Course

# 11th Standard - Physics Tutorial - Maharashtra Board

We will cover below topics.
• Units and Measurements
• Mathematical Methods
• Motion in a Plane
• Laws of Motion
• Gravitation
• Mechanical Properties of Solids
• Thermal Properties of Matter
• Sound
• Optics
• Electrostatics
• Electric Current Through Conductors
• Magnetism
• Electromagnetic Waves and Communication System
• Semiconductors

# 12. Magnetism

## Law of magnetic poles

According to Law of magnetic poles,
• Every magnet has both a north pole and a south pole.
• If a magnet is cut into smaller pieces, each piece will still have its own north and south pole.
• If you break a bar magnet in half, you will not end up with a single isolated north pole and a single isolated south pole. Instead, you will have two smaller magnets, each with its own north and south pole.
This behavior is in contrast to electric charges, where isolated positive or negative charges can exist independently. In the case of magnetic poles, they always come in pairs, and you cannot isolate one pole from the other. This is a fundamental characteristic of magnetism.

## Magnetic lines of force

• The magnetic lines of force of a magnet or a solenoid form closed loops. This is in contrast to the case of an electric dipole, where the electric lines of force originate from the positive charge and end on the negative charge, without forming a complete loop
• The direction of the net magnetic field B $\vec{B}$ at a point is given by the tangent to the magnetic line of force at that point in the direction of line of force.
• The number of lines of force crossing per unit area decides the magnitude of the magnetic field $\vec{B}$
• The magnetic lines of force do not intersect. This is because had they intersected, the direction of magnetic field would not be unique at that point.
Density of lines of force i.e., the number of lines of force per unit area normal to the surface force? 4. If you freely hang a bar magnetic horizontally, in which direction will it become stable? 222 around a particular point determines the strength of the magnetic field at that point. The number of lines of force is called magnetic flux (φ ).$\Phi = B \cdot A \cdot \cos(\theta)$

## Electrostatic Analogue

Maxwell suggested that electricity and magnetism could be studied analogously.
QuantityElectrostaticMagnetism
Basic Physical QuantityElectrostatic ChargeMagnetic Pole
FieldElectric Field $\vec{E}$ Magnetic Field $\vec{B}$
Constant $\frac{1}{4 \pi \epsilon_0}$ $\frac{\mu_0}{4 \pi}$
Dipole Moment$\vec{p} = q (2\vec{l})$ Along negative to positive $\vec{m} = q_m (2\vec{l})$ Along S to N pole
Force$\vec{F} = q \vec{E}$ $\vec{F} = q_m \vec{B}$
Energy (In external field) of a dipole$U = - \vec{p} \cdot \vec{E}$ $U = - \vec{m} \cdot \vec{B}$
Coulomb's law $F = (\frac{1}{4 \pi \epsilon_0}) \frac{q_1 q_2}{r^2}$ Magnetic Monopoles do not exist
Axial field for a short dipole $(\frac{2p}{4 \pi \epsilon_0 r^3})$ along $\vec{p}$$(\frac{\mu_02 \vec{m}}{4 \pi r^3})$
Equatorial field for a short dipole $(\frac{p}{4 \pi \epsilon_0 r^3})$ opposite to $\vec{p}$$(\frac{-\mu_0 \vec{m}}{4 \pi r^3})$

## Gauss' Law of Magnetism

The Gauss' law for electric field states that the net electric flux through a closed Gaussian surface is proportional to the net electric charge enclosed by the surface. The Gauss' law for magnetic fields states that the net magnetic flux through a closed Gaussian surface is zero
$\Phi_B = \int \vec{B} \cdot \vec{dS} = 0$
This law proves that there are no magnetic monopoles (single magnetic charges) in nature.

## Earth's Magnetism

Earth is a huge magnet!

# 14. Semiconductors

Semiconductors are tiny electronic devices used inside gadgets like Mobile phone, smartwatch, laptop etc. Key points to remember about Semiconductors

## Types of Electrical Material

Before the discovery of Semiconductor, We had 2 categories of Electric materials - Conductors (e.g. Copper) and Insulators (e.g. glass or Rubber). Then came the semiconductor! Electrical conductivity of Semiconductor lies between that of Conductors and Insulators.
• Conductors - Metals like copper and silver have a lot of free electrons (around $10^{29} \text{ per } m^3$) available for conduction!
• Insulators - Insulators like glass and wood have less number of free electrons (around $10^{23} \text{ per } m^3$) available for conduction!
• Semiconductors - Semiconductors like Silicon, germanium, gallium arsenide, gallium nitride, cadmium sulphide have more number of free electrons as compared to insulators but less number of free electrons as compared to Conductors available for conduction! In fact conductivity of Semiconductor can be adjusted via the process called as doping. In Doping, we add some impurity atoms to the silicon crystal lattice.

