Table Of ContentCHAPTER
1
Motivation
1.1 WHY “QUANTITATIVE” SCANNING PROBE MICROSCOPY?
Despite its tremendous advancement in the last 20 years, scanning probe micros-
copy (SPM) is still not understood as a really quantitative experimental technique.
Besides dimensional SPM measurements that are regularly accepted as providing
accurate results, there is an increasing number of other physical quantities measuring
and mapping modes that are producing more or less qualitative results, with no firm
relation to any absolute value. The reason is very simple. The nanoscale tip-sample
interaction is very complex, containing many different components, and some of
them are still not properly understood. Moreover, the geometry and composition of
both tip and sample are not known (we measure only result of their mutual interac-
tion), which makes all the models even more complicated. The more advanced SPM
techniques we use, the farther they are from being a metrology tool.
As most of the SPM users have no access to a specialized metrology SPM sys-
tem, their ability of converting results to quantitative ones (i.e. accurate and trace-
able, with known uncertainty) is limited to a proper instrument calibration, a good
measurement strategy and a detailed analysis of obtained results. Proper understand-
ing of basic physical phenomena taking place between tip and sample is crucial for
this task. Similarly, knowledge of all typical artifacts, accuracy bottlenecks and use
of artifact detection, and removal techniques should be a daily bread for an SPM
researcher.
The aim of this book is to provide the reader with a reference for a quantitative
SPM analysis in practical situations, namely when using commercial instruments.
We provide a description of the basic ideas necessary for the quantitative under-
standing of different SPM techniques operation, including dimensional, mechanical,
electrical, magnetic, thermal, and optical modes. We discuss the physical model of
the tip-sample interaction for each particular case and list basic calibration and trace-
ability strategies. The influence of different tip and sample geometry or their mate-
rial properties on quantitative measurements is analyzed. Techniques for modeling
realistic data and processing the measurement results are reviewed and their practical
application to user data is described. Whenever possible, publicly available software
tools are reviewed from the point of their applicability and accuracy.
Quantitative Data Processing in Scanning Probe Microscopy. http://dx.doi.org/10.1016/B978-1-45-573058-2.00001-2 1
© 2013 Elsevier, Inc. All rights reserved.
2 CHAPTER 1 Motivation
This book would like to address the typical questions of a newcomer or a casual
user. Scientific literature is full of excellent results obtained using SPM, like indi-
vidual atom chemical identification [1] or building fascinating nanostructures. When
this is compared to the possibilities of a standard commercial instrument, even a new
and really expensive one, the reader can get significantly disappointed. The data that
are produced by the instrument are at first sight only colorful images. Most of the
measured quantities have unphysical units like nanoamperes for force or volts for
temperature. If there is some calibration of quantitative data treatment built-in in the
instrument, it is limited to the very basic approaches only, even those proved in the
literature as very poor ones. In this book we would like to show what needs to be
done to get maximum of data that a “standard” commercial instrument produces and
which directions to take to improve accuracy and reliability of such results.
For illustration, we can sketch several sample questions that this book would like
to address:
• How can I calibrate my SPM to get accurate results?
• How precisely can I measure dimensions of nano-objects?
• How can I interpret force-distance curves?
• What spatial resolution can I expect in thermal/magnetic/electric/optical
measurements and how to evaluate it?
• Can I resolve different chemical species in ambient SPM measurements?
• Can I measure local material refractive index using SPM?
And what does the book not address? We focus on data processing and analysis;
all the information related to the measurement process itself is limited to its influence
on the obtained data. Technical discussion on how microscopes are built is therefore
only short and we do not describe most of the modes that need special equipment,
which is not available in any commercial instruments, even if these could lead to
challenging results. If the use of some additional equipment is suggested, it is usually
outside of the microscope, used only for obtaining some additional information (e.g.
calibration of the probes). The majority of this text is related to ambient measure-
ments, even if most of the approaches are valid also in vacuum conditions. We do not
discuss special issues related to ultrahigh vacuum (UHV) and low temperature SPMs
as this is still a statistically minor field of SPM use. We also limit the description
of numerical models and tools to basic understanding and use. For a more detailed
description, reader should follow books on concrete numerical methods, that are also
numerous.
1.1.1 Book Organization
When referring to a scanning probe microscope, some concrete instrument comes
usually to mind, typically the one that we own. We treat it as a single instrument.
