γd
l
= 2 γd
s + γp
s
γp
l
γd
l
(9.36)
9.4. SURFACE FREE ENERGY EVALUATION 103
The Extended Fowkes method
In case of the Extended Fowkes method the total surface free energy of
the studied solid is divided in three components: dispersion γd, polar γp
and γH components. The γH component results from hydrogen bridges.
The interaction energy of the non - dispersive forces at the interface was
quantified and included as geometric mean of the non-dispersive components
and hydrogen bridge components of solid and liquid:
γsl = γs + γl − 2( γd
s γd
l + γp
s γp
l + γh
s γh
l ) (9.37)
Combining this equation with Dupr`e`s formula the following term was ob-
tained
γl(1 + cos Θ) = 2( γd
s γd
l + γp
s γp
l + γh
s γh
l ) (9.38)
The most appropriate solution is to do first the measurement of the dispersion
part using a non-polar liquid. In the second step it is recommended to
measure the polar part with liquid which exhibits a hydrogen bridge part
equal to zero γh
l = 0. Finally the hydrogen bridge component of the surface
free energy of the solid can be determined using a liquid which exhibits
nonzero hydrogen bridge component of surface tension.
Wu Theory (Harmonic Mean)
On the basis of the method of Wu [96] the surface free energy of the solid is
given as the sum of the disperse γd and polar γp components of the surface
free energy. The interfacial energy between the solid surface and the liquid
γsl could be detemined according to following formulaes.
γsl = γs + γl − 4
γd
s γd
l
γd
s + γd
l
+
γp
s γp
l
γp
s + γp
l
(9.39)
Combination of the formulae Eq. 9.39 with equation of Dupr`e and YoungDupr`e
gives the final formulae for the calculation of the surface free energy
components
WA = γli(1 + cos Θi) = 4
γd
s γd
li
γd
s + γd
li
+
γp
s γp
li
γp
s + γp
li
(9.40)
Suffix li refers to measurements using several different liquids. This equation
is useful for systems with high energy (i.e. glasses, oxides, graphite, metals
etc.) [12-17].
104 CHAPTER 9. SURFACE ENERGY ANALYSIS
Combination of the harmonic mean and geometric mean gives:
γli(1 + cos Θi) = 2 γd
s γd
li + 4
γp
s γp
li
γp
s + γp
li
(9.41)
or
γli(1 + cos Θi) = 2 γp
s γp
li + 4
γd
s γd
li
γd
s + γd
li
(9.42)
Dalal [97] performed a comparative study of the two approaches, geometric
mean and harmonic mean, on 12 common polymers using the published
data with six liquids. It is found that the total surface energy of the solid
obtained by the two methods are generally quite close.
Combination of two liquids with similar values of polar and dispersion components
gives wrong values of the surface free energy. Value D for two
liquids i and j used for the calculation should be higher than 10 mJm−2:
D = γd
liγp
lj − γd
ljγp
li (9.43)
Acid-Base Theory
The Lifshitz & van der Waals - acid-base approach was proposed by van Oss,
Good and Chaudhury [86]. This method enables to determine the electron
- acceptor and electron - donor parameters of the surface free energy. The
total surface free energy is a sum of its Lifshitz & Van der Waals (LW) and
acid/base (AB) components:
γTOT = γLW
+ γAB
, (9.44)
where LW indicates the total Lifshitz-Van der Walls interactions and AB
refers to the acid-base or electron-acceptor and electron-donor interaction
according to Lewis. The surface energy can be calculated according to
Young-Dupr`e equation expressed by LW component, acid component γ+
(acceptor effect) and basic component γ− (donor effect):
(1 + cos Θ)γl = 2( γLW
li γLW
s + γ+
li γ−
s + γ−
li γ+
s ), (9.45)
where li refers to liquid and s refers to solid material. The values can be
determined from contact angle measurement with three liquids of which two
must have polar component. The polar component is given by
γAB
= 2 γ+ + γ−. (9.46)
The equations of the form of Eq. 9.45 may be written in matrix form Ax = B
with the contact angle data of various liquids on solid. The system can
9.4. SURFACE FREE ENERGY EVALUATION 105
be over - determined with more than three liquid contact angles and the
least square method may be used to determine the coefficients in equation
Eq. 9.47.
(1 + cos Θli)
2
γli
γLW
li
= γLW
s + γ+
s
γ−
li
γLW
li
+ γ−
s
γ+
li
γLW
li
(9.47)
In comparison with the three-liquid method the regression method is much
more stable against the wrong selection of the testing liquids. The result of
the regression method is usually very close to the product of the three-liquid
method on the recommended liquid combinations [85].
106 CHAPTER 9. SURFACE ENERGY ANALYSIS
Figure 9.4: Overview on most often used methods of surface free energy
evaluation [85].
Chapter 10
Instrumented indentation
techniques
Mgr. Luk´aˇs Z´abransk´y, Ph.D.
10.1 Introduction
Indentation test is a simple method consisting of pressing of a well-defined
material whose mechanical properties and geometry are known (indenter)
into a measured material whose mechanical properties are unknown (measured
specimen, e.g. a thin film). It is one of the most convenient ways how
to measure mechanical properties such as hardness or Young’s modulus in
absolute terms. It is considered as nondestructive, the analysis procedure
is well standardized, and the method can be used for wide variety of materials
with different mechanical properties such as glass, metals, ceramics,
etc. The established widely known Vickers, Brinell, Knoop and Rockwell
tests are based on pressing of an indenter with a certain shape (which is
different in case of each method) into a material. Afterwards, the projected
(contact) area of a residual crater (indent), which is a result of the indentation
process, is measured by an optical microscope and the mechanical
properties are calculated from the known applied load and the size of the
projected area. This procedure is time consuming and the determination of
the projected area is subjective. However, the main disadvantage is when
the measurement scale of displacement is in nanometers (10−9 m) instead of
millimeters or micrometers (10−6 m), which are typical measurement scales
in indentation or microindentation tests. In the nanometer range, in which
we most definitely are if we want to measure mechanical properties of thin
films, we are talking about nanoindentation. The size of residual imprints is
so small that it is very complicated to even find them under an optical microscope.
Thus, other methods of determination of the contact area needed
for further analysis must be sought for.
107
108 CHAPTER 10. INSTRUMENTED INDENTATION TECHNIQUES
0 . 0 0 . 5 1 . 0 1 . 5 2 . 0
0
1 0 0
2 0 0
3 0 0
4 0 0
5 0 0
L m a x
h r
B K 7
Y o u n g ' s m o d u l u s = ( 9 2 . 0 3 ± 0 . 3 1 ) G P a
h a r d n e s s = ( 1 0 . 2 5 ± 0 . 0 3 ) G P a
L 2
( h )
L 1
( h )
h m a x
loadL[mN]
d e p t h h [ µm ]
Figure 10.1: Load-displacement curve measured on BK7 standard.
It is possible to measure this using atomic force microscopy (AFM); however,
this is also time-consuming and demands a precise knowledge of the location
of residual imprints on a specimen surface. The other possibility is to use the
so-called Instrumented Indentation Technique (IIT), also known in literature
as Depth Sensing Indentation (DSI) which is a smart and fast method where
the contact area is calculated from the known geometry of the indenter and
actual penetration depth of the indenter into the specimen. In the case of
this method, the instantaneous depth of an imprint is detected during the
entire loading and unloading processes, depending on the instantaneous load
value. Fully automated recording of the test progress allows fast processing
of measured dependencies. By analyzing the loading and unloading curves
(so-called load-displacement curve) obtained from the test, the hardness,
modulus of elasticity, fracture toughness, resistance to indentation creep,
thin film adhesion to the substrate and other useful characteristics can be
determined.
10.2 Load-displacement curve
In a typical nanoindentation test, load L and depth of penetration h are
recorded as load is applied from zero to some maximum Lmax and then
from the maximum load back to zero. The load-displacement curve L(h) is
a result of a recording of one nanoindentation measurement. This curve has
two main parts (see Fig. 10.1): first, there is a part of the gradual increase
of the load or the loading part L1(h) which is followed by a second part of
gradual decrease of the load or the unloading part L2(h).
For the case of pure elastic reversible deformation, the loading and unloading
10.3. ANALYSIS OF LOAD-DISPLACEMENT CURVE 109
parts overlap perfectly. If plastic deformation occurs during the test, then
the unloading curve will follow a different path compared to the loading
curve and there is a residual impression of depth hr left on the surface of
the specimen. From the plastically deformed volume, or more precisely, the
area of the residual impression and the known applied load it is possible to
calculate the hardness H of the specimen. The methods of analysis rely on
the assumption of an elastic-plastic loading followed by an elastic unloading,
with no reverse plasticity during the unloading sequence. There is only some
degree of recovery due to the relaxation of elastic strains within the material
which occurs mostly in the later part of the unloading curve. The beginning
is considered approximately linear; therefore, the initial portion of the elastic
unloading response is used for calculation of the reduced elastic modulus Er
of the indented specimen.
