Module 7 Notes: Other Electronic Materials

Dielectric Materials and Insulation

The capacitance equation for a parallel plate capacitor with free space as an insulator is given by: $C = \frac{\varepsilon_0 A}{d}$ Where:
- $\varepsilon_0$ is the absolute permittivity.
- $A$ is the plate area.
- $d$ is the separation between the plates.
If a material medium is present, the capacitance increases by a factor of $\varepsilon_r$ , known as the dielectric constant or relative permittivity.
The increase in capacitance results from the polarization of the medium, where positive and negative charges are displaced.
Opposite surfaces of the dielectric medium acquire opposite surface charge densities, related to the amount of polarization.
$Electric Dipole$ Moment:
- Defined as $p = Qa$ , where $Q$ is the charge and $a$ is the separation distance.
- It gives rise to an electric field and interacts with external electric fields.
Relative permittivity is frequency dependent.
Practical capacitors exhibit losses, similar to $I^2R$ losses in resistors.
Power dissipation depends on frequency.
A defining property of a dielectric medium is its insulating behavior or low conductivity.
Dielectric materials insulate current-carrying conductors.
- Air cannot be used as insulation between high-voltage conductors.
Dielectric Breakdown:
- Occurs when the electric field exceeds a critical field called the dielectric strength.
- Results in a large discharge current through the dielectric.
- A significant cause of utility generator failures.

Matter Polarization and Relative Permittivity

Parallel Plate Capacitor with Vacuum:
- Capacitance $C0$ is defined as $C0 = \frac{Q0}{V}$ , where $Q0$ is the charge and $V$ is the voltage.
- The electric field $E = -\frac{dV}{dx}$ , simplifies to $E = \frac{V}{d}$ between the plates.
Dielectric Slab Insertion:
- The charge on the electrodes increases from $Q_0$ to $Q$ .
- The relative permittivity $\epsilonr$ is defined as $\epsilonr = \frac{C}{C0} = \frac{Q}{Q0}$ .
The electric field remains unchanged if the insulator fills the entire space between the plates.

Dipole Moment and Electronic Polarization

Electric Dipole Moment: $\vec{p} = Q\vec{a}$ , where $Q$ is the charge and $\vec{a}$ is the vector from negative to positive charge.
Neutral Atom: Has zero net charge, and the center of negative charge coincides with the positive nuclear charge.
Induced Dipole Moment:
- Occurs when an atom is placed in an external electric field.
- Electrons are displaced, leading to charge separation.
- Atom is polarized if it possesses an effective dipole moment.
Polarizability: $\vec{P}_{induced} = \alpha \vec{E}$ , where $\alpha$ is the polarizability of the atom.
Electronic Polarization: Involves displacement of electrons, denoted as $\alpha_e$ .
The Coulombic attraction between the electrons and nuclear charge “pulls in” the electrons and tries to restore the electron cloud back to its original position.
In equilibrium, the net force on the negative charge center is zero: $ZeE = \beta x$ , where $\beta$ is a constant.
The induced electronic dipole moment $pe$ is given by: $pe = (Ze)x = \frac{Z^2e^2}{\beta}E$
Electronic polarizability:
$\alpha = \frac{Z^2e^2}{\beta} = 4 \pi \varepsilon0 r0^3$
Where $r_0$ is the atomic radius.
After removing the electric field, the restoring force is $F_r = -\beta x$ .
The equation of motion is $-\beta x = Zm_e \frac{d^2x}{dt^2}$ .
The displacement at any time is sinusoidal: $x(t) = x0 \cos(\omega t)$ , where $\omega = \sqrt{\frac{\beta}{Zme}}$ .
Electronic polarization resonance frequency is $\omega_0$ .
The frequency $\omega_0$ of the electronic cloud about the nucleus is called electronic polarization resonance frequency.
Accelerating charge radiates electromagnetic energy, causing oscillations to die out with time.
Final expression for $\alpha$ :
$\alpha = \frac{Ze^2}{m_e \omega^2}$

