Class 12 Physics Notes Chapter 14 (Semiconductor) – Examplar Problems (English) Book

Alright class, let's delve into Chapter 14: Semiconductor Electronics. This is a crucial chapter, not just for your board exams but also forms the foundation for many questions in competitive government exams. We'll cover the essentials systematically.

Chapter 14: Semiconductor Electronics: Materials, Devices and Simple Circuits

1. Introduction to Semiconductors

• Materials are broadly classified based on their electrical conductivity:
  • Conductors: Have very low resistivity (or high conductivity). Examples: Copper, Aluminium, Silver. (ρ ~ 10⁻² - 10⁻⁸ Ωm, σ ~ 10² - 10⁸ S/m)
  • Insulators: Have very high resistivity (or low conductivity). Examples: Glass, Rubber, Wood. (ρ ~ 10¹¹ - 10¹⁹ Ωm, σ ~ 10⁻¹⁹ - 10⁻¹¹ S/m)
  • Semiconductors: Have resistivity intermediate between conductors and insulators. Examples: Silicon (Si), Germanium (Ge). (ρ ~ 10⁻⁵ - 10⁶ Ωm, σ ~ 10⁻⁶ - 10⁵ S/m)
• The conductivity of semiconductors is significantly affected by temperature and the presence of impurities.

2. Energy Bands in Solids

• In isolated atoms, electrons occupy discrete energy levels. In solids, these levels spread out into continuous bands due to interatomic interactions.

• Valence Band (VB): The energy band formed by valence electron energy levels. It is usually completely filled or partially filled at 0K.

• Conduction Band (CB): The next higher permitted energy band above the valence band. It is usually empty at 0K. Electrons in this band are free to move and conduct electricity.

• Forbidden Energy Gap (E<0xE1><0xB5><0x8A>): The energy gap between the top of the valence band (E<0xE1><0xB5><0x9B>) and the bottom of the conduction band (E<0xE1><0xB5><0x84>). Electrons cannot exist within this gap. E<0xE1><0xB5><0x8A> = E<0xE1><0xB5><0x84> - E<0xE1><0xB5><0x9B>.

• Classification based on Energy Bands:

  • Conductors: Valence and conduction bands overlap (E<0xE1><0xB5><0x8A> ≈ 0), or the valence band is partially filled. Electrons are readily available for conduction.
  • Insulators: Have a large forbidden energy gap (E<0xE1><0xB5><0x8A> > 3 eV). Electrons cannot easily jump from VB to CB.
  • Semiconductors: Have a small forbidden energy gap (E<0xE1><0xB5><0x8A> < 3 eV). For Si, E<0xE1><0xB5><0x8A> ≈ 1.1 eV; for Ge, E<0xE1><0xB5><0x8A> ≈ 0.7 eV at room temperature. Electrons can be excited from VB to CB by thermal energy or light.

3. Intrinsic Semiconductors

• Pure semiconductors (e.g., pure Si or Ge).
• At 0K, they behave like insulators (VB full, CB empty).
• At higher temperatures, thermal energy breaks some covalent bonds, creating electron-hole pairs.
  • Electron: Moves to the conduction band, becoming a free charge carrier.
  • Hole: The vacancy left in the valence band acts as a positive charge carrier.
• In an intrinsic semiconductor, the number density of free electrons (n<0xE1><0xB5><0x8A>) equals the number density of holes (p<0xE1><0xB5><0x8A>). This common density is called the intrinsic carrier concentration (nᵢ).
  • n<0xE1><0xB5><0x8A> = p<0xE1><0xB5><0x8A> = nᵢ
• Total current I = I<0xE1><0xB5><0x8A> + I<0xE1><0xB5><0x8A> (sum of electron current and hole current).
• Conductivity increases with temperature because nᵢ increases exponentially with temperature.

4. Extrinsic Semiconductors

• Semiconductors with deliberately added impurities to increase conductivity. This process is called doping.

• The impurity atoms are called dopants. Doping concentration is typically very small (e.g., 1 part per million).

• n-type Semiconductor:

  • Doped with pentavalent impurities (Group 15, e.g., Phosphorus (P), Arsenic (As), Antimony (Sb)).
  • The pentavalent atom forms 4 covalent bonds with Si/Ge atoms, leaving one extra electron loosely bound.
  • This extra electron easily moves to the conduction band, even at room temperature.
  • The impurity atom becomes a positive ion but is fixed in the lattice.
  • Pentavalent impurities are called donor impurities because they donate electrons.
  • Majority carriers: Electrons (n<0xE1><0xB5><0x8A>).
  • Minority carriers: Holes (p<0xE1><0xB5><0x8A>).
  • n<0xE1><0xB5><0x8A> >> p<0xE1><0xB5><0x8A>.
  • The donor energy level (E<0xE1><0xB5><0x86>) lies slightly below the conduction band (E<0xE1><0xB5><0x84>).