10.3 Analysis of load-displacement curve
The results of the analysis can largely depend on the model used to evaluate
the load/depth dependencies. The use of an analysis based on the elastic
contact model assumes that the following conditions are met:
1. no reverse plasticity occurs during the unloading part of the test;
2. for calculation of the so-called reduced elastic modulus Er, the Sneddon’s
equation [102, 103] can be used; here the compliances of the
indenter and the sample are summed according to the relationship
describing elasticity of springs connected in series:
1
Er
=
1 − µ2
i
Ei
+
1 − µ2
s
Es
, (10.1)
where E is the Young’s modulus, µ is the Poisson’s ratio and indices
i and s denote indenter and sample material;
3. the indenter has a precisely defined shape and the test surface is perfectly
smooth;
4. the contact can be modelled using an analytical model [104,105] for the
contact between a rigid indenter of a defined shape and an elastically
homogeneous isotropic half-space:
dL
dh
=
2
π
Er Ap, (10.2)
where Ap is so-called projected contact area of an indenter contacting
the surface of measured specimen.
110 CHAPTER 10. INSTRUMENTED INDENTATION TECHNIQUES
Figure 10.2: Comparison of total and projected contact areas.
Figure 10.3: Schematic of indentation process with important characteristics:
a is diameter of the indenter, hmax is maximum depth at maximum
load, hr denotes for residual depth, hc is contact depth and hs is depth of
sink-in.
In Fig. 10.2 the difference between total contact area Ad and contact area
projected into the surface plain (projected contact area Ap or an area as it
is seen and measured under an optical microscope) is explained.
The side view of a specimen surface in contact with an indenter and after
unloading is depicted in Fig. 10.3. It is clear that while the load is at the
maximum Lmax and the depth is at hmax, the true contact depth hc, i.e. the
depth of contact between the indenter and surface of the specimen, is lower
than hmax and higher than hr (the influence of pile-up is not accounted
here).
After unloading, the residual indentation imprint partially recovers in the
depth direction; however, its radius a remains mostly unchanged. This is
an important conclusion because it means that right from the hc it is easy
to calculate the diameter a and if the geometry of the indenter is known,
it is possible to calculate from parameter a the projected contact area Ap.
The main task of IIT analysis is to substitute the direct measurement of the
projected contact area of residual imprint which is here reduced to the task of
finding the contact depth. Both hmax and hr can be extracted explicitly from
the load-displacement curve without the need of any assumptions; however,
for determination of contact depth hc we need to have a model assuming
the geometry of the indenter. The contact area is generally a function of
contact depth depending on the geometry of the indenter [105]:
Ap(hc) ∼ hm
c (10.3)
10.3. ANALYSIS OF LOAD-DISPLACEMENT CURVE 111
The cylindrical indenter has an index m = 0 and the contact area is constant
with depth, the spherical tip has m = 1 and the cone or pyramid has m =
2. For the spherical indenter, the contact depth is exactly half of the actual
depth during loading, for cylinder it is lower and for pyramid or cone it is
slightly higher. According to Oliver and Pharr [105,106], this behaviour can
be summarized into an equation where the hc is fully expressed in measurable
quantities:
hc = hmax − hs = hmax −
Lmax
S
; hs = (hmax − hp), (10.4)
where hs is a depth of sink in, hp is the intersection of tangent of the unloading
curve at maximum load and the depth axis, is a constant depending
on indenter geometry (0.72 for cone tip and 0.75 for spherical indenter) and
S is contact stiffness calculated from the power law fit of the initial part of
the unloading curve with m as a fitting parameter:
S =
dL
dh
(hmax) = mAp(hmax − hp)m−1
. (10.5)
An example of analysis by the Oliver and Pharr method is depicted in Fig.
10.4 with important characteristics highlighted. Another way how to estimate
the contact depth, described by Doerner and Nix [107] in 1986, is to
use the intercept of the tangent to upper part of the unloading curve and the
depth axis hp. This older method provides reasonable values of calculated
contact area for materials with relatively high E/H ratio (elastic modulus E
to hardness H), e.g. metals; however, for materials with low value of E/H,
where significant elastic recovery occurs, the whole of the unloading curve
is not linear and the power law fit and the method according to Oliver and
Pharr should be used instead.
For perfectly sharp Berkovich (three-sided pyramid) or Vickers (four-sided
pyramid) indenters, commonly used to study mechanical properties of thin
films, the relationship describing their geometry is:
Ap = 24.5h2
c. (10.6)
However, it is impossible to manufacture such precise shape of an indenter;
therefore, corrections of the indenter shape need to be done during
calibration on a specimen whose mechanical properties are known. This is
especially important for measurements with low depths which is the case for
most measurements on thin films. The function of Ap(hc) after corrections
is:
Ap(hc) = 24.5h2
c +
7
j=1
cj
2j
hc, (10.7)
where cj is a calibration constant for a specific indenter geometry.
112 CHAPTER 10. INSTRUMENTED INDENTATION TECHNIQUES
0 . 0 0 . 5 1 . 0 1 . 5 2 . 0
0
1 0 0
2 0 0
3 0 0
4 0 0
5 0 0
S
h r
h s
h c
f i t : L 2
( h ) = B ( h - h r
)
m
h p
h m a x
load[mN]
d e p t h [ µm ]
Figure 10.4: The example of analysis of load-displacement curve according
to Oliver and Pharr method with important parameters: hs is depth of sink
in, hc is contact depth, hp is the intercept of tangent to the unloading curve
and depth axis, S is contact stiffness, hmax is maximum depth, hr is residual
depth and B and m are fitting constants.
10.4 Elastic-plastic contact
Indentation tests on many materials result in elastic-plastic deformation of
the specimen material which cannot be considered as superposition of elastic
and plastic properties obtained from models of ideal plastic and ideal
elastic solid. It turns out, for example, that the stress field generated by
the elastic-plastic deformation when using the pyramidal indenter is similar
to the stress field generated from the spherical indenter with no plastic
deformation in the specimen. For the pyramidal indenter, the mean contact
pressure pm is constant during the loading phase. However, this does
not apply to the unloading phase if the plastic deformation occurs. In the
plastically deformed volume, the hydrostatic pressure is generated which
decreases during the unloading phase. In brittle materials, plastic deformation
most commonly occurs with pointed indenters; in ductile materials,
plasticity may be readily induced with blunter indenters such as a sphere or
cylindrical punch.
The model for ideal elastic-plastic behaviour of a material was created by
Tabor [108,109]. According to his research, the ideal elastic-plastic material
has a linear curve of stress-strain dependence. This dependency is constant
until the elastic limit (yield strength) is reached. Then it starts to behave
plastically under the stress of the yield strength Y, which remains constant
even when we consider the presence of permanent plastic deformation. The
relationship between Y and the maximum strain load Lmax can be found.
10.5. HARDNESS 113
This direct relationship depends on the material. In general, three areas
of material behaviour can be distinguished by the mean pressure value pm
compared to Y [104]:
1. pm < 1.1Y — fully elastic recovery occurs without the presence of
plastic deformation;
2. 1.1Y < pm < CY — plastic deformation exists under the surface, but
is limited by surrounding elastically deformed material. The C value is
the so-called constraint factor. This is dependent on the material and
tip geometry. In addition, the C value changes during the formation
of the plastic zone from C ∼= 1 to C ∼= 3;
3. CY = pm — the plastic zone is fully formed and the further increase in
load no longer increases the mean pressure. Here, the mean pressure is
equal to the hardness of the material. When the plastically deformed
volume stops being constrained by the elastically deformed material,
then material is buckled around the tip which is known as pile-up [110].
It is clear that the hardness can be defined only if the plastic zone is fully
formed and then it is equal to the mean pressure.
10.5 Hardness
Historically, the first scale of hardness is the so-called Mohs hardness scale
from 1812 [111], which was created on the basis of the scratch test where
the harder material is able to scratch the softer one. According to the
definition given by A. Martens, hardness is seen as resilience of a material
against penetration of another material. Hardness is resistance to plastic
deformation. However, this simple definition is inadequate, as it does not say
anything how to quantify the hardness as a physical quantity. This was not
possible before the indentation test came. The indentation hardness derived
from the indentation test can define hardness as physical variable [112].
Hardness H is defined here as the proportion of applied load L and size of
the deformed area of impression A as follows:
H =
L
A
. (10.8)
10.5.1 Hardness models
Depending on what exactly we substitute for A in Eq. 10.8, we can have several
hardness theories and models, each describing slightly different property.
114 CHAPTER 10. INSTRUMENTED INDENTATION TECHNIQUES
The indentation hardness HIT which is equal to the mean contact pressure,
as described in the previous section, is defined as:
HIT =
Lmax
Ap
=
Lmax
kch2
c
, (10.9)
where Ap is the projected area which is calculated from contact depth hc
and a constant kc depending on the indenter geometry. The value of indentation
hardness has a physical meaning of a mean contact pressure under
the indenter and describes the resistance to plastic deformation. The second
equation in Eq. 10.9 is correct only for perfectly sharp indenter (see
Eq. 10.6); otherwise, it is necessary to use the equation for indenter shape
correction (see Eq. 10.7).
