Characteristics of crystalline solid

Solid State Chemistry
Sagar Kumar Dutta
ID: 111815
Chemistry Discipline
Khulna University

2
Section-A
Solids are characterized by their definite
shapes and fixed volumes. The rigid
structure is indicative of the fact that the
atoms, molecules or ions in solids are held
together by strong forces of attraction and
the constituents are places in fixed positions
from which they cannot move appreciably.
As a result the solids assume rigidity and
mechanical strength and have definite
shapes. The forces holding the constituent
atoms, molecules or ions are different and
give rise to differences in physical
properties of the solids.
The branch of physics that deals with solids
is called solid-state physics, and is the main
branch of condensed matter physics (which
also includes liquids).Materials science is
primarily concerned with the physical
and chemical properties of solids. Solid-
state chemistry is especially concerned with
the synthesis of novel materials, as well as
the science of identification and chemical
composition
Properties of solid surface
Introduction
A crystalline solid exists as small crystals, each crystal having a characteristic geometrical shape. In a
crystal, the atoms, molecules or ions are arranged in a regular, repeating three dimensional patterns called
the crystal lattice. Sugar and salt are crystalline solids.
An amorphous solid (Gr amorphous = no form) has atoms, molecules or ions arranged at random and
lacks the ordered crystalline lattice. Examples are rubber, plastics and glass. In their disordered structure,
amorphous solids resemble liquids. Thus glasses are to be regarded as super-cooled or highly viscous
liquids. The liquid nature of glass is sometimes apparent in very old window panes that have become
slightly thicker at the bottom due to gradual downward flow.
Gases and liquids can flow and take up the shape of
their container. Solids, on the other hand, have a
definite volume and shape. They are rigid and lack
the ability to flow. In both gases and liquids, atoms,
ions and molecules continually move. They translate
randomly as well as rotate and vibrate. This
determines the ability of gases and liquids to flow. In
solids, atoms, ions and molecules are held together
by relatively strong chemical forces-ionic bond,
covalent bond, or by intermolecular van der Waals’
forces. They do not translate although they vibrate to
some extent in their fixed positions. This explains
why solids are rigid and have definite shape.
TYPES OF SOLIDS
Broadly speaking, solids are of two types:
(a) Crystalline solids; also called true solids
(b) Amorphous solids

3
Characteristics of Crystalline Solid:
Geometrical shape:
The crystals of every crystalline solid have a definite Geometrical shape due to definite and
orderly arrangement in three dimensional shapes.
Melting point:
There are many crystalline solids which do not change directly to liquid state and also there are
many crystalline solids which decompose before going into the liquid state. The crystalline solids
which directly change into liquid state do so at a definite temperature e.g. the melting point of
such crystalline solids is definite.
Cleavage planes:
When a crystal of a crystalline solid is hammered, it readily breaks up into smaller crystals along
particular planes which are called cleavage planes. These planes are inclined to one another at a
particular angle for a given crystalline solid. Thus the magnitude of this angle varies from
substance to substance

4
.
Isotropic and Anisotropic Properties:
Crystalline substances, on the other hand, are anisotropic and the magnitude of a physical
property varies with directions. For example, in a crystal of silver iodide, the coefficient of
thermal expansion is positive in one direction and negative in the other. Similarly, velocity of
light in a crystal may vary with direction in which it is measured. Thus a ray of light passing
through a Nicol prism splits up into two components, each travelling with different velocity
(double refraction).
Symmetry:
Crystalline solids have crystal symmetry, i.e. when a crystalline solid is rotated about an axis, its
appearance does not change (i.e. remain the same).
Seven Crystal Systems:

5
A lattice is "an infinite three dimensional regular arrangement of points, each of which has
identical surroundings". There are 7 unique unit-cell shapes that can fill all three dimensional
space. These are the 7 Crystal systems. We define the size of the unit cell using lattice parameters
(sometimes called lattice constants, or cell parameters). These are 3 vectors, a, b, c. The angles
between these vectors are given by α (angle between b and c), β (angle between a and c), and γ
(angle between a and b).
Single Crystal:

6
A single crystal or mono-crystalline solid is a material in which the crystal lattice of the entire
sample is continuous and unbroken to the edges of the sample, with no grain boundaries. The
absence of the defects associated with grain boundaries can give mono-crystals unique properties,
particularly mechanical, optical and electrical, which can also be anisotropic, depending on the
type of crystallographic structure.
These properties, in addition to making them precious in some gems, are industrially used in
technological applications, especially in optics and electronics. Because entropic effects favor the
presence of some imperfections in the microstructure of solids, such as impurities,
inhomogeneous strain and crystallographic defects such as dislocations, perfect single crystals of
meaningful size are exceedingly rare in nature, and are also difficult to produce in the laboratory,
though they can be made under controlled conditions. On the other hand, imperfect single crystals
can reach enormous sizes in nature: several mineral species such as beryl, gypsum and feldspars
are known to have produced crystals several metres across.
The opposite of a single crystal is an amorphous structure where the atomic position is limited to
short range order only. In between the two extremes exist polycrystalline, which is made up of a
number of smaller crystals known as crystallites, and paracrystalline phases.
Polycrystalline:
Polycrystalline materials are solids that are
composed of many crystallites of varying size
and orientation. The variation in direction can
be random (called random texture) or directed,
possibly due to growth and processing
conditions. Fiber texture is an example of the
latter.
Almost all common metals, and many ceramics are polycrystalline. Some elements such as sulfur,
while usually occurring in polycrystalline form, may also occur as single crystals. The crystallites
are often referred to as grains, however, powder grains are a different context. Powder grains can
themselves be composed of smaller polycrystalline grains.
Polycrystalline is the structure of a solid material that, when cooled, forms crystallite grains at
different points within it. The areas where these crystallite grains meet are known as grain
boundarie

7
Difference between Crystalline and Polycrystalline:
 Polycrystalline solids are composed of many numbers of crystalline solids.
 Crystalline solids or crystals have ordered structures and symmetry, but, in a
polycrystalline structure, the long-range order has been disrupted.
 Crystalline structure is uniform and has no boundaries, but polycrystalline structure differs
from this. It does not have a continuous structure, and it has boundaries between grains.
 Crystalline structure is hard to produce, and it is rare in nature in contrast to
polycrystalline structure.
Surface Cleaning:
Surface cleaning can be carried out either as a wet or dry process depending on the nature of the
soiling present, the product, the process and type of production equipment. Dry cleaning is used
mainly for processes where dry or particulate products are handled. Wet cleaning is employed
wherever possible due to the higher efficacy of the wet cleaning process (better soil removal from
surfaces).
Techniques of characterization of solid surfaces:
 LEED (Low-Energy Electron Diffraction)
 XPS (X-ray Photoelectron Spectroscopy)
 Auger Diffraction
Low Energy Electron Diffraction (LEED):
Introduction
Low-energy electron diffraction (LEED) is a technique for the determination of the surface
structure of crystalline materials by bombardment with a collimated beam of low energy electrons
(20–200 eV) and observation of diffracted electrons as spots on a fluorescent screen
LEED is the principal technique for the determination of surface structures. It may be used in one
of two ways:
1. Qualitatively: where the diffraction pattern is recorded and analysis of the spot positions
yields information on the size, symmetry and rotational alignment of the adsorbate unit
cell with respect to the substrate unit cell.

8
2. Quantitatively: where the intensities of the various diffracted beams are recorded as a
function of the incident electron beam energy to generate so-called I-V curves which, by
comparison with theoretical curves, may provide accurate information on atomic
positions.
In this section, we will only consider the qualitative application of this experimental technique.
Experimental Details
The LEED experiment uses a beam of electrons of a well-defined low energy (typically in the
range 20 - 200 eV) incident normally on the sample. The sample itself must be a single crystal
with a well-ordered surface structure in order to generate a back-scattered electron diffraction
pattern. A typical experimental set-up is shown below.
Only the elastically-scattered electrons contribute to the diffraction pattern ; the lower energy
(secondary) electrons are removed by energy-filtering grids placed in front of the fluorescent
screen that is employed to display the pattern.
Basic Theory of LEED
By the principles of wave-particle duality, the beam of electrons may be equally regarded as a
succession of electron waves incident normally on the sample. These waves will be scattered by
regions of high localised electron density, i.e. the surface atoms, which can therefore be
considered to act as point scatterers.
The wavelength of the electrons is given be the de Broglie relation :
Wavelength, λ = h / p ( where p - electron momentum )
Now , p = m.v = (2mEk )1/2
= (2m.e.V)1/2
From the above examples the range of wavelengths of electrons employed in LEED experiments
is seen to be comparable with atomic spacings, which is the necessary condition for diffraction
effects associated with atomic structure to be observed.

