Semiconductor Electronics Class 12 Physics Chapter 14 Notes

Electronic Devices and Semiconductors

Basic Electronic Devices:
- Controlled flow of electrons is fundamental to electronic circuits.
- Before the transistor’s discovery in 1948, vacuum tubes (valves) were common electronic devices.
- Vacuum tubes included vacuum diodes (2 electrodes), triodes (3 electrodes), tetrodes, and pentodes (4 and 5 electrodes, respectively).
Operation of Vacuum Tubes:
- In vacuum tubes, electrons are emitted from a heated cathode.
- Controlled electron flow is achieved by varying voltage between different electrodes.
- Vacuum is essential in the inter-electrode space to prevent energy loss due to collisions with air molecules.
- Electrons can only flow from cathode to anode, giving them the name “valves.”
- Vacuum tubes are bulky, high-power devices, operating at high voltages with limited life and reliability.
Semiconductor Electronics:
- The development of modern solid-state semiconductor electronics began in the 1930s.
- Solid-state semiconductors and their junctions allow control of charge carriers’ number and direction.
- Simple stimuli like light, heat, or small applied voltage can change the number of mobile charges in a semiconductor.
- Charge carriers flow within the solid in semiconductor devices, eliminating the need for external heating or a vacuum.
- Semiconductor devices are compact, low-power, operate at low voltages, and have long life and high reliability.
- They have largely replaced vacuum tube-based devices, such as Cathode Ray Tubes (CRTs), in applications like television and computer monitors.
Radio Wave Detector:
- Before the full understanding of semiconductor devices, a naturally occurring galena crystal (Lead sulphide, PbS) with a metal point contact was used as a radio wave detector.

Classification of Materials Based on Conductivity

Metals:
- Characteristics:
  - Very low resistivity (high conductivity).
- Resistivity (r) range:
  - r ~ 10^(-2) to 10^(-8) ohm-meter (Ω·m).
- Conductivity (s) range:
  - s ~ 10^2 to 10^8 Siemens per meter (S/m).
Semiconductors:
- Characteristics:
  - Resistivity and conductivity values intermediate between metals and insulators.
- Resistivity (r) range:
  - r ~ 10^(-5) to 10^6 ohm-meter (Ω·m).
- Conductivity (s) range:
  - s ~ 10^5 to 10^(-6) Siemens per meter (S/m).
Insulators:
- Characteristics:
  - High resistivity (low conductivity).
- Resistivity (r) range:
  - r ~ 10^11 to 10^19 ohm-meter (Ω·m).
- Conductivity (s) range:
  - s ~ 10^(-11) to 10^(-19) Siemens per meter (S/m).

Types of Semiconductors

Elemental Semiconductors:
- Examples: Silicon (Si) and Germanium (Ge).
Compound Semiconductors:
- Inorganic Compound Semiconductors:
  - Examples: Cadmium Sulfide (CdS), Gallium Arsenide (GaAs), Cadmium Selenide (CdSe), Indium Phosphide (InP), etc.
- Organic Compound Semiconductors:
  - Examples: Anthracene, doped phthalocyanines, etc.
- Organic Polymers as Semiconductors:
  - Examples: Polypyrrole, polyaniline, polythiophene, etc.
The majority of semiconductor devices in use are based on elemental semiconductors like Silicon (Si) or Germanium (Ge) and compound inorganic semiconductors.
Since 1990, some semiconductor devices have been developed using organic semiconductors and semiconducting polymers, which has led to the emergence of futuristic technologies such as polymer electronics and molecular electronics.

Classification of Materials Based on Energy Bands

Atomic Model vs. Solid State Behavior:

According to the Bohr atomic model, an electron’s energy in an isolated atom depends on its orbit. However, in a solid, atoms are closely packed, and electrons from neighboring atoms interact, leading to different electron behavior.

Formation of Energy Bands:

Inside a crystal, each electron occupies a unique position, and no two electrons experience the same surrounding charges. This results in each electron having a different energy level.
These energy levels with continuous energy variations form what are known as energy bands.
Two primary energy bands are significant: the valence band (lower energy) and the conduction band (higher energy).

Valence Band and Conduction Band:

The valence band contains energy levels of valence electrons.
The conduction band is above the valence band and generally empty under normal conditions.
If the lowest conduction band level is lower than the highest valence band level, valence electrons can move into the conduction band, facilitating electrical conduction, as seen in metallic conductors.

Energy Band Gap (Eg):

The energy gap between the valence band and conduction band is called the energy band gap (Eg).
Eg can be large, small, or zero, depending on the material.