A different approach is used in case of plastic hardness HUpl which describes
the plastic behaviour of the specimen and can be expressed as:
HUpl =
Lmax
Ad
=
Lmax
kh2
p
. (10.10)
Here the total area Ad (see Fig. 10.2) is used instead of projected area (the
constant k = 26.43 for Vicker’s indenter). The total area is calculated from
hp, i.e. the intercept of a tangent to unloading curve with the depth axis,
which is the same as hc value calculated by Oliver and Pharr method for
= 1 (see Eq. 10.7). This hardness model is mostly used in industry and
for characterization of metallic specimens where the unloading curve can be
fitted by linear function without the need of power law relation.
It is also possible to determine the hardness as a function of load and depth.
This is how the Marten’s hardness HM is defined:
HM =
L
Ad
=
L
kh2
. (10.11)
If the L = Lmax and h = hmax, then Marten’s hardness is equal to the universal
hardness HU. It should be noted that the Marten’s hardness describes
the resistance to both elastic and plastic deformation mixed together.
A special case is the differential hardness Hdif , which is defined as the
derivative of the applied load dL with respect to the contact area, which is
dependent on h2, as follows:
Hdif = const
dL
d(h)2
. (10.12)
Differential hardness is calculated by numerical methods from the loaddisplacement
curve during the nanoindentation test to provide information
on the continuous deformation response of the material (plastic and elastic)
10.5. HARDNESS 115
0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5
2
4
6
8
1 0
1 2
differentialhardness[GPa]
d e p t h [ µm ]
Figure 10.5: An example of three measurements of differential hardness.
[117]
for a small change in applied load. It describes the momentary resistance
of the material to deformation, on the other hand, the common hardness
described in previous paragraphs integrates over all deformation states from
the initial contact of the tip with the specimen to the actual depth [113,114].
Differential hardness measurement results in a continuous dependency of this
hardness on depth. Sudden changes in differential hardness may result from
events such as cracking or grain rearrangement. The initial few dozens of
nanometres of depth are strongly affected by the microstructure of the coating
or by the surface roughness because the deformed area is not yet large
enough to avert potential local inhomogeneities such as grains in the case of
nanocomposite material. From a change in the differential hardness curve
it is also possible to recognize when mechanical properties of a substrate
or an underlying layer affect the measurement, which is often associated
with a gradual change of differential hardness curve [115,116]. Figure 10.5
represents examples of such gradual shifts. Here, three differential curves
represent three nanoindentation tests performed on a specimen containing
a TiC (titanium carbide) thin film. Initial sequences at lower depths vary
quite a lot, and for higher depths the measurements are more averaged due
to larger distorted volume. From about 1 µm there is a decrease that is
caused by the influence of the lower layer, in this case, a substrate on which
the thin film was deposited. With this technique it is possible to find safe
loads and indentation depths where the measured hardness is not affected
by the unwanted influence of the substrate — in the case presented in Fig.
10.5 the safe indentation depth would be < 1 µm.
116 CHAPTER 10. INSTRUMENTED INDENTATION TECHNIQUES
10.5.2 The influence of the substrate on measured hardness
Hardness is one of the most important material parameters of thin films but
due to their small thickness, however its measured value is often influenced
by the substrate itself and is not the real hardness of the thin film. One of the
ways to find the hardness of a thin layer without the influence of a substrate
is to use a nanoindentation test with a tip penetration of up to 10 % of the
depth of the thin film. However, in the case of a very thin film, this option is
sometimes impossible. In addition, there is a combination of substrates and
thin films where not even 10 % of depth is sufficient because the substrate
and the thin film have very different mechanical properties [110]. There are
several models to separate the hardness of the thin film from the substrate
or from lower layers in the multilayered system [118].
During the nanoindentation test performed into a thin film, the material
at different depths under the indenter has a different effect on the resulting
hardness value. Let us consider a small volume of material at depth h. Its
contribution to the resulting hardness is proportional to two factors — the
actual hardness H(h) of the material in a given volume, and the weighting
coefficient which determines the weight of the material hardness contribution
at depth h on the measured result and which is also proportional to the
distance from the point we measure. This weighting coefficient can be, for
example, linear (Jonsson-Hogmark model) [119] or quadratic (Burnett-Page
model) [120]. There are also different models considering cracks in a thin film
emerging during the nanoindentation test, such as the Korsunsky’s model
[121], where one parameter determines whether the plastic deformation or
the effect of the resulting cracks prevails.
10.6 Elastic modulus
The elastic modulus expresses the ability of the material to resist elastic
deformation and is defined as the ratio of stress and strain. Depending
on the type and direction of stress and deformation, we divide the elastic
modulus into several types:
1. Young’s modulus of elasticity is defined as the ratio of tensile stress
and relative elongation of the body in the direction of applied stress.
It is labelled as E and given in GPa.
2. The shear modulus is defined as the shear stress and shear deformation
ratio. It is denoted as G and for isotropic materials it can be
expressed using Young’s modulus of elasticity and Poisson’s ratio µ as:
G =
E
2(1 + µ)
; (10.13)
10.7. FRACTURE TOUGHNESS 117
3. The bulk modulus, denoted as K or B, represents the resistance of
a material to uniform pressure. It is defined as the ratio of the increase
of this pressure dp and the reduction of the volume dV. Using Young’s
elastic modulus E and the Poisson’s ratio µ, the bulk modulus can be
expressed as:
B =
E
3(1 − 2µ)
. (10.14)
The modulus of elasticity in the case of thin films can be obtained by means
of a nano-indentation measurement from the so-called contact stiffness S
(see Eq. 10.2), which is obtained from fitting of the upper 60 % (in older
literature 80 % [122]) part of the unloading curve with an assumption that
first about 5 % of the curve length is not used for the fitting by default.
According to the Eq. 10.2, the contact area Ap in which the contact stiffness
is determined is required to calculate reduced modulus Er. Thus, Er is
typically measured in the initial part of the unloading curve [112] as the
contact area for evaluation of hardness is usually determined here as well.
From the reduced modulus using Eq. 10.1, it is possible to calculate effective
elastic modulus Eef and from it the Young’s modulus E if the Poisson’s ratio
of the measured material µs is known. The effective elastic modulus of the
specimen Eef,s is defined as:
Eef,s =
Es
1 − µ2
s
, (10.15)
where Es is the Young’s modulus of the specimen. The value of Eef,s describes
better the elastic properties of the specimen itself than Er because
the later one characterize combined elastic properties of the specimen and
the indenter. If the diamond indenter is used, the Et and µt are 1140 GPa
and 0.07, respectively, and it is easy to express the effective elastic modulus
of the specimen from Eq. 10.1 as a function of the Er which is the only
variable.
10.7 Fracture toughness
Fracture toughness is defined as the critical stress intensity factor (KIC)
at which a brittle failure occurs. The stress intensity factor expresses the
magnitude of the stress field at a given point around the crack and depends
on the stresses due to external forces and the crack length. This dependency
differs for different ways of applying external forces. It is true that malleable
materials have higher fracture toughness than brittle materials of the same
hardness because they can absorb energy in their plastic zone [123], i.e. it
is harder to produce a crack since the material complies rather plastically.
118 CHAPTER 10. INSTRUMENTED INDENTATION TECHNIQUES
Figure 10.6: The image of a radial crack spreading from one indent corner
including important length parameters that are necessary for the fracture
toughness calculation.
The fracture toughness is calculated for the plain strain condition, which is
difficult to achieve in the case of thin films as it imposes certain requirements,
among other things, on their thickness [124]. There are several ways to
determine fracture toughness of thin films using nanoindentation. The most
common option is to measure the length of the radial crack c from the
residual impression after the indentation test [125–128] and use the following
equation which is applicable for the Berkovich tip:
KIC = χv
a
l
1
2 E
H
2
3 Lmax
c
3
2
, (10.16)
where c is the length of the radial crack measured from the indentation
centre to the tip of the emanated cracks as shown in Fig. 10.6, a is the size
of the residual indent made by Berkovich tip, l is the length of the emanated
crack, E is the Young’s modulus and H is the hardness. The parameter χv
was determined by Ouchterlony [129] — for Berkovich tip it is equal to 0.016.
The Eq. 10.16 is suitable for calculating the fracture toughness of composite
materials consisting of brittle and malleable phases [130]. The reliability of
the measured fracture toughness values depends on the crack lengths and Eq.
10.16 works well only when cracks are shorter than 10 µm. Of course, it is
necessary that the indentation measurement is not affected by the substrate
(see section 10.5.2); otherwise, the obtained KIC values do not represent
the fracture toughness of the coating standalone but rather properties of
the coating-substrate system as a whole.
10.8. RATIOS OF H/E AND H3/E2 119
10.8 Ratios of H/E and H3
/E2
Mechanical properties such as fracture toughness or resilience are important
parameters when studying thin films. For their at least approximate
estimation in the case of ceramic materials, it is possible to use the results
of the hardness measurement H and the effective elastic modulus Eef [131]
obtained from the nanoindentation test.
Several authors [132–135] show that the fracture toughness of the studied
thin films depends on the H/Eef ratio. By increasing the H/Eef ratio, we
can in many cases achieve high crack resistance. The low H/Eef allows the
applied load to be decomposed into a larger volume, inhibiting the formation
of plastic deformation in the substrate and at the substrate-coating interface.
This plastic deformation is the cause of tensile stresses and subsequent
cracking at the interface.
