1. Nano Measurement
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1. Introduction:
The introduction and invention of Scanning Tunneling Microscope (STM), Atomic Force
Microscope (AFM), Magnetic Force Microscope (MFM) and other Scanning Probe
Microscopes (SPM) (where around 25 types are available currently) bought a wave of
change in the way we see and study the structures and properties of the surfaces. With
this development, we are now able to realize novel properties in nanotechnology such
as creation of unique structures by manipulating atoms and molecules. This has also
lead to new developments in the field of electronics, information storage, multicore
processors and sensors. There has been a massive interest in this field ever since its
inception in 1982 [1]. One of the main factors behind the rapid development of SPM is
the high availability of commercial instruments, the required conditions which were
available easily (like vacuum, liquid and gas from 4 to 700 K) and renewed interest
amongst scientist and engineers to be able to manipulate matter at a atomic level and
understand its properties [1]. From January 1, 2002 to December 31 2003, there were
around 11,000 cited publications solely devoted to the physics and the applications of
SPM [2]. By using STM, one can, with slight modifications to the current technology,
image non conductive materials such as DNA and oxides to sub-nanometer level. The
processes were observed continuously thanks to the ability of STM and AFM which gives
no damage or interference to the sample. One of such example is that the entire
process of a living cell infected by virus has been seen in detail using AFM [3].
Figure 1: General visual representation of SPM [4]

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2. SPM Techniques (Questions 1 and 2):
There are around 25 types of SPM related techniques. Although most of the techniques
are mere modifications of STM or AFM, the following list shows some of frequently used
and widely known SPM techniques:
- Atomic Force Microscopy (AFM):
AFM is one of the most high resolution type SPM where the resolution is
of the order of few nanometers. It was developed in the early 1980s by
Gerd Binning and Heinrich Rohrer at the IBM Research Labs in Zurich.
Since then, AFM has become the foremost tool for nano based imaging
and measurements. More detailed explanation of AFM will be discussed
further in the report.
- Scanning Tunneling Microscopy (STM):
STM is widely used for imaging surfaces at atomic level. It was invented
at IBM-Zurich by Gerd Binning and Heinrich Rohrer in 1986 [5] and this
earned them a Nobel Prize in 1986 in Physics [6]. The resolution of STM is
about 0.1 nm (lateral) and 0.01 nm (depth) which enables the images to
be viewed at atomic level precision with as low as single atoms can be
viewed separately within the materials. STM is based on a quantum
phenomenon known as quantum tunneling. This will be explained in
detail further in the report.
- Near Field Scanning Optical Microscopy (NSOM/SNOM):
NSOM/SNOM measures local optical properties by exploiting near field
effects which in turn allows the characterization (such as structural,
mechanical, optical and electronic) of the material (such as metals,
semiconductors, insulators, biomolecules) [7] with a specific environment
(vacuum, liquid, ambient air conditions) [1] [7]. This is basically done by
breaking the resolution limit through the properties of evanescent wave1
.
The detector is placed very close to the sample (usually at smaller
wavelength) and by using this method, the spatial, and spectral and
resolution of the image is highly improved. The resolution is limited by
the size of the detector’s aperture but not by the wavelength of the
illuminating light which is usually the case. The lateral resolution
achieved is 20 nm and vertical resolution is 2-5 nm [8].
1
Evanescent wave is a near-field standing wave with the intensity having an exponential decay which
starts from the boundary at which the wave is being formed initially [55].

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Figure 2: Differences in the probe tip between STM, AFM and SNOM [7]
Figure 3: Tip differences in (A)-STM, (B)-AFM, (C)-SNOM, (D)-A probe kept in ambient conditions [9]

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- Ballistic Electron Emission Microscopy (BEEM):
BEEM is a three terminal STM which was invented in 1988 at Jet
Propulsion Lab by L. Douglas Bell and William Kaiser [10]. BEEM has been
used usually for the study of Metal-Semiconductor Schottky diodes.
- Chemical Force Microscopy (CFM):
CFM is another variation of AFM. It was developed by Charles Lieber at
Harvard University in 1994 [11]. The only difference between them is that
in CFM the interactions between the probes tip and sample is done
through chemical methods. Typically a gold-coated tip is used with its
surface having R-SH thiols2
(where R is any carbon containing atoms
functional group) [12]. CFM’s main usage is to determine the chemical
nature of surfaces regardless of their morphology and this enables to
understand the chemical bonding enthalpy and surface energy of the
samples [12].
- Magnetic Force Microscopy (MFM):
MFM is another technique derived from AFM. A sharp magnetic tip is
used to scan the sample. The interaction between the tip and sample are
detected which in turn are used to reconstruct the magnetic topography
of the material. It’s often used in scanning Magnetic images of Hard
Drives (or ant recording media), nanowires, Carbon Nanotube (CNT), thin
films etc. MFM will be discussed in more detail further in the report.
Optical SEM/TEM Confocal SPM
Magnification 103
107
104
109
Price(USD $) $10k $250k $30k $100k
Technology Age 200 years 40 years 20 years 20 years
Applications Ubiquitous Science and
technology
New and
Unfolding
Cutting Edge
Market Since
1998
$800 million $400 Million $80 Million $100 Million
Growth Rate 10% 10% 30% 70%
Table 1: Conventional Microscopes in comparison with SPM techniques [7]
2
A thiol is a organosulfur (organic compounds containing sulfur) compound which contains R-SH or C-SH
group (where R is alkane, alkene or other carbon containing atoms)

