Conductors, Semiconductors And Insulators

BANDGAP ENERGY & TEMP VARIATION OF RESISTANCE

Slide 1

Conductors, Semiconductors, and Insulators are materials that differ in their ability to conduct electricity.
The behavior of these materials is determined by their energy band structures.
Bandgap energy is an important concept in understanding the conductivity of materials.
In this lecture, we will explore the bandgap energy and the temperature variation of resistance in conductors, semiconductors, and insulators.

Slide 2

Conductors have a large number of free electrons available for conduction.
In a conductor, the valence band and conduction band overlap, allowing easy flow of electrons.
Examples of conductors include metals like copper, silver, and gold.
Conductors have a very low resistivity, and their resistance decreases with increasing temperature.

Slide 3

Semiconductors have a smaller number of free electrons compared to conductors.
The valence band in semiconductors is completely filled, while the conduction band is partially filled or empty.
The energy gap between the valence and conduction bands is relatively small.
Examples of semiconductors include silicon (Si), germanium (Ge), and gallium arsenide (GaAs).

Slide 4

Insulators have a large energy gap between the valence and conduction bands.
The valence band is completely filled, and the conduction band is empty.
Insulators have a very low electrical conductivity.
Examples of insulators include rubber, glass, and plastic.

Slide 5

The bandgap energy (Eg) is the energy difference between the valence band and the conduction band.
In conductors, the valence and conduction bands overlap, so the bandgap energy is zero.
In insulators, the bandgap energy is large, typically in the range of 1 to 10 eV.
Semiconductors have a bandgap energy between conductors and insulators, typically ranging from 0.1 to 3 eV.

Slide 6

The bandgap energy determines the electrical conductivity of a material.
In conductors, the electrons can easily move from the valence band to the conduction band.
In insulators, the energy gap is so large that electrons cannot jump to the conduction band easily.
In semiconductors, the bandgap energy is small enough that electrons can be easily excited to the conduction band, but thermal energy is not sufficient to promote extensive electron movement.

Slide 7

Temperature variation of resistance is an important aspect of conductors, semiconductors, and insulators.
In conductors, the resistance decreases with increasing temperature.
This is due to an increase in collision between electrons and lattice vibrations at higher temperatures, which helps in overcoming the resistance offered by the lattice.
This phenomenon is known as positive temperature coefficient.

Slide 8

In semiconductors, the temperature variation of resistance is more complex.
At low temperatures, the resistance decreases due to a decrease in the number of collisions between electrons and lattice vibrations.
As the temperature increases, the resistance first decreases, then reaches a minimum, and finally increases.
This behavior is due to the combined effects of thermal excitation and impurity scattering.

Slide 9

At higher temperatures, the collisions between electrons and impurities dominate, leading to an increase in resistance.
This increase in resistance with temperature is known as the negative temperature coefficient.
The temperature at which the resistance is minimum is known as the compensation temperature.

Slide 10

Insulators have a very high resistance and show a negative temperature coefficient.
The number of charge carriers in the valence band decreases with increasing temperature, leading to an increase in resistance.
The resistance of insulators increases monotonically with increasing temperature.

Electrical Conductivity

Electrical conductivity is a measure of a material’s ability to conduct electric current.
It is denoted by the symbol σ and is given by the formula: σ = nqµ
- n = Charge carrier density
- q = Charge of the charge carrier
- µ = Charge carrier mobility
Conductors have high electrical conductivity due to a large number of free charge carriers.

Charge Carrier Density

In conductors, the charge carrier density is high, typically on the order of 10^22 to 10^29 charge carriers per cubic meter.
The charge carriers in conductors are free electrons, which are delocalized and can move freely within the material.
The high charge carrier density contributes to the high electrical conductivity of conductors.

Charge Carrier Mobility

Charge carrier mobility is a measure of how easily the charge carriers can move through a material under the influence of an electric field.
It is denoted by the symbol µ and is expressed in units of meters squared per volt-second (m^2/Vs).
Charge carriers in conductors have high mobility, allowing them to move quickly in response to an applied electric field.

Examples of Conductors

Copper (Cu) is an excellent conductor, commonly used in electrical wiring and transmission lines.
Aluminum (Al) is another commonly used conductor in power distribution systems.
Silver (Ag) has the highest electrical conductivity among all metals and is used in high-performance electrical contacts.

