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CHAPTER-2
EXPERIMENTAL METHODS / TECHNIQUES
USED
2.0 INTRODUCTION
In this chapter, all the experimental techniques/methods involved in the present
work are described briefly.
Materials are made of atoms. Knowledge of how atoms are arranged into
solids is known as crystal structure of materials. The crystal structures are the
foundation on which we build our understanding of the synthesis and physical
properties of materials. There are also many ways for measuring chemical
compositions of materials and methods based on inner-shell electron spectroscopes
are covered here. The larger emphasis is on measuring spatial arrangements of atoms
in the range from 10-8 to 10-4 cm, bridging from the unit cell of the crystal to the
microstructure of the material. To date, most of our knowledge about the spatial
arrangements of atoms in materials has been gained from diffraction experiments. In a
diffraction experiment, an incident wave either an electromagnetic wave e. g. X-rays
or matter waves i.e. electron / neutron wave is directed into a material and a detector
is typically moved about to record the directions and intensities of the outgoing
diffracted waves.
The basic aims of the scientist in the area of micro analytical analysis have
been to unravel the structural details of materials down to the atomic level. Keeping in
view, one of the fundamental aspects of physics that resolution can never be better
than wavelength of illumination used. One needs to replace the visible light
(wavelength = 4000-8000 Å) by some other waves e.g. X-rays, electrons or neutrons.
Where as the wavelength of X-ray, depend upon the target element e. g. CuKα =
1.5418 Å, in the case of electrons it can be controlled by accelerating voltage e.g.
wavelength λ = 0.037 Å for 100kV electrons. One of the major themes of the present
work is to study the structural and microstructural techniques employed for this
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purpose correspond to the “X-ray diffraction and Electron microscopy”. So it will be
appropriate to describe these techniques in some details. The following sections
embody the descriptions for characterization of as synthesized (bulk form) as well as
the transformed materials.
2.1 THE POWDER X-RAY DIFFRACTOMETER
More than 95% of all solid materials can be described as crystalline. When Xrays interact with a crystalline substance, X-ray diffraction results from an
electromagnetic wave (the X-ray) impinging on a regular array of scattering sites
(repeating arrangement of atoms within the crystal). An x-ray diffraction pattern of
the pure substance is therefore like a fingerprint of the substance. The powder
diffraction method is thus ideally suited for characterization and identification of
polycrystalline phases.
An instrument for studying crystalline and nanocrystalline materials by
measurements of the ways in which they diffract x-rays of known wavelength has
been aptly called a diffractometer. An X-ray diffractrometer [1-3] consist of two
elements: X-ray tube and a goniometer. X-rays are generated in a cathode ray tube by
heating a filament to produce electrons accelerating the electrons towards a target by
applying a voltage and bombarding the target material with electrons. When electrons
have sufficient energy to dislodge inner shell electrons of the target material,
characteristic X-rays spectra and Brehmsstrahlung are produced. Copper is the most
common target material for single-crystal diffraction, with CuKα radiation 0.5418A.
These x-rays are collimated and directed onto the sample. The goniometer employs a
large flat sample combined with a parafocussing arrangement to increase the intensity
of diffraction and x-ray detector / counter in place of film for measuring diffraction
angles and number of electronic circuits for determining the intensity of diffraction at
any angle. As the sample and detector are rotated, the intensity of the reflected X-rays
is recorded. The interaction of the incident rays with the sample produces constructive
interference (and a diffracted ray) when the conditions satisfy Bragg's Law (nλ = 2d
sin θ). This law relates the wavelength of electromagnetic radiation to the diffraction
angle and the lattice spacing in a crystalline sample. These diffracted X-rays are then
detected, processed and counted. The counter transforms the radiation spectrum
emitted by the sample into a pulse spectrum, which after suitable amplification, is fed
into the circuit panel and measured in one of a number of ways. The pubes, smoothed
into a fluctuating current, may be caused to actuate a pen on a strip chart and produce
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a permanent graphic record of intensity against diffraction angle and these by remains
tangent to the focusing circle about the same axis as the specimen but at twice the
angular speed. Thus by scanning the sample through a range of 2θ angles, all possible
diffraction directions of the lattice should be attained due to the random orientation of
the powdered material.
The x-ray optical system of a commercial diffractometer is shown in figure 2.1
and Rigaku 18 kW powder X-ray diffractometer of UGC-DAE consortium for
scientific research (CSR) at Indore used in present investigation is shown in figure
2.2. The focusing error is kept small by the use of an x-ray beam that is very narrow
in the plane of the focusing circle (the focusing plane). Such a beam is obtained by
viewing the line-shaped focal spot longitudinally and at an angle of about 30 to the
surface of the target. The effective source-beam width of this arrangement is less than
1/10 mm. The actual angular aperture of the beam is determined by the width of a
divergence slit. The length of specimen irradiated by the beam through a given slit
increase with decreasing angle of incidence. This sets a lower limit on the angular
range that can be scanned with a particular slit-width without exceeding the total
length of the sample and counting the risk of detecting stray radiation scattered by the
specimen holder. A line-focus beam has an inherently greater divergence in the plane
normal to the focusing circle (the axial plane), but this is limited to a few degrees by
the use of a parallel plate assembly. A slit and a parallel-plate collimator similarly
control the diffracted beams. The purpose of the scatter slit near the window of the
counter is to exclude non-diffracted radiation, thereby reducing the background of the
powder spectrum. This diffractometer has a goniometer radius of 170mm to take full
advantage of the increase in resolution gained through the use of line-focus source
and the increase in intensity afforded by a large specimen.
A number of instrumental factors, such as diffraction at various depths in the
sample, divergence of incident and diffracted beams, and the use of a flat sample,
affect the position and shape of a diffractometer peak. In general, the influence of
these factors is counted with a careful experimental peak. In general, the influence of
these factors is counted with involves the use of a highly absorbing sample to limit
diffraction to the sample surface and the use of slits and parallel-plate assemblies
already described to reduce the divergence of the beams. The parafocussing condition
is not met by a flat sample only a narrow region can diffract at the proper 2θ angle.
The remainder diffracts at a lower angle of incidence with the result that the peak is
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broadened and its center of gravity is shifted to a lower 2θ value. These effects are
most pronounced for the low-angle diffraction. It has been shown that the flat sample
factor has a minor effect, relative to the effect of cross-divergence, for example when
the incident beam is held to a 10 divergence in the focusing plane, but a consequence
of the narrowed beam is a loss of intensity. Ogilvie [4] has described a device for
automatically curving the sample to match the curvature of the focusing circle as the
2θ angle of the diffractometer is varied over its range. “Coherent scattering” preserves
the precision of wave periodicity. Constructive or destructive interference then occurs
along different directions as atoms of different types and positions emit scattered
waves. There is a profound geometrical relationship between the directions of waves
that interfere constructively, which comprise the “diffraction pattern,” and the crystal
structure of the material. The diffraction pattern is a spectrum of real space
periodicities in a material. Atomic periodicities with long repeat distances cause
diffraction at small angles, while short repeat distances (as from small interplanar
spacing) cause diffraction at high angles. It is not hard to appreciate that diffraction
experiments are useful for determining the crystal structures of materials. Much more
information about a material is contained in its diffraction pattern. However, crystals
with precise periodicities over long distances have sharp and clear diffraction peaks.