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SPL3
Method Instruments Environment Key
Mechanism
Typical
Resolution
Patterning
Materials
Possible
Applications
Nanoscale
Pen Writing
Dip-Pen
Nanolithography
AFM Ambient Thermal
Diffusion of
Soft Solids
10nm SAM4
,
Biomolecule
s, Sol-Gel,
Metal etc
Biochip,
Nanodevice,
Mask Repair
etc
Nanoscale
Printing of
Liquid Ink
NSOM5
Ambient Liquid Flow 100nm Etching
Solution,
Liquid
Mask Repair
etc
Nanoscale
Scratching
Nanoscale
Indentation
AFM Ambient Mechanical
Force
10nm Solid Mask Repair
etc
Nanografting AFM Liquid Cell Mechanical
Force
10nm SAM Biochip etc
Nanoscale
Melting
AFM Ambient Mechanical
Force and
Heat
10nm Low Melting
Point
Materials
Memory etc
Nanoscale
Manipulation
Atomic and
Molecular
Manipulation
STM Ultra High
Vacuum
Van der Waals
or
Electrostatic
Forces
0.1nm Metals,
Organic
Molecules
etc
Molecular
Electronics etc
Manipulation of
Nanostructures
AFM Ambient Van der Waals
or Mechanical
Force
10nm Nanostructu
res,
Biomolecule
s
Mask Repair,
Nanodevices
etc
Nanoscale
Tweezers
AFM Ambient Van der Waals
or Mechanical
Force
100nm Nanostructu
res
Electrical
Measure etc
Nanoscale
Chemistry
Nanoscale
Oxidation
STM or AFM Humid Air Electrochemic
al Reaction in
a Water
Meniscus
10nm Si, Ti etc Nanodevices
etc
Nanoscale
Desorption of
SAM
STM or AFM Humid Air Electrochemic
al Reaction in
a Water
Meniscus
10nm SAM Nanodevices
etc
Nanoscale
Chemical Vapor
Deposition
STM Ultra High
Vacuum with
Precursor Gas
Nanoscale
Chemical
Vapor
Deposition
10nm Fe, W etc Magnetic
Array etc
Nanoscale
Light
Exposure
Nanoscale Light
Exposure
NSOM Ambient Photoreaction 100nm Photosensiti
ve Materials
Nanodevices
etc
Table 2: Applications of SPM related techniques into different SPM Processes and their practical applications [9].
3
Scanning Probe Lithography.
4
Self Assembled Monolayer – It is an organized layer of amphiphilic molecules in which the one end of
the molecule (named as the “head group”) shows specific affinity for the substrate.
5
aka SNOM

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2.1. Scanning Tunneling Microscope(STM)(Question 3 and 4):
During its inception, the STM was the first and one of its kind device which was able to
get 3-D images of solid structures with atomic resolution [13]. STM works on the
principle of quantum tunneling and this was first proposed by I. Giaver [14].
Figure 4: Basic Schematic of a STM [15]
According to him if there is a potential difference applied to two metals which are
separated by a thin insulating film, a current will flow due to the ability of electrons to
penetrate through the potential barrier. Binning et al. later introduced lateral scanning
and vacuum tunneling and also demonstrated that the preferable distance between the
two metals should be 10nm [13]. Due to the lateral scanning, the resolution laterally is
about 1nm and vertically is about 0.1nm which is sufficient to acquire an image of single
atoms.
The working of STM is fairly simple. The metallic tip is bought close to the sample
surface such that after applying a bias voltage (of about 10mV – 1V [7]), the tunneling
current between the tip and the surface of the sample is measured. The tunneling
current is usually from 0.2nA – 10nA [7]. Figure 5 shows the schematic of the two modes.
STM works in two modes; constant current mode and constant height mode.
The tunneling current normally gets reduced by a factor of 2 (𝑒2
) when the separation
(from the tip and the surface) is more than 0.2 nm [7]. This will be explained further in
this section with the introduction of quantum mechanics and the concept of quantum
tunneling.

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Figure 5: The two modes of the STM; constant current and constant height mode are illustrated in the above image.
The concept of Quantum Tunneling can be explained through classical mechanics; let’s
assume an electron has an energy E and having a Potential Energy U(x), then the
following can be deduced:
𝒑 𝒙
𝟐
𝟐𝒎
+ 𝑼( 𝒙) = 𝑬 1
Where m = 9.1 𝑋10−28
𝑔 which is the electron mass. This can be further elaborated into
two cases. If E > U(x) the electron has a non zero momentum and if E < U(x) then
electron cannot penetrate into any region and hence creating a potential barrier. This is
better described by using the wave function Schrödinger’s Equation:
−
ℏ 𝟐
𝟐𝒎
𝒅 𝟐
𝒅𝒙 𝟐 𝝍( 𝒙) + 𝑼( 𝒙) 𝝍( 𝒙) = 𝑬𝝍( 𝒙) 2

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Image 1: Difference between classical and quantum physics [16].
In the image above, there is a constant energy and a piece-wise constant potential. In
the first half of the above image, classical physics allowed region E > U, then equation 1
has solutions of the wave function which is also a wave vector and can be represented
as:
𝝍( 𝒙) = 𝝍(𝟎)𝒆±𝒊𝒌𝒙
3
Where k is:
𝒌 =
√𝟐𝒎(𝑬−𝑼)
ℏ
4
The electron is moving in positive/negative direction having a constant momentum 𝑝 𝑥 =
ℏ𝑘 = √2𝑚(𝐸 − 𝑈) with a constant velocity which can be derived from the momentum
equation 𝑣 𝑥 =
𝑝 𝑥
𝑚
. When the electron is in the classically forbidden/impenetrable
region then equation 2.2 becomes:
𝝍( 𝒙) = 𝝍(𝟎)𝒆−𝒌𝒙
5