Supercapacitor

Supercapacitors have a very high power density compared to common capacitors (about 100 times greater) and are also known as Electric Double Layer Capacitors (EDLC) or Ultracapacitors.
Capacitance range: 100 Farad to 5 KiloFarad.
Construction:
- Two metal foils coated with an electrode material (e.g., activated carbon).
- An ion-permeable membrane (separator) insulates the electrodes.
- Rolled or folded into cylindrical or rectangular shape and packed in aluminum can.
Working:
- No conventional dielectric.
- Plates soaked in an electrolyte and separated by a thin insulator.
- An opposite charge forms on both sides of the separator, forming an electric double layer.
Electric Double Layer:
- Electrochemical capacitor with two electrodes and a separator.
- Applying voltage results in an electric double layer.
Features:
- Stores a high amount of energy.
- High capacitance, charge and discharge rates, cycle efficiency (95%).
- Low toxicity.
Applications:
- Start-up mechanism for automobiles, diesel engine start-up in submarines & tanks.
- Backup power system in missiles.
- Power source for laptops, flash in cameras.
- Voltage stabilizer.
Super Capacitor Buses:
- Powered via energy stored in large onboard super-capacitors.
- Connects to stationary electrical installation at bus stops for charging.
Advantages:
- High energy storage, wide working temperature (-40°C to 60°C), eco-friendly.
- Quick charging time, maximum life cycle, high cycle efficiency (95%).
- High specific power up to 17 kW/kg, extremely low internal resistance, safe.
Disadvantages:
- Low energy density.
- Voltage varies with the energy stored.
- High self-discharge rate.
- Requires expert electronic control.
- Cannot be used in AC and high-frequency circuits.
- High cost.
Conclusion:
- Suitable for high power or energy storage requirements.
- Widely usable due to long life & short charging time.
- Limitations include high cost, self-discharge, packaging problems, etc.

Carbon Nanotubes

Introduction:
- CNT is a tubular form of carbon with diameter as small as 1nm. Length: few nm to microns.
- CNT is equivalent to a two dimensional graphene sheet rolled into a tube.
- A CNT is characterized by its Chiral Vector: $Ch = n \hat{a}1 + m \hat{a}2, \theta$ → Chiral Angle with respect to the zigzag axis.
Structure Types:
- Armchair: $(n,m) = (5,5), \theta = 30^\circ$
- Zig Zag: $(n,m) = (9,0), \theta = 0^\circ$
- Chiral: (n,m) = (10,5), 0^\circ < \theta < 30^\circ
Reasons for Formation:
- Graphite (Ambient conditions): sp2 hybridization: planar
- Diamond (High temperature and pressure): sp3 hybridization: cubic
- Nanotube/Fullerene (certain growth conditions): sp2 + sp3 character: cylindrical
- Finite size of graphene layer has dangling bonds.
- Eliminates dangling bonds Nanotube formation.
  - Total Energy Increases Strain Energy decreases.
Types of CNTs:
- Single Wall CNT (SWCNT)
- Multiple Wall CNT (MWCNT)
- Can be metallic or semiconducting depending on their geometry.
CNT Properties:
- The strongest and most flexible molecular material because of C-C covalent bonding and seamless hexagonal network architecture.
- Young's modulus of over 1 TPa vs 70 GPa for Aluminum, 700 GPA for C-fiber.
  - strength to weight ratio 500 time > for Al; similar improvements over steel and titanium; one order of magnitude improvement over graphite/epoxy.
- Maximum strain ~10% much higher than any material.
- Thermal conductivity ~3000 W/mK in the axial direction with small values in the radial direction.
Electrical conductivity six orders of magnitude higher than copper.
Can be metallic or semiconducting depending on chirality.
'tunable' bandgap.
electronic properties can be tailored through application of external magnetic field, application of mechanical deformation…
Very high current carrying capacity.
Excellent field emitter; high aspect ratio and small tip radius of curvature are ideal for field emission.
Implications for electronics:
- Carrier transport is 1-D.
- All chemical bonds are satisfied  CNT Electronics not bound to use SiO2 as an insulator.
- High mechanical and thermal stability and resistance to electromigration  Current densities upto109 A/cm2 can be sustained.
- Diameter controlled by chemistry, not fabrication.
- Both active devices and interconnects can be made from semiconducting and metallic nanotubes.
Nanotube Growth Methods:
- Arc Discharge & Laser Ablation:
  - Involve condensation of C-atoms generated from evaporation of solid carbon sources.
  - Temperature ~ 3000- 4000K, close to melting point of graphite.
  - Both produce high-quality SWNTs and MWNTs.
  - MWNT: 10’s of m long, very straight & have 5-30nm diameter.
  - SWNT: needs metal catalyst (Ni,Co etc.).
  - Produced in form of ropes consisting of 10’s of individual nanotubes close packed in hexagonal crystals.
- Chemical Vapor Deposition:
  - Hydrocarbon + Fe/Co/Ni catalyst at 550-750°C.
  - CNT Steps: Dissociation of hydrocarbon, Dissolution and saturation of C atoms in metal nanoparticles, Precipitation of Carbon.
  - Choice of catalyst material?
  - Base Growth Mode or Tip Growth Mode?
  - Metal support interactions.
Growth Mechanisms:
- Electronic and Mechanical Properties are closely related to the atomic structure of the tube.
- Mechanism should account for the experimental facts: metal catalyst necessary for SWNT growth, size dependent on the composition of catalyst, growth temperature etc.
- MWNT Growth Mechanism: - Open or close ended? Lip Lip Interaction Models
- SWNT Growth Mechanism: - Catalytic Growth Mechanism
- Simulations & Observations  No! Spontaneous closure at experimental temperatures of 2000K to 3000K. Closure reduces reactivity.
Catalytic SWNT Growth Mechanism Catalytic SWNT Growth Mechanism:
- Transition metal surface decorated fullerene nucleates SWNT growth around periphery.
- Catalyst atom chemisorbed onto the open edge. Catalyst keeps the tube open by scooting around the open edge, ensuring and pentagons and heptagons do not form.
Phenomenal mechanical properties and unique electronic properties make them both interesting as well as potentially useful in future technologies.
Significant improvement over current state of electronics can be achieved if controllable growth is achieved.
Growth conditions play a significant role in deciding the electronic and mechanical properties of CNTs.
Growth Mechanisms yet to be fully established.