But if we start discussing all the interactions, probe types, and quantities that can
be measured we see that we have many different instruments mixed together, linked
only by the basic concept—scanning with a small probe in proximity to the surface.
1.1 Why “Quantitative” Scanning Probe Microscopy? 3
If we want to discuss quantitative aspects of all these distinct instruments, the easi-
est way is to go method by method, always showing the key phenomena, necessary
instrumentation, metrology issues, and related data processing steps. This approach
is followed in most of the chapters.
The book starts with a description of what is common to all the methods. In this
and the next chapter we discuss the very basics of SPM that are probably known to
the reader—more to reference them than to bring some novel information. We review
briefly the key instrumentation principles and basic phenomena behind the measure-
ment. We review basics of metrology in order to help following the discussions on
quantitative data processing. We also describe how the SPM is related to other ana-
lytical methods.
The following three chapters describe more in detail the concepts that are com-
mon to all SPM techniques. The third chapter focuses on basic data acquisition and
storage models in SPM, including a discussion of factors limiting SPM precision
during the measurement, like drift or noise. The fourth chapter describes basics of
data visualization, correction, and processing. The fifth chapter refers to dimensional
measurements using inter-atomic force-based feedback that is common to most of
the discussed techniques. It also covers major issues of uncertainty analysis in SPM
based dimensional measurements. As dimensional measurements are the key part of
every more complex SPM technique, this analysis is valid also in all the following
chapters.
The next eight chapters are related to different analytical techniques available in
SPM. They have almost the same basic structure as shown below.
First, key phenomena that can be measured and that are used as a source of the
analytical information are discussed (normal and lateral forces, electric field, thermal
transport, etc.). This should cover the basic questions of why to use these techniques
and what we can measure with them. Theoretical analysis starts from very simple
models and even very basic concepts to make reading easier for SPM users from
non-physical fields. More complex approaches are discussed briefly as well, how-
ever their rigorous development is often left to referred monographs as their detailed
description would be outside the scope and size of this book. Theoretical descriptions
often include also basic information about numerical modeling techniques, that can
be helpful in the interpretation of the data. Simply usable software is often recom-
mended for the practical demonstration of the efficiency of the numerical methods
even if the results and general remarks are valid for all the other software packages
as well.
The instrumentation necessary for each particular analytical method is reviewed,
to show how the discussed quantities can be measured. This section is namely focus-
ing on possibilities how to get the method calibrated and traceable. As the book is
namely concentrated on data processing and interpretation, we do not discuss special
modes and techniques that need special equipment (usually custom built) and would
be probably not available for the reader.
The most important section on data interpretation follows, showing how both the
analytical models and numerical techniques can be used for better understanding of
4 CHAPTER 1 Motivation
what was measured. Typical error sources and artifacts are reviewed and ways how to
detect and suppress them are discussed. This covers the main question discussed through
the whole book: how precise SPM can be for different quantities measurements. The
chapter is then finished by examples of what the reader could practically try, often using
attached software, and with some tips for making the measurement as quantitative as
possible. Recommended further reading is listed as well as this book does certainly not
contain all the information that the user would need when going deeper.
There are two special chapters at the end of the book. The first one (Chapter 13) lists
all the available data—measurement samples and software available on the associated
web content. The second one (Chapter 14) provides some more technical details about
how the different numerical methods work and what they are based on.
1.1.2 Available Numerical Techniques
While reading the book, you might ask why there is such an emphasis on numerical
modeling techniques? It is clear that the availability of any numerical method cannot
substitute the understanding of physics behind the problem. Numerical modeling could
be understood as no better than the “second best” approach. But for many SPM related
phenomena the analytical approach needs so many assumptions that it cannot cover
the tip-sample interaction in whole, including all effects seen in the real world (e.g.
roughness or material inhomogeneities). That is why we need numerical modeling.
Numerical modeling tools are very popular nowadays in physics, as the large
computational power and ubiquity of computers makes their use very simple.