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Where k becomes:
𝒌 =
√𝟐𝒎(𝑼−𝑬)
ℏ
6
The U-E is present which signifies a decay of electron in positive x direction (+x). The
probability density of finding an electron which is having a non-zero value near the point
x is proportional to |𝜓(0)|2
𝑒−2𝑘𝑥
and if the decay is in negative direction then the
probability is 𝜓(0)𝑒 𝑘𝑥
which signifies the decay stage.
Image 2.2: Grey Scale Images. The two images are of Si (111) -7X7 with dimensions 100X125Å 𝟐
taken from a STM
[17]
Using the concepts above, we can now prove the metal-vacuum-metal tunneling. We
can now include the concept of work function which states that it’s the minimum energy
required to remove an electron from the surface of the metal. The work function of a
metal depends on two things; the material itself and on the crystallographic orientation
of the surface (or lattice arrangement). Table 2.1 shows all commonly used metals in
STM based experiments. Assuming that the work function of the tip and the sample in
the STM are the same, then the electron can tunnel from the sample to the tip [13] [16].
Element Al Au Cu Ir Ni Pt Si W
𝝓(𝒆𝑽) 4.1 5.4 4.65 5.6 5.2 5.7 4.8 4.8
Table 3.1: Typical work function values of metals commonly used in STM experiments [18]

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- Derivation and equations the tunneling current acting within the STM:
Figure 2.5: A 1-D barrier between two metals. A bias voltage is applied in between two electrodes [9]
Let’s assume a 1-D barrier and a vacuum barrier in between two electrodes as shown in
the above image where the two electrodes’ work functions are the same and hence
having a same barrier height Φ, bias voltage V and barrier width d, then according to
quantum physics’ first order perturbation theory [19], the tunneling current can be
written as:
𝑰 =
𝟐𝝅𝒆
ℏ
∑ 𝒇( 𝑬 𝝊)[ 𝟏 − 𝒇( 𝑬 𝝊 + 𝒆𝑽)]|𝑴 𝝁,𝝊|
𝟐
𝜹(𝑬 𝝁 − 𝑬 𝝊)𝝁,𝝊 7
Where 𝑓( 𝐸) is the Fermi function, 𝑀𝜇,𝜐 is the tunneling matrix element between the
quantum states 𝜓 𝜇 𝑎𝑛𝑑 𝜓 𝜐 of the electrodes. 𝐸𝜇and 𝐸𝜐 are the energies within the
states 𝜓 𝜇 𝑎𝑛𝑑 𝜓 𝜐. If we assume that we are working at cryogenic temperatures and
small voltages, then the equation 7 can be simplified to as follows:
𝑰 =
𝟐𝝅𝒆 𝟐
ℏ
𝑽 ∑ |𝑴 𝝁,𝝊|
𝟐
𝜹(𝑬 𝝊 − 𝑬 𝑭)𝜹(𝑬 𝝁 − 𝑬 𝝊)𝝁,𝝊 8
Under certain conditions [19], the tunneling matrix element can be expressed as:
𝑴 𝝁𝝊 =
ℏ 𝟐
𝟐𝒎
∫ 𝒅𝑺⃑⃑⃑⃑⃑ . ( 𝝍 𝝁 𝛁∗⃑⃑⃑⃑⃑ 𝝍 𝝊 − 𝝍 𝝊 𝛁∗⃑⃑⃑⃑⃑ 𝝍 𝝁) 9
The integral mentioned in equation 9 is the integral over the entire barrier region [9].
Now we will estimate the magnitude of 𝑀𝜇𝜐.

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To estimate, we will expand the wave function of 𝜓 𝜐 in a plane-wave form which is as
follows:
𝝍 𝝊 =
𝟏
√𝛀 𝑺
∑ 𝒂 𝑮 𝒆
[√ 𝒌 𝟐+|𝒌 𝑮
⃑⃑⃑⃑⃑ |
𝟐
𝒛]
𝑮 𝒆[𝒊𝒌 𝑮
⃑⃑⃑⃑⃑ .𝒙⃑⃑ ]
10
Where Ω 𝑆 is the volume of the sample, 𝑘 =
√2𝑚ϕ
ℏ
is the decay constant/rate, ϕ is the
work function of the electrodes, 𝑘 𝐺
⃑⃑⃑⃑ = 𝑘||
⃑⃑⃑⃑ + 𝐺⃑⃑ where 𝑘||
⃑⃑⃑⃑ is the surface component of
the Bloch vector6
and 𝐺 is the surface reciprocal vector [9].
Figure 6: If we assume the radius of the edge of the tip to be R, the distance from the sample to the tip to be d,
then the position of the centre of the sphere will be 𝒓 𝟎 [20].
Using the principle mentioned in the Figure 6 above, the wave function of the tip can be
expressed as:
𝝍 𝝁 =
𝟏
√𝛀 𝒕
𝒄𝒕 𝒌𝑹𝒆 𝒌𝑹( 𝒌| 𝒓⃑ − 𝒓 𝟎⃑⃑⃑⃑ |)−𝟏
𝒆−𝒌|𝒓⃑ −𝒓 𝟎⃑⃑⃑⃑ |
11
where 𝜓 𝜇 is the voltage of the tip, 𝑐𝑡 is the sharpness of the tip which is a constant.
6
Bloch vector is a unit vector which is used to represent points in a Bloch Sphere.
Sample
R𝑟0
Tip

