C O N D E N S E D M AT T E R
PHYSICS
INTRODUCTION
• Condensed matter physics is the field of physics that deals with
the macroscopic and microscopic physical properties of matter,
especially the solid and liquid phases which arise from
electromagnetic forces between atoms.
• Main Topics:
• Semiconductors (Diodes)
• Superconductors
• Crystals
REVIEW TOPICS
TYPES OF BONDS
• Ionic bond: forms when an electron transfers from one
atom to another
• Covalent bond: occurs when two or more atoms share
electrons
• Metallic bond: occur among metal atoms
• van der Waals bond: occurs due to the attraction of
charge-polarized molecules and is considerably weaker
than ionic or covalent bonds
Ionic Bonds
Ionic Bonds
• When an ionic bond is formed, electrons are transferred from one chemical unit to
another. Charged ions are produced as a consequence.
• Anions are negatively charged atoms that gain electrons as a consequence of the
creation of ionic bonds. Cations are positively charged atoms that have lost electrons
during the creation of ionic bonds.
• Metal ions act as cations most of the time, whereas non-metal ions act as anions due
to their electrical configuration.
• Electrostatic forces of attraction as well as repulsion between opposite charges as well
as similar charges, respectively, generate ionic bonds. The final product of ionic
bonding is known as an ionic compound.
• Ionic bonding is also seen in acid-base neutralization reactions. These molecules are
commonly referred to as salts.
Condition for Ionic Bonding
1. The charges of the two elements or ions engaged in the creation of the ionic bond must be
opposing. Metals as well as non-metals are the most prevalent kinds of elements that form
ionic bonding.
2. One of the atoms (metal) participating in the bond formation must have a low ionization or
electron affinity, allowing it to easily shed electrons as well as create positively charged ions
(cations).
3. The next atom should have a high ionization energy or electron affinity, allowing it to rapidly
gain electrons as well as produce negatively charged ions (anions).
4. The electronegativity difference between the two atoms engaged in the creation of an ionic
bond should be more than 1.7.
5. In order to be stable, the ionic molecule generated as a consequence of bonding must have
high lattice energy.
6. The bond’s ionic property should be greater than its covalent property.
Covalent Bonds
Covalent Bonds
• formed by the equal sharing of electrons from both participating atoms
• The pair of electrons participating in this type of bonding is called a shared pair or
bonding pair.
• are also called molecular bonds
• Elements having very high ionization energies are incapable of transferring electrons,
and elements having very low electron affinity cannot take up electrons. The atoms of
such elements tend to share their electrons with the atoms of other elements or with
other atoms of the same element in a way that both the atoms obtain octet
configuration in their respective valence shells, and thus achieve stability which is
similar to the atoms of noble gases.
Single Bond
• is formed when only one pair
of electrons is shared between
the two participating atoms
• is represented by one dash (-)
• has a smaller density and is
weaker than a double and
triple bond, but it is the most
stable
Double Bond
• is formed when two pairs of
electrons are shared between
the two participating atoms
• is represented by two dashes
(=)
Triple Bond
• is formed when three pairs of
electrons are shared between
the two participating atoms
• represented by three dashes
(≡) and are the least stable
type of covalent bonds
Polar Covalent Bond
• exists where the unequal
sharing of electrons occurs due
to the difference in the
electronegativity (0.5 to 0.19) of
combining atoms
• more electronegative atoms will
have a stronger pull for
electrons and as a result, the
shared pair of electrons will be
closer to that atom
Nonpolar Covalent Bond
• formed whenever there is an
equal share of electrons
between atoms
• the electronegativity difference
between two atoms is zero
• occurs wherever the combining
atoms have similar electron
affinity (diatomic elements)
Coordinate Bond
• aka dative covalent bond
• a type in which both electrons
come from the same atom
BAND THEORY OF SOLIDS
• In gaseous substances, the arrangement of molecules is spread apart and is not
so close to each other. In liquids, the molecules are closer to each other.
• But in solids, the molecules are closely arranged together, and due to this,
atoms of molecules tend to move into the orbitals of neighbouring atoms.
Hence, the electron orbitals overlap when atoms come together.
• In solids, several bands of energy levels are formed due to the intermixing of
atoms in solids. We call these sets of energy levels energy bands.
E n e r g y B a n d Ty p e s
Valence Band
• The electrons in the outermost shell are known as valence electrons. These valence electrons contain a
series of energy levels and form an energy band known as the valence band. The valence band has the
highest occupied energy.