Numerical methods that required supercomputers some 10 years ago are now acces-
sible within a few minutes or hours on a regular computer and with the extreme
market demands for innovations we can expect them to run even on a toaster 10 years
from now. The increasing market need for consumption is from this point certainly
a large benefit for computational physicists. A large number of both commercial
and non-commercial software tools has been created for different physics areas and
applications. Even if they can help a lot in SPM data analysis, there is a significant
barrier for a beginner to use them. Some of the numerical packages are intended for
general purposes, but to set up a simulation of a concrete problem needs many hours
of preparation. Others are optimized for the particular field of application of their
authors and application for any other field is almost impossible. In this book several
numerical methods and software packages are discussed in detail for illustration of
data processing concepts. It should be said that these were selected on the basis of
their simplicity (and author’s knowledge) and the reader is encouraged to try any
possible alternative that would fit his/her needs.
For practical purposes the numerical techniques description is scattered through-
out the book, discussing each particular technique in the chapter when it has some
application. Here we summarize the techniques discussed in the book:
• Classical molecular dynamics and quantum molecular dynamics based on
Density Functional Theory (DFT) are discussed in Chapter 6 when forces
1.2 What is Scanning Probe Microscopy? 5
and local mechanical properties are discussed. DFT is then again used in
Chapter 10 for scanning tunneling microscopy (STM) modeling. Generally,
these methods are appropriate when dealing with effects at a very small scale,
starting from few atoms up to some millions of atoms.
• Finite Difference and Finite Element methods are discussed also in Chapter 6
and then in Chapter 8 following electrostatic fields in SPM description and in
Chapter 9 discussing micromagnetic modeling. These methods are designed to
treat the material as a continuum, and so are used from computation space sizes
of some micrometers up to the macroscale.
• Finite Difference in Time Domain method is discussed in Chapter 12 when
talking about optics in SPM. This is a time-based extension of Finite Difference
method, solving coupled Maxwell equations.
Many more simpler algorithms are introduced in different chapters, like tip
manipulation routines (dilation, erosion), neural network analysis, surface simula-
tions, virtual SPM, etc. When possible, the reader has the possibility to try them
directly in the attached open source software packages, in most cases as modules in
the open source software Gwyddion, briefly introduced here.
Gwyddion [2] is a modular multi-platform software for SPM data analysis. Its
main task is to provide fast and reproducible data processing routines that will be
available for many SPM users. Gwyddion can be downloaded from http://gwyddion.
net or taken from the associated web content. It allows the user to perform all basic
operations necessary for the successful evaluation of data obtained using an SPM.
It can read over 80 file formats and it can be used for the easy development of soft-
ware modules, scripting and other, even relatively complex tasks. The selection of
Gwyddion as a key sample software for this book is however based only on the
authors’ knowledge of it and the reader is encouraged to try also other software pack-
ages, some of which are listed in Chapter 4.
On the associated web content there are also the sample data discussed in the next
chapters (in native Gwyddion file format) and some more open source software pack-
ages discussed in this book. Note that both Gwyddion and other software packages
evolve rapidly, so it might be helpful to download the actual versions when reading
this book.
1.2 WHAT IS SCANNING PROBE MICROSCOPY?
As the whole SPM history fits only a few decades, we can briefly introduce it here in
just one paragraph. The principal ideas of scanning probe microscopy can be dated
back to 1928, when E.H. Synge proposed a theoretical approach for overcoming dif-
fraction limit in conventional optical microscopy by scanning a small sub-wavelength
aperture in distance of 100 nm from the sample surface. Even if this pioneering study
did not introduce most of the key parts of a scanning probe microscope, its basic idea—
a nanoscale probe in proximity to the surface—was already incorporated. The first
6 CHAPTER 1 Motivation
instrument that already consisted of the key SPM parts and concepts (scanner, probe,
imaging by scanning) was the Topografiner in 1971 from R.D. Young et al., an ances-
tor of the scanning tunneling microscope. Ten years later, the first scanning tunneling
microscope was built by Binnig et al. [3] (Nobel Prize in 1986), followed by the first
atomic force microscope in 1986 by Binnig et al. [4], and followed by a large amount of
different other microscopes and related analytical techniques in the next two decades.