Classification Based on Energy Band Gap:

Metal (Case I):
- Conduction and valence bands can overlap or partially fill.
- This allows a large number of electrons to be available for electrical conduction.
- Materials in this category have low resistance and high conductivity.
Insulator (Case II):
- A significant energy gap (Eg > 3 eV) exists.
- The conduction band is empty, making electrical conduction impossible.
- Electrons cannot be thermally excited from the valence band to the conduction band due to the large energy gap.
Semiconductor (Case III):
- A small energy gap (Eg < 3 eV) exists.
- At room temperature, some electrons in the valence band can acquire enough energy to cross the gap and enter the conduction band.
- These electrons, though limited in number, can conduct electricity.
- Semiconductors have intermediate resistance compared to metals and insulators.

Classification Summary:

Metals have overlapping or partially filled energy bands, offering high conductivity.
Insulators have a large energy gap, making them non-conductive.
Semiconductors have a small energy gap, allowing some electrons to conduct, and their resistance falls between that of metals and insulators.
The energy band theory helps classify materials based on their electrical conductivity and provides insight into their electrical properties.

Intrinsic Semiconductors

Crystal Lattice Structure:

Intrinsic semiconductors, such as Ge (Germanium) and Si (Silicon), have diamond-like lattice structures. Each atom is surrounded by four nearest neighbor atoms.

Covalent Bonds:

In their crystalline structure, each Si or Ge atom shares one of its four valence electrons with each of its four nearest neighbors.
These shared electron pairs form covalent bonds, holding atoms together strongly.

Covalent Bond Behavior:

At low temperatures, covalent bonds are intact, and electrons in these bonds shuttle back and forth between associated atoms.
As temperature increases, thermal energy becomes available, causing some electrons to break away from their covalent bonds and become free electrons contributing to conduction.

Holes in the Crystal:

When an electron breaks away, it effectively ionizes an atom and creates a vacancy in the bond.
This vacancy with an effective positive electronic charge is called a hole.
Holes act as apparent free particles with effective positive charge.

Intrinsic Carrier Concentration (ni):

In intrinsic semiconductors, the number of free electrons (ne) is equal to the number of holes (nh), denoted by ni.
Mathematically: ne = nh = ni

Hole Movement:

Holes in semiconductors move, creating hole current (Ih) under an applied electric field.
The motion of holes is a convenient way to describe the movement of bound electrons when there is an empty bond in the crystal.

Total Current (I):

The total current in an intrinsic semiconductor is the sum of the electron current (Ie) and the hole current (Ih).
Mathematically: I = Ie + Ih

Generation and Recombination:

Intrinsic semiconductors experience both generation and recombination of charge carriers.
Generation occurs when thermally excited electrons break free from their covalent bonds.
Recombination happens when electrons collide with holes.
At equilibrium, the rate of generation equals the rate of recombination of charge carriers.

Temperature Effect:

Intrinsic semiconductors behave like insulators at absolute zero temperature (T = 0 K).
As temperature increases (T > 0 K), some electrons are thermally excited from the valence band to the conduction band, partially occupying the conduction band.
The energy-band diagram of an intrinsic semiconductor reflects this behavior, with electrons in the conduction band and an equal number of holes in the valence band.

Extrinsic Semiconductors

Enhancing Semiconductor Conductivity:

Intrinsic semiconductors have low conductivity at room temperature, limiting their practical applications.
To improve conductivity, extrinsic semiconductors are created by introducing suitable impurities through a process called doping.
Impurity atoms introduced in the semiconductor are called dopants.

Dopant Selection:

Dopants must be chosen carefully to match the size of the semiconductor lattice and not distort its structure.
There are two types of dopants for tetravalent Si or Ge:
- Pentavalent (valency 5): Examples include Arsenic (As), Antimony (Sb), and Phosphorus (P).
- Trivalent (valency 3): Examples include Indium (In), Boron (B), and Aluminum (Al).

n-type Semiconductor:

Doping with a pentavalent element introduces additional electrons into the crystal lattice.
The pentavalent dopant is called a donor impurity because it donates one extra electron for conduction.
These added electrons are highly mobile at room temperature and become the majority carriers.
In n-type semiconductors, the number of electrons (ne) is much greater than the number of holes (nh).

p-type Semiconductor:

Doping with a trivalent element results in the creation of holes in the crystal lattice.
The trivalent dopant is called an acceptor impurity because it accepts an electron from the neighboring Si or Ge atom.
Holes are the majority carriers in p-type semiconductors, while electrons are the minority carriers.
The number of holes (nh) is much greater than the number of electrons (ne) in p-type semiconductors.

Charge Neutrality:

The addition of dopants does not disrupt the overall charge neutrality of the crystal.