Crystals with defects (such as impurities, dislocations, planar faults, internal strains,
or small precipitates) are less precisely periodic in their atomic arrangements, but they
still have distinct diffraction peaks. Their diffraction peaks are broadened, distorted,
and weakened, however, and “diffraction line shape analysis” is an important method
for studying crystal defects. Diffraction experiments are also used to study the
structure of amorphous materials, even though their diffraction patterns lack sharp
diffraction peaks. In a diffraction experiment, the incident waves must have
wavelengths comparable to the spacing between atoms.
2.2 THE MICROSCOPIC TECHNIQUE
In an electron microscope when a high-energy electron beam strikes a solid or
electron transparent specimen a number of interactions occur, the most important of
these being illustrated in figure 2.3. Electrons may be backscattered from the front
face of the specimen with little or no energy loss, or they may interact with surface
atoms to produce secondary (low energy) electrons. Some electrons may be absorbed
by the specimen with transfer of energy to heats and sometimes to lights. Whereas
transmitted electrons may be unchanged in direction or scattered at different angles.
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Scattered electrons may be elastic (no energy loss) or inelastic (having lost some
energy). If energy is transmitted to specimen, it may also result in the production of
Auger electrons or X-ray. Each of these events can provide information about the
atoms within the specimen. Among these, backscattered and secondary electrons are
used in scanning electron microscope (SEM) to form surface images while
transmitted and
.
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Figure 2.1 Rigaku 18 kW powder X-ray diffractometer and Rotating anode X-ray
Generator used in present study operated at UGC-DAE Consortium for Scientific
Research, Indore.
Figure 2.2 Schematic of an X-ray powder diffractometer.
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scattered electrons are utilized in transmission electron microscope (TEM) to form
images and diffraction patterns while. However, the interaction of specimens with
high energy electrons which generates X-ray, give the information about the atoms
within the specimen in the region being irradiated and thus provide a means of
correlating the ultra structural information in the electron microscope image with
chemical analysis of very small regions of the specimen. The detection of X-ray
scattered from atoms of specimen in SEM is carried out by using electron probe
microanalysis (EPMA). In principle, a universal analytical electron microscope
(AEM) would have access to all those signals that are generated within the specimen
due to high energy electrons, such as X-rays, Auger electrons and visible light
(cathodoluminiscence) as well as in semiconducting specimens, electron-hole pairs,
and induced conductivity effects.
2.2.1 SCANNING ELECTRON MICROSCOPY (SEM)
The SEM is used primarily for the examination of thick (i.e. electron-opaque)
samples. Electrons which are emitted or backscattered from
the specimen are
collected to provide: (1) topological information (i.e. the detailed shape of the
specimen surface) if the low energy secondary electrons (≤ 50eV) are collected. (2)
Atomic number or orientation information if the higher energy, back scattered
electrons are used, or if leakage current to earth is used. Imaging of magnetic samples
using secondary and / or backscattered electrons reveals magnetic domain contrast. In
addition two other signals can be collected; the electron beam induced current and
light cathodoluminescence.
The output from any detector may be used to modulate the intensity of a cathode ray
tube (CRT), which is scanned synchronously with the scan of the probe on the
specimen. The magnification of the image is given immediately by the ratio of the
CRT scan size to the specimen scan size. The image obtained in this way is simply the
variation in intensity of the signal, which is collected by the detector, as a function of
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position of the incident probe. A systematic ray diagram for a SEM is shown in fgure
2.4. The most commonly used electron detector is a scintillator-photo multiplier. If
the low energy secondary electrons are to be efficiently collected a positive bias of
200 V is applied to the grid in front of the detector and if only the high energy
backscattered electrons are to be collected the grid is biased to about -200V, which
will deflect virtually all the secondary electrons will not be influenced by this small
change in bias and the line of sight backscattered electrons will contribute to the
image in both cases. Solid state backscattered detectors can be fitted to the bottom
probe-forming lens and are particularly useful in STEMs because they are so much
smaller then scintillator-photo multiplier detectors. If the electron probe is rocked
through a range of angles about a fixed point on the specimen, then the angular
dependence of the backscattered electron intensity can be obtained. If these electrons
are used to modulate the intensity of the CRT then a channeling pattern is obtained.
Backscattered electron patterns can be obtained by setting the specimen so that the
electrons strike the surface at a glancing angle. Electrons, which are scattered through
less than about 90 and subsequently, Bragg diffracted, such that they re-emerge from
the specimen, then form a backscattered electron pattern. Because the probe is held
stationary in this mode of operation the backscattered / Bragg diffracted electrons are
detected using films, since no time-dependent signal is available. This technique thus
requires a special camera to be inserted into the specimen chamber. Because the
signal is generally generated as a function of time in as SEM (in contrast to the TEM
where the whole area of interest is illuminated simultaneously with electrons) it is
straightforward to process images (e.g. to differentiate the signal, to back the signal
off, etc.). In addition to the secondary electrons or primary electrons it is possible to
collect X- rays generate by the probe, and hence to determine local chemistry. Both
wavelength and energy dispersive detectors can be used and the analysis can be
carried out either by placing the probe on the specific region of interest or by
continuing scanning and using X-rays generated by the element of interest to
modulate the intensity of the CRT. By selecting different energy X-rays for
successive scans the distribution of specified elements can be obtained fairly rapidly
unless the scan speed is slowed down significantly, these X-ray maps tend to be very
noisy. SEMs are also used in the cathodoluminescent mode and if the light emitted
from the sample is used to modulate the CRT intensity, information on the
distribution of light-emitting regions can be obtained.
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Figure 2.3 Schematic showing main electron interaction with thin specimen and the
information available by analytical microscopy.
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This imaging mode is useful for studying light-emitting semiconductors.
In addition the beam-induced conductively can be investigated by applying a potential
across the specimen and using the current in this circuit to modulate the CRT. Clearly
regions which give rise to significant increased conductivity will show different
contrast from regions which give rise to little or no conductivity. SEMs operate
generally in the range 2.5 to 50 kV with probe sizes available at the specimen between
5nm and 2µm. The convergence angle of the probe at the specimen is controlled by
the diameter of As 10 nm the value of F is 2µm, this is a very large depth of field for
such a high resolution image which underlines the value of high magnification SEM
images of rough surfaces. The resolution of an SEM is different for the various
imaging modes and it is clear that at least three factors are important in determining
the resolution:(1) The number of lines on the CRT is related to the maximum useful
magnification by the expression M = δ/d, where d referred to the specimen is
taken here as the probe size and δ is the screen resolution, defined by the
number of lines. The number of lines is usually 1000 on a 10cm screen so the
lines are 0.1mm apart (which is approximately the resolution of the human
eye) so that δ = 0.1mm. The maximum useful magnification is given in this
case by M = 0.1/d if d is also measured in millimeters, and if M is 1000 the
optimum probe size would be 100nm. If a smaller probe size is used the image
will be achieved since the resolution is limited to 100nm by the number of
lines on the CRT at this magnification. Most manufactures provide charts
which link magnification and probe size so that it is straightforward to choose
the appropriate probe for the magnification required.
(2) The probe size is an important factor in determining the resolution of images
obtained in a SEM and it seems reasonable that a probe of the same order as
the required resolution should be used. However, especially at small probe
sizes high angle elastic scattering degrades the resolution significantly.
(3) As pointed out above, the volume of the specimen is important in determining
resolution because electron scattering takes place within the sample. The
extent of the degradation of the resolution is different for the different signals
and these will therefore be considered separately.
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Figure 2.4 Systematic ray diagrams for a scanning electron microscope.
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Figure 2.5 JEOL JSM 5600 Scanning Electron Microscopy (SEM) used in present study
operated at UGC-DAE Consortium for Scientific Research, Indore.