Since that time we can observe a large development of both custom built and
commercial systems and SPM matured to become a standard technique in the field of
materials science, surface physics, microelectronics, life sciences, and even metrol-
ogy. Two main branches were established soon after—microscopes working in UHV
conditions, used namely by surface physicists, and microscopes working in ambient
conditions used by everyone else. Both branches were improved significantly during
some 20 years of development, so the state-of-the-art instruments are really excellent
pieces of equipment. Even with relatively simple instruments we can observe many
different phenomena on many different samples, like morphology of surfaces from
living cells [5] to diamonds (see Figure 1.1a and b), mechanical properties differ-
ences (Figure 1.1c), magnetic stray field effects (Figure 1.1d), thermal conductivity
variations on microelectronic samples [6] (Figure 1.1e), or luminescence of locally
concentrated dyes [7] (Figure 1.1f).
The definition of a scanning probe microscope is almost completely given already by
its name. During the last 30 years so many different methods emerged, that any instru-
ment obtaining any data by scanning with a small probe of any kind in the close proxim-
ity to the sample surface (with distance preserved by any feedback principle) belongs to
the family of scanning probe microscopes and probably even has its own name.
A typical realization of an SPM instrument consists of a very precise position-
ing stage that enables sub-nm positioning, a probe, usually in form of a sharp cone
or pyramid, and finally an electronic system detecting the probe-sample interaction
and enabling a closed loop feedback for probe positioning. Despite its primary func-
tion—scanning—the probe is also doing other activities, like collecting local spec-
troscopic data. A slightly more detailed description of how an SPM can look like is
given in Chapter 2.
An important difference between scanning probe microscopy and “classical
microscopy” is that we are not looking at the sample, but we are more or less touch-
ing it. A profilometer or a gramophone is therefore much closer to an SPM than an
optical microscope. Let us briefly describe what happens when we bring a small
solid body—probe—close to the sample surface. Of course, this depends namely on
the properties of both the bodies, but in general we can observe several interactions
(having different ranges as schematically sketched in Figure 1.2), that, as we will see
later, will be responsible for different SPM imaging modes and analytical techniques:
• Probe-sample distance 1 μm: If we bring two bodies to this distance, we will
not observe anything special. If the bodies are charged, we might measure
electrostatic force, if they are magnetized we will observe magnetic interaction.
There will not be probably any significant energy transfer, except radiative heat
1.2 What is Scanning Probe Microscopy? 7
Figure 1.1 (a) AFM topography of Escherichia coli bacteria, (b) AFM topography of a natural
diamond, (c) Z-modulation measurement showing mechanical properties of a nanocomposite
sample, (d) MFM magnetic field distribution above a hard disk surface, (e) SThM thermal
conductivity map of a microelectronic chip, and (f) NSOM image showing a luminescence of
a rhodamine dye intercalated in montmorillonite.
transfer in case that temperatures differ significantly, but also this effect will be
rather small.
• Probe-sample distance 10–100 nm: If the bodies come closer, they can start
sensing some other long range interactions, like van der Waals forces. Even
closer, in ambient conditions, first water bridges can appear due to capillary
8 CHAPTER 1 Motivation
Figure 1.2 Ranges in which typical interactions are observed in SPM experiments.
condensation. Convective heat transfer due to surrounding air or even liquid
layer can appear. This is the probe-sample distance where we can already
collect some interesting data with resolution in tens of nanometers, e.g. in
magnetic force microscopy (MFM).
• Probe-sample distance 1–10 nm. Charge transfer via tunneling appears, van der
Waals forces can become dominant. If there is a native water layer, the probe is
immersed into it. We can set up a feedback loop using attractive forces.
• Contact (probe-sample distance equal to or less than inter-atomic distance).
Repulsive interactions due to the Pauli exclusion can be used for feedback. We
observe charge and heat transfer. For higher forces sample and probe deformation
can occur, so we can determine mechanical properties of the sample.
As we can see, even if there are only few basic interactions that we will observe
in SPM their combination and presence of third bodies (like water molecules) leads
to a surprisingly rich mixture of different physical phenomena that we can observe.
The basic data acquisition and feedback mechanisms in SPM that will be dis-
cussed in this book are as follows:
• Repulsive chemical interaction: Atomic force microscopy (AFM) imaging
and nanoindentation, topography measurements by nearly all the techniques,
described in Chapter 5.
• Attractive or repulsive van der Waals interaction: AFM, topography
measurements by nearly all the techniques (Chapter 5).
• Electrostatic forces and potentials: Electrostatic force microscopy (EFM),
scanning capacitance microscopy (SCM), Kelvin probe force microscopy
(KFPM), described in Chapter 8.