The resilience of the material is defined as resistance to plastic deformation.
This is the energy the material can hold before plastic deformation occurs.
The wear resistance [133] is derived from the resilience which is related
to the proportion of H3/E2
ef where the higher proportion indicates higher
resistance to wear.
10.9 Fischerscope measuring device
Fischerscope H100C XYp (see Fig. 10.7) is a computer-controlled measuring
system with programable XY stage for automated testing and determination
of material parameters according to ISO 14577 [136]. A Vickers or Berkovich
pyramid is generally used as an indenter and is pressed into the material or
coating whose parameters are to be determined. Without requiring special
sample preparation, test specimens are positioned by hand and material parameters
such as Martens hardness, Vickers hardness, differential hardness,
plastic and elastic parts of the indentation work, effective elastic modulus or
creep (determined after loading as well as unloading) are measured quickly
and accurately.
10.9.1 Parameters and calibration
Key parameters of the measuring device are summarized in following points:
Measuring head
• load range: 0.4 — 1000 mN,
• load resolution: 0.02 mN,
120 CHAPTER 10. INSTRUMENTED INDENTATION TECHNIQUES
Figure 10.7: The image of the Fischerscope H100C XYp measuring device
covered in a plastic box, with running WIN-HCU software on the screen.
[117]
• maximum displacement: 700 µm,
• displacement resolution: 2 nm.
Positioning device and optics
• optical microscope with 40x, 200x and 400x magnification,
• programmable measuring stage 80 x 80 mm.
Prior to the measurement it is necessary to ensure that the indenter is free
of any mechanical impurities, to check the measuring stage parallelism and
to ensure that the indenter shape is well calibrated. For the indenter shape
calibration, it is important to have a standardized sample which mechanical
parameters are precisely known. One of the best candidate for indenter
shape calibration in the case of Fischerscope H100C device is a certified
boron silicate BK7 plate 5 x 5 x 1 cm with universal hardness of 4150 ±
80 MPa. If the measurement of universal hardness with the load of 300
mN fits in the error range of the universal hardness value of BK7, then
the indenter shape calibration is not needed. Otherwise, the area function
needs to be modified to obtain the correct universal hardness. In case of the
Fischerscope H100C, the values of calibration constants Cj (see Eq. 10.7)
are fixed and the contact depth hc is corrected to a value of hcorr where the
obtained universal hardness fits in the error range of the universal hardness
value of BK7. The value of hcorr then represents virtually the correct contact
depth as it would be for the perfect Berkovich or Vickers indenter (see Eq.
10.6). This value is then used for all calculations instead of the true hc.
10.9. FISCHERSCOPE MEASURING DEVICE 121
10.9.2 WIN-HCU software
The entire measurement process is controlled via WIN-HCU software. By
using this software and the built-in optical microscope, it is possible to
program multiple measurements or imprints with different loads. In Fig.
10.8 there is a print screen of the welcoming main window of this program
where one may find all necessary buttons, bars and sub-menus. On the
upper right-hand side of the window there is an optical microscope screen
with magnification that is currently used, and x and y coordinates that
serve as scales. With a small attached joystick, it is possible to move the
stage in x and y axes and control the movement with the optical microscope
screen. Below the optical screen there is a result table with measured and
calculated parameters as Marten’s, plastic or indentation hardness, ratio
of the elastic work to total work done during one indentation test nIT ,
effective elastic modulus, maximum depth, creep etc., which are related
to a certain load chosen in a drop-down list located above. Selected as
well as averaged values including standard errors and deviations, minima
and maxima are generally shown in separated rows. All load-displacement
curves measured with the chosen load are displayed in the middle graph
ˆa€“ by clicking on a curve, one can display corresponding parameters in the
result table. It is also convenient to erase measurements that are wrong,
i.e. due to imperfect contact with the surface of the specimen or due to
unwanted cracking of the specimen; otherwise, their calculated values of
parameters distort the averages in the result table. The measurement or
set of programmed measurements can be started or aborted via buttons
in the start bar located in the lower left-hand side of the main window.
The magnification is changed manually directly on the attached microscope
and, at the same time, it is convenient to change it also by the software
— on the toolbar there is a corresponding icon for it. After changing the
magnification via software, the displayed magnification and the scales on
the optical microscope screen will change as well.
The whole measurement process is very simple: first, the desired spot is
found on the specimen, then the load is chosen, and the single measurement
can be performed just by one click. The X/Y programming of several
following measurements can be done by clicking on the corresponding icon
X/Y-Programming in the toolbar. In the programming window, there is possible
to program individual measurements, line of measurements or matrices
where it is necessary to set the first and the last point and number of points
between. The selection is done by stage movement which can be done either
by using the joystick, or mouse-clicking. Afterwards, the load is selected
and by confirmation the programming is finished. After clicking back on
the Measurement Screen icon in the toolbar, one may notice that the Run
button in the start bar is now green and can be pressed. The Run button
122 CHAPTER 10. INSTRUMENTED INDENTATION TECHNIQUES
Figure 10.8: The print screen of the main window of WIN-HCU software.
serves for starting the programmed measurements whereas the Start button
is for a single measurement by using a load chosen in the drop-down list in
the right-hand side of the window.
After the measurement and evaluation is done, the data might be exported
as Excel, text or ASCII files via User-defined export located on the
measurement bar on the right-hand side. However, prior clicking on it,
one needs to first set what exactly is to be exported and how. Click on
Settings on the upper main bar, then go to Options - User-defined
export. Here, ensure that Settings of test parameters, Statistics
of block, Characteristic material parameters - over all test
parameters, and Excel as a target are crossed, and confirm. Then, after
clicking on the measurement bar the Excel file with exported data should
open automatically.
Chapter 11
Advanced ellipsometry and
spectrophotometry
Mgr. Daniel Franta, Ph.D., Mgr. Jiˇr´ı Voh´aˇnka, Ph.D., Mgr. David Neˇcas,
Ph.D.
11.1 Polarization of light and optical quantities
The properties of the light beams between the light sources, detectors, measured
samples and optical elements of the real optical instruments can be
effectively described using the formalism of the Stokes vectors and Mueller
matrices [137]. This formalism allows us to describe the intensity and the
polarization state of light but the information about the absolute phase
is lost. Therefore, this formalism is usable for expressing the incoherent
superposition of individual light beams falling onto the detector and for expressing
the influence of the area non-uniformity of the measured samples,
i.e. varying properties along the area of the samples.
The intensity and the polarization state of quasi-monochromatic light is
completely specified by the Stokes vectors
S =




S0
S1
S2
S3



 =




I
I − I⊥
I+ − I−
I − I



 , (11.1)
where I = I + I⊥ = I+ + I− = I + I is the total intensity of light I , I⊥,
I+, I−, I , I are the intensities measured after light passes through ideal
polarizers for the following polarization states: I – linear polarization at
angle 0ˆA° (i.e. in the reference direction), I⊥ – linear polarization at angle
90ˆA°, I+ – linear polarization 45ˆA°, I− – linear polarization −45ˆA°, I –
right circular polarization, I – left circular polarization.
123
124 CHAPTER 11. ELLIPSOMETRY AND SPECTROPHOTOMETRY
From the Stokes vector it is possible to express other quantities describing
the polarization of the light, for example the degree of polarization
P =
1
S0
S2
1 + S2
2 + S2
3 . (11.2)
The changes in the intensity and the polarization state of the light beam
after it is reflected from or transmitted through the linear optical system is
then expressed by means of the matrix which relates the Stokes vector of
the outgoing (i.e. reflected or transmitted) beam Sout to the Stokes vector
of the incident beam Sin:
Sout = MSin . (11.3)
The matrix M is called the Mueller matrix. The optical quantities measured
using the optical instruments, such as reflectance, transmittance and
ellipsometric quantities can be expressed using the elements of this matrix.
Although the Mueller matrix has 16 elements, the number of independent
elements is often much smaller. For simple systems which do not exhibit
complicated combinations of effects such as anisotropy and depolarization
a number of elements of the Mueller matrix vanishes or could be expressed
using the other elements. In particular for reflection of light from the system
of ideal isotropic thin films placed on semi-infinite substrate the Mueller
matrix has only three independent elements. Although the real substrate is
never semi-infinite, it is possible to view it as semi-infinite if the reflections
from the back side do not have to be taken into account. This happens, for
example, if the substrate is sufficiently absorbing or if the back-side is very
rough.
The special system discussed above does not cause depolarization and it is
possible to investigate the reflection of light independently for light polarized
in the plane of incidence and light polarized perpendicular to the plane of
incidence, i.e. for the p-polarization (from German parallel for parallel) and
the s-polarization (from German senkrecht for perpendicular). The electric
field corresponding to the p- and s-polarized light is depicted in figure 11.1.