Ferroelectrics

Non-conducting materials may have a net electrostatic polarisation induced by an external electric field.
Where the affects upon observable properties such as elastic, optical and thermal behaviour is large, these materials are termed ferroelectrics.
The local alignment of dipoles can exist over any length scale.
Different regions may exist with different polarisation orientations, known as domains.
In contrast with magnetism, domain walls are abrupt.
External field:
- When an electric field is applied, dipoles will switch direction is the field is strong enough.
- The dipoles are polarized by the applied field.
- Domain walls move.
Polarisation vs. E-field:
- If we apply a small electric field, such that it is not able to switch domain alignments, then the material will behave as a normal dielectric: PE.
- As E is increased, we start to flip domains and rapidly increase P.
- When all domains are switched, we reach saturation.
- The value at zero field is termed the remnant polarisation.
The value of P extrapolated back from the saturation limit is the spontaneous polarisation.
Reversal of the field will eventually remove all polarisation.The field required is the coercive field.
The essential feature of a ferroelectric is not that there is a spontaneous polarisation, but that the spontaneous polarisation can be reversed by the application of an electric field.
Curie temperature:
- Above a critical temperature the spontaneous polarisation will be lost due to one of two effects:
  - A change of structure such that there is a single minimum in the energy mid-way between sites.
  - The rate that the small ions hop is so high that on average there is no net polarisation.
- This temperature is termed the Curie temperature, Tc, in light of the analogy with the transition temperature between ferromagnetism and paramagnetism.
- Above the Curie temperature, ferroelectrics behave as nonpolar dielectrics, sometimes termed a paraelectric phase.
- Some ferroelectrics do not have a Curie temperature.
Temperature effects:
- In addition to the change in spontaneous polarization, temperature affects the dielectric constant of the material, normally defined as the rate of change of dielectric displacement with electric field.
In some ferroelectrics, the temperature dependence of  can be reasonably accurately represented by the Curie-Weiss law: • = 0+C/(T-T0)
- $C$ is the Curie constant.
- $T0$ is the Curie-Weiss temperature, which in general differs from the Curie temperature (Tc).
- Close to T0  becomes very large.
- In the model, we have picked out pairs of atoms, and attributed point dipoles associated with the combination of their charges and separations.
- More realistically, each unit cell carries a dipole moment: d = ∫∫∫(r).r.dv  0
  - (r) is the charge density (inc. ions), the integral is with respect to an arbitrary origin, and d is independent of its choice.
  - The definition allows the polarisation to be as influenced by distortions in the electron density as it is by displacements in the point-like ion sites.
Crystal classes with a unique polar axis are called polar.
- The spontaneous polarisation can be seen in terms of its change with temperature.
- The pyroelectric effect.
- The 10 polar classes are therefore sometimes referred to as the pyroelectric classes.
- Ferroelectric crystals must belong to the pyroelectric classes.
- But Ferroelectrics must exhibit the hysteresis, so we define ferroelectric crystals as pyroelectric crystals that exhibit reversible polarisation.
Antiferroelectrics:
- If the free energy of an antipolar phase is comparable to the polar state then the material is termed antiferroelectric.
- If a material exhibits ferroelectric effects in one polar direction, and antiferroelectric effects perpendicular, it may be termed ferrielectric.
Perovskites:
- Perovskite is a naturally occurring mineral with chemical formula CaTiO3.
- This is a prototype for many ABO3 materials which are very important in ferroelectrics.
- These materials may be envisaged by consideration of a non-polar, cubic basic building block…
- Below the Curie temperature, these crystals undergo symmetry lowering distortions. We’ll initially focus up the distortions of BaTiO3.
- There are three phase transitions in order of decreasing temperature: 120oC, 5oC, and -90oC.
  - From 120oC down to ~5oC, there is a distortion to a tetragonal phase.
  - All of the cube directions can undergo this type of distortion: this leads to complexity in domain formation.
PbTiO3 internal structure • X-ray and neutron scattering yield the internal structure:
- a=3.904Å, c=4.150Å, so that c/a=1.063.
- Taking the Pb site as the origin, the displacements are • zTi=+0.040 • zOI=+0.112 • zOII=+0.112
  - Here OI are the polar O-sites, and OII are the equatorial.