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In this case we will be focusing only on s-wave function of the tip7
and this due to:
𝟏
𝒌𝒓⃑
𝟏
𝒆−𝒌𝒓⃑ = ∫ 𝒅 𝟐
𝒒𝒃( 𝒒⃑⃑ ) 𝒆^[−√𝒌 𝟐 + 𝒒 𝟐| 𝒛|] 𝒆𝒊𝒒⃑⃑ .𝒙⃑⃑
12
𝒃( 𝒒) =
𝟏
𝟐𝝅 𝒌
𝟐√ 𝟏+
𝒒 𝟐
𝒌 𝟐
13
Substituting 12 and 13 into 9 we get:
𝑴 𝝁𝝊 =
ℏ 𝟐
𝟐𝒎
𝟒𝝅
𝒌√𝛀 𝒕
𝒌𝑹𝒆 𝒌𝑹
𝝍 𝝊(𝒓 𝟎⃑⃑⃑⃑ ) 14
Substituting 8 into 2 we get:
𝑰 = 𝟑𝟐𝝅 𝟑 𝟏
ℏ
𝒆 𝟐
𝑽𝝓 𝟐
𝑫𝒕( 𝑬 𝑭) 𝑹 𝟐 𝟏
𝒌−𝟒
𝒆 𝟐𝒌𝑹 ∑ | 𝝍 𝝊( 𝒓 𝟎)| 𝟐
𝜹(𝑬 𝝊 − 𝑬 𝑭)𝝊 15
where 𝐷𝑡( 𝐸 𝐹) is the local density of states at Fermi level for the tip [9]. By substituting
typical values for metals for density of states in 15, we get:
𝑰𝜶𝑽𝑫𝒕( 𝑬 𝑭) 𝒆 𝟐𝒌𝑹
𝝆( 𝒓 𝟎, 𝑬 𝑭)
𝝆( 𝒓 𝟎, 𝑬 𝑭) = ∑| 𝝍 𝝊( 𝒓 𝟎)| 𝟐
𝜹(𝑬 𝝊 − 𝑬 𝑭) 16
Equation 11 shows that the STM tip would only measure 𝜌(𝑟0, 𝐸 𝐹).
Since,
|𝜓 𝜐(𝑟0)⃑⃑⃑⃑⃑ |2
𝛼 𝑒−2𝑘(𝑅+𝑑)
, ℎ𝑒𝑛𝑐𝑒 𝐼 𝛼 𝑒−2𝑘𝑑
This proves that the tunneling current depends on the tunneling gap distance d. This
allows the resolution to be around 0.1 Å. This makes STM have atomic resolution and
this will be discussed further in this section with examples.
7
It is a type of elastic wave also known as the secondary wave.

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Another very important issue in STM is the noise level requirements. This is a big burden
for STM manufacturers to decide whether a huge amount of money should be put in to
create a vibration isolated room which can be very expensive. But this has to be
determined depending on the use of the STM. Preamplifiers can also be used and placed
at low cryogenic temperatures. There are two ways of reducing noise:
 Noise Calculations:
- Mechanical Noise Cancellation Method (Vibration Control):
In Mechanical Noise cancellation method, a suspension spring with
magnetic damping is used. This is done due to the fact that the tunneling
current is extremely sensitive to height of the tip. In other words, if the
tip-sample separation has an offset of a few angstroms then there would
be a big deviation in the images taken from the STM and there would be
hardly any useful/meaningful data acquired due to the noise generated.
- Electronic Noise:
There are three major form of electronic noise namely; Johnson noise,
shot noise and 1/f noise (or time period dependent noise). Johnson noise
across a resistor is given by:
∆𝑽 = √ 𝟒𝒌𝑻𝑹∆𝒇 17
The noise increases with resistance and since 𝑉 = 𝐼𝑅, having larger
resistor values will result in less noise ratio. The rms Johnson current
noise through the resistor is given by:
𝑰 = √
𝟒𝒌𝑻∆𝒇
𝑹
18
Using the above equations 2.7 and 2.8, we can calculate the noise level
required for the STM, assuming the work function to be 4eV and the
vertical mapping distance to be 0.01Å. Note that at low cryogenic
temperatures, the tunneling current is proportional to the exponential of
the decay constant (k) and vertical mapping distance (d) which can be
expression as follows:
𝑰 ∝ 𝒆−𝟐𝒌𝒅
19

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Where the decay constant is given by:
𝒌 =
√ 𝟐𝒎𝚽
ℏ
20
Then we can do the calculation as follows:
𝑘 =
√2𝑋9.1𝑋10−31 𝑋6.4𝑋10−19
1.05𝑋10−34
= 1010
Hence, the decay constant is 1010
. Using this we can calculate the noise
level by using equation 2.8:
𝐼 = 𝑒−2𝑋0.01𝑋1010 𝑋10−10
= 0.98 𝐴 ≈ 1𝐴
∆𝐼
𝐼
= −2𝐾𝑑 = −2 ∗ 1010
∗ 10−12
= 0.02 = 2%
STM offers atomic resolution in every clean surface of metals and
semiconductors. Normally to achieve atomic scale resolution, a lateral
resolution of 2Å is required. If we assume that each point on the tip the
tunneling current density follows the equation for 1-D quantum tunneling
case then the current distribution is and by using the experiment done by
Quate et al [21]:
𝐼 = 𝐼0 𝑒−2𝑘
∆𝑥2
2𝑅
Where 𝑘 = 1Å
−1
, 𝑅 = 1000Å, ∆x = 45Å(∆x is current column) [21], the
current drops by a factor of 𝑒−2
. If 𝑅 = 100Å, the current stays at around R=
14 Å which enables atomic precision. Hence a high lateral resolution is
achieved [16]. The following images show a good example of some images
achieved through STM with atomic level precision.