Therefore, it is possible to decompose light into the p-component and scomponent,
which are not mixed in the simplest case discussed here. This
means that p-polarized light is reflected and refracted to p-polarized light
and s-polarized light is reflected and refracted into s-polarized light. The
relations between the complex amplitudes of the electric fields of the incident,
reflected and refracted waves are expressed using the Fresnel reflection
coefficients (ˆrp, ˆrs) and the transmission coefficients (ˆtp, ˆts) for individual
polarizations:
ˆErp = ˆrp
ˆEip , ˆErs = ˆrs
ˆEis , ˆEtp = ˆtp
ˆEip , ˆEts = ˆts
ˆEis . (11.4)
The Mueller matrix describing the reflection from the system is then given
11.1. POLARIZATION OF LIGHT AND OPTICAL QUANTITIES 125
p-polarization s-polarization
Eip Erp
Etp
Eis Ers
Ets
Figure 11.1: Schematic diagram of the electric field corresponding to the pand
s-polarized light.
as:
M =
1
2





|ˆrp|2 + |ˆrs|2 |ˆrp|2 − |ˆrs|2 0 0
|ˆrp|2 − |ˆrs|2 |ˆrp|2 + |ˆrs|2 0 0
0 0 2 (ˆrpˆr∗
s ) 2 (ˆrpˆr∗
s )
0 0 −2 (ˆrpˆr∗
s ) 2 (ˆrpˆr∗
s )





. (11.5)
The reflectance of the sample, which is defined as the ratio of the intensity
of reflected light Ir to the intensity of incident light I0 (we assume that light
is not polarized), is then equal to the element M00 of the Mueller matrix
R =
Ir
I0
= M00 =
1
2
(|ˆrp|2
+ |ˆrs|2
) . (11.6)
This result is exactly what we expect since for unpolarized light the reflectance
is given as the average (Rp + Rs)/2 of the reflectances for the pand
s-polarized light (Rp = |ˆrp|2, Rs = |ˆrs|2).
While the reflectance describes the change of the intensity upon the reflection
of light from the sample, the other two remaining quantities (recall that there
are three independent elements of the Mueller matrix) describe the change
in the polarization state. The ellipsometric ratio
ˆρ = ˆrp/ˆrs , (11.7)
is often used to describe the change in the polarization state. Since ˆρ is a
complex number, it corresponds to two real quantities. The real quantities
azimuth Ψ and the phase change ∆ related to the ellipsometric ratio as
tan Ψ exp(i∆) = ˆrp/ˆrs . (11.8)
are also often used to describe the change in the polarization state.
126 CHAPTER 11. ELLIPSOMETRY AND SPECTROPHOTOMETRY
The disadvantage of these quantities is that they are periodic, discontinuous
and in some cases they can be infinite. Therefore, the changes in the
polarization state that are close to each other from the physical point of
view do not necessarily result in values of ˆρ, Ψ and ∆ lying close to each
other. This may cause problems in processing of the experimental data. It
is more practical to describe the changes in the polarization state using the
elements of the normalized Mueller matrix, which is defined as the Mueller
matrix divided by the reflectance R:
M = R





1 −In 0 0
−In 1 0 0
0 0 Ic Is
0 0 −Is Ic





. (11.9)
The quantities Is, Ic and In take values from the interval [−1, 1] and the
changes of the polarization states that are close to each other correspond
to values lying close to each other. Since there are only two independent
quantities describing the change in the polarization state only two of these
quantities are independent. In particular it holds
I2
s + I2
c + I2
n = 1 . (11.10)
Another advantage of the quantities Is, Ic and In is that they can be used
even if the system exhibits depolarization, which can be caused, for example,
by the reflection on the back sides of the substrates, area non-uniformity
of the samples, etc. In this case the Mueller matrix has the same form as
presented above but the ellipsometric quantities Is, Ic and In represent three
independent quantities constrained by the condition
I2
s + I2
c + I2
nˆa1 . (11.11)
In the ellipsometric literature, these quantities are often denoted by letters
S ≡ Is, C ≡ Ic and N ≡ In (mostly by researchers using the Woollam
instruments) or by symbols IS ≡ Is, ICII ≡ Ic and ICIII ≡ In (mostly by
researchers using the Horiba, Jobin Yvon instruments).
The transmittance of the sample is defined as the ratio of the intensity of
transmitted light It to the intensity of incident light I0:
T = It/I0 . (11.12)
It does not make sense to consider transmittance for the layered system on
the semi-infinite substrate and, moreover, the reflections on the back side of
the substrate must be taken into account.
If the substrate is transparent, then the reflectance (or transmittance) must
be calculated as incoherent superposition the intensities corresponding to the
11.1. POLARIZATION OF LIGHT AND OPTICAL QUANTITIES 127
Figure 11.2: Summation scheme used for total reflectance or transmittance
on the thick substrate.
situations in which there are zero, one, two, etc. reflections from the back
side of the substrate. The contributions that must be summed together are
depicted in figure 11.2. Let us denote: R1 reflectance of the layered system
on the upper (front) side of the substrate for light incident from top, R1
reflectance of the layered system on the upper side of the substrate for light
incident from bottom, R2 reflectance of the layered system on the lower
(back) side of the substrate for light incident from top, T1 transmittance of
the layered system on the upper side of the substrate for light incident from
top, T1 transmittance of the layered system on the upper side of the substrate
for light incident from bottom, T2 transmittance of the layered system on
the lower side of the substrate and U transmittance of the substrate. The
reflectance and transmittance of the whole system is then given as
R = R1 +
T1T1R2U2
1 − R1R2U2
, T =
T1T2U
1 − R1R2U2
. (11.13)
If we want to calculate the Mueller matrices instead of reflectance and transmittance,
then the same summation scheme can be used but it is necessary
to replace the reflectances and transmittances with corresponding Mueller
matrices:
R = R1 + T1(1 − U2
R2R1)−1
R2T1U2
, T = UT2(1 − U2
R1R2)−1
T1 .
(11.14)
When the above formulae were derived it was assumed that the Mueller
matrix describing the attenuation of the light in the substrate is given as
U = U1, U = exp −
4πd
λ
(ˆn cos ˆθ) , (11.15)
where ˆn is the complex refractive index of the media forming the substrate,
ˆθ is complex refraction angle of the light traveling in the substrate, d is
the thickness of the substrate and λ is the wavelength of light in vacuum.
The Mueller matrices for transmitted light have the same form as for the
reflected light (11.5) but with the reflection coefficients replaced by transmission
coefficients.
128 CHAPTER 11. ELLIPSOMETRY AND SPECTROPHOTOMETRY
11.2 Thin film systems
θ1
n2
n1
θ1
θ2
1
2
Figure 11.3: Schematic diagram of reflection and refraction of the light on
single boundary.
In the optical characterization it is necessary to use the relations between
the optical quantities and the properties of the materials, thicknesses of the
films and other parameters.
First, we will look at the reflection and refraction of light on a boundary
between two different isotropic media with refractive indices ˆn1 and ˆn2 (see
figure 11.3). The incidence angle from the side of media 1 will be denoted
ˆθ1. The refraction angle in the media 2 follows from the Snell’s law
ˆn1 sin ˆθ1 = ˆn2 sin ˆθ2 . (11.16)
It is evident that this law is transitive. Although the angles and refractive
indices are complex quantities if the media are absorbing, the Snell’s law and
other formulae that will be introduced below take exactly the same form as
for non-absorbing media.
The boundary conditions for the Maxwell equations can be used to derive the
Fresnel coefficients for the reflection on the smooth boundary. The reflection
coefficients for the p- and s-polarization are as follows
ˆrp =
ˆErp
ˆEip
=
ˆn2 cos ˆθ1 − ˆn1 cos ˆθ2
ˆn2 cos ˆθ1 + ˆn1 cos ˆθ2
, ˆrs =
ˆErs
ˆEis
=
ˆn1 cos ˆθ1 − ˆn2 cos ˆθ2
ˆn1 cos ˆθ1 + ˆn2 cos ˆθ2
.
(11.17)
In the special case of normal incidence these formulae take especially simple
form
ˆrp = −ˆrs =
ˆn2 − ˆn1
ˆn2 + ˆn1
. (11.18)
The Fresnel transmission coefficients are given as
ˆtp =
ˆEtp
ˆEip
=
2ˆn1 cos ˆθ1
ˆn2 cos ˆθ1 + ˆn1 cos ˆθ2
, ˆts =
ˆEts
ˆEip
=
2ˆn1 cos ˆθ1
ˆn1 cos ˆθ1 + ˆn2 cos ˆθ2
.
(11.19)
11.2. THIN FILM SYSTEMS 129
For the normal incidence they can be written as:
ˆtp = ˆts =
ˆn1
ˆn2 − ˆn1
. (11.20)
It is necessary to note that the ideal boundary between two media is almost
never encountered in the real world. Therefore, it is often necessary to use
more complicated models which take into account adsorbed layers or slight
roughness of the boundaries. This is especially true for ellipsometry which
is very sensitive to these effects.
In order to calculate the optical quantities of more complicated layered systems
it is convenient to use the 4 × 4 matrix formalism (Yeh matrix formalism).