9
Consider, first, a one dimensional (1-D) chain of atoms (with atomic separation a ) with the
electron beam incident at right angles to the chain. This is the simplest possible model for the
scattering of electrons by the atoms in the topmost layer of a solid; in which case the diagram
below would be representing the solid in cross-section with the electron beam incident normal to
the surface from the vacuum above.
If you consider the backscattering of a wave front from two adjacent atoms at a well-defined
angle, θ , to the surface normal then it is clear that there is a "path difference" (d) in the distance
the radiation has to travel from the scattering centres to a distant detector (which is effectively at
infinity) - this path difference is best illustrated by considering two "ray paths" such as the right-
hand pair of green traces in the above diagram.
The size of this path difference is a sin θ and this must be equal to an integral number of
wavelengths for constructive interference to occur when the scattered beams eventually meet and
interfere at the detector i.e.
d = a sin θ = n λ
For two isolated scattering centres the diffracted intensity varies slowly between zero (complete
destructive interference ; d = (n + ½) λ ) and its maximum value (complete constructive
interference ; d = n λ ) - with a large periodic array of scatterers, however, the diffracted intensity
is only significant when the "Bragg condition"
a sin θ = n λ
is satisfied exactly. The diagram below shows a typical intensity profile for this case.

10
There are a number of points worth noting from this simple 1-D model
1. the pattern is symmetric about θ = 0 (or sin θ = 0)
2. sin θ is proportional to 1 / V 1/2
(since λ is proportional to 1 / V 1/2
)
3. sin θ is inversely proportional to the lattice parameter , a
The aforementioned points are in fact much more general - all surface diffraction patterns show a
symmetry reflecting that of the surface structure, are centrally symmetric, and of a scale showing
an inverse relationship to both the square root of the electron energy and the size of the surface
unit cell.
As an example we can look at the LEED pattern from an fcc(110) surface. In the diagram below
the surface atomic structure is shown on the left in plan view, as if you are viewing it from the
position of the electron gun in the LEED experiment (albeit greatly magnified). The primary
electron beam would then be incident normally on this surface as if fired from your current
viewpoint and the diffracted beams would be scattered from the surface back towards yourself.
The diffraction pattern on the right illustrates how these diffracted beams would impact upon the
fluorescent screen.
The pattern shows the same rectangular symmetry as the substrate surface but is "stretched" in the
opposite sense to the real space structure due to the reciprocal dependence upon the lattice

11
parameter. The pattern is also centrosymmetric about the (00) beam - this is the central spot in the
diffraction pattern corresponding to the beam that is diffracted back exactly normal to the surface
(i.e. the n = 0 case in our 1-D model).
The above illustration of the diffraction pattern shows only the "first-order" beams i.e. it is
representative of the diffraction pattern visible at low energies when only for n = 1 is the angle of
diffraction, θ , sufficiently small for the diffracted beam to be incident on the display screen.
By contrast, the diagram below shows the diffraction pattern that might be expected if the energy
of the incident electrons is doubled - some of the second order spots are now visible and the
pattern as a whole has apparently contracted in towards the central (00) spot.
This is what the real diffraction patterns might look like …
In the case of such simple LEED patterns, it is possible to explain the diffraction pattern in terms
of scattering from rows of atoms on the surface. For example, the rows of atoms running
vertically on the screen would give rise to a set of diffracted beams in the horizontal plane,
perpendicular to the rows, thus leading to the row of spots running in a line horizontally across the
diffraction pattern through the (00) spot. The further the rows are apart, then the closer in are the
diffracted beams to the central (00) beam. This is, however, a far from satisfactory method of
explaining LEED patterns from surfaces.
X-ray photoelectron spectroscopy (XPS)

12
Introduction
XPS is a quantitative spectroscopic technique that measures the elemental composition, empirical
formula, chemical state and electronic state of the elements that exist within a material. XPS
spectra are obtained by irradiating a material with a beam of X-rays while simultaneously
measuring the kinetic energy and number of electrons that escape from the top 1 to 10 nm of the
material being analyzed. XPS requires ultra high vacuum (UHV) conditions.
XPS is a surface chemical analysis technique that can be used to analyze the surface chemistry of
a material in its "as received" state, or after some treatment, for example: fracturing, cutting or
scraping in air or UHV to expose the bulk chemistry, ion beam etching to clean off some of the
surface contamination, exposure to heat to study the changes due to heating, exposure to reactive
gases or solutions, exposure to ion beam implant, exposure to ultraviolet light.
XPS is also known as ESCA, an abbreviation for Electron Spectroscopy for Chemical Analysis.
X-ray Photoelectron Spectroscopy (XPS) involves irradiating a sample with X-rays of a
characteristic energy and measuring the flux of electrons leaving the surface. The energy
spectrum for the ejected electrons is a combination of an overall trend due to transmission
characteristics of the spectrometer, energy loss processes within the sample and resonance
structures that derive form electronic states of the material under analysis. The instrumental
contribution is an unwelcome fact of the measurement process, but the background and resonance
peaks offer information about the sample surface

13
XPS is also known as ESCA (Electron Spectroscopy for Chemical Analysis), an abbreviation
introduced by Kai Siegbahn's research group to emphasize the chemical (rather than merely
elemental) information that the technique provides.
Instrumentation
Fig: XPS (X-ray Photoelectron Spectroscopy
 Electron energy analyzer
 X-ray source
 Ar ion gun
 Neutralizer
 Vacuum system
 Electronic controls
 Computer systemUltrahigh
 vacuum system< 10-9Torr (< 10-7 Pa)
 Detection of electrons
 Avoid surface reactions/contamination

14
XPS mechanism process
Photoelectron spectroscopy works by directing a beam of monoenergetic photons in the direction
of a sample. The photons have certain energy that when they hit electrons in the atoms of the
sample with the energy necessary the electrons from the atoms in the sample are ejected from
the atom. The electrons ejected are analyzed in the XPS detector by measuring electrons kinetic
energy which provides the information to determine the kind of elements present in the sample
figure 1 illustrates the schematic representation of the x-ray photoelectron process.
In principle XPS detects all elements. In practice, using typical laboratory-scale X-ray sources,
XPS detects all elements with an atomic number (Z) of 3 (lithium) and above. It cannot easily
detect hydrogen (Z = 1) or helium (Z = 2).
 Detection limits for most of the elements (on a modern instrument) are in the parts
per thousand range. Detection limits of parts per million (ppm) are possible, but
require special conditions: concentration at top surface or very long collection time
(overnight).
 XPS is routinely used to analyze inorganic compounds, metal alloys,
semiconductors, polymers, elements, catalysts, glasses, ceramics, paints, papers,
inks, woods, plant parts, make-up, teeth, bones, medical implants, bio-materials,
viscous oils, glues, ion-modified materials and many others.
 XPS is less routinely used to analyze the hydrated forms of some of the above
materials by freezing the samples in their hydrated state in an ultra pure
environment, and allowing or causing multilayers of ice to sublime away prior to
analysis.
 Such hydrated XPS analysis allows hydrated sample structures, which may be
different from vacuum-dehydrated sample structures, to be studied in their more
relevant as-used hydrated structure. Many bio-materials such as hydrogels are
examples of such samples.

15
Wide-scan or survey spectrum of a somewhat dirty silicon wafer, showing all elements present. A
survey spectrum is usually the starting point of most XPS analyses because it shows all elements
present on the sample surface, and allows one to set up subsequent high-resolution XPS spectra
acquisition. The inset shows a quantification table indicating all elements observed, their binding
energies, and their atomic percentages.
High-resolution spectrum of an oxidized silicon wafer in the energy range of the Si 2p signal. The
raw data spectrum (red) is fitted with five components or chemical states, A through E. The more
oxidized forms of Si (SiOx, x = 1-2) appear at higher binding energies in the broad feature
centered at 103.67 eV. The so-called metallic form of silicon, which resides below an upper layer
of oxidized silicon, exhibits a set of doublet peaks at 100.30 eV (Si 2p1/2) and 99.69 eV (Si 2p3/2).
The fact that the metallic silicon signal can be seen "through" the overlayer of oxidized Si
indicates that the silicon oxide layer is relatively thin (2-3 nm). Attenuation of XPS signals from
deeper layers by overlayers is often used in XPS to estimate layer thicknesses and depths.