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The secondary electrons, which give rise to the topological information, are generated
both by the incident electrons as they enter the specimen and by backscattered
electrons and X-rays. Figure 2.6 shows schematically the form of the variation in
intensity of the secondary electron signal as a function of distance away from the
incident electron probe.
The central peak in intensity is generated by the incident electrons and therefore has a
peak shape, which reflects the variation in intensity across the incident probe. The full
width at half-maximum higher (FWHM) of the incident probe is thus a measure of the
FWHM of the main secondary electron signal. This signal is superimposed on the
much weaker secondary electron signal generated by electrons which have been either
singly elastically scattered, so that they travel significant distances close to the surface
of the sample outside the area defined by the initial probe. The intensity of this
secondary electron signal generated by high angle elastically scattered electrons is
clearly going to
be far smaller than that of the signal generated within the area of the probe because
(apart from those few high energy electrons scattered such that they travel close to the
surface), all backscattered electrons which give rise to secondary electrons, which are
close enough to the surface to escape, must suffer at least two high angle elastic
scattering events. The probability of an electron being scattered electrons will be
reduced with respect to the main secondary signal, by the product of the probabilities
of scattering through the two angles. Similarly the intensity of secondary electrons
generated by x-rays (generated by the incident high-energy electrons) will be small
because the probability of X-ray generation is small.
The probability of subsequent secondary electron generation, near the surface of the
sample, is also small. On the basis of the above discussion the resolution of a
secondary image in a SEM is potentially significant degraded by high angle elastic
scattering. The fact that secondary images can be obtained in which detail is visible
on a scale of the FWHM of the incident probe is due to the ability to process images.
Thus if the background level is adjusted so that the information visible on the CRT
corresponds to intensities above the dashed line on figure 2.7 the secondary electrons
generated by the backscattered electrons will not contribute to the secondary image
and the resolution will be virtually the defined by the incident probe size. In principle
the resolution can be improved even further by raising the background level to a
higher level than indicated on Figure 2.6 so that image detail which is smaller than the
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probe at FWHM can be observed. The ultimate limit to resolution is defined by
signal-to-noise considerations since this sets the limit to extent to which the
background level can be raised. An ideal sample consisting say of gold particles on
aluminum would generate a large secondary signal from the gold and a small
backscatter-generated secondary signal from the aluminum substrate and in such a
sample resolution could be better than the initial probe size. With more typical
samples the optimum resolution of secondary images would be
Figure 2.6 Schematic diagram illustrating the use of an SEM to generate electron beam
induced current (EBIC) information from a sample containing a p-n junction.
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Figure 2.7 Schematic diagram illustrating the intensity of secondary electrons generated
from a
solid specimen by a stationary probe. The dashed line represents the label to
about 5nm but the above discussion should make it clear that resolution is a somewhat
difficult parameter to define in this imaging mode.
Which the background must be set to remove any contribution to the secondary image
from secondary’s generated by backscattered electrons outside the initial probe
diameter.
The spatial resolution of backscattered electron images is also affected by
electron, which suffer two or more high angle scattering events and which emerge
from the specimen travelling in a direction such that they are collected by the
backscattered electron detector. The intensity profile of backscattered images and a
typical figure for X-ray resolution would be about 2µm. In this case electrons have to
be scattered through a high angle only once, after which they may degrade the X-ray
resolution if they ionize an atom. Characteristic X-rays are generated with spherical
symmetry and at whatever depth in the sample they are generated some will
contribute to the signal which are of very low energy in which case they may be
absorbed. Electrons, which have lost a significant fraction of their initial energy, and
could not therefore be scattered out of the sample, can nevertheless generate X-rays,
so that the spatial resolution of X-ray signals will be expected, on this basis also, to be
worse than secondary and backscattered images.
Somewhat similar arguments apply to cathodoluminescence and beam induced
conductivity and these techniques have typical resolutions of about 2 µm. Indeed it is
the limitation of the spatial resolution of SEM, which has been responsible in part for
the development of STEM.
2.2.1(a) Interpretation of Scanning Electron Microscopy Images
The interpretation of images in SEM is straight forward compared with the
interpretation in STEM or TEM, because of the relative insensitivity to
crystallographic influences on electron specimen interactions and to their overall
similarity to optical micrographs, but it is nevertheless necessary to consider the
factors which lead to and which limit, the information in SEM images. In the case of
magnetic samples contrast is observed from the individual domains and the origin of
this contrast will be briefly considered below.
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If only secondary electrons are collected (i.e. electrons with energies ≤ 50eV)
the contrast can arise from the following sources: changes in surface topology, (since
if the surface is locally nearly parallel with the electron beam direction a high
secondary electron signal will be generated since a large number of incident electrons
will be elastically scattered so that they travel near the surface of the samples), surface
magnetic fields, surface electric fields and differences in secondary electron emission
characteristics of phases. Of these the topological contrast is the most widely used.
Because the parts of the specimen which have the most direct path to the detector
appear brightest, the image of a rough specimen appears as if it is viewed from above,
when being illuminated from the detector. The fact that the low energy electrons are
bent into the detector from regions which do not have a direct line of sight into the
detector allows details within holes and shaded regions to be observed- especially if
standard image processing is used to enhance contrast within the dark regions. The
strength of SEM in topological model is of course in the very large depth of field.
If second phase particles are present in the specimen it is possible that the
intensity of the image will be influenced by the relative efficiency of secondary
electron production and this may make interpretation of the topology less straight
forward. Stereo pairs taken by tilting the specimen through the appropriate angle can
remove any such problem and in addition make the interpretation of any height
difference far more obvious. As in TEM, the tilt angle between stereos which are
suitable for an individual can vary but are influenced by the height difference for an
individual can vary but are influenced by the height difference and the magnification.
If there are large changes in height (which would require a small divergence angle to
obtain an adequate depth of field) and if the magnification is high then the required
tilt angle between the stereo pairs will be small. Typically 100 tilt is appropriate for a
print magnification of 1000 times from a rough fracture surface. The stereo pair
should be varied in a stereo viewer with the tilt axis perpendicular to the line joining
the viewer’s eyes. Measurements of height difference can be made on most
commercial stereo viewers provided the tilt angle and magnification are accurately
known. It should be noted that the magnification is influenced by the tilt angle, the
influence being largest in the direction perpendicular to the tilt axis. This effect can be
compensated for on-line on modern SEM’s and STEM’s.
If backscattered high-energy electrons are used to image the sample the
contrast mechanisms, which underlie the common imaging mode, involve atomic
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number contrast and orientation contrast. Orientation contrast arises because, as
discussed earlier, the backscattered intensity is a function of the incident angle of the
electron beam with respect to the crystal planes. The intensity backscattered from a
crystal for a given electron beam direction is thus determined by the orientation of
that particular crystal and the intensity variation from a polycrystalline sample will
cover the range in intensities visible in channeling patterns. This imaging mode,
although one of low contrast is very useful when examine specimens which are
difficult to etch or which, because of the particular experiment cannot be etched.
Again a minimum beam divergence will maximize the contrast but it is evident that
the image intensity decreases with decrease in divergence angle and signal: noise
problems can reduce the contrast; only by increasing gun brightness and / or
increasing the scan time can this problem be overcome. It cannot be emphasized too
strongly that imaging in SEM requires the operator to select the appropriate balance
between probe size, beam divergence and magnification in order to optimize
condition for each application.