In this formalism we work with four-dimensional complex vectors and
with complex matrices relating these vectors. The components of the vectors
correspond to amplitudes of four plane waves (there are two polarizations
and two directions of propagation). Since this formalism works with amplitudes
of the waves it is usable if the fields are summed coherently. Therefore,
this formalism is usable for systems of thin films, where the interference effects
must be taken into account. In this formalism the layered system is
described by the matrix of the system, which relates the amplitudes of the
waves on both sides of the system. For example, the matrix of the two-layer
system with smooth boundaries is expressed as follows:
ˆM = ˆB(na, ˆnf1) ˆT(ˆnf1, df1) ˆB(ˆnf1, ˆnf2)ˆT(ˆnf2, df2) ˆB(ˆnf2, ˆns) , (11.21)
where the arguments in the brackets indicate dependencies of the individual
matrices on the complex refractive indices and thicknesses of the layers. The
indices a, f1, f2, and s correspond to the ambient, first layer, second layer
and substrate. In the case of smooth boundaries and homogeneous media
the Yeh matrices are expressed as follows:
B(ˆn1, ˆn2) =




1/ˆtp ˆrp/ˆtp 0 0
ˆrp/ˆtp 1/ˆtp 0 0
0 0 1/ˆts ˆrs/ˆts
0 0 ˆrs/ˆts 1/ˆts



 (11.22)
and
T(ˆn, d) =





exp(i ˆX) 0 0 0
0 exp(−i ˆX) 0 0
0 0 exp(i ˆX) 0
0 0 0 exp(−i ˆX)





, (11.23)
where
ˆX =
2π
λ
d ˆn cos ˆθ . (11.24)
130 CHAPTER 11. ELLIPSOMETRY AND SPECTROPHOTOMETRY
It is also possible to include anisotropy or various defects, such as roughness,
inhomogeneity, etc., into this 4 × 4 matrix formalism. The concrete forms
of the matrices for anisotropic media or mentioned defects can be found in
literature [137,138].
11.3 Universal dispersion models
If the aim of the optical characterization is more than determination of the
refractive index in the transparent region and the thickness of the layer, it is
necessary to perform the optical characterization in a wide spectral range.
In this case the absorption caused by excitations of electrons, i.e. in the
visible and ultraviolet ranges, as well as the absorption caused by vibrations
of the atomic lattice, i.e. in the phonon absorption in the infrared region,
must be taken into account. A suitable dispersion model describing the mentioned
absorption processes must be used for the optical characterization.
In the program newAD2 it is possible to use the dispersion model called
the Universal Dispersion Model (UDM) [139], which provides the means to
describe the dielectric response of almost all materials.
The description of the UDM model and its use in the newAD2 software can
be found at newad.physics.muni.cz.
11.4 Spectroscopic ellipsomety
Ellipsometry is an optical technique, in which the changes in the polarization
state of light upon reflection or transmission by the sample are measured.
The instrument used for these measurements is called ellipsometer.
Within ellipsometry we distinguish several techniques differing in the construction
of the used instruments and the quantities that can be measured.
The number of the measured quantities is in the range from two (e.g. ∆
and Ψ) to fifteen (i.e. all the elements of the normalized Mueller matrix).
All types of ellipsometers contain polarizers in the optical path before and
after the sample. The one before the sample is called polarizer while the one
after the sample is called analyzer. Most types of ellipsometers also contain
one or more compensators (optical elements shifting the phase between the
waves corresponding to two mutually perpendicular directions). By analyzing
the dependence of the intensity of the detected light on the on the
rotation angles of the optical elements or changes of their parameters it is
possible to determine how the sample changes the polarization state of the
light (see figure 11.4).
11.5. SPECTROPHOTOMETRY 131
Detector
and
Monochromator
Analyzer
Compensator
Polarizer
Light source
Sample
Modulator
Figure 11.4: Shematic diagram of ellipsometers in PCSA (polariser–
compensator–sample–analyser) configuration.
11.5 Spectrophotometry
The spectrophotometers can be constructed as one-channel or two-channel
instruments. The schematic diagram of the two-channel spectrophotometer
is depicted in figure 11.5. In two-channel instruments the light beam
between the light source and the detector is divided into two paths using
appropriate beamsplitter, the first path corresponds to the sample channel
and the second path corresponds to the reference channel. Both channels
use the same detector and the channel measured at a given time is chosen for
example by using the rotating mirrors as beamsplitter to select appropriate
path of the light beam. Two measurements are performed on the sample
channel. The first measurement is performed for the investigated sample
and the second measurement is performed for the normal (i.e. sample with
known reflectivity). The silicon single crystal in the UV–VIS range and gold
plated sample in the NIR range are often used. Therefore, we measure the
relative reflectance of the sample with respect to the normal. The reference
channel is used to compensate for the fluctuations in the intensity of the
light source and sensitivity of the detector. The sample with arbitrary reflectivity
(usually identical with the normal) is placed in this channel. The
following relations hold for the intensities Iv, In measured on the sample
channel and the intensities Ir1, Ir2 measured on the reference channel:
Iv = RvZ1D1Gv , Ir1 = RrZ1D1Gr , (11.25)
In = RnZ2D2Gn , Ir2 = RrZ2D2Gr , (11.26)
where Rv, Rn and Rr are the reflectances of the sample, normal and reference,
respectively. The symbols Z1,2 denote the intensity of the light source
at the time of measurement, the symbols D1,2 denote the sensitivity of the
detectors at the time of measurement and Gv, Gn, Gr are geometrical factors
for individual channels which take into account different positions of the
samples and they also include different technical realization of these channels.
If the channels are switched sufficiently fast during one measurement,
132 CHAPTER 11. ELLIPSOMETRY AND SPECTROPHOTOMETRY
Light source
Mirrors
Sample/Normal
Detector
Reference
Mono-
chromator
Figure 11.5: Shematic diagram of two-channel spectrophotometers.
it is possible to neglect the fluctuations in the intensity of the light source
and the sensitivity of the detector (i.e. D a Z are the same for both the
channels but different for subsequent measurements).
By combining the above relations we obtain
Rv
Rn
=
Iv
Ir1
In
Ir2
Gn
Gv
= Rrel . (11.27)
The factors corresponding to fluctuations of the light source and the detector
were canceled and, moreover, it is reasonable to assume that the ratio Gv/Gn
is very close to unity, since it relates factors for the same channel (only
the measured samples are different). The reflectance of the sample is then
calculated as
Rv = RrelRn . (11.28)
The measurement of the transmittance using the two-channel spectrophotometer
is almost identical to measurement of the reflectance. The only
difference is that an empty channel (corresponding to 100% transmittance)
is used instead of the reference sample. Therefore, the measurement of transmittance
does not require the knowledge of the reflectance of the reference.
11.6 FTIR - Fourier Transform InfraRed
FTIR (Fourier Transform InfraRed) is a method for measuring spectrophotometric
and ellipsometric quantities in the infrared region.
11.6. FTIR - FOURIER TRANSFORM INFRARED 133
IR source
Colilimation
mirror
SampleDetector
Fixed mirror
Moving
mirror
Beam splitter
IR beam
Figure 11.6: Schematic diagram of the Michelson interferometers for FTIR
measurements.
The FTIR instrument does not contain monochromator. Instead, it uses
the Michelson interferometer (see figure 11.6) and the output of the measurement
is interferogram (the dependence of the intensity of the detected
radiation on the position of the mirror in the interferometer). The spectral
dependence of the intensity is obtained from the interferogram using the
Fourier transform.
134 CHAPTER 11. ELLIPSOMETRY AND SPECTROPHOTOMETRY
Bibliography
[1] R.F. Bunshah, (Ed.) Handbook of Deposition Technologies for Films and
Coatings: Science, Technology and Applications. 2nd ed. Park Ridge:
Noyes Publications, 1994. 888 p. ISBN 0-12-533026-X
[2] P. Sigmind, Nucl. Instrum. Meth. B 27/1-2 (1987) 1
[3] R.A. Powell, S. Rossnagel, (Eds.) PVD for Microelectronics: Sputter Deposition
Applied to Semiconductor Manufactoring. San Diego: Academic
Press, 1999. 420 p. ISBN 0-8155-1337-2
[4] K. Besocke, S. Berger, W.O. Hofer, U. Littmark, Radiat. Eff. 66 (1982)
35
[5] W.O. Hofer, K. Besocke, B. Stritzker, Appl. Phys. A 30/2 (1983) 83
[6] Y. Yamamura, H. Tawara. Atomic and Nuclear Data Tables. Academic
Press, vol. 62, 1996.
[7] O.A. Fouad, A.K. Rumaiz, S.I. Shah, Thin Solid Films. 517/19 (2009)
5689
[8] J.F. Ziegler, Particle Interactions with Matter. http://www.srim.org/,
Cited July 15th, 2013.
[9] W.M. Posadowski, Vacuum 46/8-10 (1995) 1017
[10] J. Fu, P. Ding, F. Dorleans, Z. Xu, F. Chen, J. Vac. Sci. Technol. A.
17/5 (1999) 2830
[11] A. Anders, J. Andersson, A. Ehiasarian, J. Appl. Phys. 102 (2007)
113303-1
[12] D. Depla, S. Mahieu, (Eds.). Reactive Sputter Deposition. Springer
Berlin Heidelberg, 2008, ISBN 978-3-540-76664-3
[13] T. Motohiro, Y. Taga, Thin Solid Films 112/2 (1984) 161
135
136 BIBLIOGRAPHY
[14] G.M. Turner, I.S. Falconer, B.W. James, D.R. McKenzie, J. Appl. Phys.