16
XPS is used to measure:
 Elemental composition of the surface (top 1–10 nm usually)
 Empirical formula of pure materials
 Elements that contaminate a surface
 Chemical or electronic state of each element in the surface
 Uniformity of elemental composition across the top surface (or line profiling or mapping)
 Uniformity of elemental composition as a function of ion beam etching (or depth
profiling)
XPS can be performed using either a commercially built XPS system, a privately built XPS
system or a synchrotron-based light source combined with a custom designed electron analyzer.
Commercial XPS instruments in the year 2005 used either a highly focused 20 to 200 micrometer
beam of monochromatic aluminium Kα X-rays or a broad 10–30 mm beam of non-
monochromatic (polychromatic) magnesium X-rays. A few, special design, XPS instruments can
analyze volatile liquids or gases, materials at low or high temperatures or materials at roughly 1
torr vacuum, but there are relatively few of these types of XPS systems.
AUGER ELECTRON SPECTROSCOPY
INTRODUCTION
Auger electron spectroscopy (AES) is a nondestructive core-level electron spectroscopy for semi-
quantitative determination of the elemental composition of surfaces, thin films, and interfaces.
The popularity of this ultrahigh vacuum technique may be attributed to high surface sensitivity
(an analysis depth of less than 100 Å) and a relatively low detection limit (~0.1 atomic percent).
In addition to having an elemental coverage from lithium to uranium and beyond, AES has the
ability to distinguish between two elements that are close to each other in the periodic table. In

17
addition, AES has an atomic number-dependent sensitivity that varies at most by one order of
magnitude.
AES chemical shifts and line shapes can also yield bonding (chemical state) information, albeit
with less precision than is possible with X-ray photoelectron spectroscopy (XPS) (Chapter 11),
another core-level electron spectroscopy. Auger electron spectroscopy has a depth resolution of
5–25 Å, and can be used, with simultaneous ion sputtering, for depth profiling. With a lateral
resolution (< 100 Å) that is significantly better than that of XPS, scanning Auger microscopy
(SAM) can be used effectively for imaging nanoscale structures and to produce two-dimensional
maps of surface elemental composition. Survey Auger spectra typically take less than five
minutes, providing for rapid data acquisition. Although somewhat sophisticated and expensive,
Auger instrumentation is relatively simple to use and is readily available from many different
commercial sources. The reasons enumerated above explain why Auger electron spectroscopy has
become perhaps the most widely used surface analytical technique. Auger Electron Spectroscopy
structure. Finally, results of recent experiments have demonstrated that angle-resolved Auger
electron spectroscopy can provide a means to study excitation processes in solids. The Auger
process is a three-electron process. When a beam of electrons, typically with an energy range of
3-20 keV, strikes a solid atom, a core-level (inner) electron is ejected producing a singly ionized
excited atom. An outer level electron can fill the resulting vacancy in the core level. Following
this radiationless transition, the excess energy of the resulting excited state ion may be removed
by emitting either
 An X-ray (the basis for X-ray fluorescence (XRF)/electron microprobe (EMP) analysis) or
another electron from the atom. The emitted electrons in process are called Auger
electrons, after Pierre Auger, who discovered this process in the 1920s.
 Although Lise Meitner independently discovered the effect around the same time, she is
given very little recognition in the literature. While the emission of X-rays produces singly
ionized atoms, the emission of Auger electrons results in doubly ionized atoms. Because
Auger is a three-electron process, hydrogen and helium cannot be detected by this
technique. Although Li has three electrons, an isolated ground state Li atom does not yield
Auger peaks because the atom has only two energy levels that contain electrons.
 Auger peaks, however, have been detected from multiply excited Li atoms. The presence
of electrons in the valence band of solid Li also allows for Auger transitions of the type
KVV. The surface sensitivity of AES is due to the short mean free path of the relatively
low energy Auger electrons.

18
BASIC PRINCIPLES OF AES:
X-Ray Notation
In Auger electron spectroscopy, electron energy states are denoted by using X-ray notation.
Because removing an electron from a complete shell is equivalent to placing a single electron in
an empty shell, X-ray spectra are similar to one-electron alkali atom spectra. Hence, we first
examine the fine structure in the optical spectra of alkali atoms. The fine structure, the splitting of
lines (with the exception of those due to s-state electrons) in the spectra of Spin-orbit coupling
splits non-s energy terms in alkali atoms
into two levels. We now discuss the terminology used for electronic energy levels for light atoms,
for which Russell-Saunders coupling (also called L-S coupling) is a valid approximation. In the
general case, each level is specified by the principle quantum number (n) and a level symbol
(2S+1LJ). In this symbol, S is
the total electronic spin angular momentum quantum number, L is the code for the total electronic
orbital angular momentum quantum number, and J is the total electronic angular momentum
quantum number. Because X-ray spectra are similar to one-electron alkali atom spectra, the
following simplification is made to yield the XPS notation.

19
Auger Transitions
The Auger process for a solid is schematically illustrated in Figure 10.2. The KL2L3 Auger
transition, illustrated in this diagram, involving ionization, an relaxation, and emission, may be
visualized as follows:
 A core- electron in the atom is removed by the high-energy incident electron creating a
vacancy in the K shell and yielding an electronically excited ion (ionization).
 An electron from the L2 level falls down almost immediately in a radiation less transition
to fill t he vacancy in the K shell (relaxation).
INSTRUMENTATION
Electron Optical Column:
In AES instrumentation, the electron beam from an electron source is focused onto the specimen
surface by a suitable optical column. In addition to being mono-energetic, the electron beam used
in AES instrumentation should be small in size with high brightness. The sample to be analyzed is
irradiated with electrons with energy of 2�10 keV and beam current of 10-8 to 10-5 A. In the
case of scanning Auger microscopy, energies as high as 35 keV and currents as low as 10 �9 A
are used to produce beam diameters as small as 100 Å.

20
Ion Optical Column:
For depth profiling and/or sputter cleaning, an electron impact-type ion source is usually
employed in conjunction with AES instruments. Electrons from a heated filament are accelerated
by a cylindrical grid to an energy sufficient to ionize gas atoms by collisions. The resulting ions
are accelerated into a focusing lens column. Inert gases such as argon (Ar) or xenon (Xe) are used
in a typical electron impact-type ion source with a hot tungsten filament.
Electron Energy Analyzers:
Electron energy analyzers are used to measure the number of ejected electrons (N) as a function of
electron energy (E). The most commonly used energy analyzers in AES are:
 The retarding field analyzer (RFA),
 The cylindrical mirror analyzer (CMA),

21
 The concentric hemispherical analyzer (CHA). Because of the limited energy resolution
and poor signal-to-noise ratio resulting from mediocre transmission efficiency, the
retarding field analyzer, commonly used for low energy electron diffraction studies, is not
an optimal choice for Auger electron spectroscopy.
The high transmission efficiency, compact size, and ease of use of the cylindrical mirror analyzer.
combine to make it the analyzer of choice for Auger electron spectroscopy. Because of its higher
resolution, the concentric hemispherical analyzer (Figure 10.8) is used in Auger electron
spectroscopy when chemical state information is desired. The CHA consists of an input lens and
the hemispherical analyzer. All XPS energy analyzers are concentric hemispherical analyzers.