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- Some Interesting Images from STM showing atomic scale resolution:
Image 2: This image shows the atomic resolved image of Cu (111). The atomic distance of Cu here is 2 Å [16]

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Image 3: STM images of evaporated 𝑪 𝟔𝟎 film on a gold coated mica [22]
Image 4: In the image above, individual atoms and their electronics structure can be seen clearly. This is the first
STM image of Si (111) achieved by Binnig et al [13]. The height of each step is 12 Å [16].
Image 5: In the first image from the STM of Si(111)[-7X7] surface, the individual atomic bonds can be clearly seen.
The above images were taken in the first year of the inception of the STM. The individual nearest-neighbor bond

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distance in the first image is 7.68 Å. The second image above is taken after the Si substrate is evaporated with
Chlorine. After this the bond distance is 3.84 Å [16]
Image 6: In the above STM image, defects in the Si(100) topographic image are revealed [16]

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Image 7: The above image is of Gi(111) surface as seen through the STM. Individual dangling atomic bonds can be
clearly seen [16]
Image 8: STM image of GaAs (001) with bias voltage = -1.8V and tunneling current = 40pA [23]

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Image 9: STM images of Au (001) [24]
Image 10: Atomically resolved image of carbon nanotube taken through an STM. T represents the tube axis and H
represents the nearest neighbor hexagon rows [25]
Image 11: (A) – STM image of 𝑪 𝟐 𝑯 𝟐 molecule (left) and 𝑪 𝟐 𝑫 𝟐, the imaged area is 48 Å X 48 Å. The same images
were recorded at (B) – 358 mV, (C) – 266 mV, (D) – 311mV with tunneling current 1nA DC [26]

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Image 12: “Quantum Coral” created by using 48 Fe atoms on top of Cu (111) surface and seen through an STM [27]
Image 13: STM imaged of patterns generated by (A) dodecanethiol and (B) decanethiol [28]

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2.2. Atomic Force Microscopy/Scanning Force
Microscopy(AFM/SFM)(Question 5):
AFM relies on 3-D scanning same as the STM. AFM measures ultra-small forces between
the tip and the surface of the sample (a force of around 1nN [7]).One big difference
between STM and AFM is that STM requires the surface of the sample to be electrically
conductive in nature but AFM can scan conductive and isolators with atomic scale
precision. The sample is generally is generally scanned instead of the tip because AFM
measures the relative displacement between the cantilever surface (shown in the image
below) and the tip surface (also known as the reference surface).
Figure 7: Schematic of the operation of AFM [7]
There are typically three methods or variations of AFM:
- Contact Mode
- Non-Contact Mode
- Tapping Mode
In the contact mode/static mode/Repulsive Force mode, the tip is bought in contact
with the surface of the sample. The atoms at the end of the tip experience a weak
repulsive force due to the orbital overlap8
on the surface of the sample. The cantilever is
8
Orbital Overlap is a concept first introduced by Linus Pauling which states that the s orbital are special in
shape and p orbitals have a 90 degree orientation which means that bonds are created due to the overlap
of adjacent atomic orbitals. If the overlap is greater, the resulting bonds are much stronger than the
individual orbitals [56].

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then dragged across the surface of the sample. The force on the tip makes the cantilever
deflect and this is measured by tunneling, capacitive or optical detectors. Typically the
detectors can detect if the deflection is about 0.02nm and the spring constant of the
cantilever is about 10 N/m with a force of 0.2 nN [7]. The reason cantilevers are used in
the contact mode of AFM is because the static signal is prone to noise.
In Non-Contact mode/Dynamic mode/Attractive Force mode, the tip is bought very
close to the sample surface but the tip is not allowed to made contact with the surface.
The cantilever is on purpose vibrated in Amplification Modulation [29] or Frequency
Modulation [29] [30] [31] [32] just above its resonant frequency. Weak Vanderwall
attractive forces (which are strongest from 1 nm to 10 nm above the surface of the
sample) are seen between the tip and the sample. This makes the resonant frequency
drop. Unlike the static method, dynamic method’s measurement is done by the
vibration in AM or FM and due to this a force gradient is obtained which in turn allows
to measure the resonant frequency of the cantilever. The tip-sample distance is
captured by the software which recreates the topographic image of the surface of the
sample. If the vibration is done in Frequency Modulation (FM), the changes in the
frequency of the oscillation give the tip to sample information. If Amplitude Modulation
(AM) is used, then the phase of the oscillation can be measured and by using this
information the sample’s material can be identified and more information about the
material itself can be given. This method is very slow and time consuming and usually
this type of AFM techniques are only used in research based laboratory rather than
commercial. Major differences in two of the techniques can be seen in the table below:
AFM Static Mode AFM Dynamic Mode
The interaction force between the tip and
the sample is measured by the deflection
of the cantilever
The force gradient between the tip and the
sample is measured due to the deflection
of the cantilever by vibrating the cantilever
in AM or FM
Has comparatively lower resolution Have comparatively higher resolution
Resolution is about 0.02 nm (lateral) Resolution is about 0.01 nm (lateral)
Assuming the spring constant of the
cantilever is 10 N/m, the measurable force
is about 0.02nN
Assuming the spring constant of the
cantilever is 10 N/m, the measurable force
is about 1nN
Table 4: Major differences between Static and Dynamic modes of AFM
Typically in the contact mode, the friction acts as a major role and disadvantage because
it can vastly affect the accuracy of the topographic images [33]. To overcome this, the
third technique of AFM known as the tapping method is used.

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In tapping method, the friction is reduced substantially and it can also get topographic
images of soft materials as well. The working principle is similar to dynamic mode hence
this is called Dynamic Force Mode. The cantilever is vibrated by a piezoelectric on top of
the cantilever. The tip, which is oscillating, slightly taps the surface of the sample with a
frequency of 70-400Hz and amplitude of 20-100nm in a vertical direction9
[7].
Image 14: AFM image of Au(111) evaporated gold on mica [34].
9
The scanning angle is usually not important but it has been seen that if the scanned vertically, the
topographic images are much clearer as compared to parallel scanning. This is due to the friction
generated between the tip and the sample surface by the cantilever.

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Image 15: AFM image of Au(111) after exposed to air for sometime [34]
Image 16: A 3-D AFM image of Platinum [34].