• Magnetic forces: Magnetic force microscopy (MFM) and similar techniques
discussed in Chapter 9.
• Current between probe and sample: Scanning tunneling microscopy (STM) and
conductive AFM (C-AFM), discussed in Chapter 10.
1.3 Basic Metrology Concepts 9
• Heat exchange: Scanning thermal microscopy (SThM) discussed in Chapter 11.
• Electromagnetic field enhancement and scattering: Near-field scanning optical
microscopy (NSOM), tip enhanced Raman scattering (TERS), see Chapter 12.
In this book we will discuss how to get quantitative information from all these
techniques and numerical tools that can help us with this, often hard, task. Note that
there are many other acronyms often seen in the SPM related literature, sometimes
referring to the same techniques. A typical example is SNOM (scanning near-field
optical microscopy) versus NSOM (near-field scanning optical microscopy) that in
some 90% of articles means the same. A list of different acronyms used in SPM and
their meaning is given in Table 1.1, together with the location of their description in
the book (if there is any).
1.3 BASIC METROLOGY CONCEPTS
As this book is dedicated to quantitative measurements, we would like to review here
basic concepts of metrology that will be often referenced. Even if a measurement
is the key concept in science, metrology certainly does not belong among the most
popular science fields. However, there is no quantitative measurement without metrol-
ogy. The basic terms that will be often used in this book are discussed in this section.
1.3.1 Measurement Traceability
When people are buying a new SPM, they typically request a particular range, resolu-
tion, noise level, or if they go to more technical details, e.g. some bit depth of analog-
to-digital converters. Better instruments have typically higher resolution and smaller
noise levels. But this has nothing to do with measurement accuracy. Even if our SPM
can beautifully image an atomic lattice in ambient conditions it could measure the
distances between atoms wrong by tens of percent. In this book we will try to empha-
size the measurement accuracy issues in SPM.
When we look at the definition of basic SI units we see that a primary realiza-
tion of the unit is always mentioned, which is by definition understood as the most
accurate realization. Even if for mass this is still (2012) a prototype, which cannot
be independently realized in an other laboratory, in most of the cases it is an experi-
ment based on some physical effect, that could be repeated anywhere with the same
accuracy. Usually, at the top level, these basic SI unit realizations are maintained by
national metrology institutes, that are using a set of inter-comparisons to ensure that
all the realizations give the same results.
If we have a commercial SPM and we want to perform accurate measurements,
we need to get a connection to the basic realization of appropriate units, most fre-
quently for length. By measurement traceability we understand a chain of relations
between measurements starting from the international etalons for a given quantity
and ending in our experiment. The relation is usually established by calibrating a
lower level etalon by a higher level one.
10 CHAPTER 1 Motivation
Table 1.1 List of most frequently used SPM abbreviations and their
meanings
Abbreviation Full name Main applications Chapter
AFAM Acoustic Force Mechanical 6
Atomic Microscopy properties
AFM Atomic Force Dimensional 5, 6
Microscopy and mechanical
properties
C-AFM Conductive Electrical properties 5, 6
Atomic Force
Microscopy
FFM Friction Force Friction 7
Microscopy
IETS Inelastic Molecular 10
Electron Tunneling composition
Spectroscopy
KPFM Kelvin Probe Force Dimensional and 8
Microscopy electronic properties
LFM Lateral Force Friction 7
Microscopy
MFM Magnetic Force Magnetic properties 9
Microscopy
MRFM Magnetic Magnetic and 9
Resonance Force chemical properties
Microscopy
NSOM Near-Field Equal to SNOM 12
Scanning Optical
Microscopy
PFM Piezoresponse Piezoelectric –
Force Microscopy properties
SECM Scanning Local 10
Electrochemical electrochemistry
Microscopy
SCM Scanning Electrical 8
Capacitance properties, dopant
Microscopy concentration
SNOM Scanning Optical properties 12
Near-Field Optical
Microscopy
SThM Scanning Thermal Temperature and 11
Microscopy thermal conductivity
STM Scanning Tunneling Dimensional and 10
Microscopy electronic properties
STS Scanning Tunneling Electronic properties 10
Spectroscopy
TERS Tip Enhanced Optical and 12
Raman Scattering chemical properties