22
Applications:
 Auger electron spectroscopy is a very powerful surface analytical
technique that has found applications in many fields of solid-state physics
and chemistry of surfaces during physical property measurements.
 Several phenomena such as adsorption desorption, surface segregation
from the bulk, measurement of diffusion coefficients, and catalytic activity
of surfaces have been investigated using AES.
 It has also been used to study the surface compositional changes in alloys
during ion sputtering. Chemical properties such as corrosion, stress
corrosion, oxidation and catalytic activity and mechanical properties such
as fatigue, wear, adhesion, resistance to deformation processes, and surface
cracking depend on surface properties.
 Similarly, grain boundary chemistry Influences mechanical properties such
as low- and high-temperature ductility and fatigue, chemical properties
such as inter-granular corrosion and stress corrosion, and electrical
properties.
 AES has been used to relate surface and grain boundary chemistry to
properties of materials. AES has proved to be extremely valuable
compared to most other techniques, which are limited by either large
sampling depth or poor sensitivity.
ADVANTAGES AND DISADVANTAGES

23
The main advantages of AES can be summarized as follows:
 Spatial resolution is high.
 Analysis is relatively rapid.
 Surface or subsurface analysis can be performed.
 It is sensitive to light elements (except H and He).
 It provides reliable semi quantitative analysis.
 Chemical information is available in some cases.
The disadvantages of this technique are as follows:
 Insulators are difficult to study due to surface charging.
 Surface may be damaged by the incident electron beam.
 Precise quantitative analysis may require extensive work.
 Sensitivity is modest (0.1 to 1 atom %).
 Depth profiling by ion sputtering or sectioning is destructive
Conclusion:
Electrical conductivity of solids may arise through the motion of electrons and positive holes
(electronic conductivity) or through the motions of ions (ionic conductivity). The conduction
through electrons is called n-type conduction and through positive holes is called p – types
conduction. Electrical conductivity of metal is due to motion of electrons and it increases with the
number of electrons available to participate in the conduction process. Pure ionic solids where
conduction can take place only through motion of ions are insulators. However, the presence of
defects in the crystal structure increases their conductivity

24
Introduction to Molecular Adsorption
The adsorption of molecules on to a surface is a necessary prerequisite to any surface mediated
chemical process.
For example, in the case of a surface catalysed reaction it is possible to break down the whole
continuously-cycling process into the following five basic steps :
1. Diffusion of reactants to the active surface
2. Adsorption of one or more reactants onto the surface
3. Surface reaction
4. Desorption of products from the surface
5. Diffusion of products away from the surface
The above scheme not only emphasizes the importance of the adsorption process but also its
reverse - namely desorption. It is these two processes which are considered in this Section.
TYPES OF ADSORPTION:
The adsorption of a gas into a solid surface is mainly of two types:
(a) Physical Adsorption:
This is due to the gas molecules being held to the solid surface by van der Waal’s
attractive forces. It is also referred to as van der Waal’s Adsorption. For example,
adsorption of hydrogen or oxygen on charcoal is Physical Adsorption.
(b) Chemical Adsorption or Chemisorption

25
In this kind of adsorption, the gas molecules or atoms are held to the solid surface by
chemical bonds. These bonds may be covalent or ionic in nature. For example, hydrogen is
chemisorbed on nickel. Hydrogen molecules are first adsorbed by van der Waal’s forces and
then dissociates. The hydrogen atoms are thus chemisorbed on nickel.
The adsorbed atoms or molecules can be held on the surface of a metal such as platinum (Pt) by
physical van der Waal’s force or chemical forces due to residual valence bonds. Thus the
adsorption of hydrogen on platinum may take place in two ways (molecularly or atomically as
shown above).

26
A catalyst is defined as a substance which alters the rate of a chemical reaction, itself remaining
chemically unchanged at the end of the reaction. The process is called Catalysis.
Berzelius (1836) realized that there are substances which increase the rate of a reaction without
themselves being consumed. He believed that the function of such a substance was to loosen the
bonds which hold the atoms in the reacting molecules together. Thus he coined the term Catalysis
(Greek kata = wholly, lein = to loosen). There is no doubt that usually a catalyst accelerates a
reaction as was originally through by Berzelius. But a number of cases are now known where the
catalyst definitely retards (slows down) the rate of reaction. As evident from the above definition,
a catalyst may increase or decrease the rate of a reaction.
A catalyst which enhances the rate of a reaction is called a Positive catalyst and the process
Positive catalysis or simply Catalysis.
A catalyst which retards the rate of a reaction is called a Negative catalyst and the process
Negative catalysis.
There are two main types of catalysis:
(a) Homogeneous catalysis
(b) Heterogeneous catalysis
Also, there is a third types of catalysis known as Enzyme catalysis which is largely of biological
interest. This will be discussed separately at a later stage.
HOMOGENEOUS CATALYSIS
In homogeneous catalysis, the catalyst is in the same phase as the reactants and is evenly
distributed throughout. This type of catalysis can occur in gas phase or the liquid (solution)
phase.
Examples of Homogeneous Catalysis in Gas Phase:
(a) Oxidation of sulphur dioxide (SO2) to sulphur trioxide (SO3) with nitric oxide (NO) as
catalyst,
2SO2 + O2 + [NO] 2SO3 + [NO]
gas gas gas gas
(b) Decomposition of acetaldehyde (CH3CHO) with iodine (I2) as catalyst,
Catalysis

27
CH3CHO + (I2) CH4 + CO
vapour vapour gas gas
Examples of Homogeneous Catalysis in Solution Phase
Many reactions in solutions are catalysed by acids (H+
) and bases (OH–
).
(a) Hydrolysis of cane sugar in aqueous solution in the presence of mineral acid as catalyst,
(b) Hydrolysis of an ester in the presence of acid or alkali,
(c) Decomposition of hydrogen peroxide (H2O2) in the presence of iodide ion (I–
) as catalyst,
HETEROGENEOUS CATALYSIS
The catalysis in which the catalyst is in a different physical phase from the reactants is
termed Heterogeneous catalysis. The most important of such reactions are those in which the
reactants are in the gas phase while the catalyst is a solid. The process is also called Contact
catalysis since the reaction occurs by contact of reactants with the catalyst surface. In contact
catalysis, usually the catalyst is a finely divided metal or a gauze. This form of catalysis has great
industrial importance.
Examples of Heterogeneous Catalysis:
Some examples of heterogeneous catalysis with reactants in the gas, liquid or the solid phase are
listed below.
(1) Heterogeneous catalysis with gaseous reactants (Contact catalysis)
(a) Combination of sulphur dioxide (SO2) and oxygen in the presence of finely divided
platinum or vanadium pentoxide, V2O5, (Contact Process for Sulphuric acid).

28
Vegetable oils are triesters of glycerol with higher unsaturated acid (oleic acid). When hydrogen
is passed through the vegetable oils in the presence of nickel, the carbon-carbon double bonds of
the acid portions are hydrogenated to yield solid fats (Vanaspati ghee).
CHARACTERISTICS OF CATALYTIC REACTIONS
Although there are different types of catalytic reactions, the following features or characteristics
are common to most of them.
(1) A catalyst remains unchanged in mass and chemical composition at the end of the
reaction
Qualitative and quantitative analysis show that a catalyst undergoes no change in mass of
chemical nature. However, it may undergo a physical change. Thus granular manganese dioxide
(MnO2) used as a catalyst in the thermal decomposing of potassium chlorate is left as a fine
powder at the end to the reaction.
(2) A small quantity of catalyst is generally needed to produce almost unlimited reaction
Sometimes a trace of a metal catalyst is required to affect very large amounts of reactants. For
example, one ten-millionth of its mass of finely divided platinum is all that is needed to catalyse
the decomposition of hydrogen peroxide. On the other hand, there are catalysts which need to be
present in relatively large amount to be effective. Thus in Friedel-Crafts reaction
anhydrous aluminium chloride functions as a catalyst effectively when present to the extent of 30
per cent of the mass of benzene. For the acid and alkaline hydrolysis of an ester,
the rate of reaction is proportional to the concentration of the catalyst (H+
or OH–
).
(2) A catalyst is more effective when finely divided

29
In heterogeneous catalysis, the solid catalyst is more effective when in a state of fine subdivision
than it is used in bulk. Thus a lump of platinum will have much less catalytic activity than
colloidal or Platonized asbestos. Finely divided nickel is a better catalyst than lumps of solid
nickel.
(3) A catalyst is specific in its action
While a particular catalyst works for one reaction, it will not necessarily work for another
reaction. Different catalysts, moreover, can bring about completely different reactions for the
same substance. For example, ethanol (C2H5OH) gives ethene (C2H4) when passed over hot
aluminium oxide,
(4) A catalyst cannot, in general, initiate a reaction
In most cases a catalyst speeds up a reaction already in progress and does not initiate (or start) the
reaction. But there are certain reactions where the reactants do not combine for very long period
(perhaps years). For example, a mixture of hydrogen and oxygen, which remains unchanged
almost indefinitely at room temperature, can be brought to reaction by the catalyst platinum black
in a few seconds.
Thus it is now considered that the catalyst can initiate a reaction. According to this view, the
reacting molecules (in the absence of catalyst) do not possess minimum kinetic energies for
successful collisions. The molecules rebound from collision without reacting at all.
(5) A catalyst does not affect the final position of equilibrium, although it shortens the
time required to establish the equilibrium
It implies that in a reversible reaction the catalyst accelerates the forward and the reverse reactions
equally. Thus the ratio of the rates of two opposing reactions i.e., the equilibrium constant,
remains unchanged. The effect of a catalyst on the time required for equilibrium to be established
for the reaction:
To start with the concentrations of A and B are at the maximum and hence the rate of forward
reaction is maximum. As the time passes the rate of the reaction decreases till the equilibrium is
established. For the reverse reaction the initial concentrations of C and D are zero and the rate of
reaction is lowest. At the time passes, the rate of reaction increases till the equilibrium is