65 (1989) 3671
[15] S.M. Rossnagel, J. Vac. Sci. Technol. A 6 (1988) 19
[16] G.M. Turner, J. Vac. Sci. Technol. A. 13/4 (1995) 2161
[17] F.J. Jimenez, S.K. Dew, J. Vac. Sci. Technol. A. 30/4 (2012) 041302
[18] C. Huo, M.A. Raadu, D. Lundin, J.T. Gudmundsson, A. Anders, N.
Brenning, Plasma Sources Sci. Technol. 21 (2012) 045004
[19] N. Brenning, D. Lundin, M. A. Raadu, C. Huo, C. Vitelaru, G. D.
Stancu, T. Minea, and U. Helmersson, Plasma Sources Sci. Technol. 21
(2012) 025005
[20] F. Mitschker, M. Prenzel, J. Benedikt, C. Maszl, A. von Keudell, J.
Phys. D: Appl. Phys. 46 (2013) 155204
[21] N. Hardy, Planar Magnetrons In PVD Coatings: Essential Basics.
http://www.semicore.com/ news/ 50-planar-magnetron-pvd-coating,
Cited July 22nd, 2013.
[22] D.L. Smith, Thin Film Deposition: Principles & Practice. McGrawHill,
New York, 1995
[23] R.S. Rastogi, V.D. Vankar, K.L. Chopra, Rev. Sci. Instrum. 58/8 (1987)
1505
[24] Gencoa high yield magnetic option. hhttp://www.gencoa.com/
hy high yield rectangular magnetron/ index.asp, Cited July 22nd, 2013.
[25] The ONYX-Revolution: Angstrom Sciences — Cylindrical Magnetrons.
www.angstromsciences.com, Cited July 22nd, 2013.
[26] P.S. McLeod, L.D. Hartsough, J. Vac. Sci. Technol. 14(1) (1977) 263
[27] R.K. Waits, J. Vac. Sci. Technol. 15(2) (1978) 179
[28] P.J. Kelly, R.D. Arnell Vacuum 56 (2000) 159
[29] B. Window, N. Savvides, J. Vac. Sci. Technol. A 4(2) (1986) 196
[30] K.L. Chopra, Thin film phenomena, McGRAW-HILL book company
USA, 1969
[31] R.V. Stuart, Vacuum Technology, thin films and sputtering, Academic
press, 1983, ISBN 0-12-674780-6
[32] D.M. Mattox, Handbook of Physical Vapor Deposition (PVD) Processing,
Elsevier Inc. , 2010, ISBN 978-0-8155-2037-5
BIBLIOGRAPHY 137
[33] H.O. Pierson, Handbook of Chemical Vapor Deposition (CVD). Noyes
Publications,Park Ridge, New Jersey, U.S.A., 1992
[34] M.A. Lieberman, A.J. Lichtenberg, Principles of Plasma Discharges
and Material Processing.Second Edition, Wiley, 2005
[35] L. Martinu, O. Zabeida and J.E. Klemberg-Sapieha, Plasma Enhanced
Chemical Vapor Deposition of Functional Coatings.In Handbook of Deposition
Technologies for Films and Coatings, Third Edition,Science, Applications
and Technology (2010), 392
[36] L. Martinu, J.E. Klemberg-Sapieha, O.M. Kuettel, A. Raveh, M.R.
Wertheimer, J. Vac. Sci. Technol. A 12 (1994) 1360
[37] K. Kohler, D.E. Horne, J.W. Coburn, J. Appl. Phys. 58 (1985), 3350
[38] R.N. Franklin, J. Phys. D: Appl. Phys. 36 (2003) R309
[39] A.Stoica, Preparation of nanostructured carbon films by Plasma Enhanced
Chemical Vapor Deposition ,Dissertation work, Masaryk University,
Brno, 2012
[40] M. V. Alves, M. A. Lieberman, V. Vahedi, and C. K. Birdsall, J. Appl.
Phys. 69/7 (1991) 3823
[41] C. Corbella Roca. Thin film structures of diamond-like carbon prepared
by pulsed plasma techniques. PhD dissertation. Universitat de Barcelona,
2005
[42] L. K¨orner, Diffusion Barrier Coatings for Polymer Containers processed
by Plasma Enhanced Chemical Vapor Deposition PhD dissertation.
Eidgen¨ossische Technische Hochschule ˆa€“ ETH Z¨urich 2010
[43] R.d´Agostino, P. Favia, F. Fracassi, Plasma Processing of Polymers,
Kluwer Academic Publishers, The Netherlands, 1997
[44] J. Goldstein, D. E. Newbury, D. C. Joy, C. E. Lyman, P. Echlin, E.
Lifshin, L. Sawyer, J. R. Michael, Scanning Electron Microscopy and
X-Ray Analysis, Kluwer, NY, 2003
[45] P. B. Hirsch, Electron Microscopy of Thin Crystals, Butterworths,
Washington, 1965 or later edition
[46] C. W. Oatley, The Scanning Electron Microscope, part 1: The Instrument.,
Cambridge University Press, 1972
[47] L. Reimer, Scanning Electron Microscopy, Springer, 1998
[48] Handbook of Charged Particle Optics, Ed. J. Orloff, CRC Press, 1997
138 BIBLIOGRAPHY
[49] V. Hul´ınsk´y, K. Jurek, Zkoum´an´ı l´atek elektronov´ym paprskem, SNTL
Praha, 1982
[50] Tescan, Mira 3. https://www.tescan.com/en-us/technology/sem/mira3
[51] Quorum Technologies, Q150R Rotary-Pumped Sputter Coater/Carbon
Coater.
https://www.quorumtech.com/quorum-product/q150r-rotary-pumped-
sputter-coatercarbon-coater
[52] Oxford Instruments, Oxford Instruments NanoAnalysis.
https://www.oxford-instruments.com/products/microanalysis/energy-
dispersive-x-ray-systems-eds-edx,
https://www.oxford-instruments.com/products/microanalysis/wavelength-
dispersive-systems-wds
[53] JEOL, Scanning Electron Microscope A To Z.
https://www.jeol.co.jp/en/applications/pdf/sm/sem atoz all.pdf
[54] ThermoFischer Scientific, Electron Microscopy.
https://www.thermofisher.com/cz/en/home/industrial/electron-micro-
scopy.html,
https://www.fei.com/introduction-to-electron-microscopy/
[55] GlobalSino, Practical Electron Microscopy.
http://www.globalsino.com/EM/
[56] ´Ustav pˇr´ıstrojov´e techniky Brno, Podzimn´ı ˇskola elektronov´e
mikroskopie.
https://www.isibrno.cz/cs/podzimni-skola-zakladu-elektronove-
mikroskopie-2017
[57] B.L. Dutrow, X-ray Powder Diffraction (XRD),
https://serc.carleton.edu/research education/geochemsheets/techniques/
XRD.html
[58] PRAKTIKUM Z PEVNYCH LATEK (1B) — F6390,
http://www.physics.muni.cz/ufkl/Vyuka/Praktika/F6390-
PraktikumFPL-Navody-2018.pdf
[59] G. Binnig, C.F. Quate, and Ch. Gerber Phys. Rev. Lett. 56 (1986)
930
[60] https://warwick.ac.uk/fac/sci/physics/current/postgraduate/
regs/mpagswarwick/ex5/techniques/structural/afm/
[61] G. Fantner, Advanced bioengineering methods, Atomic Force Microscopy,
https://lbni.epfl.ch/
BIBLIOGRAPHY 139
[62] P. Klapetek, Quantitative Data Processing in Scanning Probe Microscopy.
SPM Applications for Nanometrology, A volume in Micro and
Nano Technologies, 2013
[63] https://www.ntmdt-si.com/resources/spm-principles
[64] S. Magonov, J. Alexander, and S. Wu Advancing characterization of
materials with Atomic Force Microscopy - based electric techniques In
Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging
and Spectroscopy; Kalinin, S. V.; Gruverman, A., Eds.; Springer: Berlin,
Germany, (2010) 33.
[65] X-ray diffraction, Rigaku corporation,
www.rigaku.com/en/techniques/xrd
[66] S.A. Speakman, Basics of X-Ray Powder Diffraction,
http://prism.mit.edu/xray
[67] P. Scherrer, Bestimmung der Groesse und der inneren Struktur von
Kolloidteilchen mittels Roentgenstrahlen, Nachr. Ges. Wiss. Goettingen
26 (1918) 98-100
[68] http://www.eagle-regpot.eu/EAgLE-Equipment XPS.html
[69] C.J. Powell, A. Jablonski, S. Tanuma et al. J. Electron Spectrosc. Relat.
Phenom, 68, (1994)
[70] D. F. Mitchell, K. B. Clark, W. N. Lennard, et al. Surf. Interface Anal,
21 (1994) 44
[71] B. Hergelova, A. Zahoranova, D. Kovacik, et al. Open Chemistry, 13
(2015) 564
[72] P. Willmott, An Introduction to Synchrotron Radiation — Techniques
and Applications, J. Wiley & Sons Ltd., 2011.