Energy Band Structure in Extrinsic Semiconductors:

The energy band structure of extrinsic semiconductors includes additional energy states due to donor and acceptor impurities.
Donor energy levels (ED) are slightly below the conduction band, while acceptor energy levels (EA) are slightly above the valence band.
Donor impurities contribute to the majority carrier concentration in n-type semiconductors, while acceptor impurities increase the hole concentration in p-type semiconductors.

Carrier Concentration in Thermal Equilibrium:

In thermal equilibrium, the product of the electron concentration (ne) and hole concentration (nh) is equal to the square of the intrinsic carrier concentration (ni).
Mathematically: ne * nh = ni^2

Energy Gap and Resistivity:

The difference in resistivity between carbon (C), silicon (Si), and germanium (Ge) semiconductors depends on the energy gap between their conduction and valence bands.
C (diamond) has the highest energy gap (5.4 eV), Si has an intermediate energy gap (1.1 eV), and Ge has the lowest energy gap (0.7 eV).
Sn, although a group IV element, is a metal because it has a zero energy gap.
Extrinsic semiconductors significantly enhance the conductivity of semiconductors, making them suitable for various electronic applications. The choice of dopant type determines whether a semiconductor becomes n-type or p-type.

p-n Junction

Importance of p-n Junction:

A p-n junction is a fundamental component of many semiconductor devices, such as diodes and transistors.
Understanding the behavior of a p-n junction is essential for analyzing the operation of various semiconductor devices.

Formation of a p-n Junction:

To create a p-n junction, a thin p-type silicon (p-Si) semiconductor wafer is used.
By adding a small quantity of pentavalent impurity, part of the p-Si wafer is converted into n-Si.
The wafer contains both p- and n-regions, with a metallurgical junction between them.

Two Key Processes in p-n Junction Formation:

Diffusion: Due to a concentration gradient, holes diffuse from the p-side to the n-side, and electrons diffuse from the n-side to the p-side.
Drift: As electrons and holes diffuse, they create a space-charge region on either side of the junction.
- On the n-side, the diffusion of holes leaves behind positively charged ionized donors.
- On the p-side, the diffusion of electrons leaves behind negatively charged ionized acceptors.
- The resulting electric field is directed from the positive space-charge region to the negative space-charge region, causing electron and hole motion.
- This motion due to the electric field is called drift, and it generates a drift current opposite in direction to the diffusion current.
- Initially, the diffusion current is more substantial than the drift current.

Depletion Region:

The space-charge regions on either side of the junction collectively form the depletion region.
This region is called “depletion” because the initial movement of electrons and holes depletes it of free charges.
The depletion region’s thickness is typically around one-tenth of a micrometer.

Equilibrium and Barrier Potential:

The loss of electrons from the n-region and the gain of electrons by the p-region result in a potential difference across the junction.
This potential opposes further carrier movement and is termed a barrier potential.
At equilibrium, there is no net current in a p-n junction.

Barrier Potential and Polarity:

The n-material becomes positively charged relative to the p-material due to the loss of electrons from the n-region.
The potential across the junction is such that it inhibits the flow of electrons from the n-region to the p-region.
This potential is known as the barrier potential.
In a p-n junction, the formation of the depletion region, the electric field, and the barrier potential create conditions of equilibrium, preventing any net current flow.

A Semiconductor Diode

A semiconductor diode is essentially a p-n junction with metallic contacts at the ends for external voltage application, making it a two-terminal device.
The direction of the arrow in the diode symbol indicates the conventional direction of current flow when the diode is forward-biased.
By applying an external voltage V across the diode, the equilibrium barrier potential of the p-n junction can be modified.

P-n Junction Diode Under Forward Bias:

When an external voltage V is applied to a semiconductor diode with the p-side connected to the positive terminal of the battery and the n-side connected to the negative terminal, the diode is considered forward-biased.
Under forward bias, most of the applied voltage drops across the depletion region, and the voltage drop across the p-side and n-side is minimal. This is because the resistance of the depletion region, where there are no charges, is much higher than the resistance of the p-side and n-side.
The direction of the applied voltage (V) is opposite to the built-in potential (V0), leading to a decrease in the width of the depletion region and a reduction in the barrier height.
The effective barrier height under forward bias is (V0 – V).
Increasing the applied voltage reduces the barrier potential, allowing more carriers to cross the junction, leading to an increase in the current.
Minority carrier injection occurs as electrons from the n-side cross the depletion region to reach the p-side (where they are minority carriers), and holes from the p-side cross the junction to reach the n-side.
Due to this, the concentration of minority carriers at the junction boundary increases significantly compared to locations far from the junction.
This concentration gradient results in injected electrons on the p-side diffusing from the junction edge to the other end of the p-side, and similarly, injected holes on the n-side diffuse from the junction edge to the other end of the n-side.
This movement of charged carriers on either side generates current, with the total diode forward current being the sum of hole diffusion current and conventional current due to electron diffusion.