30
established. Similar curves of the rates of reactions with the catalyst show that the rates of the
forward reaction and the reverse reaction are altered equally but the equilibrium is established in a
much shorter time. For example, in the Haber Process for ammonia,
the reaction is very slow. In the presence of the catalyst, the equilibrium is reached much sooner
but the percentage yield remains unchanged. The iron catalyst shortens the time to attain
equilibrium but cannot alter the percentage yield.
Energy considerations also show that the final state of equilibrium cannot be changed by the
catalyst. Suppose the catalyst accelerates the forward reaction more than the reverse reaction. This
will shift the equilibrium point, which cannot happen without the supply of energy to the system.
But a catalyst unchanged in mass and composition at the end of the reaction, cannot supply the
required energy.
(6) Change of temperature alters the rate of a catalytic reaction as it would do for the
same reaction without a catalyst:
We have already studied the effect of temperature change on reversible reactions under Le
Chatelier principle. Some catalysts are, however, physically altered by a rise in temperature and
hence their catalytic activity may be decreased. This is particularly true with colloidal solutions
like that of platinum, since a rise in the temperature may cause their coagulation. In such a case
the rate of reaction increases up to a certain point and then gradually decreases. The rate of
reaction is maximum at a particular temperature called the optimum temperature.
PROMOTERS
The activity of a catalyst can often be increased by addition of a small quantity of a second
material. This second substance is either not a catalyst itself for the reaction or it may be a feeble
catalyst. A substance which, though itself not a catalyst, promotes the activity of a catalyst is
called a promoter.

31
Example of Promoters”
Molybdenum (Mo) or aluminium oxide (Al2O3) promotes the activity of iron catalyst in the Haber
synthesis for the manufacture of ammonia.
In some reactions, mixtures of catalysts are used to obtain the maximum catalytic efficiency.
For example, in the synthesis of methanol (CH3OH) from carbon monoxide and hydrogen, a
mixture of zinc and chromium oxide is used as a catalyst.
Explanation of Promotion Action
The theory of promotion of a catalyst is not clearly understood. Presumably :
(1) Change of Lattice Spacing. The lattice spacing of the catalyst is changed thus enhancing
the spaces between the catalyst particles. The absorbed molecules of the reactant (say H2)
are further weakened and cleaved. This makes are reaction go faster.
(2) Increase of Peaks and Cracks. The presence of the promoter increases the peaks and
cracks on the catalyst surface. This increases the concentration of the reactant molecules
and hence the rate of reaction. The phenomenon of promotion is a common feature of
heterogeneous catalysis.
CATALYTIC POISONING:
Very often a heterogeneous catalyst in rendered ineffective by the presence of small amounts of
impurities in the reactants. A substance which destroys the activity of the catalyst to accelerate
a reaction, is called a poison and the process is called Catalytic poisoning.
Examples of Catalytic Poisoning

32
(1) The platinum catalyst used in the oxidation of sulphur dioxide (Contact Process), is poisoned
by arsenic oxide (As2O3)
(2) The iron catalyst used in the synthesis of ammonia (Haber Process) is poisoned by H2S.
(3) The platinum catalyst used in the oxidation of hydrogen is poisoned by carbon monoxide.
Explanation of Catalytic Poisoning
The poison is adsorbed on the catalyst surface in preference to the reactants. Even a
monomolecular layer renders the surface unavailable for further adsorption of the reactants. The
poisoning by As2O3 or CO appears to be of this kind.
(2) The catalyst may combine chemically with the impurity. The poisoning of iron catalyst by
H2S falls in this class.
AUTOCATALYSIS
When one of the products of reaction itself acts as a catalyst for that reaction the
phenomenon is called Autocatalysis.
In autocatalysis the initial rate of the reaction rises as the catalytic product is formed, instead of
decreasing steadily. The curve plotted between reaction rate and time shows a maximum when the
reaction is complete.

33
ACTIVATION ENERGY AND CATALYSIS
According to the collision theory, a reaction occurs by the collisions between the reactant
molecules (or ions). At ordinary temperature, the molecules do not possess enough energy and
hence the collisions are not effective. However, when the temperature of the system is raised, the
kinetic energy of the molecules increases. But the molecules do not react unless they attain a
minimum amount of energy. The minimum amount of energy required to cause a chemical
reaction is known as the Activation Energy. The activated molecules on collision first form an
Activated Complex. As a result of breaking and forming of new bonds, the activated complex
dissociates to yield product molecules.
A catalyst lowers the activation energy of the reaction by providing a new pathway
(mechanism). Thus larger number of effective collisions occur in the presence of the catalyst than
would occur at the same temperature without the presence of the catalyst. In this way the presence
of the catalyst makes the reaction go faster, other conditions remaining the same.

34
THEORIES OF CATALYSIS
There are two main theories of catalysis:
 Intermediate Compound Formation theory
 The Adsorption theory.
In general, the Intermediate Compound Formation theory applies to homogeneous catalytic
reactions and the Adsorption theory applies to heterogeneous catalytic reactions.
The Intermediate Compound Formation Theory
As already discussed a catalyst functions by providing a new pathway of lower activation energy.
In homogeneous catalysis, it does so by forming an intermediate compound with one of the
reactants. The highly reactive intermediate compound then reacts with the second reactant to yield
the product, releasing the catalyst. Let us illustrate it by taking the general reaction
The activation energies of the reactions (2) and (3) are lower than that of the reaction (1) Hence
the involvement of the catalyst in the formation of the intermediate compound and its subsequent
decomposition, accelerates the rate of the reaction (1) which was originally very slow.

35
Example 1. Catalytic oxidation of sulphur dioxide (SO2) in the presence of nitric oxide (NO) as
catalyst. (Chamber Process of Sulphuric acid)
It may be noted that the actual isolation of intermediate compounds which would prove their
existence is very difficult. As already stated, by their very nature they are unstable. In general, the
intermediate compounds suggested as being formed are usually plausible rather that proved.
The Adsorption Theory:
This theory explains the mechanism of a reaction between two gases catalysed by a solid
(Heterogeneous or Contact Catalysis). Here the catalyst functions by adsorption of the reacting
molecules on its surface. Generally speaking, four steps can be put forward for heterogeneous
catalysis. For example, if the reaction is :
Step 1. Adsorption of Reactant molecules:
The reactant molecules A and B strike the catalyst surface. They are held up at the surface by
weak van der Waals forces (Physical adsorption) or by partial chemical bonds (Chemisorption).
Step 2. Formation of Activated complex
The particles of the reactants adjacent to one another join to form an intermediate complex (A–B).
The activated complex is unstable. It has only fleeting existence.
Step 3. Decomposition of Activated complex
The activated complex breaks to form the products C and D. The separated particles of the
products hold to the catalyst surface by partial chemical bonds.

36
Step 4. Desorption of Products
The particles of the products are desorbed or released from the surface. They are stable and can
lead an independent existence. The mechanism of contact catalysis may vary in details, depending
on the nature of the reactants.
HYDROGENATION OF ETHENE (ETHYLENE) IN PRESENCE OF NICKEL
Ethane adds hydrogen in the presence of nickel as a catalyst to yield ethane.

37
The catalyst operates by the following steps.
Step 1. Adsorption of Hydrogen molecules
Hydrogen molecules are adsorbed on the nickel surface due to the residual valence bonds of the
nickel atoms.
Step. 2 H–H Bonds are broken
The H–H bond is smaller (0.74Å) than Ni–Ni bond. Therefore, the H–H bond of the adsorbed
hydrogen molecule is stretched and weakened. The weakened bond breaks, separating the
hydrogen atoms. The separated hydrogen atoms are held to the nickel surface by chemical bonds.
Step 3. Formation of the Activated complex
The chemisorbed hydrogen atoms then attach to ethene molecule by partial chemical bonds. The
unstable activated complex is thus formed.