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Image 17: An AFM image of protein surface layer [35].
Image 18: (a) – AFM image taken by tapping mode with carbon probe of polydiacetylene crystal. (b) – Molecular
arrangement of polydiacetylene crystal. (c) – Contact mode image of the bc-plane of the polydiacetylene crystal.
(d) – Tapping mode image of the bc-plane of the polydiacetylene [36]
Image 19: (A) – Dual height and (B) dual amplitude image of multiphase film structure in films of 𝟐 𝟑. (𝑫𝑬𝑩 𝟏𝟐) on
HOPG [nanorod (a), crystal (b), granular (c), and gas/liquid phase (d)] [37]

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Image 20: Multiwalled Nanotube attached to a silicon tip image taken through an AFM [38]

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Image 21: Creation of a deflated bacterium because of high vertical forces. (A), (C), (E), and (G) are height images,
whereas (B), (D), (F), and (H) are deflection images. The bacterium is deflated in (C) and (D) at the dotted line. A
similar deflated bacterium is shown in (G) and (H) [37]
Image 22: Image of a living S. cerevisiae [(height = 6 X 6 𝝁m and z range = 1 𝝁m)] immobilized on a porous polymer
membrane [37]
Image 23: von Willebrand factor adsorption onto OTS. Atomic force microscopy image (2 mm 2 mm scan) of VWF
multimers adsorbed on hydrophobic OTS and imaged under PBS. Most VWF multimers display the characteristic
compact ball of yarn structures observed by electron microscopy. Each VWF multimer is closely packed with
intramolecular overlap and crossover of chains. Intramolecular structural features of the VWF multimer chain are
resolved. However, the compact arrangement of the chain makes it difficult to discern the structural features

29. Atif Syed
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belonging to neighboring repeat units. In some multimer chains, short sections are not as compact and appear
extended (arrows). Completely extended chains are rare. None are seen in this image area. The average lateral
dimensions of the VWF multimers are 256 X 74nm and 152 X 62 nm in dimensions [37] [39]
Image 24: IC-1000 polishing pad surface imaged by using an AFM [37] [40]
Image 25: AFM image of DNA on top of Mica surface [9]

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- Experimental Work using AFM on Silicon Solar Cell:
The AFM experiment was carried out by using silicon based solar cell. The solar cell is
kept on the AFM’s sample stage/holder and the tip is added as well. After the initial set
up the laser beam is aligned in such a way that the focus of the beam is that the top of
the tip. The laser beam reflected back is detected by a photodiode. In the figure below,
the screw C and D are used to adjust the position of the laser and the screws E and F are
used to adjust the position of the photodiode.
Figure 8: Left-(www.ems.psu.edu/~ryba/coursework/..../class%20slides/AFM.ppt), where 1-Laser Source, 2- Laser
reflection Mirror, 30 Sample stage, 4- Laser reflection mirror (fixed), 5-Photodiode, Right- Experimental setup of
the AFM in the JEOL Nanocentre York.
Screws A and B are used to move the position of the sample stage. A computer aided
movement can also be employed for precise measurements. Once the setup is
completed and the working distance is acquired and set, the line by line scan can be
done. In the demonstration we have used the tapping mode method of the AFM (which
is also described above in this section). The scan speed can be controlled; slower scan
will result in high resolution images and better clarity which is seen in the image next
page.

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Image 26: Computer output of the AFM image

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2.3. Magnetic Force Microscopy(MFM)(Question 7 and 8):
The concept of MFM is similar to AFM. The tip is magnetically coated and the difference
is that the static cantilever deflection due to magnetic force on the tip is detected. This
allows the MFM images of the material to be produced. The sensitivity can be handled
by vibrating the cantilever to near resonant frequency. When the tip encounters a
magnetic field, the magnetic gradient along with the resonant frequency is shifted [7].
The magnetic field gradient image is created by measuring the oscillation amplitude as
the tip is scanning over the surface of the sample [7].
The topography of the sample is usually taken by a method called as the lift mode which
is done by separating the magnetic gradient from the magnetic field images. The
measurements taken during the lift mode is done by scanning twice over the sample.
During the first scan, the topographic information of the sample is recorded by using the
tapping method where the tip is oscillating and the oscillating tip slightly taps the
surface of the sample. During the second scan, the tip is lifted up and the distance of the
lift between the tip and surface of the sample is upon the discretion of the user (but
ideally 20nm-200nm is preferred [7]). At this stage, the image taken from the first scan
is used as a reference rather than the standard feedback hereby making the separation
constant. This height allows the cantilever amplitude to be sensitive to electric field
gradients without being influenced by topographic features [7]. The two scanning
method allows the two different kinds of images to be produced; topographic and
magnetic force images [7].
Figure 9: Flow chart of the electronics for constant electronic frequency scanning [41]

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Figure 10: The block controller scheme of the MFM. This figure is the illustration of the working principle of the
MFM [42]
Image 27: The image on the left is obtained after the first scan is performed. After the first scan, the image is
stored. The image on the right is taken after the second scan of the MFM image. The second scan is made after
taking the first image as reference rather than the conventional standard feedback system (the block diagram is
shown in Figure 9) [16].