Atomic number contrast arises because the backscattering efficiency is a
function of atomic weight; heavy elements scatter electrons more efficiently than do
light elements. It is therefore possible to use backscattered images to detect
differences in composition if the differences result in a change in the mean atomic
weight. The technique is in fact sensitive enough to detect differences corresponding
to a change in mean atomic weight of less than one atomic mass unit.
The contrast observed from magnetic samples has been classified as Type I
and Type II magnetic contrast [5]. In Type I contrast the magnetic fields above the
surface of the sample influence the trajectory of the low energy secondary electrons.
Hence contrast between domains is observed when the secondary electron signal is
used. In Type II contrast, this is observed with secondary backscattered and specimen
current signals, the trajectories of electrons in particular domains so that they travel
close to the surface. In these domains the backscattered and secondary electron yield
will therefore be increased and contrast observed. These specialized applications of
SEM imaging are summarized in [5] and are not elaborated further here.
2.2.2 ATOMIC FORCE MICROSCOPY (AFM)
Atomic force microscopy (AFM) is part of a microscopy group called scanning
probe microscopy. Atomic force microscopy has roots in scanning tunneling
microscopy (STM) which measures topography of surface electronic states using the
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tunneling current which is dependent on the separation between the probe tip and a
highly conductive sample surface. The STM also includes viewing charge density
waves (CDW). Atomic force microscopy (AFM) or scanning force microscopy (SFM)
is a very high-resolution type of scanning probe microscopy, with demonstrated
resolution on the order of fractions of a nanometer, more than 1000 times better than
the optical diffraction limit. The precursor to the AFM, the scanning tunneling
microscope, was developed by Gerd Binnig and Heinrich Rohrer in the early 1980 at
IBM Research - Zurich, a development that earned them the Nobel Prize for Physics
in 1985. Binnig, Quate and Gerber invented the first atomic force microscope (AFM)
in 1986 [6 &7]. The first commercially available atomic force microscope was
introduced in 1989.
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Figure 2.11 Nano Scope – E Digital Instruments Inc. U. S. A. contact mode A. F. M. used
in present study operated at UGC-DAE Consortium for Scientific Research, Indore.
The AFM is one of the foremost tools for imaging, measuring, and manipulating
matter at the nanoscale. The information is gathered by "feeling" the surface with a
mechanical probe. Piezoelectric elements that facilitate tiny but accurate and precise
movements on (electronic) command enable the very precise scanning. In some
variations, electric potentials can also be scanned using passed through the tip to
probe the electrical conductivity or transport of the underlying surface, but this is
much more challenging with very few groups reporting reliable data. Beam deflection
system, using a laser and photodector to measure the beam position. As shown in
figure2.12. The AFM consists of a cantilever with a sharp tip (probe) at its end that is
used to scan the specimen surface. The cantilever is typically silicon or silicon nitride
with a tip radius of curvature on the order of nanometers. When the tip is brought into
proximity of a sample surface, forces between the tip and the sample lead to a
deflection of the cantilever according to Hooke's law. Depending on the situation,
forces that are measured in AFM include mechanical contact force, van der Waals
forces, capillary forces, chemical bonding, electrostatic forces, magnetic forces (see
magnetic force microscope, MFM), Casmir forces, salvation forces, etc. The parts of
an approach-retraction cycle of the tip as shown in figure 2.13. Along with force,
additional quantities may simultaneously be measured through the use of specialized
types of probe (see scanning thermal microscopy, photo thermal micro spectroscopy,
etc.). Typically, the deflection is measured using a laser spot reflected from the top
surface of the cantilever into an array of photodiodes. Other methods that are used
include optical interferometry, capacitive sensing or piezoresistive AFM cantilevers.
These cantilevers are fabricated with piezoresistive elements that act as a strain gauge.
Using a Wheatstone bridge, strain in the AFM cantilever due to deflection can be
measured, but this method is not as sensitive as laser deflection or interferometry. If
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the tip was scanned at a constant height, a risk would exist that the tip collides with
the surface, causing damage. Hence, in most cases a feedback mechanism is
employed to adjust the tip-to-sample distance to maintain a constant force between the
tip and the sample. Traditionally, the sample is mounted on a piezoelectric tube that
can move the sample in the z direction for maintaining a constant force, and the x and
y directions for scanning the sample. Alternatively a 'tripod' configuration of three
piezo crystals may be employed, with each responsible for scanning in the x, y and z
directions. This eliminates some of the distortion effects seen with a tube scanner. In
newer designs, the tip is mounted on a vertical piezo scanner while the sample is
being scanned in X and Y using another piezo block. The resulting map of the area s
= f(x, y) represents the topography of the sample. The AFM can be operated in a
number of modes, depending on the application. In general, possible imaging modes
are divided into static (also called contact) modes and a variety of dynamic (or noncontact) modes where the cantilever is vibrated. Atomic Fource Microscopy (AFM)
used in present study operated at UGC-DAE Consortium for Scientific Research,
Indore.
2.2.2(a) AFM Modes of Operation
(i) Contact Mode
The first and foremost mode of operation, contact mode is widely used. As
the tip is raster-scanned across the surface, it is deflected as it moves over the surface
corrugation. In constant force mode, the tip is constantly adjusted to maintain a
constant deflection, and therefore constant height above the surface. It is this
adjustment that is displayed as data. However, the ability to track the surface in this
manner is limited by the feedback circuit. Sometimes the tip is allowed to scan
without this adjustment, and one measures only the deflection. This is useful for
small, high-speed atomic resolution scans, and is known as variable-deflection mode.
Because the tip is in hard contact with the surface, the stiffness of the lever needs to
be less that the effective spring constant holding atoms together, which is on the order
of 1 - 10 nN/nm. Most contact mode levers have a spring constant of < 1N/m. The
contact mode of AFM is shows that figure 2.14.
(ii) Non-contact Mode
In this mode, the tip of the cantilever does not contact the sample surface. The
cantilever is instead oscillated at a frequency slightly above its resonance frequency
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where the amplitude of oscillation is typically a few nanometers (<10 nm). The van
der Waals forces, which are strongest from 1 nm to 10 nm above the surface, or any
other long range force which extends above the surface acts to decrease the resonance
frequency of the cantilever. This decrease in resonance frequency combined with the
feedback loop system maintains a constant oscillation amplitude or frequency by
adjusting the average tip-to-sample distance. Measuring the tip-to-sample distance at
each (x, y) data point allows the scanning software to construct a topographic image
of the sample surface. Non-contact mode AFM does not suffer from tip or sample
degradation effects that are sometimes observed after taking numerous scans with
contact AFM. This makes non-contact AFM preferable to contact AFM for measuring
soft samples. In the case of rigid samples, contact and non-contact images may look
the same. However, if a
Figure 2.12 Beam deflection system, using a laser and photodector to measure the beam
position.
61
Figure 2.13 The parts of an approach-retraction cycle of the tip.
few monolayers of adsorbed fluid are lying on the surface of a rigid sample, the
images may look quite different. An AFM operating in contact mode will penetrate
the liquid layer to image the underlying surface, whereas in non-contact mode an
AFM will oscillate above the adsorbed fluid layer to image both the liquid and
surface. Schemes for dynamic mode operation include frequency modulation and the
more common amplitude modulation. In frequency modulation, changes in the
oscillation frequency provide information about tip-sample interactions. Frequency
can be measured with very high sensitivity and thus the frequency modulation mode
allows for the use of very stiff cantilevers. Stiff cantilevers provide stability very close
to the surface and, as a result, this technique was the first AFM technique to provide
true atomic resolution in ultra-high vacuum conditions [8]. The non-contact mode of
AFM is shows that figure 2.15.