38
Step 4. Decomposition of the Activated complex and desorption of ethane molecules
The unstable activated complex decomposes to release ethane molecules. The freed catalyst
surface is again available for further action.
Active Centres on Catalyst Surface
Just like surface tension, the catalyst has unbalanced chemical bonds on it. The reactant gaseous
molecules are adsorbed on the surface by these free bonds. This accelerates the rate of the
reaction. The distribution of free bonds on the catalyst surface is not uniform. These are crowded
at the ‘peaks’, ‘cracks’ and ‘corners’ of the catalyst. The catalytic activity due to adsorption of
reacting molecules is maximum at these spots. These are, therefore, referred to as the active
centres.
The active centres increase the rate of reaction not only by increasing the concentration of the
reactants but they also activate the molecule adsorbed at two such centres by stretching it.
The Adsorption Theory Explains Catalytic Activity
(1) Metals in a state of fine subdivision or colloidal form are rich in free valence bonds and hence
they are more efficient catalysts than the metal in lumps.
(2) Catalytic poisoning occurs because the so-called poison blocks the free valence bonds on its
surface by preferential adsorption or by chemical combination.

39
(3) A promoter increases the valence bonds on the catalyst surface by changing the crystal lattice
and thereby increasing the active centres.
ENZYME CATALYSIS
Numerous organic reactions are taking place in the body of animals and plants to maintain the life
process. These reactions being slow remarkably catalysed by the organic compounds known as
Enzymes. All enzymes have been found to be complex protein molecules. Thus : Enzymes are
protein molecules which act as catalysts to speed up organic reactions in living cells. The
catalysis brought about by enzymes is known as Enzyme Catalysis.
Each enzyme is produced in a particular living cell to catalyse a reaction occurring in that cell.
Many enzymes have been identified and obtained in pure crystalline state from the cells to which
they belong. However the first enzyme as prepared by synthesis in the laboratory in 1969.
Examples of Enzyme Catalysis
Some common examples of the biochemical reactions catalysed by enzymes are:
MECHANISM OF ENZYME CATALYSIS
The long chains of the enzyme (protein) molecules are coiled on each other to make a rigid
colloidal particle with cavities on its surface. These cavities which are of characteristic shape and
abound in active groups (NH2, COOH, SH, OH)] are termed Active centres. The molecules of
substrate which have complementary shape, fit into these cavities just as key fits into a lock
(Lock-and- Key theory). By virtue of the presence of active groups, the enzyme forms an
activated complex with the substrate which at once decomposes to yield the products. Thus the
substrate molecules enters the cavities, forms complex and reacts, and at once the products get out
of the cavities. Michaelis and Menten (1913) proposed the following mechanism for enzyme
catalysis (Fig. 21.11).

40
CHARACTERISTICS OF ENZYME CATALYSIS
In general, enzyme behave like inorganic heterogeneous catalysts. However, they are unique in
their efficiency and high degree of specificity. Some more important features of enzyme catalysis
are listed below.
(1) Enzymes are the most efficient catalysts known
The enzyme catalysed reactions proceed at fantastic high rates in comparison to those catalysed
by inorganic substances. Thus one molecule of an enzyme may transform one million molecules
of the substrate (reactant) per minute. Like inorganic catalysts, enzymes function by lowering the
activation energy or a reaction. For example, the activation energy of the decomposition of
hydrogen peroxide,
without a catalyst is 18 kcal/mole. With colloidal platinum (inorganic catalyst), the activation
energy is lowered by 11.7 kcal/mole. The enzyme catalase lowers the activation energy of the
same reaction to less than 2 kcal/mole.
(2) Enzyme catalysis is marked by absolute specificity
An enzyme as a rule catalyses just one reaction with a particular substance. For example, urease
(an enzyme derived from soya bean) catalyses the hydrolysis of urea and no other amide, not even
methylurea.

41
Enzyme catalysed reactions are often marked by absolute specificity. Thus where a compound can
exist in optically active isomers (identical in every respect except the space arrangement of
groups), an enzyme which can act on one of the isomers is unable to act on the other. For
example, the enzyme present in ordinary mould (Penicillium glaucum) when added to a (±)-
mixture of tartaric acid, decomposes the (+)-form only, leaving the (–)-form behind.
(2) The rate of enzyme catalysed reactions is maximum at the optimum temperature
The rate of an enzyme catalysed reaction is increased with the rise of temperature but up to a
certain point. Thereafter the enzyme is denatured as its protein structure is gradually destroyed.
Thus the rate of reaction drops and eventually becomes zero when the enzyme is completely
destroyed. The rate of an enzyme reaction with raising of temperature gives a bell-shaped curve.
The temperature at which the reaction rate is maximum is called the optimum temperature.

42
For example, the optimum temperatures, of enzyme reactions occurring in human body is 37°C
(98.6°F). At much higher temperatures, all physiological reactions will cease due to loss of
enzymatic activity. This is one reason why high body temperature (fever) is very dangerous.
(3) Rate of enzyme catalysed reactions is maximum at the optimum pH
The rate of an enzyme catalysed reaction varies with pH of the system. The rate passes through a
maximum at a particular pH, known as the optimum pH. The enzyme activity is lower at other
values of pH. Thus many enzymes of the body function best at pH of about 7.4, the pH of the
blood and body fluids.
(4) Enzymes are markedly inhibited or poisoned
The catalytic activity of an enzyme is often reduced (inhibited) or completely destroyed
(poisoned) by addition of other substances. These inhibitors or poisons interact with the active
functional groups on the enzyme surface. For example, heavy metal ions (Ag+, Hg2+) react with
the – SH groups of the enzyme and poison it.
The physiological activity of many drugs is related to their action as enzyme inhibitors in the
body. Thus sulpha drugs, penicillin, and streptomycin inhibit the action of several bacteria and
have proved effective in curing pneumonia, dysentery, cholera, and many other infectious
diseases.
(5) Catalytic activity of enzymes is greatly enhanced by the presence of Activators or
Coenzymes
Activators are metal ions Na+, Mn2+, CO2+, Cu2+, etc., which get weakly bonded to enzyme
molecules and promote their catalytic action. Thus it has been found that the addition of sodium
chloride (Na+) makes amylase catalytically very active. Often, a small non-protein (vitamin)

43
termed a coenzyme when present along with an enzyme, promotes the catalytic activity of the
latter.
Conclusion:
Solid surface materials have many applications. Some applications are harsher than others while
others rely on different attributes of solid surface materials to provide the performance benefit
needed for the application. Some of the more common applications are listed below. One
application area is Countertop applications, e.g. flat surfaces in commercial, residential, industrial,
and medical area sand cook top areas.
It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a
liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill
the entire volume available to it like a gas does.

44
Typical metals are good conductors of electricity while elements like silicon and germanium are
nonconductors at ordinary temperature. However, they exhibit appreciable conductivity upon
addition of impurities as arsenic and boron. The resulting materials are called semiconductors
(poor conductors).
Now let a boron atom be introduced in place of silicon atom in the crystal lattice. A boron atom
has only three valence electrons. It can form only three of the four bonds required for a perfect
lattice. Thus it is surrounded by seven electrons (one of Si) rather than eight. In this sense, there is
produced an electron vacancy or a ‘positive hole’ in the lattice. Another electron from the bond of
the adjacent Si atom moves into this hole, completing the four bonds on the B atom. This electron
also leaves a hole at its original site. In this way electrons move from atom to atom through the
crystal structure and the holes move in the opposite direction. Therefore the conductivity of the
material improves.
There are two types of semi-conductors-
 n-type semi-conductors
 p-type semi-conductors
Band Theory of Solids
A useful way to visualize the difference between conductors, insulators and semiconductors is
to plot the available energies for electrons in the materials. Instead of having discrete energies as
in the case of free atoms, the available energy states form bands. Crucial to the conduction
process is whether or not there are electrons in the conduction band. In insulators the electrons in
the valence band are separated by a large gap from the conduction band, in conductors like metals
the valence band overlaps the conduction band, and in semiconductors there is a small enough gap
between the valence and conduction bands that thermal or other excitations can bridge the gap.
With such a small gap, the presence of a small percentage of a doping material can increase
conductivity dramatically.
An important parameter in the band theory is the Fermi level, the top of the available electron
energy levels at low temperatures. The position of the Fermi level with the relation to the
conduction band is a crucial factor in determining electrical properties.
SEMICONDUCTORS