## Electrical Conductivity formula

Electrical conductivity is measured in Siemens per Meter (s/m). Device used to measure the conductivity is called as conductivity meter or Conductance meter. e.g. Electrical Conductivity of Copper is  $5.96 \times 10^7$ and that of Silicon is $1.56 \times 10^{-3}$ and that of Glass is $10^{-11}$ to $10^{-15}$.

The electrical conductivity $\sigma$ of a semiconductor can be calculated using the formula:

$\sigma = n \cdot q \cdot \mu$

Where:

• $\sigma$ is the electrical conductivity (in Siemens per meter, S/m).
• $n$ is the charge carrier density or concentration (in number of charge carriers per cubic meter, $m^{-3}$ )
• $q$ is the charge of an electron (in Coulombs, C).
• $\mu$ is the mobility of carriers (in square meters per volt-second,$m^2/Vs$ ).

## Semiconductor Material

When the temperature of a semiconductor is increased, its electrical conductivity also increases. The electrical conductivity of a metal decreases with increase in its temperature!
• Elemental semiconductors: Silicon, germanium - Semiconductors silicon and germanium are from the fourth group of elements in the periodic table. They have a valence of four. Their atoms are bonded by covalent bonds. At absolute zero temperature, all the covalent bonds are completely satisfied in a single crystal of pure silicon or germanium.
• Compound Semiconductors: Cadmium sulphide, zinc sulphide
• Organic Semiconductors: Anthracene, doped pthalocyanines, polyaniline

## Band Theory

Band theory, in simple terms, is a way to understand how electrons are arranged and move within solids like metals and semiconductors. Imagine a ladder with many steps. In a solid, the energy levels that electrons can have are like the steps on the ladder. However, in band theory, we group these energy levels into bands, like sections of the ladder.
Valence Band: The lower bands are called the valence bands. These are the steps closer to the ground. Electrons in these bands are tightly bound to the atoms in the solid and cannot move freely.
Conduction Band: The higher bands are called the conduction bands. These are the steps higher up. Electrons in these bands have more energy and are free to move throughout the solid, creating electrical conductivity.
Band Gap: The gap between the valence band and the conduction band is called the "band gap." It's like an empty space between the lower and higher steps of the ladder.

Now, here's the key idea: In insulators, there is a large band gap, so it's hard for electrons to jump from the valence band to the conduction band. That's why insulators don't conduct electricity well. In conductors like metals, the valence and conduction bands overlap, so electrons can easily move from one to the other, allowing electricity to flow freely. In semiconductors, there's a small band gap. This means that under certain conditions (like adding a little energy), electrons can jump from the valence band to the conduction band, making semiconductors conduct electricity, but not as well as metals.

## Semiconductor Types

### Intrinsic

A pure semiconductor such as pure silicon or pure germanium is called an intrinsic semiconductor. Silicon (Si) has atomic number 14 and its electronic configuration is$\text{ } 1s^2 \text{ } 2s^2 \text{ } 2p^6\text{ } 3s^2 \text{ }3p^2$. Its valence is 4. Each atom of Si forms four covalent bonds with its neighbouring atoms. At absolute zero temperature, all valence electrons are tightly bound to respective atoms and the covalent bonds are complete. Electrons are not available to conduct electricity through the crystal because they cannot gain enough energy to get into higher energy levels. At room temperature, however, a few covalent bonds are broken due to thermal agitation and some valence electrons can gain energy. Once covalent bonds are broken, electrons move to conduction band. So if say n electrons move to conduction band, exact n number of holes are created in valence band.

$n_h = n_e$

If external battery is connected to the intrinsic semiconductor, at room temperature, electrons in conduction band will flow to positive terminal and holes will move to negative terminal of battery. But conductivity is still very low! Intrinsic semiconductors have an equal number of electrons and holes (electron-hole pairs) generated at room temperature due to thermal excitation. This means that their carrier concentration (number of charge carriers per unit volume) is relatively low. In electronic devices, precise control over carrier concentration is crucial for controlling device behavior and that's why we use extrinsic semiconductor.