In amplitude modulation, changes in the oscillation amplitude or phase provide
the feedback signal for imaging. In amplitude modulation, changes in the phase of
oscillation can be used to discriminate between different types of materials on the
surface. Amplitude modulation can be operated either in the non-contact or in the
intermittent contact regime. In dynamic contact mode, the cantilever is oscillated such
62
that the separation distance between the cantilever tip and the sample surface is
modulated. Amplitude modulation has also been used in the non-contact regime to
image with atomic resolution by using very stiff cantilevers and small amplitudes in
an ultra-high vacuum environment.
(iii) Tapping Mode
In tapping mode, the cantilever is driven to oscillate up and down at near its
resonance frequency by a small piezoelectric element mounted in the AFM tip holder
similar to non-contact mode. However, the amplitude of this oscillation is greater than
10 nm, typically 100 to 200 nm. Due to the interaction of forces acting on the
cantilever when the tip comes close to the surface, Van der Waals force, dipole-
dipole interaction,
electrostatic forces, etc cause the amplitude of this oscillation to decrease as the tip
gets closer to the sample.
An electronic servo uses the piezoelectric actuator to control the height of the
cantilever above the sample. The servo adjusts the height to maintain a set cantilever
oscillation amplitude as the cantilever is scanned over the sample. A tapping AFM
image is therefore produced by imaging the force of the intermittent contacts of the tip
with the sample surface. This method of 'tapping' lessens the damage done to the
surface and the tip compared to the amount done in contact mode. Tapping mode is
gentle enough even for the visualization of supported lipid bilayers or adsorbed single
polymer molecules (for instance, 0.4 nm thick chains of synthetic polyelectrolyte)
under liquid medium. With proper scanning parameters, the conformation of single
molecules can remain unchanged for hours [9].
2.2.2(b) Advantages and disadvantages
AFM has several advantages over the scanning electron microscope (SEM).
Unlike the electron microscope which provides a two-dimensional projection or a
two-dimensional image of a sample, the AFM provides a true three-dimensional
surface profile. Additionally, samples viewed by AFM do not require any special
treatments (such as metal/carbon coatings) that would irreversibly change or damage
the sample. While an electron microscope needs an expensive vacuum environment
for proper operation, most AFM modes can work perfectly well in ambient air or even
a liquid environment. This makes it possible to study biological macromolecules and
even living organisms. In principle, AFM can provide higher resolution than SEM. It
63
has been shown to give true atomic resolution in ultra-high vacuum (UHV) and, more
recently, in liquid environments. High resolution AFM is comparable in resolution to
SEM and TEM.
A
disadvantage of AFM compared with the (SEM) is the single scan image size. In one
pass, the SEM can image an area on the order of square millimeters with a depth of
field on the order of millimeters. Whereas the AFM can only image a maximum
height on the order of 10-20 micrometers and a maximum scanning area of about
150×150 micrometers. One method of improving the scanned area size for AFM is by
using parallel probes in a fashion similar to that of millipede data storage. The
scanning speed of an AFM is also a limitation. Traditionally, an AFM cannot scan
images as fast as a SEM, requiring several minutes for a typical scan, while a SEM is
capable of scanning at near real-time, although at relatively low quality. The relatively
slow rate of scanning during AFM imaging often leads to thermal drift in the image
[10-13] making the AFM microscope less suited for measuring accurate distances
between topographical features on the image. However, several fast-acting designs
[14-18] were suggested to increase microscope scanning productivity including what
is being termed video AFM (reasonable quality images are being obtained with video
AFM at video rate: faster than the average SEM). To eliminate image distortions
induced by thermal drift, several methods have been introduced.
64
Figure 2.14 The intermittent-contact mode.
65
Figure 2.15 AFM - non-contact mode
AFM images can also be affected by hysteresis of the piezoelectric material [19] and
cross-talk between the x, y, z axes that may require software enhancement and
filtering. Such filtering could "flatten" out real topographical features. However,
newer AFMs utilize closed-loop scanners which practically eliminate these problems.
66
Some AFMs also use separated orthogonal scanners (as opposed to a single tube)
which also serve to eliminate part of the cross-talk problems.
2.2.3 THE TRANSMISSION ELECTRON MICROSCOPE (TEM)
The transmission electron microscope (TEM) is a powerful tool for imaging
materials and organic structures at the atomic level. The images are projections
through thin films between 10nm and several microns thick. The TEM also provides
diffraction patterns from nanoscale regions, and chemical analysis using secondary
emissions such as X-rays, cathodoluminescence, secondary or backscattered
electrons, and energy-loss spectra from nanoscale regions. Diffraction patterns from
the smallest (sub-nanometer) region are called convergent-beam electron diffraction
patterns (CBED). The resolution of the best high-resolution electron microscopes
(HREM) is now about one Angstrom (0.1nm), so that columns of atoms may be seen
directly in projection. High-resolution electron diffraction (HRED) is also a powerful
method. Energy-loss spectra (ELS), which provide similar information to soft X-ray
absorption spectra, may be obtained from
sub-nanometer regions of these films.
The carbon nanotube (CNT) was recently discovered by TEM, and
amongst many other macromolecules (e.g. membrane proteins), the structure of the
ribosome has recently been solved to 1nm resolution by tomographic cryomicroscopy
(TCM).
2.2.3(a) The Concept of Resolution
The smallest distance between two points that we can resolve by our eyes is
about 0.1-0.2 mm, depending on how good our eyes are. This distance is the
resolution or resolving power of our eyes. The instrument that can show us pictures
revealing detail finer than 0.1 mm could be described as a microscope. The Rayleigh
criterion defines the resolution of light microscope as:

0.61
 sin 
……………………………………(2.1)
Where λ is the wavelength of the radiation, μ is the refractive index of the view
medium and β is the semi-angle of collection of the magnifying lens. The variable of
refractive index and semi-angle is small, thus the resolution of light microscope is
mainly decided by the wavelength of the radiation source. Taking green light as an
example, its 550nm wavelength gives 300nm resolution, which is not high enough to
separate two nearby atoms in solid-state materials. The distance between two atoms in
67
solid is around 0.2nm. Based on wave-particle duality, we know that electron has
some wave-like properties:

h
p
………………………………………..(2.2)
If an electron is accelerated by an electrostatic potential drop eU, the electron
wavelength can be described as:

h

eU 
2m0eU 1 
2 
 2m0c 
……………………….(2.3)
If we take the potential as 100keV, the wavelength is 0.0037nm. The resolution of
electron microscope should be better than that of light microscope.
2.2.3(b) Instrumentation
1. Illumination system. It takes the electrons from the gun and transfers them to
the specimen giving either a broad beam or a focused beam. In the raydiagram, the parts above the specimen belong to illumination system.
2. The objective lens and stage. This combination is the heart of TEM.
3. The TEM imaging system. Physically, it includes the intermediate lens and
projector lens.
The diffraction pattern and image are formed at the back focus plane and
image plane of the objective lens. If we take the back focus plane as the objective
plane of the intermediate lens and projector lens, we will obtain the diffraction pattern
on the screen. It is said that the TEM works in diffraction mode (Figure 2.16 b). If we
take the image plane of the objective lens as the objective plane of the intermediate
lens and projector lens, we will form image on the screen. It is the image mode
(Figure 2.16 a). In present investigation Tecnai 20 G2 transmission electron
microscope is used figure 2.17.