45
Energy Bands for Solids
Energy Bands Comments
Insulator Energy Bands
Most solid substances are insulators, and in terms of the band theory of solids this implies that
there is a large forbidden gap between the energies of the valence electrons and the energy at
which the electrons can move freely through the material (the conduction band).
Glass is an insulating material which may be transparent to visible light for reasons closely
correlated with its nature as an electrical insulator.The visible light photons do not have enough
quantum energy to bridge the band gap and get the electrons up to an available energy level in the
conduction band. The visible properties of glass can also give some insight into the effects of
"doping" on the properties of solids. A very small percentage of impurity atoms in the glass can
give it color by providing specific available energy levels which absorb certain colors of visible

46
light. The ruby mineral (corundum) is aluminum oxide with a small amount (about 0.05%) of
chromium which gives it its characteristic pink or red color by absorbing green and blue light.
While the doping of insulators can dramatically change their optical properties, it is not enough to
overcome the large band gap to make them good conductors of electricity. However, the doping
of semiconductors has a much more dramatic effect on their electrical conductivity and is the
basis for solid state electronics.
Semiconductor Energy Bands
For intrinsic semiconductors like silicon and germanium, the Fermi level is essentially halfway
between the valence and conduction bands. Although no conduction occurs at 0 K, at higher
temperatures a finite number of electrons can reach the conduction band and provide some
current. In doped semiconductors, extra energy levels are added.
The increase in conductivity with temperature can be modeled in terms of the Fermi function,
which allows one to calculate the population of the conduction band.
Conductor Energy Bands
In terms of the band theory of solids, metals are unique as good conductors of electricity. This
can be seen to be a result of their valence electrons being essentially free. In the band theory, this
is depicted as an overlap of the valence band and the conduction band so that at least a fraction of
the valence electrons can move through the material
Doping
Doping means the introduction of impurities into a semiconductor crystal to the defined
modification of conductivity. Two of the most important materials silicon can be doped with, are
boron (3 valence electrons = 3-valent) and phosphorus (5 valence electrons = 5-valent). Other
materials are aluminum, indium (3-valent) and arsenic, antimony (5-valent).

47
The dopant is integrated into the lattice structure of the semiconductor crystal, the number of
outer electrons define the type of doping. Elements with 3 valence electrons are used for p-type
doping, 5-valued elements for n-doping. The conductivity of a deliberately contaminated silicon
crystal can be increased by a factor of 106
.
n-doping
The 5-valent dopant has an outer electron more than the silicon atoms. Four outer electrons
combine with ever one silicon atom, while the fifth electron is free to move and serves as charge
carrier. This free electron requires much less energy to be lifted from the valence band into the
conduction band, than the electrons which cause the intrinsic conductivity of silicon. The dopant,
which emits an electron, is known as an electron donor (donare, lat. = to give).The dopants are
positively charged by the loss of negative charge carriers and are built into the lattice, only the
negative electrons can move. Doped semimetals whose conductivity is based on free (negative)
electrons are n-type or n-doped. Due to the higher number of free electrons those are also named
as majority charge carriers, while free mobile holes are named as the minority charge carriers.
n-doping with phosphorus
Arsenic is used as an alternative to phosphorus, because its diffusion coefficient is lower. This
means that the dopant diffusion during subsequent processes is less than that of phosphorus and
thus the arsenic remains at the position where it was introduced into the lattice originally.
p-doping
In contrast to the free electron due to doping with phosphorus, the 3-valent dopant effect is
exactly the opposite. The 3-valent dopants can catch an additional outer electron, thus leaving a
hole in the valence band of silicon atoms. Therefore the electrons in the valence band become
mobile. The holes move in the opposite direction to the movement of the electrons. The necessary
energy to lift an electron into the energy level of indium as a dopant, is only 1 % of the energy
which is needed to raise a valence electron of silicon into the conduction band.
With the inclusion of an electron, the dopant is negatively charged, such dopants are called
acceptors (acceptare, lat. = to add). Again, the dopant is fixed in the crystal lattice, only the
positive charges can move. Due to positive holes these semiconductors are called p-conductive or
p-doped. Analog to n-doped semiconductors, the holes are the majority charge carriers, free
electrons are the minority charge carriers.

48
p-doping with boron
Doped semiconductors are electrically neutral. The terms n- and p-type doped do only refer to the
majority charge carriers. Each positive or negative charge carrier belongs to a fixed negative or
positive charged dopant.
N- and p-doped semiconductors behave approximately equal in relation to the current flow. With
increasing amount of dopants, the number of charge carriers increases in the
semiconductor crystal. Here it requires only a very small amount of dopants. Weakly doped
silicon crystals contain only 1 impurity per 1,000,000,000 silicon atoms, high doped
semiconductors for example contain 1 foreign atom per 1,000 silicon atoms.
Electronic band structure in doped semiconductors
Through the introduction of a dopants with five outer electrons, in n-doped semiconductors there
is an electron in the crystal which is not bound and therefore can be moved with relatively little
energy into the conduction band. Thus in n-doped semiconductors one finds a donator energy
level near the conduction band edge, the band gap to overcome is very small.
Analog, through introduction of a 3-valent dopant in a semiconductor, a hole is available, which
may be already occupied at low-energy by an electron from the valence band of the silicon. For p-
doped semiconductors one finds an acceptor energy level near the valence band.

49
Semiconductor Doping Technology
Without exaggeration almost all of the basic MOSFET parameters are affected by the distribution
of dopants in the device. Doping refers to the process of introducing impurity atoms into a
semiconductor region in a controllable manner in order to define the electrical properties of this
region. The doping with donors and acceptors allows to modify the electron and hole
concentration in silicon in a very large range from 10 cm up to 10 cm . The carrier
concentration can also be varied spatially quite accurately which is used to produce pn-junctions
and built-in electric fields. All electronic and optical semiconductor devices incorporate dopants
as a crucial ingredient of their device structure.
Semiconductor Types
 An intrinsic semiconductor is a pure semiconductor having no impurities and equal
numbers of excited electrons and holes, i.e., n = p.
 A semiconductor in which doping has been introduced, thus changing the relative number
and type of free charge carriers, is called an extrinsic semiconductor
Fundamentals of Semiconductor Doping
The starting material used for the fabrication of semiconductor devices is monocrystalline silicon.
Silicon wafers are produced either by the Czochralski crystal pull method or by the floating-zone
crystal growth technique . Dopants are added to the silicon during the growth process in order to
set the resistivity of the wafer in the range from 1m cm - 30 cm . Defects in the silicon
crystal become much more severe for smaller device dimensions. Today, silicon wafers with a
surface plane are commonly used in semiconductor manufacturing , because the lowest defect
density at the Si/SiO2 interface can be achieved by thermal oxidation of silicon. In this work we
consider crystalline substrates of silicon, silicon-germanium, and germanium. At zero temperature
the conductivity in a pure semiconductor crystal is zero, because the vacant conduction band is
separated by an energy gap from the filled valence band. As the temperature is increased,
electrons are thermally excited from the valence band to the conduction band. Both the electrons
in the conduction band and the vacant orbitals or holes left behind in the valence band contribute
to the electrical conductivity.
Intrinsic Semiconductor:
An intrinsic semiconductor is one that contains a negligibly small amount of impurities compared
with thermally generated electrons and holes. The energy distribution of electrons in solids is
given by the Fermi-Dirac statistics . The probability that an electronic state at energy is
occupied by an electron in thermal equilibrium is given by the Fermi-Dirac distribution
(2.1)