Conduction Band
• The valence electrons are not tightly held to the nucleus due to which a few of these valence electrons
leave the outermost orbit even at room temperature and become free electrons. The free electrons conduct
current in conductors and are therefore known as conduction electrons. The conduction band is one that
contains conduction electrons and has the lowest occupied energy levels.
Forbidden Energy Gap
• The gap between the valence band and the conduction band is referred to as the forbidden gap. As the
name suggests, the forbidden gap doesn’t have any energy and no electrons stay in this band. If the
forbidden energy gap is greater, then the valence band electrons are tightly bound or firmly attached to the
nucleus. We require some amount of external energy that is equal to the forbidden energy gap.
Ty p e s o f M a t e r i a l s
Conductors
• allow an electric current to flow through them
• have less than 3 valence electrons
• Examples: Gold, Aluminium, Silver, Copper
• There is no forbidden gap between the valence band and conduction band which results in the
overlapping of both bands. The number of free electrons available at room temperature is large.
Insulators
• do not allow electricity to pass through them
• have high resistivity and very low conductivity
• have more than 5 valence electrons
• Examples: Glass and wood
• The energy gap in the insulator is very high, up to 7 eV. The material cannot conduct because
the movement of the electrons from the valence band to the conduction band is not possible.
Ty p e s o f M a t e r i a l s
Semiconductors
• electrical properties lie in between semiconductors and insulators
• have four valence electrons
• Examples: Germanium and Silicon
• The energy band diagram of semiconductors is shown where the conduction
band is empty and the valence band is completely filled but the forbidden gap
between the two bands is very small that is about 1 eV.
• Germanium = 0.72 eV
• Silicon = 1.1 eV
• Thus, the semiconductor requires small conductivity.
S E M I C O N D U C TO R S
SEMICONDUCTOR AND DOPING
• pure or intrinsic semiconductor = a semiconducting material that is
composed only of a single type of atom, such as a silicon atom
• impurities = added into a semiconductor to actually increase the electric
conductivity
• doping = the process of adding an impurity into the semiconductor to increase
its ability to conduct electricity
• doped semiconductors = impure semiconductor
• n-type semiconductor
• p-type semiconductor
N - Ty p e S e m i c o n d u c t o r
• produced by adding pentavalent atoms to silicon
• pentavalent atoms (donor atoms)
• group V elements in the periodic table like Arsenic
(As), Antimony (Sb), and Phosphorous (P)
• have 5 valence electrons that can form covalent
bonds with the 4 valence electrons that silicon
atoms have
• the extra valence electron present when the two
atoms bond is free to participate in conduction
• therefore, more electrons are added to the
conduction band and hence increase the number of
electrons present
P - Ty p e S e m i c o n d u c t o r
• produced by adding trivalent atoms to silicon
• trivalent atoms (acceptor atoms)
• group III elements in the periodic table like Boron
(B), Indium (In), and Aluminum (Al)
• have 3 valence electrons with which to interact with
silicon atoms
• net result is a hole, as not enough electrons are
present to form the 4 covalent bonds surrounding
the atoms
• the number of electrons trapped in bonds is higher,
thus effectively increasing the number of holes
P r o p e r t i e s o f S e m i c o n d u c t o r Ty p e s
Dopant
Bonds
Majority Carriers
Minority Carriers
N-Type
Group V
P-Type
Group III
Excess Electrons
Electrons
Holes
Missing Electrons
Holes
Electrons
The Diode
• created by joining a p-type semiconductor to an n-type semiconductor
• the junction between these materials is called a PN junction
• When a PN junction is formed, electrons from the conduction band of the n-type
material diffuse to the p-side, where they combine with holes in the valence band.
• This migration of charge leaves positive ionized donor ions on the n-side and negative
ionized acceptor ions on the p-side, producing a narrow double layer of charge at the
PN junction called the depletion region.
• The electric field associated with the depletion layer prevents further diffusion.
The Diode
(a) Representation of a p-n junction. (b) A comparison
of the energy bands of p-type and n-type silicon prior
to equilibrium.
Near the junction, electrons from the n-type material
can fall into holes in the p-type material, releasing
energy by a process called recombination as the
electron drops from the conduction band to fill the
hole in the valence band. This process reaches an
equilibrium and no net current flows.
The Diode
At equilibrium, (a) excess charge resides near the
interface and the net current is zero, and (b) the
potential energy difference for electrons (in light blue)
prevents further diffusion of electrons into the p-side.