### Extrinsic

To increase the conductivity of pure semiconductor, we add impurity to it! The process of adding impurities to an intrinsic semiconductor is called doping. The semiconductor with impurity is called a doped semiconductor or an extrinsic semiconductor. The impurity is called the dopant. Silicon or Germanium can be doped with a pentavalent or trivalent impurity. Based on impurity type, we categorise the Extrinic Semiconductors as n-type or p-type
• n-type
• p-type

#### n-type semiconductor

When we add pentavalent impurity such as phosphorus (P), arsenic (As) or antimony (Sb) to pure silicon, resulting semiconductor is called as n-type semiconductor! When a dopant atom of 5 valence electrons occupies the position of a Si atom in the crystal lattice, 4 electrons from the dopant form bonds with 4 neighbouring Si atoms and the fifth electron from the dopant remains very weakly bound to its parent atom. To make this electron free even at room temperature, very small energy is required. It is 0.01 eV for Ge and 0.05 eV for Si. Since every pentavalent dopant atom donates one electron for conduction, it is called a donor impurity . As this semiconductor has large number of electrons in conduction band and its conductivity is due to negatively charged carriers, it is called n-type semiconductor. For n-type semiconductor,
$n_e >> n_h$
. The free electrons donated by the impurity atoms occupy energy levels which are in the band gap and are close to the conduction band. They can be easily available for conduction.

#### p-type semiconductor

When we add trivalent impurity such as boron (B), aluminium (Al) or indium (In). to pure silicon, resulting semiconductor is called as n-type semiconductor! The dopant trivalent atom has one valence electron less than that of a silicon atom. Every trivalent dopant atom shares its three electrons with three neighbouring Si atoms to form covalent bonds. But the fourth bond between silicon atom and its neighbour is not complete. The acceptor atoms acquire electron and become negatively charged-ions. For p-type semiconductor,
$n_h >> n_e$
.

#### Charge neutrality

The n-type semiconductor has excess of electrons but these extra electrons are supplied by the donor atoms which become positively charged. Since each atom of donor impurity is electrically neutral, the semiconductor as a whole is electrically neutral. Here, excess electron refers to an excess with reference to the number of electrons needed to complete the covalent bonds in a semiconductor crystal. These extra free electrons increase the conductivity of the semiconductor.

Similarly, a p-type semiconductor has holes or absence of electrons in some energy levels. When an electron from a host atom fills this level, the host atom is positively charged and the dopant atom is negatively charged but the semiconductor as a whole is electrically neutral. Thus, n-type as well as p-type semiconductors are electrically neutral.

#### Amount of Impurity

The amount of impurities is expressed as part per million or ppm, that is, one impurity atom per one million atoms of the host.
$n_h \cdot n_e = n_i ^ 2$
.

## p-n combination

### p-n junction

When n-type and p-type semiconductor materials are fused together, a p-n junction is formed.

Diffusion - Process of transfer of electrons and holes across the p-n junction is called as diffusion!

Depletion Region - The diffusion of carriers across the junction and resultant accumulation of positive and negative charges across the junction builds a potential difference across the junction. This potential difference is called the potential barrier. The magnitude of the potential barrier for silicon is about 0.6 - 0.7 volt and for germanium, it is about 0.3 - 0.35 volt. This potential barrier always exists even if the device is not connected to any external power source. It prevents continuous diffusion of carriers across the junction. A state of electrostatic equilibrium is thus reached across the junction. Free charge carriers cannot be present in a region where there is a potential barrier. The regions on either side of a junction, therefore, becomes completely devoid of any charge carriers. This region across the p-n junction where there are no charges is called the depletion layer or the depletion region.The n-side near the boundary of a p-n junction becomes positive with respect to the p-side because it has lost electrons and the p-side has lost holes. Thus the presence of impurity ions on both sides of the junction establishes an electric field across this region such that the n-side is at a positive voltage relative to the p-side.

As a result of potential barrier across depletion region, charge carriers require some extra energy to overcome the barrier. A suitable voltage needs to be applied to the junction externally, so that these charge carriers can overcome the potential barrier and move across the junction.

### Forward Bias

If the p-region is connected to the positive terminal and the n-region is connected to the negative terminal of an external voltage source, it creates external voltage which opposes the built-in potential of the junction. The width of potential barrier is thus reduced. Also, negative charge carriers (electrons) from the n-region are pushed towards the junction. A similar effect is experienced by positive charge carriers (holes) in the p-region and they are pushed towards the junction. Both the charge carriers thus find it easy to cross over the barrier and contribute towards the electric current. Such arrangement of a p-n junction in an electric circuit is called forward bias.