Energy Band Diagram

An energy band diagram is a graphical representation of the energy levels of electrons in a material.
In conductors, the valence and conduction bands overlap, indicating the presence of a large number of free electrons.
The Fermi level lies within the valence band, signifying that some electrons are available for conduction.

Temperature Coefficient of Resistance

The temperature coefficient of resistance (α) is a measure of how much a material’s resistance changes with temperature.
It is given by the formula: α = (1/R)(∆R/∆T)
- R = Resistance
- ∆R = Change in resistance
- ∆T = Change in temperature
The temperature coefficient of resistance can be positive, negative, or close to zero.

Positive Temperature Coefficient (PTC)

Conductors exhibit a positive temperature coefficient (PTC) of resistance.
The resistance of conductors increases with increasing temperature due to increased collisions between electrons and lattice vibrations.
This phenomenon is utilized in devices such as self-regulating heating elements.

Negative Temperature Coefficient (NTC)

Semiconductors and insulators typically exhibit a negative temperature coefficient (NTC) of resistance.
The resistance of semiconductors and insulators decreases with increasing temperature due to increased thermal excitation of charge carriers.
Negative temperature coefficient behavior is utilized in thermistors, which are temperature-sensitive resistors.

Energy Band Gap and Conductivity

The bandgap energy plays a crucial role in determining the conductivity of a material.
Conductors have a zero or very small bandgap energy, allowing easy movement of electrons.
Semiconductors have a moderate bandgap energy that can be surpassed by thermal excitation.
Insulators have a large bandgap energy that prevents easy movement of electrons.

Summary

Conductors have a high charge carrier density, high mobility, and a positive temperature coefficient of resistance.
Semiconductors have a moderate charge carrier density and mobility, and their resistance decreases with increasing temperature.
Insulators have a low charge carrier density, low mobility, and a negative temperature coefficient of resistance.
The bandgap energy determines the electrical conductivity of a material.

Here are slides 21 to 30 on the topic "Conductors, Semiconductors and Insulators - BANDGAP ENERGY & TEMP VARIATION OF RESISTANCE":

Slide 21

Conductors:

Have a high electrical conductivity due to a large number of free charge carriers.
Are used in various electrical devices and circuitry.
Examples: Copper, Aluminum, Silver.

Slide 22

Semiconductors:

Have a moderate electrical conductivity between conductors and insulators.
Are widely used in electronic devices like transistors and diodes.
Examples: Silicon, Germanium.

Slide 23

Insulators:

Have very low electrical conductivity due to a lack of free charge carriers.
Act as good electrical insulators and are used for insulation purposes.
Examples: Rubber, Glass, Plastic.

Slide 24

Thermal Conductivity:

Conductors have high thermal conductivity, allowing heat to flow easily.
Semiconductors have lower thermal conductivity compared to conductors.
Insulators have very low thermal conductivity, making them good thermal insulators.

Slide 25

Superconductors:

Superconductors exhibit zero resistance to the flow of electric current.
They experience a drastic drop in resistivity at very low temperatures.
Superconductors are used in various applications like magnetic resonance imaging (MRI) and particle accelerators.

Slide 26

Band Theory:

The band theory explains the behavior of electrons in solids.
Electrons in solids occupy energy bands rather than discrete energy levels.
The valence band is the highest filled band, while the conduction band is the next empty or partially filled band.

Slide 27

Band Overlap:

In conductors, the valence and conduction bands overlap, allowing the easy movement of electrons.
In semiconductors, the valence and conduction bands have a small energy gap.
In insulators, the valence and conduction bands are separated by a large energy gap.

Slide 28

Temperature Dependence:

The electrical resistance of conductors increases with increasing temperature.
Semiconductors show a decrease in resistance with increasing temperature up to a certain point.
Insulators show an increase in resistance with increasing temperature.

Slide 29

Thermal Excitation:

At higher temperatures, thermal energy can excite electrons across the band gap in semiconductors.
This leads to an increase in the number of charge carriers and a decrease in resistance.

Slide 30

Impurity Scattering:

Impurities in semiconductors can scatter charge carriers, increasing resistance.
At high temperatures, the number of impurity scattering events dominates, leading to an increase in resistance.