Diode Biasing
There are two operating regions and three possible “biasing” conditions for the standard Junction
Diode and these are:
1. Zero Bias – No external voltage potential is applied to the PN junction diode, and a
natural potential barrier (threshold voltage) is developed across the depletion layer. This is
approximately 0.5V to 0.7V for silicon diodes and approximately 0.3V for germanium
diodes.
2. Reverse Bias – The voltage potential is connected negative, (-ve) to the P-type material
and positive, (+ve) to the N-type material across the diode which has the effect of
increasing the width of the depletion region.
3. Forward Bias – The voltage potential is connected positive, (+ve) to the P-type material
and negative, (-ve) to the N-type material across the diode which has the effect of
decreasing the width of the depletion region.
Diode Biasing
Ty p e s o f S e m i c o n d u c t o r D i o d e
• LED
• Zener diode
• Rectifier diode
• Tunnel diode
• Variable capacitance diode
• Photodiode
• Switching diode
• Gunn diode, etc.
Applications of
Semiconductor Diode
• Rectifier diode which is used for the rectification of alternating current.
• Gunn diode which is one of the components of high-frequency electronics.
• Zener diodes are used for the stabilisation of current and voltage in electronic
systems.
• Photodiode works as a photo-detector.
• Switching diode which is used for fast switching requirements.
• A tunnel diode is a special diode that is used in the negative dynamic resistance
region.
• LED is used for emitting an infrared light spectrum.
• A variable capacitance diode is used when a voltage is applied in reverse
biased condition.
S U P E R C O N D U C TO R S
SUPERCONDUCTORS
• defined as a substance that offers no resistance to electric
current when it becomes colder than a critical
temperature
• popular examples of superconductors are aluminum,
magnesium diboride, niobium, copper oxide, yttrium
barium, and iron pnictides
• Superconductors have a wide variety of everyday
applications, from MRI machines to super-fast maglev
trains that use magnets to levitate the trains off the track
to reduce friction.
• Researchers are now trying to find and develop
superconductors that work at higher temperatures, which
would revolutionize energy transport and storage.
History of Superconductivity
• 1911: Dutch physicist Heike Kamerlingh Onnes was studying the electrical
properties of mercury in his laboratory at Leiden University in The Netherlands
when he found that the electrical resistance in the mercury completely vanished
when he dropped the temperature to below 4.2 Kelvin — that's just 4.2 degrees
Celsius (7.56 degrees Fahrenheit) above absolute zero.
• To confirm this result, Onnes applied an electric current to a sample of
supercooled mercury, then disconnected the battery. He found that the electric
current persisted in the mercury without decreasing, confirming the lack of
electrical resistance and opening the door to future applications of
superconductivity.
History of Superconductivity
• 1933: Physicists Walther Meissner and Robert Ochsenfeld discovered that
superconductors "expel" any nearby magnetic fields, meaning weak magnetic
fields can't penetrate far inside a superconductor. This phenomenon is called
the Meissner effect.
• 1950: Theoretical physicists Lev Landau and Vitaly Ginzburg published a theory
of how superconductors work. While successful in predicting the properties of
superconductors, their theory was "macroscopic," meaning it focused on the
large-scale behaviours of superconductors while remaining ignorant of what
was going on at a microscopic level.
History of Superconductivity
• 1957: Physicists John Bardeen, Leon N. Cooper and Robert Schrieffer
developed a complete, microscopic theory of superconductivity. To create
electrical resistance, the electrons in a metal need to be free to bounce around.
But when the electrons inside a metal become incredibly cold, they can pair up,
preventing them from bouncing around. These electron pairs, called Cooper
pairs, are very stable at low temperatures, and with no electrons "free" to
bounce around, the electrical resistance disappears. Bardeen, Cooper and
Schrieffer put these pieces together to form their theory, known as BCS theory,
which they published in the journal Physical Review Letters.
C r i t i c a l Te m p e r a t u r e f o r
Superconductors
• is the temperature at which the electrical resistivity of metal falls to zero
• most materials show superconducting phase transitions at low temperatures
• until 1986: highest critical temperature was about 23K
• 2020: a room-temperature superconductor made from carbon, hydrogen, and
sulfur under pressures of around 270 GPa was identified to possess the highest
temperature at which any material has shown superconductivity
Material
Critical Temperature (TC) in K
Aluminum
1.2 K
Indium
3.4 K
Mercury
4.2 K
Lead
7.2 K
Superconductor Working
• When the temperature of the metal decreases below the critical temperature, the
electrons in the metal form bonds known as Cooper pairs. The electrons can’t offer any
electrical resistance when bonded like this—allowing electricity to flow through the
metal smoothly.