### Reverse Bias

If the p-region is connected to the negative terminal and the n-region is connected to the positive terminal of the external voltage source, This external voltage effectively adds to the built-in potential of the junction. The width of potential barrier is thus increased. Also, the negative charge carriers (electrons) from the n-region are pulled away from the junction. Similar effect is experienced by the positive charge carriers (holes) in the p-region and they are pulled away from the junction. Both the charge carriers thus find it very difficult to cross over the barrier and thus do not contribute towards the electric current. Such arrangement of a p-n junction in an electric circuit is called reverse bias.

### p-n junction diode

A p-n junction, when provided with metallic connectors on each side is called a junction diode or simply, a diode. The p-side is called the anode and the n-side is called the cathode of the diode.

Forward biased mode The positive terminal of the external voltage is connected to the anode (p-side) and negative terminal to the cathode (n-side) across the diode. In case of forward bias, the width of the depletion region decreases and the p-n junction offers a low resistance path allowing a high current to flow across the junction. The barrier potential is reduced in forward biased mode.

Reverse biased mode The positive terminal of the external voltage is connected to the cathode (n-side) and negative terminal to the anode (p-side) across the diode. In case of reverse bias, the width of the depletion region increases and the p-n junction behaves like a high resistance. Practically, no current flows through it with an increase in the reverse bias voltage. However, a very small leakage current does flow through the junction. The barrier potential is increased in reverse biased mode.

Zero Biased Junction Diode When a diode is connected in a zero bias condition, no external potential energy is applied to the p-n junction

Static and dynamic resistance of a diode An ideal diode offers zero resistance in forward biased mode and infinite resistance in reverse biased mode.Static (DC) resistance: When a p-n junction diode is forward biased, it offers a definite resistance in the circuit. This resistance is called the static or DC resistance ($R_{\text{g}}$) of a diode.

$R_{\text{g}} = \frac{V} {I}$
Dynamic (AC) resistance: When a p-n junction diode is forward biased, The dynamic (AC) resistance of a diode ($r_{\text{g}}$) at a particular applied voltage, is defined as
$r_g = \frac{\Delta V}{\Delta I}$

### Thermistor

Thermistor is a temperature sensitive resistor. There are two types of thermistors.
• Negative Temperature Coefficient (NTC) - Resistance of a NTC thermistor decreases with increase in its temperature. Its temperature coefficient is negative. They are commonly used as temperature sensors and also in temperature control circuits.
• Positive Temperature Coefficient (PTC) - Resistance of a PTC thermistor increases with increase in its temperature. They are commonly used in series with a circuit. They are generally used as a reusable fuse to limit current passing through a circuit to protect against over current conditions, as resettable fuses.
Thermistors are made from thermally sensitive metal oxide semiconductors. They can measure temperature variations of a small area due to their small size.

• Electronic properties of semiconductors can be controlled to suit our requirement
• They are smaller in size and light weight
• They can operate at smaller voltages (of the order of few mV) and require less current (of the order of μA or mA), therefore, consume lesser power.
• Almost no heating effects occur, therefore these devices are thermally stable
• Faster speed of operation due to smaller size.
• Fabrication of ICs is possible
• They are sensitive to electrostatic charges.
• Not vary useful for controlling high power.
• They are sensitive to radiation.
• They are sensitive to fluctuations in temperature.
• They need controlled conditions for their manufacturing.
• Very few materials are semiconductors

## Applications of semiconductors

• Solar cell: Converts light energy into electric energy. Useful to produce electricity in remote areas and also for providing electricity for satellites, space probes, and space stations.
• Photo resistor: Changes its resistance when light is incident on it.
• Bi-polar junction transistor: A transistor can be a p-n-p or n-p-n transistor.
• Photodiode: It conducts when illuminated with light.
• LED: Light Emitting Diode: Emits light when current passes through it. They consume less power, are smaller in size, have a longer life, and are cost-effective.
• Solid State Laser: Special type of LED that emits light of specific frequency. It is smaller in size and consumes less power.
• Integrated Circuits (ICs): Hundreds of diodes and transistors are used to make integrated circuits that are used in mobile phones and laptops.

## Exercises

• Electric conduction through a semiconductor is due to: both electrons and holes . Electrons and holes both are charge carriers
• The energy levels of holes are in the valence band
• Current through a reverse biased p-n junction, increases abruptly at breakdown voltage !
• A reverse biased diode, is equivalent to an off switch
• The potential barrier in p-n diode is due to accumulation of positive and negative charges near the junction