P-n Junction Diode Under Reverse Bias:

When an external voltage (V) is applied across the diode such that the n-side is positive and the p-side is negative, the diode is reverse-biased.
Under reverse bias, the applied voltage mainly drops across the depletion region, and the direction of the applied voltage matches the barrier potential. This increases the barrier height and widens the depletion region due to changes in the electric field.
The effective barrier height under reverse bias is (V0 + V).
This configuration suppresses the flow of electrons from the n-side to the p-side and holes from the p-side to the n-side, leading to a significant decrease in the diffusion current.
Under reverse bias, the electric field direction at the junction sweeps carriers from their minority side to their majority side, creating drift current.
The drift current is of the order of a few mA and is primarily due to the motion of carriers across the junction from their minority side to their majority side.
The diode’s reverse current is not highly dependent on the applied voltage but is limited by the concentration of minority carriers on either side of the junction.
The reverse current remains almost constant until it reaches a critical reverse bias voltage known as the breakdown voltage (Vbr).
Beyond Vbr, even a slight increase in bias voltage causes a sharp increase in the reverse current. Exceeding the rated value of the reverse current can lead to diode destruction due to overheating.

Characteristics of a Diode:

The V-I (voltage-current) characteristics of a diode are typically studied using a circuit that varies the applied voltage and measures the resulting current.
In forward bias, the diode current remains nearly constant until the voltage across the diode reaches the threshold voltage or cut-in voltage (around 0.2V for germanium diodes and 0.7V for silicon diodes). Beyond this voltage, the current increases significantly (exponentially).
In reverse bias, the diode current is very small and nearly constant. It is called reverse saturation current. However, at high reverse bias (breakdown voltage), the diode current can suddenly increase. General-purpose diodes are not typically used beyond the reverse saturation current region.
Diodes exhibit low resistance under forward bias compared to high resistance under reverse bias.
The dynamic resistance of a diode, defined as the ratio of a small change in voltage (ΔV) to a small change in current (ΔI), characterizes its behavior.

Application of Junction Diode as a Rectifier

A junction diode can be used as a rectifier to convert alternating current (AC) into direct current (DC). A rectifier allows current to flow in only one direction, which is useful for converting AC voltage to a unidirectional voltage. There are two common types of rectifiers: half-wave rectifiers and full-wave rectifiers.

Half-Wave Rectifier:
- In a half-wave rectifier circuit, a diode is used to allow current to flow only during one half of the AC cycle, while the other half is blocked.
- The circuit consists of a diode connected in series with a load resistor (RL) across the secondary of a transformer.
- During the positive half-cycle of the AC input, when the diode is forward-biased, current flows through the diode and the load resistor, producing an output voltage.
- During the negative half-cycle, when the diode is reverse-biased, no current flows.
- The output voltage of a half-wave rectifier is a pulsating DC voltage that only utilizes one half of the AC waveform.
Full-Wave Rectifier:
- In a full-wave rectifier circuit, two diodes are used to allow current to flow during both the positive and negative half-cycles of the AC input, resulting in a more efficient rectification.
- The diodes are connected in a bridge configuration or using a center-tap transformer.
- During the positive half-cycle of the AC input, one diode conducts, while during the negative half-cycle, the other diode conducts. Both diodes do not conduct simultaneously.
- The output voltage of a full-wave rectifier is closer to a continuous DC voltage compared to a half-wave rectifier.
- Filters, such as capacitors, are often used to smooth the pulsating DC voltage and provide a more constant DC output.

Filtering:

The rectified output voltage from both half-wave and full-wave rectifiers is in the form of pulsating DC voltage, which contains ripples.
To obtain a steady DC output, a filter is often connected across the output terminals in parallel with the load resistor (RL).
Capacitors are commonly used as filters in rectifier circuits.
When the voltage across the capacitor is rising, it gets charged, and when there is no external load, it remains charged at the peak voltage of the rectified output.
When there is a load, the capacitor discharges through the load, causing the voltage to fall.
The rate of voltage fall depends on the capacitance (C) and the effective resistance (RL) in the circuit and is referred to as the time constant.
A larger capacitance results in a larger time constant, which allows the output voltage to remain closer to the peak voltage of the rectified waveform.
The addition of a capacitor effectively filters out the AC ripples from the rectified output, producing a smoother, nearly constant DC voltage.

Overall, both half-wave and full-wave rectifiers play a crucial role in converting AC to DC, and filtering components help provide a more stable and smooth DC output for various electronic applications, such as power supplies.