• Nevertheless, this only works at low temperatures. When the metal gets warm, the
electrons gain enough energy to break the bonds of the Cooper pairs and go back to
offering resistance.
Cooper Pair Formation
S u p e r c o n d u c t o r Ty p e s
Type I Superconductors
• consists of fundamental conductive elements that are used in everything from
electrical wiring to computer microchips
• have critical temperatures between 0.000325K and 7.8K
• few need tremendous amounts of pressure in order to achieve the
superconductive state
• example: sulfur which needs a pressure of 9.3 million atmospheres (9.4 x 1011
Pa) and a temperature of 17K to reach superconductivity
• approximately half of the elements in the periodic table are superconductive
S u p e r c o n d u c t o r Ty p e s
Type II Superconductors
• comprises metallic compounds such as lead or copper
• achieve a superconductive state at much higher temperatures compared to type
I superconductors
• can be penetrated by a magnetic field, whereas type I cannot
S u p e r c o n d u c t o r Ty p e s
Superconductor Properties
Infinite Conductivity
• A material has zero resistance in the superconducting state. When the
temperature of the material is below the critical temperature, its resistance
abruptly lowers to zero. For example, Mercury shows zero resistance below 4K.
Critical Temperature
• The critical temperature is the temperature below which the material changes
from conductors to superconductors. The critical temperature is also called
transition temperature. The transition from conductors to superconductors is
sudden and complete.
Superconductor Properties
Magnetic Field Expulsion
• When a material transitions from the normal to the superconducting state, it
expels magnetic fields from its interior; this is called the Meissner effect.
Critical Magnetic Field
• The value of the magnetic field beyond which the superconductors return to
conducting state, is known as the critical magnetic field. The value of the critical
magnetic field is inversely proportional to the temperature.
Superconductor Applications
• Superconductors are used in particle accelerators, generators, transportation,
computing, electric motors, medical, power transmission, etc.
• Superconductors are primarily employed for creating powerful electromagnets
in MRI scanners.
• These conductors are used to transmit power for long distances.
• They are used in memory or storage elements.
CRYSTALS
C R Y S TA L S
• a crystal is a form of matter in which the atoms, molecules, or ions are arranged
in a highly ordered three-dimensional lattice
• also called crystalline solids because most crystals are solid
• however, liquid crystals also exist
• liquid crystal is a thermodynamic stable phase characterized by anisotropy
of properties without the existence of a three-dimensional crystal lattice,
generally lying in the temperature range between the solid and isotropic
liquid phase, hence the term mesophase
• the word “crystal” comes from the Greek word krustallos, which means both
“rock crystal” and “ice”
• the study of crystals is named crystallography
Examples of Crystals
• diamond (crystal carbon)
• salt (sodium chloride crystals)
• quartz (silicon dioxide crystals)
• snowflakes (water ice crystals)
• many gems are crystals, including
emerald, citrine, ruby, and sapphire
• other materials look like crystals but
don’t consist entirely of ordered lattices
• Example: polycrystals (like ice,
many metals, and ceramics) form
when crystals fuse together
The crystalline structure of quartz allows it to cleave into smooth planes that refract light, making it suitable for jewelry.
Silicon, the main element in quartz, also forms crystals in its pure form, and these crystals form the basis for the
worldwide semiconductor electronics industry.
14 Bravais Lattices
Bravais lattices are named
for crystallographer and
physicist Auguste Bravais,
who described threedimensional arrays in
terms of points.
How Crystals Form
• Crystals grow via a process called crystallization.
• Basically, one particle bonds to another and so on until a structure forms.
• The beginning of the process is called nucleation.
• Most crystals people grow form from a liquid solution. As the solution cools or
the liquid evaporates, the particles draw closer together. Eventually, chemical
bonds form.
• Other crystals grow as solids deposited from the gas phase or from a melted
pure solid (e.g., bismuth).
What is Not a Crystal?
• Despite the names, leaded crystal and crystal glass aren’t actually crystals.
• They are glass, which is an amorphous solid, that has been cut to resemble
the sharp faces of crystals.
• Many gemstones are crystals, but not all of them.
• For example, turquoise is cryptocrystalline.
• This means it contains many tiny crystals, but is not crystalline overall.
• Similarly, pearl forms from concentric layers of crystalline calcium carbonate,
but the gem is not a single crystal.
• Any material that has to be cut to look like a crystal isn’t usually a crystal.
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