Superconductors

Superconductors are materials with almost zero resistivity, behaving as diamagnetic below the superconducting transition temperature.
Superconductivity is the flow of electric current without resistance in certain materials at temperatures near absolute zero.
Superconductivity was first discovered in 1911 by Heike Kammerlingh Onnes.
At 4.2K, the Electrical Resistance (opposition of a material to the flow of electrical current through it) Vanished, Meaning Extremely Good Conduction of Electricity-Superconductivity.
General Properties of Superconductors:
- Electrical resistance: Virtually zero electrical resistance.
- Effect of impurities: When impurities are added to superconducting elements, the superconductivity is not loss but the T is lowered.
  *Effects of pressures and stress: certain materials exhibits superconductivity on increasing the pressure in superconductors, the increase in stress results in increase of the T value.
Isotope effect:
- The critical or transition temperature Tc value of a superconductors is found to vary with its isotopic mass. i.e. "the transition temperature is inversely proportional to the square root of isotopic mass of single superconductors."
  $T α 1/ 2√M$
Magnetic field effect:
- If Strong magnetic field applied to a superconductors below its T, the superconductors undergoes a transition from superconducting state to normal state.
Meissner effect: The complete expulsion of all magnetic field by a superconducting material is called "Meissner effect"
Important Factors to define a Superconducting State:
- The superconducting state is defined by three very important factors: critical temperature (Tc), critical field (Hc), critical current density (Jc).
- Each of these parameters is very dependant on the other two properties present.
CRITICAL TEMPERATURE:
- The temperature at which a material electrical resistivity drops to absolute zero is called the Critical Temperature or Transition Temperature.
- Below critical temperature, material is said to be in superconducting and above this it is said to in normal state.
  - Below this temperature the superconductors also exhibits a variety of several astonishing magnetic and electrical properties.
Critical magnetic field (He) Above this value of an externally applied magnetic field a superconductor becomes non-superconducting. This minimum magnetic fields required to destroy the superconducting state is called the critical magnetic field H
- Electrical Resistivity Vs Temperature Plot for Superconductors and Normal Metals: from the figure it can be seen that the electrical resistivity of normal metal decreases steadily as the temperature is decreased and reaches a low value at OK called Residual Resistivity.
  $H = H [1-(T/Tc)²]$
TYPES OF SUPERCONDUCTORS:
- TYPE I: Soft superconductors are those which can tolerate impurities without affecting the superconducting properties.
  - Also called SOFT SUPERCONDUCTORS.
  - Only one critical field exists for these superconductors.
- Critical field value is very low.
  - Exhibits perfect and complete Meissner effect.
  - The current flows through the surface only.
  - These materials have limited technical applications because of very low field strength value
- TYPE II: Hard superconductors are those which cannot tolerate impurities, i.e., the impurity affects the superconducting property.
  - Also called HARD SUPERCONDUCTORS.
  - Two critical fields Hc1(lower) & Hc2(upper) for these.
  - Critical field value is very high.
  - Don't exhibit perfect and complete Meissner effect.
  - It is found that current flows throughout the material.
  - These materials have wider technology of very high field strength value.
HIGH Te SUPERCONDUCTORS:
- Low Te Superconductors Superconductors that require liquid helium coolant are called low temperature superconductors.