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Figure 11: Illustration of the two modes of MFM. dZ signifies the cantilever being lifted up at a height z which a
change of height denoted by dZ. Due to the height dZ, the cantilever is only sensitive to long-ranged forces
(magnetic forces will be explained in detailed further in this section) [42].
As described above in this section, we will further elaborate the different modes of
operation of MFM and how it relates to the force acting upon the cantilever due to the
magnetic field and magnetic field gradients. Just as in AFM there are two modes:
- Static Mode:
In this mode the force acting upon on the cantilever follows the Hook’s Law and is given
by:
𝑭 = −𝒌∆𝒛 21
∆𝑧 is the displacement of the cantilever measured.
- Dynamic Mode:
In this mode, the cantilever is kept close to its resonant frequency. Since it’s in a
resonant frequency, the harmonic oscillator can be expressed as:
𝒇 =
𝟏
𝟐𝝅
√
𝒌 𝒆𝒇
𝒎
22
Where m is the effective mass of the system and 𝑘 𝑒𝑓 is the effective spring constant
[42]. The effective spring constant can be also expressed as:
= 𝒌 −
𝝏𝑭
𝝏𝒛
23

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k is the cantilever’s spring constant (not to be confused with 𝑘 𝑒𝑓 which is the effective
spring constant),
𝝏𝑭
𝝏𝒛
is the force gradient 10
.
Figure 12: Illustration of Tip-Sample interaction in a MFM
By substituting equation 23 into 22 we get:
𝒇 = 𝒇 𝟎
√ 𝟏 −
𝝏𝑭
𝝏𝒛
𝒌
24
Where 𝑓0 is the free resonant frequency of the cantilever when there is no tip-sample
interaction.
10
This will be explained further in this section.
z
𝝏𝑭
𝝏𝒛
k
𝑧0

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- Magnetic Interaction in the MFM:
MFM displays magnetic force and magnetic gradient based on the fluctuations on top of
the magnetic samples. One of the biggest factors in determining the topographic image
is the tip-sample distance as mentioned before. The forces acting on top of the
magnetic tip are not magnetic forces but in fact many other forces such as electrostatic,
Van der Waals (some examples given in Table 2), quantum mechanical or capillary forces
act upon the tip. The magnetic force however can take effect only if the recommended
tip-sample distance is maintained which in turn depict the magnetic image (through
magnetic contrast).
Let’s assume that the magnetic element is exposed to magnetic stray field of the surface
of the sample. Then the magnetic potential is given by:
𝑬 = −𝝁 𝟎 ∫ 𝑴𝒕𝒊𝒑𝑽
. 𝑯 𝒔𝒂𝒎𝒑𝒍𝒆 𝒅𝑽𝒕𝒊𝒑 25
where 𝑀𝑡𝑖𝑝 𝑎𝑛𝑑 𝐻𝑠𝑎𝑚𝑝𝑙𝑒 are the tip magnetization and sample stray field respectively
and the integration is done over one period of V (tip volume) [42]. The magnetic force
(gradient) can be expressed as:
𝑭 = −𝛁𝑬 = ∫ 𝛁(𝑴𝒕𝒊𝒑𝑽
. 𝑯 𝒔𝒂𝒎𝒑𝒍𝒆)𝒅𝑽𝒕𝒊𝒑 26
Some alterations have been made to the current method where the magnetic field is
allowed to alternate and the field mechanism is dependent on the shape of the tip [43]
[44] and the magnetic tip-sample interaction [45].
Figure 13: MFM tip-sample interaction and also resembling magnetic spin of electrons [46]

37. Atif Syed
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To better explain the concept in Figure 13, we need to understand a method commonly
used in the magnetic recording theory known as the spatial frequency domain method.
According to the method, 𝑴𝒕𝒊𝒑 is transformed into its Fourier derivatives into 𝑀̂ (x,y)
plane (2-D) and leaving the third plane (z) unchanged, we then get [46]:
𝑴̂ (𝒌 𝒙, 𝒌 𝒚, 𝒛) = ∫ ∫ 𝑴⃑⃑⃑ ( 𝒙, 𝒚, 𝒛) 𝒆−𝒊(𝒙𝒌 𝒙+𝒚𝒌 𝒚)
𝒅𝒙𝒅𝒚
∞
−∞
∞
−∞
27
The relation between the wavelength of a certain magnetic component and its Fourier
component is given by [46]:
𝒌⃑⃑ = (𝒌 𝒙, 𝒌 𝒚) 28
𝒌 𝒙(𝒚) =
𝟐𝝅
𝝀 𝒙(𝒚)
29
The stray field of the sample can be calculated by using Laplace transforms [47]:
(
𝑯 𝒙
̂ (𝒌 𝒙, 𝒌 𝒚, 𝒛)
𝑯 𝒚
̂ (𝒌 𝒙, 𝒌 𝒚, 𝒛)
𝑯 𝒛
̂ (𝒌 𝒙, 𝒌 𝒚, 𝒛)
) =
(
−
𝒊𝒌 𝒙
|𝒌⃑⃑ |
−
𝒊𝒌 𝒚
|𝒌⃑⃑ |
𝟏 )
𝟏
𝟐
(𝟏 − 𝒆−|𝒌⃑⃑ |𝒕
) 𝒆−|𝒌⃑⃑ |𝒛
𝝈 𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆(𝒌⃑⃑ ) 30
where 𝝈 𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆 is the effective surface charge distribution. According to Laplace’s
property, we can safely say that the stray field at height z above the sample is
determined by the stray field at height z = 0. If the sample is perpendicular (i.e. 𝑀𝑥 =
0 𝑎𝑛𝑑 𝑀 𝑦 = 0) then the surface charge distribution will be:
𝝈 𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆(𝒌⃑⃑ )
̂
= 𝑴 𝒛
̂ (𝒌⃑⃑ ) = 𝝈̂(𝒌⃑⃑ ) 31
If the magnetization is constant and the only volume we have is the charge volume
denoted by 𝜌(𝑥, 𝑦), the effective surface charge equals:
𝝈 𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆(𝒌⃑⃑ )
̂
=
𝒊𝒌⃑⃑
|𝒌⃑⃑ |
. 𝑴 𝒛
̂ (𝒌⃑⃑ ) =
𝝆̂(𝒌⃑⃑ )
|𝒌⃑⃑ |
32
The energy of the tip and the sample can be calculated by combining the equations 25
and 30.