2.2.3(c) Principles of Image Formation and Lattice Images in TEM
When an electron beam strikes an object, several things can happen. If the
electron does not strike an atom in the sample, it will continue to travel in a straight
line until it hits the imaging screen. If the electron does come into contact with the
sample, it can either bounce off elastically, that is, without any loss of energy, or in
68
elastically, i.e., transferring some of that energy to the atom. In an inelastic bounce,
the amount of energy transferred from electron to sample is variable and random.
Therefore, when the electron eventually reaches the imaging plane, it has an unknown
energy and angle of incidence. This particular electron will then generate noise in the
image. However, if the electron bounced elastically, its energy is constant, and the
law of conservation of momentum will determine the angle at which it will bounce.
This electron can be used to give
high-resolution information on the sample.
Note that an electron can have an angle of reflection greater than 900. Electrons that
follow such a trajectory are termed 'back reflected electrons' and are generally not
used in electron microscopy. Contrast arises when there is interference between
electrons coming in from different angles. Electrons that interact with the sample are
bent away from their original path, and will thus interfere (either constructively or
destructively) with the main electron beam. If a small objective aperture is used,
electrons that get deflected at a greater angle are blocked, and the contrast of the
image is enhanced. However, electrons with a high deflection contain high-resolution
information and are therefore lost. A balance needs to be achieved between having
good contrast and having a high resolution. Because the electrons of a TEM pass
through the sample before hitting the imaging screen, they contain information on the
inside structures of that sample. If a hollow sphere and a solid ball are held in front of
a flashlight, both will cast an identical shadow: a solid black disk. In a TEM,
however, the two projections will be different. The solid ball will generate a disk that
is very dark in the center and progressively drops off in darkness towards the edges
(Figure 2.18 left). The hollow sphere will also cast a circular image. However, the
darkness gradient will be in the opposite direction, with the edge being the darkest,
and the middle the lightest (Figure 2.18 right). This happens because the electron
beam passes through the least amount of matter in the middle of a hollow sphere. The
darkness of the image is proportional to the electron absorbency properties of the
material used.
69
2.2.3(d) High Resolution Transmission Electron Microscopy (HRTEM)
To obtain lattice images, a larger objective aperture has to be selected that
allows many beams including the direct beam to pass. The image is formed by the
interference of the diffracted beams with the direct beam (phase contrast).
If the point resolution of the microscope is sufficiently high and a suitable
sample oriented along a zone axis, then high-resolution TEM (HRTEM) images are
obtained. In many cases, the atomic structure of a specimen can directly be
investigated by HRTEM. The incident parallel electron beam, ideally a plane wave,
interacts elastically while passing through the specimen, and the resulting
Modulations of its phase and amplitude are present in the electron wave leaving the
specimen. The wave here, the object exit wave o(r), thus contains the information
about the object structure. Unfortunately, the objective lens is not an ideal but has
aberrations (astigmatism, spherical Cs and chromatic Cc aberration) that reduce image
quality. The intensity distribution of the exit wave function is described by the
contrast transfer function (CTF). Much HRTEM work has been done on complex
oxides with a short and two long axes. If these are observed along the short axis, the
structural model is directly accessible by evaluation of the HRTEM image.
2.2.3 (e) Electron Diffraction
The diffraction, which mathematically corresponds to a Fourier transform,
results in spots (reflections) at well-defined positions. Each set of parallel lattice
planes is represented by spots which have a distance of 1/d (d: interplanar spacing)
from the origin and which are perpendicular to the reflecting set of lattice plane. The
two basic lattice planes (blue lines) of the two-dimensional rectangular lattice shown
below (Figure 2.18) are transformed into two sets of spots (blue). The diagonals of the
basic lattice (green lines) have a smaller interplanar distance and therefore cause spots
that are farther away from the origin than those of the basic lattice. The complete set
of all possible reflections of a crystal constitutes its reciprocal lattice.
The diffraction can be described in reciprocal space by the Ewald sphere
construction (Figure 2.19). A sphere with radius 1/λ is drawn through the origin of the
reciprocal lattice. Now, for each reciprocal lattice point that is located on the Ewald
sphere of reflection, the Bragg condition is satisfied and diffraction arises.
Due to the small wavelength of electrons (e.g., λ = 1.97pm for 300keV electrons), the
radius of the Ewald sphere is larger and many reflections appear. Furthermore, the
70
lattice points are elongated in ED to form rods so that the Ewald sphere intersects
more points (Figure 2.20). Because of that, diffraction occurs even then the Bragg
condition is not exactly satisfied. In fact, ED patterns are 2D cuttings of reciprocal
lattice. The rod-shape is due to the fact that TEM specimens are very thin in real
space,
leading
to
an
elongation
in reciprocal space.
If the interplanar distance in direction of observation is large (that means a small
distance between ZOLZ and FOLZ in reciprocal space), higher order Laue zones
(HOLZ) can be observed as well. The indexing of diffraction maxima is generally
carried out in one of two ways. In the first method the effective camera length L is
either known or can be calibrated so that the measured distances OX, OY on a plate
can be used to obtain the spacing of planes which are giving rise to the maxima. It can
be seen from simple geometry (for small angle) that d1   L / OX and d2   L / OY .
These values of interplanar spacing’s d1 and d2 enable the indices of the planes to be
defined.
The second method uses the ratios of the distances OX and OY rather than absolute
distances. Distances of diffraction maxima from the direct beam are proportional to
the reciprocal of spacing’s of the corresponding {hkl} planes in real space and hence
the ratio of the squares of the interplanar spacing’s. This ratio together with the
measured angle between the maxima (the angles between the planes {h1k1l1} and
{h2k2l2} in the crystal) enables to be calculated. Point 0: origin of reciprocal lattice,
k0: wave vector of the incident wave kD: wave vector of a diffracted wave, ZOLZ:
Zero Order Laue Zone, FOLZ (SOLZ): First (Second) Order Laue Zone Electron
microscopes can also be used to generate and view diffraction patterns of samples.
These are usually from samples that contain a repeated motif, such as 2D crystals
(sheets one layer thick) of proteins. In the back focal plane of the objective lens, a
diffraction image is formed. Depending then, on the positioning of the intermediate
lens, the diffraction pattern or the image will be magnified and displayed on the view
screen.
2.3 ELECTRICAL CONDUCTIVITY AND HALL MEASURMENT
Four-point probe
The four-point probe method is widely used for the determination of the electrical
resistivity of a semiconductor layer. When an electric field E is applied to a
semiconductor material, an electric current will flow. This current density is given by:
71
J = σE……………………………………… (2.4)
where the electrical conductivity of the layer is given by σ. When a rectangularshaped sample with dimensions l.w.d (where l is the length, w the width and d the
thickness of this rectangle) is considered, the resistance is given by:
R = ρ (l/wd ) ………………………………….(2.5)
If l = w then equation 2.5 becomes:
R = ρ/d = Rs ……………………………….. (2.6)
The quantity Rs is known as the sheet resistance of one square of the film that is
independent of the size of the square. The most common method of measuring this
sheet resistance is with the four-point probe method. The instrument is made up of
four point-probes that touch the surface of the film.
Figure 2.16 Schematic ray diagrams for a transmission electron microscope (TEM) with
the specimen, illuminated with a parallel beam of electrons showing (a) image formation
and (b) diffraction pattern formation.
72
Figure 2.17 Tecnai 20 G2 transmission electron microscopes operated at 200 kV at CSR,
Indore used in present investigation.
73
Figure 2.18 Schematic ray diagram showing formation of diffraction pattern.