- Liquid helium temperature is 4.2K above absolute zero.
- High Te superconductors Superconductors having their Te values above the temperature of liquid nitrogen (77K) are called the high temperature superconductors.
MAGNETIC LEVITATION:
- Magnetic levitation, maglev, or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields.
- Magnetic force is used to counteract the effects of the gravitational and any other accelerations. The two primary issues involved in magnetic levitation are lifting force and stability.
- Maglev trains; In EMS,the electromagnets installed on the train bogies attract the iron rails. The magnets wrap around the iron & the attractive upward force is lift the train.
  - In EDS levitation is achieved by creating a repulsive force between the train and guide ways.
JOSEPHSON EFFECT: Two superconductors separated by a very thin strip of an installer forms a Josephson junction.
- The wave nature of moving particles make electrons to tunnel through the barrier.
- As a consequence of tunneling of electrons across the insulator there is net current across the junction. This is called d.c.josephson effect. The current flows even in absence of potential difference.
- The magnitude of current depends on the thickness of the insulators, the nature of the materials and the temperature. On the other hand when potential difference V is applied between the two sides of the junction there will be an oscillation of tunneling current with angular frequency v-2eV/h. This is called a.c.josephson effect.
APPLICATION OF SUPERCONDUCTORS:
- The production of sensitive magnetometers based on SQUIDS A SQUID (Superconducting Quantum Interference Device) is the most sensitive type of detector known to science. Consisting of a superconducting loop with two Josephson junctions, SQUIDS are used to measure magnetic fields.
- Powerful superconducting electromagnets used in maglev trains, Magnetic Resonance Imaging (MRI) and Nuclear magnetic resonance (NMR) machines, magnetic confinement fusion reactors (e.g. tokomaks), and the beam-steering and focusing magnets used in particle accelerators.
- Superconducting generators has the benefit of small size and low energy consumption than the conventional generators.
- Very fast and accurate computers can be constructed using superconductors and the power consumption is also very low. Superconductors can be used to transmit electrical power over very long distances without any power or any voltage drop

Graphene - The wonder material

High electrical conductivity 5000 W/mK, Zero Gap conductivity, Resistivity 10-6 Qcm, Charge carriers behave massless, Little Scattering High mobility.
Thermal Conductivity, Transparent in nature, Thinnest = 0.335 nm.
Applications:
- Integrated Circuits: High mobility of charge can be integral in IC. Replaces Silicon.
- Distillation: It allows only water to pass through it. Nanoporous graphene.
- Gas Sensors: Can detect effect of a single molecule associating with graphene, Effects the electric properties with addition of any foreign atom.
- Transistors: More Efficient than silicon transistors, Can be easily controlled by electric field, Can run at higher frequency, Increase speed of Circuits.
- Ultra-Capacitor: High surface to mass ratio, Two sheet of graphene with electrolyte in between, May replace batteries, High recharge rate and slow discharge, Long life.
- Bionic Devices: Non corrosive, Biodegradable, High conductivity, Non toxic compared to conventional electrode used in bionic device.
- Protective Coating: It is resistant to acids, alkalis etc, Being impermeable, Coating of containers, Jars etc, Paints for car body, steel structure.
- Solar Cell: It is super capacitor.
- Flexible Mobilephone. The Strongest.
Lightest, Flexible, Transparent, Electrical Conductive, Thermal Conductive.