[73] V. Prysiazhnyi, M. Stupavska, C. Kleber et al. Surf. Coat. Technol.,
258 (2014) 1082
[74] http://www.rjlg.com/2014/12/polystyrene-manufacturing-issues/
[75] https://xpssimplified.com/
[76] J. Y. Lee, D. W. Kim, W. S. Kang, J. O. Lee, M Hur, S. H. Han, J.
Phys. D: Appl. Phys. 51 (2017) 9
[77] N. Winograd, S. W. Gaarenstroom, Physical methods in modern chemical
analysis, vol. 2, Academic Press, New York, (1980)
140 BIBLIOGRAPHY
[78] Surface Analysis — the Principal Techniques, John Wiley & Sons
(1997).
[79] D. Briggs, M. Seah, Practical surface analysis, John Wiley & Sons
(1990).
[80] D. Briggs, J. T. Grant, Surface analysis by Auger and X-Ray Photoelectron
Spectroscopy, IM Publications, (2003)
[81] https://www.phi.com/surface-analysis-techniques/xps-esca.html
[82] Raman Spectroscopy — A Tutorial,
http://www.kosi.com/na en/products/raman-spectroscopy/raman-
technical-resources/raman-tutorial.php
[83] What is Raman Spectroscopy?, https://www.nanophoton.net/raman/
raman-spectroscopy.html
[84] S.M. Leeds, Characterisation of the Gas-Phase Environment in
a Microwave Plasma Enhanced Diamond Chemical Vapour Deposition
Reactor using Molecular Beam Mass Spectrometry, 1999,
http://www.chm.bris.ac.uk/pt/diamond/stuthesis/chapter2.htm
[85] V. Bursikova, P. Stahel, Z. Navratil, J. Bursik, J. Janca, Surface energy
evaluation of plasma treated materials by contact angle measurement
Masaryk University, Brno, 2004
[86] R.J. Good and C. J. van Oss, Modern Approaches to Wettability: Theory
and Applications Eds: M. E. Schrader, and G. Loeb, Plenum Press,
New York, 1992
[87] W.A. Zisman,Handbook of Adhesives Skeist, I., Ed: van Nostrand,
NewYork, Chapter 3, 1977
[88] F. M. Fowkes,Industrial and Engineering Chemistry 56/12, 40, 1964
[89] , F.M. Fowkes, J. of Adhesion, 4, 153, 1972.
[90] A.W. Neumann and R. J. Good,Techniques of Measuring Contact Angles,
In Surface and Colloid Science, Volume II, Experimental Methods,
Eds: R.J. Good and R. R. Stromberg, Plenum Pres, New York, 1979.
[Oss] C.J. van Oss,Interfacial Forces in Aqueous Media Marcel Decker
Inc., New York, 1994.
[91] D. Berthelot, Comp. Rend. Acad. Sci., 126, 1703, 1898.
[92] D.Y. Kwok and A.W. Neumann Adv. Coll. Inter. Sci. 81 (1999), p. 167.
[93] G. Antonow J. Chem. Phys. 5 (1907), p. 372.
BIBLIOGRAPHY 141
[94] D.K. Owens and R.C. Wendt J. Appl. Pol. Sci. 13 (1969), p. 1714.
[95] F.M. Fowkes In: Physico-chemical Aspects of Polymer Surfaces vol. 2,
Plenum, K.L. Mittal, Editor, New York (1983).
[96] S. Wu Polymer Interface and Adhesion, Marcel Dekker, New York
(1982).
[97] E.N. Dalal Langmuir 3 (1987), p. 1009. Inter. Sci. 49 (1974), p. 291.
[98] L.A. Girifalco and R.J. Good J. Phys. Chem. 61 (1957), p. 904.
[99] D. Li and A.W. Neumann J. Colloid Interface Sci.137 (1990), p. 304.
[100] D.Y. Kwok and A.W. Neumann Coll. Surf. A 161 (2000),31
[101] P.K. Sharma, K. Hanumantha Rao, K.S.E. Forssberg and K.A.
Natarajan Int. J. Miner. Proc. 62 (2001), p. 3.
[102] I.N. Sneddon, Proc. Cambridge Philos. Soc. (1948), 492-507
[103] I.N. Sneddon, Int. J. Eng. Sci. 3 (1965), 47-57
[104] FISCHER-CRIPPS, A. C. (2011). Nanoindentation (3th ed.). New
York: Springer
[105] W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992), 1564
[106] W.C. Oliver, G.M. Pharr, J. Mater. Res. 19 (2004), 3
[107] M.F. Doerner, W.D. Nix, J. Mater. Res. 1 (1986), 601
[108] D. Tabor, Review of Physics in Technology 1 (1970), 145
[109] D. Tabor, Philos. Mag. A 74 (1996), 1207
[110] MANN, A. B. (2005). Nanomechanical Properties of Solid Surfaces and
Thin Films, in B. BHUSHAN (Ed.), Nanotribology and Nanomechanics,
An Introduction. Berlin, Nemecko: Springer.
[111] H. King, Mohs hardness scale, http://geology.com/minerals/mohs-
hardness-scale.shtml
[112] B. Wolf, Crystal Research and Technology 35 (2000), 377
[113] B. Wolf, B. Wolf, A. Richter, New J. Phys. 5 (2003), 15.1
[114] B. Wolf, Phil. Mag. Phil. Mag. Lett. 86 (2006), 5251
[115] L. Zabransky, V. Bursikova, P. Soucek, P. Vasina, T. Gardelka, P.
Stahel, O. Caha, V. Perina, J. Bursik, Surf. Coat. Tech. 242 (2014) 62
142 BIBLIOGRAPHY
[116] L. Zabransky, V. Bursikova, J. Daniel, P. Soucek, P. Vasina, J.
Dugacek, P. Stahel, O. Caha, J. Bursik, V. Perina, Surf. Coat. Tech.
267 (2015), 32
[117] ZABRANSKY, L. (2017). Studium mechanickych vlastnosti a
mikrostruktury tvrdych ochrannych vrstev na bazi uhliku [dizertacni
prace]. Masarykova Univerzita, Brno, Ceska republika
[118] J.L. He, W.Z. Li, H.D. Li, Appl. Phys. Lett. 69 (1996), 1402
[119] B. Jonsson, S. Hogmark, Thin Solid Films114 (1984), 257
[120] P. J. Burnett, T. F. Page, J. Mater. Sci.19 (1984), 845
[121] A.M. Korsunsky, M.R. McGurk, S.J. Bull, T.F. Page, Surf. Coat. Tech.
99 (1998), 171
[122] A.C. Fischer-Cripps, P. Karvankova, S. Veprek, Surf. Coat. Tech. 200
(2006), 5645
[123] FISCHER-CRIPPS, A.C. (2000). Introduction to Contact Mechanics.
Springer, Berlin, 2000
[124] S. Zhang, X. Zhang, Thin Solid Films 520 (2012), 2375
[125] B.R. Lawn, A.G. Evans, J. Am. Cer. Soc. 63 (1980), 574
[126] BROEK, D. (1997). Elementary Engineering Fracture Mechanics,
Kluwer Academic Publishers, Dordrecht, 1997
[127] M.T. Laugier, J. Mater. Sci. Lett. 6 (1987), 897
[128] G.R. Anstis, P. Chantikul, B.R. Lawn, D.B. Marshall, J. Am. Cer.
Soc. 64 (1981), 533
[129] F. Ouchterlony, Eng. Fract. Mech. 8 (1976), 447
[130] J.J. Guo, K. Wang, T. Fujita, J.W. McCauley, J.P. Singh, M.W. Chen,
Acta Mater. 59 (2011), 1671
[131] KOHOUT, J., (2013). Nanokrystalicke multikomponentni vrstvy
pripravene pulzim magnetronovym naprasovanim [dizertacni prae]. Zapadoceska
univerzita v Plzni, Plzen, Ceska republika
[132] D. Martinez-Martinez, C. Lopez-Cartes, A. Fernandez, J.C. SanchezLopez,
Thin Solid Films 517 (2009), 1662
[133] D. Galvan, Y.T. Pei, J.Th.M. De Hosson, Surf. Coat. Tech. 201 (2006),
590
BIBLIOGRAPHY 143
[134] A. Leyland, A. Matthews, Wear 246 (2000), 1
[135] A. Leyland, A. Matthews, Surf. Coat. Tech. 177-178 (2004), 317
[136] https://www.iso.org/standard/56626.html
[137] I. Ohl´ıdal, J. Voh´anka, Martin ˇCerm´ak, D. Franta, Ellipsometry of
Layered Systems, in: Optical Characterization of Thin Solid Films 64,
ed. O. Stenzel and M. Ohl´ıdal, Springer, 2018, 233–267.
[138] I. Ohl´ıdal, D. Franta, Ellipsometry of Thin Film Systems, in: Progress
in Optics 41, ed. E. Wolf, Elsevier, 2000, 181–282.
[139] D. Franta and J. Voh´anka and M. ˇCerm´ak, Universal dispersion model
for characterization of thin films over wide spectral range, in: Optical
Characterization of Thin Solid Films 64, ed. O. Stenzel and M. Ohl´ıdal,
Springer, 2018, 31–82.