Figure 2.19 Shows a Fourier transformed diffraction pattern.
Figure 2.20 Schematic ray diagram showing the Ewald sphere construction.
74
Figure 2.21 Differentiating between a solid ball (left) and a hollow sphere (right) in a
transmission electron microscope.
A current I is passed through the outer two probes, while a potential difference V is
measured between the inner two probes.
The resistivity is given as:

V
2x ………………………………………(2.7)
I
where x is the distance between the probes. If the material is in the form of an
infinitely thin film resting on an insulating support then equation 2.7 can be written
as:

Or

d
V d
I ln 2
 Rs  4.53
V
I
……………………………………..(2.8)
Hall-effect measurement
Since the Hall-effect and its application in the determination of electrical properties of
semiconductors are standard techniques, it will only be briefly discussed. When a
current is passed through a semiconductor in the presence of a transverse magnetic
field B, the mobile charge will not only drift in the direction of the field, but also in
the direction perpendicular to both the applied electric and magnetic fields. The total
force that a hole in a p-type conductor will experience is given by:
F = qv x B or Fy = qvxBz
……………………………………………(2.9)
Where Fy is the force in the y-direction. From the equation it is clear that unless an
electric field Ey is astablished along the width of the bar, each hole will experience a
force in the y direction. To maintain a steady state flow of holes down the length of
the semiconductor, the electric field Ey , has to balance the magnetic force:
Ey = νx Bz
………………………………………………………..(2.10)
The field Ey is set up when the magnetic field shifts the hole distribution slightly.
Once the electric field becomes as large as νx Bz no net lateral force is experienced by
75
the holes as they drift through the conductor. The establishment of the electric field Ey
is known as the Hall –effect and the resulting voltage.
………………………………………………………….(2.11)
VH = Ew
is known as the Hall-voltage with w as the width of the sample. The carrier
concentration can be calculated with
n
1
eR
H
……………………………….(2.12)
V d
R  D ………………………………….(2.13)
H
IB
Where,
In equation 2.10, I is the current, d the thickness of the layer and VH the measured
Hall voltage.
The resistivity is given by

V wd
I l
…………………………………..(2.14)
Where V is the voltage across the length of the sample, l the length of the sample and
w is the width of the sample. The mobility of the carrier is calculated by

1
wdne
……………………………………………..(2.15)
The Sheet resistance was measured by a four-point probe measurement system, and
the resistivity was then calculated by considering the thickness. The carrier
concentration and Hall mobility were carried out at room temperature using the van
der Pauw method on samples with a size of 10mm×10mm by a MMR Hall and Van
der Pauw Measurment system. It is important to point out that the calculated
resistivity based on the four-point probe system and the one obtained from the Hall
Measurment equipment should be similar.
The electrical resistivity of a semiconductor thin film can be written using Ohm’s law,
76
where ‘ρ’ is the film resistivity, e is the electronic charge, n is the number of carriers
corresponding to the carrier concentration and ‘μ’ is the carrier mobility. According to
Ohm’s law the carrier mobility affects resistivity. Low resistivity can be achieved by
increasing the carrier concentration or mobility or both. Increasing carrier
concentration is self-limiting because at some point the increased number of free
carriers decreases the mobility of the film due to carrier scattering. Hence there is a
tradeoff between the carrier density and carrier mobility for achieving low resistivity.
This technique allows one to measure resistance without including contact resistance
in the result. With an ohmmeter, for example one measures the specimen resistance
plus the resistance of the wires going to the specimen plus the contact resistance
between these wires and the specimen. The latter might be large or small, depending
on whether the surfaces are oxidized or not and on how hard the contacts are pressed
together. Since the contact resistance is unpredictable, it must be excluded from the
measurement when high accuracy is desired. This is particularly important, obviously,
when one expects the measured resistance to go to zero. Figure 2.22 shows a block
diagram of the measuring circuit. In Figure 2.22a, the voltage parallel to the applied
current is measured (longitudinal measurement), while in figure 2.22 b, the voltage
perpendicular to the applied current is measured (transverse measurement). Note that
the specimen current is provided by a constant current source, that is, a source for
which the current will not change when the specimen resistance changes. This is not
an essential feature of the method but is very convenient. “Four-probe” refers to the
fact that four independent contacts are made to the specimen. “Independent” means
that the only current path between any two contacts lies in the specimen, not in the
wires or solder.
There might be a substantial resistance between each of the outer, currentsupplying contacts and the specimen. Convince yourself that this will not affect the
measurement of the resistance of the region between the two inner contacts. High
contact resistance at the outer contacts might have other disadvantages, such as high
77
power dissipation and resulting heating, but they will not affect the resistance reading
directly.
The voltmeter and a section of the specimen are in parallel, so the measuring
current will split and some will pass through the meter. Therefore, the current in that
section of the specimen is not the same as what is measured by the ammeter.
Convince yourself that this will not give an error in the resistance calculation. Taking
into account the fact that a good voltmeter will have a very high resistance. Modern
digital voltmeters may have resistance in the tens of mega ohms range while the
typical specimen resistance will be very much less than this. Another possible
problem lies in the fact that the voltmeter connections to the specimen might have a
contact resistance that is not negligible compared to that of the meter.
The presence of unwanted thermal voltages in a measuring circuit can produce
significant errors in voltage measurements, especially when various parts of the
circuit are at very different temperatures. Their presence can be detected by reversing
the direction of the current because the thermal voltages will not reverse sign when
we do this. In the van der Pauw geometry the electrical contacts are on the perimeter
of the sample. Figure 2.23shows longitudinal (a) and diagonal (b) electrical
measurements using a lock-in amplifier as an ac current source.
2.3.2 The simple Cryogenic System
The cryostat used for performing the temperature dependent measurement
consists of the specimen probe, a stand to hold the probe, and a well-insulated
container partly filled with liquid nitrogen. In keeping the rate of change of
temperature slow and to maintain thermal equilibrium inside the specimen, principal
data can be taken during warming. The specimen probe stick (Figure 2.21) is lowered
into a sealed metal sample tube that is inside an outer vessel that is filled with liquid
nitrogen (LN). The sample makes thermal contact to the LN through a dilute He
exchange gas, which is present in the sample tube. Typically, the sample tube is
completely evacuated after the sample has been inserted. Then, a small amount of
helium gas is allowed to enter the sample tube. This is accomplished by attaching a
helium gas filled latex tube to the sample tube port, pinching the tube off 10 cm from
the port, and finally opening the port valve to allow the pinched off portion of helium
gas to enter the sample tube. The port valve is then closed. If it becomes difficult to
warm the sample up to higher temperature (i.e., thermal contact between the sample
78
and the surrounding LN is too great), one can pump further on the sample tube to
reduce the amount of helium exchange gas, and thereby reduce the thermal
connection between the sample and the cold LN. As the specimen slowly warms up,
the computer can collect a graph of specimen voltage vs. diode (temperature
sensitive) voltage. If the warming rate is too slow, it can be increased using the heater.
Be careful, if the rate is too fast we will not have temperature equilibrium inside the
specimen can. Also, the current in the heater wire can generate magnetic fields that
may disturb our measurements.
2.3.3 The Vacuum Pumping System
A single mechanical pump is used to alternately pump the outer vacuum space
or the sample tube (sample space). Valves are provided for pumping and isolating
both the sample space and the vacuum isolation space. In addition, helium exchange
gas can be added independently to each space to aid in thermal contact, warming,
cooling, etc. If a vacuum is to be maintained in the sample space or in the vacuum
isolation can, close the sample space valve and the vacuum space valve before
shutting off the pump. After the pump has been turned off, allow a minimum of ten
seconds before trying to restart it. After the pump has been switched off, vent the
input to atmosphere to prevent oil from being drawn into the pumping hose.