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o Interesting Facts and Development in Magnetic Recording Media:
IBM has recently managed to make the world’s smallest bit by using only
12 atoms. The illustration below shows the Atomic-Scale Magnetic
Memory [48].
Image 28: A infograph about Atomic-Scale Magnetic Memory by IBM [48]

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3. Photovoltaic Solar Cells(Question 6):
Advancement in the field of renewable energy technology has gained the center of
attention all over the world. The solution lies within Solar Cells; or precisely photovoltaic
Solar Cells.
Figure 14: Photovoltaic Devices progress in terms of efficiency achieved [49]
One of the highest solar cells’ efficiency has been achieved in multijunction cells based
on III-V compound semiconductors as each of them have different band gaps and
multiple absorbing layers [49] which in turn should allow higher efficiencies. To
understand this better we need to analyze the atomic microstructures within the solar
cell. In this section we will focus on organic-based solar cells which are developing
rapidly as the future of solar cells.

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- Charge Transportation within organic semiconductors used in organic-based
solar cells:
Organic semiconductors can be classified into two different categories namely; small
molecules (having molecular weight less than a 1000 AMU11
) or polymers (having
molecular weight between 1000 AMU-1 Million AMU) [37]. This is highly important in
determining the lithography process required for the making of thin films and based on
this related morphologies are obtained [37]. These mechanisms are the basis of light
absorption, exciton12
diffusion and charge carrier motion within the solar cell. The
properties are primarily governed by molecular orbital which are built from 𝜋-electrons
which in turn are delocalized across the molecules [37].
Figure 15: Molecular structures of some semiconductors which are usually used in photovoltaic devices such as
solar cells [37]
The charge transfer between organic molecules can be better understood by the theory
of Marcus [50]. Using the theory, the rate of electron transfer between two molecules
can be expressed as:
𝒌 𝑬𝑻 =
𝟒𝝅 𝟐
ℏ
𝟏
√𝟒𝝅𝒌 𝑩 𝒕
𝒕 𝟐 𝒆−𝝀
𝟒𝒌 𝑩 𝑻
33
11
Atomic Mass Unit
12
It is a bound state of an electron and hole which are attracted to each other by electrostatic Coulomb
Force

41. Atif Syed
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where ℏ is the Planck’s constant, 𝑘 𝐵 is the Boltzmann’s constant, T is temperature, t is
the transfer integral describing the strength of interaction between the two molecules,
𝜆 is the reorganization energy that describes the strength of the electron-phonon
interaction [51]. For a highly ordered system, single or polycrystalline molecular films of
materials are sufficient in terms of interaction strength for band transport to be seen
[51] [52] [37]. Similarly by using Poole-Frenkel behavior [37], the charge carrier mobility
for organic semiconductors can be derived as:
𝝁(𝑬, 𝑻) 𝜶 𝝁 𝟎( 𝑻) 𝒆 𝜸(𝑻)√𝑬
34
where 𝛾( 𝑇) is the coefficient of the stretched exponential that describes the
temperature dependence of the field activation, 𝜇0 is the zero-field mobility. This
behavior has been successfully modeled and developed by B𝑎̈ssler [53]. Another much
recent development in this area has been done by Novikov et al. [54] and this one takes
the account of spatial correlations in site energies which turn out to be:
𝝁 = 𝝁∞ 𝒆
[(
𝟑𝝈̂ 𝒅
𝟓
)
𝟐
+𝑪 𝟎(𝝈̂ 𝒅
𝟑
𝟐−𝚪)√
𝒆𝒂𝑬
𝝈̂ 𝒅
]
35
Where 𝜇∞ is the mobility at limit T → ∞, 𝜎̂ 𝑑 is the width of the Gaussian distribution the
site energies divided by 𝑘 𝐵 𝑡, 𝐶0 is the empirical constant, Γ describes the geometric
disorder and a is the intersite spacing [37].
Image 29: Difference between semiemperical calculations and highest occupied molecular orbitals of
representative organic semiconductors with extended 𝝅-electron delocalization [37]

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Using the basic concept above, the light absorption in inorganic semiconductor normally
leads to an electron-hole pair while in organic semiconductor light absorption leads to
exciton. For a free carrier to be generated, the exciton has to be dissociated [37]. For
this to happen, a very high electric field should be present at the defect site of the
material or at the interface between two materials that have a sufficient mismatch of
their energetic levels. We can fabricate a device as such with the structure positive
electrode/donor/acceptor/negative electrode [37]. One of the first experiments done by
using this method was by using copper phthalocyanine layer as the donor and perylene
derivate as acceptor and was done by Tang [55]. This particular device achieved an
efficiency of about 1% in terms of solar illuminations and light absorption [55]. The
biggest obstacle in this method is that due to a lot of short exciton diffusion lengths, the
exciton that are generated at around 10nm contribute to photocurrent, the rest pose a
serious limitation to the device itself. To overcome this, research has been done to
develop a device which I an amalgamation of donor and acceptor molecules and they
are collectively called as “bulk heterojunction” solar cell [56]. Photoinduced electron
transfer from a conjugated polymer-fullerene was used and the transfer rate was
around 45fs and the recombination rate being 300ns-1ms [57] [58]. The exciton now
produce a conjugated polymer having lifetimes of 100’s of pico seconds. The free
electrons now have sufficient time to be transported before recombining. This produces
a more light-absorbed solar cell having high carrier mobility and large optical density
[37]. Some latest improvements include using nanorods, nanofibers and nanorods which
lead in using these structures in 3-D. Some images are shown on the next page taken
from an SEM [37].
Figure 16: Diagram of conjugated polymer-fullerene bulk heterojunction photovoltaic device [37]

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Image 30: Scanning electron microscopic image of TiO2 nanofibers grown from an aqueous solution at 150 C [37].
Image 31: Scanning electron microscopic image of ZnO microcrystallites grown from an aqueous solution at 95 C
[37].

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