50
In the Fermi-Dirac distribution function versus energy E-EFis presented for different
temperatures. The Fermi energy EF is the energy at which the probability of occupation by an
electron is exactly one-half. The probability of not finding an electron at energy , (1- EF) s the
probability of finding a hole there. At absolute zero temperature, = 0K, all the states below the
Fermi level are filled, f(E)=0 for E<, EF and all the states above the Fermi level are empty f(E)=0
for E> EF. At finite temperatures, continuous thermal agitation exists, which results in excitation
of electrons from the valence band to the conduction band and an equal number of holes are left in
the valence band. This process is balanced by recombination of the electrons in the conduction
band with holes in the valence band. The width of the transition from one to zero of the
probability distribution f(E)increases with the thermal energy KBT. Note that f(E)is symmetrical
around the Fermi level EF . For energies that are 3KBT above or below the Fermi energy, the
exponential term becomes larger than 20 or smaller then 0.05, respectively. The Fermi-Dirac
distribution can thus be approximated by simpler expressions according to
(2.2)
(2.3)
The electron and hole concentrations in an intrinsic semiconcuctor under thermal equilibrium
condition depend on the density of states N(E), that is, the number of allowed energy states per
unit energy per unit volume and is given by
(2.4)
The electron concentration N(E), in the conduction band is given by integrating the product of
the density of states and the probability of occupying an energy level f(E)according to
(2.5)
where ECis the energy at the bottom of the conduction band. Substituting and into and solving the
integral results in
(2.6)
where is the effective density of states in the conduction band . In a similar way the hole
concentration in the valence band can be obtained according to

51
(2.7)
where EVis the energy at the top of the valence band. Substituting (2.3) and (2.4) into (2.7) and
solving the integral yields
(2.8)
where NVis the effective density of states in the valence band
Figure : Density of states, probability distribution, and resulting electron and hole concentration
in an intrinsic semiconductor
For an intrinsic semiconductor the number of electrons in the conduction band is equal to the
number of holes in the valence band, that is, where is the intrinsic carrier concentration. In
Fig. the intrinsic electron and hole concentrations are obtained graphically from the product of
N(E) and f(E). The Fermi level for an intrinsic semiconductor is obtained by equating and which
yields
(2.9)
The intrinsic Fermi level Eg lies very close to the middle of the band gap Eg= Ec-Ev, because the
second term in is much smaller than the band gap at room temperature.
The intrinsic carrier concentration can be calculated from equations and (according

52
Donors and Acceptors
Figure : Schematic bond representation for n-type silicon doped with arsenic and p-type silicon
doped with boron.
In processing of modern semiconductor devices, doping refers to the process of introducing
impurity atoms into a semiconductor wafer by ion implantation. The purpose of semiconductor
doping is to define the number and the type of free charges in a crystal region that can be moved
by applying an external voltage. The electrical properties of a doped semiconductor can either be
described by using the ``bond'' model or the ``band'' model. When a semiconductor is doped with
impurities, the semiconductor becomes extrinsic and impurity energy levels are introduced. In
Fig. 2.4 the bond model is used to show that a tetravalent silicon atom (group IV element) can be
replaced either by a penta valent arsenic atom (group V) or a trivalent boron atom (group III).
When arsenic is added to silicon, an arsenic atom with its five valence electrons forms covalent
bonds with its four neighboring silicon atoms. The fifth valence electron has a relatively small
binding energy to its arsenic host atom and can become a conduction electron at moderate
temperature. The arsenic atom is called a donor and a donor-doped material is referred to as an n-
type semiconductor. Such a semiconductor has a defined surplus of electrons in the conduction
band which are the majority carriers, while the holes in the valence band, being few in number,
are the minority carriers. In a similar way, demonstrates the behavior, if a boron atom with its
three valence electrons replaces a silicon atom, an additional electron is ``accepted'' to form four
covalent bonds around the boron, and a hole carrier is thus created in the valence band. Boron is
referred to as an acceptor impurity and doping with boron forms a p-type semiconductor. The
dopant impurities used in controlling the conductivity type of a semiconductor usually have very
small ionization energies, and hence, these impurities are often referred to as shallow impurities.
The energy required to remove an electron from a shallow donor impurity such as arsenic,
phosphorus, and antimony can be estimated based on the Bohr model of the hydrogen atom . The
ionization energy of hydrogen is given by
(2.12)

53
where m0 is the free electron mass, q is the elementary charge, E0is the dielectric constant, and
is the Planck constant. The evaluation of results in for the ionization energy EHof the
free hydrogen atom. The hydrogen atom model may be modified to take into account the
dielectric constant of the semiconductor and the effective mass of an electron in the periodic
potential of the crystal. Thus, the donor ionization energy is obtained by replacing q2with
⁄ and moby the effective mass me according to
(2.13)
The Bohr radius of the donor can also be derived from the hydrogen atom model according to
(2.14)
The applicability to silicon and germanium is complicated due to the anisotropic effective mass of
the conduction electrons. To obtain a first order approximation of the impurity levels we use for
electrons in silicon and in germanium. Then the ionization energy for donors, measured from the
conduction band edge, can be calculated from , and is for silicon and for
germanium. Calculations using the correct anisotropic mass tensor predict for silicon
and for germanium. According to (, the Bohr radius for donors is in silicon and
in germanium, which is much larger than the Bohr radius of for the hydrogen atom.
Therefore, the average distance between the electron and the positive charged donor ion is also
much larger than the inter-atomic spacing of the semiconductor crystal. These large radii of the
donor orbits overlap at relatively low donor concentrations in the crystal and an ``impurity band''
is formed from the donor states, which enables electron hopping from donor to donor.
Shallow acceptor impurities in silicon and germanium are boron, aluminium, gallium, and indium.
An acceptor is ionized by thermal energy and a mobile hole is generated. On the energy band
diagram, an electron rises when it gains energy, whereas a hole sinks in gaining energy. The
calculation of the ionization energy for acceptors is similar to that for donors, it can be thought
that a hole is located in the central force field of a negative charged acceptor. The calculated
ionization energy for acceptors, measured from the valence band edge, is in silicon and
in germanium. The used approach for the calculation of the ionization energy is based
on a hydrogen-like model and the effective mass theory. This approach does not consider all
influences on the ionization energy, in particular it cannot predict the ionization energy for deep
impurities. However, the calculated values do predict the correct order of magnitude of the true
ionization energies for shallow impurities.
For shallow donors, it can be assumed that all donor impurities are ionized at room temperature.
A donor atom which has released an electron becomes a positive fixed charge. The electron
concentration under complete ionization is given by
(2.15)

54
where NDis the donor concentration. From (2.6) and (2.15), we obtain the distance of the Fermi
level from the conduction band edge according to
(2.16)
Under complete ionization, the hole concentration is equal to the acceptor concentration NA,
(2.17)
In a similar way we obtain the distance of the Fermi level from the top of the valence band,
(2.18)
Figure: Density of states, probability distribution, and carrier concentration in an n-type
semiconductor.
Equation states that the higher the donor concentration, the smaller the energy difference EC-ED,
which means that the Fermi level will move up closer to the conduction band edge. On the other
hand side, for a higher acceptor concentration, the Fermi level will move closer to the top of the
valence band according to . According to the implanted impurity type, either n- or p-type carriers
will dominate, but the product of and is equal to. Note that this result is equal to the intrinsic
case, Equation (2.10), which is called the mass action law. Fig. 2.5 shows the graphic procedure
for obtaining the carrier concentrations in an n-type semiconductor under thermal equilibrium.
If donor and acceptor impurities are introduced together, the impurity present in a higher
concentration determines the type of conductivity in the semiconductor. The Fermi level must
adjust itself to preserve charge neutrality. Overall charge neutrality requires that the negative
charges (electrons and ionized acceptors) must be equal to the total positive charges (holes and
ionized donors):
(2.19)

55
Combining (2.10) and (2.19) results in the equilibrium electron and hole concentrations in an n-
type semiconductor:
(2.20)
(2.21)
The index refers to the n-type semiconductor. In a similar way the holes and electrons can be
calculated in a p-type semiconductor:
(2.22)
(2.23)
The index pindicates the majority carrier type being holes.
(2.24)
(2.25)
Conclusion:
Electrical conductivity of solids may arise through the motion of electrons and positive holes
(electronic conductivity) or through the motions of ions (ionic conductivity). The conduction
through electrons is called n-type conduction and through positive holes is called p – types
conduction. Electrical conductivity of metal is due to motion of electrons and it increases with the
number of electrons available to participate in the conduction process. Pure ionic solids where
conduction can take place only through motion of ions are insulators. However, the presence of
defects in the crystal structure increases their conductivity

Characteristics of crystalline solid

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Was ist angesagt?

Was ist angesagt? (20)

Ähnlich wie Characteristics of crystalline solid

Ähnlich wie Characteristics of crystalline solid (20)

Kürzlich hochgeladen

Kürzlich hochgeladen (20)

Characteristics of crystalline solid