The cryostat (dewar) is used for low temperature measurements. This dewar
has three independent spaces as shown in figure 2.24. The first is the vacuum space
that is evacuated to provide thermal insulation. The second space consists of a
reservoir that contains the liquefied cryogen, in this case liquid nitrogen. The third
and innermost region is the central sample tube, which contains the sample stick.
Typically, one first pumps out the vacuum space for 15 minutes. After that space
evacuated, the vacuum space valve is closed and the pump is used to evacuate the
sample space. After the sample
79
(a)
(b)
Figure 2.22 dc longitudinal (a) and transverse (b) voltage measurements using fourprobe configuration.
(a)
(b)
Figure 2.23 ac longitudinal (a) and diagonal (b) voltage measurements using the
reference output of the lock-in amplifier as a voltage source.
80
Figure 2.24 Sample probe stick
Figure 2.25 Cryostat for making low temperature measurements.
81
space is evacuated, liquid nitrogen (LN2) can be poured into the reservoir through the
fill funnel. Be sure the sample space is well evacuated, or water may freeze on the
sample. To aid in cooling the sample, a small amount of helium exchange gas can be
introduced into the sample tube.
2.4 OPTICAL PROPERTIES MEASURMENTS
2.4 (a) Photoluminescence Spectroscopy
Introduction
Photoluminescence spectroscopy is a powerful tool used for the characterization of
semiconductors, especially those applicable for optoelectronic devices. It is a simple,
versatile, contactless, nondestructive method of probing the electronic structure of
materials. Photoluminescence (PL) involves the irradiation of the crystal to be
characterized with photons of energy greater than the band-gap energy of that
material. Light is directed onto a sample, where it is absorbed and imparts excess
energy into the material in a process called "photo-excitation". One way this excess
energy can be dissipated by the sample is through the emission of light, or
luminescence.
In the case of photo-excitation, this luminescence is called
"photoluminescence." The intensity and spectral content of this photoluminescence is
a direct measure of various important material properties. Photo-excitation causes
electron-hole pairs within the material to move into permissible excited states. When
these electrons and holes recombine, the excess energy is released and may include
the emission of light (a radiative process) or may not (a nonradiative process). We can
briefly say photoluminescence process includes three main phases [20].
1. Excitation: Electrons can absorb energy from external sources, such as lasers,
arc discharge lamps, and tungsten-halogen bulbs, and be promoted to higher
energy levels. In this process electron-hole pairs are created.
2. Thermalisation: Excited pairs relax towards quasi-thermal equilibrium
distributions.
3. Recombination: The energy can subsequently be released, in the form of a
lower energy photon, when the electron falls back to the original ground state.
This process can occur radiatively or non-radiatively.
PL is the spontaneous emission of light from a material under optical excitation.
Because the sample is excited optically, electrical contacts and junctions are
82
unnecessary and high-resistivity materials pose no practical difficulty. Moreover, PL
can be used to study virtually any surface in any environment. PL investigations can
be used to characterize a variety of material parameters. The excitation energy and
intensity are chosen to probe different regions and excitation concentrations in the
sample. PL spectroscopy provides electrical characterization, and it is a selective and
extremely sensitive probe of discrete electronic states. Features of the emission
spectrum can be used to identify surface, interface, and impurity levels and to gauge
alloy disorder and interface roughness. The intensity of the PL signal provides
information on the quality of surfaces and interfaces. Moreover, PL is generally not
sensitive to the pressure in the sample chamber. Hence, it can be used to study surface
properties in relatively high-pressure semiconductor growth reactors.
Although PL does depend quite strongly on temperature, liquid helium temperatures
being required for the highest spectral resolution, room-temperature measurements are
sufficient for many purposes. In addition, PL has little effect on the surface under
investigation. Photoinduced changes and sample heating are possible, but low
excitation can minimize these effects. Compared with other optical methods of
characterization like reflection and absorption, PL is less stringent about beam
alignment, surface flatness, and sample thickness. The fundamental limitation of PL
analysis is that of working with materials which have poor radiative efficiency, such
as low-quality indirect bandgap semiconductors. Indirect-bandgap semiconductors,
where the conduction band minimum is separated from the valence band maximum in
momentum space, have inherently low PL efficiency. Nonradiative recombination
tends to dominate the relaxation of excited populations in these materials. This
problem can be augmented by poor surface quality, where rapid nonradiative events
may occur.
Instrumentation
The basic equipment setup needed to perform conventional photoluminescence
consists of three main parts. (1) a light source to provide above- or below-band-gap
excitation; (2) from the sample (Figure 2.26). a dewar to maintain the samples at low
temperatures while allowing optical access to the sample surface; and (3) a detection
system to collect and analyse the photons emitted
83
Figure 2.26 The schematic representation of a basic PL set-up.
Figure 2.27 Systematic ray- diagram of Photoluminescence. (a) An electron absorbs a
photon and is promoted and is promoted from the Valence band to the conduction
band.(b) The electron cools down to the different widths placed in one single chip
bottom of the conduction band. (c) The elrctron produced with the hole resulting in the
emission of light with energy hν.
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2.4 (b) UV-Vis SPETROSCOPY (Transmission and Reflection of Light)
Optical transmission and reflection data are normally collected with a UV-VisibleNIR spectrophotometer capable of measuring in the wavelength range 190-1100 nm.
This apparatus uses a monochromator and a double silicon diode detector. A xenon
flashlight is used as illumination source, and the dual beam operation mode is able to
correct for intensity fluctuations of the source our surroundings. The resolution and
scan speed can be adjusted. In most experiments the wavelength interval is 1 nm
measured at 10 nm/s. A baseline can be recorded in order to use the bare substrate as a
reference. By using the 45º incidence specular reflectance attachment, reflection mode
data can be recorded. From the obtained optical data, values for the absorption can be
deduced from the equation 2.5 and subsequently the bandgap value can be obtained
from the arheneous plot. Moreover, the film thickness can be calculated for known
refractive index from a fringe pattern, or vice versa. Collimated light incident on a
transparent substrate with a thin film may be transmitted or reflected, as shown in
figure 2.28. The incident light impinges on the sample at some arbitrary angle θi with
respect to the direction normal to the sample surface. At the boundary, part of the
light will be reflected at angle qr while the other part will be transmitted through the
sample at angle θt .
Snell's law requires that all three beams and the normal to the surface be in the plane
of incidence (shaded green in figure 2.28). The transmission and reflection
measurements acquire the intensity ratios, T and R respectively, over a given range of
wavelengths. T and R are defined as the ratio of the light intensity being transmitted It
or reflected It over the incident light intensity Ii on the sample, as shown in eqs. (2.16)
and (2.17):
I
T  t
Ii
I
R r
Ii
…………………
(2.16)
……………. ……… (2.17)
The light from the light source is converged and enters to the monochromator and is
dispersed by the grating in the monochromator and converges onto the exit slit. The
light that has passed through the exit slit is monochromatic. This light is split into two
beams, one going to the sample to be measured and the other to the reference sample.
The light that passed through the sample or reference sample is incident upon the
silicon photodiode alternatively.
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Figure 2.28 Schematic diagram of the incident, reflected, and transmitted beams.
Figure 2.29 Schematic Diagram of Double Beam UV-Vis Spectrophotometer.
86
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