• p-type Semiconductor:

  • Doped with trivalent impurities (Group 13, e.g., Boron (B), Aluminium (Al), Gallium (Ga), Indium (In)).
  • The trivalent atom forms 3 covalent bonds, leaving a deficiency of one electron (a hole) in the fourth bond.
  • This hole can easily accept an electron from a neighbouring covalent bond, effectively making the hole move.
  • The impurity atom becomes a negative ion after accepting an electron but is fixed in the lattice.
  • Trivalent impurities are called acceptor impurities because they create holes that accept electrons.
  • Majority carriers: Holes (p<0xE1><0xB5><0x8A>).
  • Minority carriers: Electrons (n<0xE1><0xB5><0x8A>).
  • p<0xE1><0xB5><0x8A> >> n<0xE1><0xB5><0x8A>.
  • The acceptor energy level (E<0xE1><0xB5><0x82>) lies slightly above the valence band (E<0xE1><0xB5><0x9B>).

• Mass Action Law: In any semiconductor (intrinsic or extrinsic) at thermal equilibrium, the product of electron and hole concentrations is constant and equals the square of the intrinsic carrier concentration.

  • n<0xE1><0xB5><0x8A> * p<0xE1><0xB5><0x8A> = nᵢ²

5. p-n Junction

• Formed when a p-type semiconductor is brought into close contact (usually fabricated) with an n-type semiconductor.
• Formation Process:
  • Due to concentration difference, holes diffuse from p-side to n-side, and electrons diffuse from n-side to p-side (Diffusion Current).
  • This leaves behind immobile negative acceptor ions (N<0xE1><0xB5><0x82>⁻) on the p-side and immobile positive donor ions (N<0xE1><0xB5><0x86>⁺) on the n-side near the junction.
  • This region containing immobile ions is devoid of free charge carriers and is called the Depletion Region or Space Charge Region.
  • An electric field develops across the depletion region, directed from the n-side to the p-side. This field opposes further diffusion.
  • This electric field creates a potential difference across the junction called the Potential Barrier (V<0xE1><0xB5><0x83>). (Typically ~0.7V for Si, ~0.3V for Ge at room temp).
  • The electric field causes minority carriers (electrons from p-side, holes from n-side) to drift across the junction (Drift Current).
• Equilibrium: In an unbiased p-n junction, the diffusion current equals the drift current, resulting in zero net current.

6. Semiconductor Diode (p-n Junction Diode)

• A p-n junction with metallic contacts at the ends. Allows current flow primarily in one direction.
• Symbol: Arrow points from p-type to n-type (direction of conventional current flow when forward biased).
• Biasing: Applying an external voltage across the diode.
  • Forward Bias: Positive terminal of the battery connected to the p-side, negative terminal to the n-side.
    • Applied voltage opposes the barrier potential (V<0xE1><0xB5><0x83>).
    • Effective barrier height decreases (V<0xE1><0xB5><0x83> - V).
    • Depletion region width decreases.
    • Resistance becomes low.
    • Majority carriers easily cross the junction (diffusion current dominates).
    • Current increases significantly (mA range) once the applied voltage exceeds the barrier potential (knee voltage).
  • Reverse Bias: Positive terminal of the battery connected to the n-side, negative terminal to the p-side.
    • Applied voltage supports the barrier potential (V<0xE1><0xB5><0x83>).
    • Effective barrier height increases (V<0xE1><0xB5><0x83> + V).
    • Depletion region width increases.
    • Resistance becomes very high.
    • Majority carrier flow is blocked.
    • A small current (μA range) flows due to minority carriers drifting across the junction (drift current). This is called Reverse Saturation Current and is largely independent of the applied reverse voltage but depends on temperature.
• V-I Characteristics: A graph showing the relationship between voltage across the diode and the current through it.
  • Forward Characteristic: Current remains negligible until the voltage reaches the knee voltage (≈ barrier potential), after which it increases rapidly.
  • Reverse Characteristic: Current is very small (reverse saturation current) until the breakdown voltage is reached, where the current increases sharply. This can be due to Zener breakdown or Avalanche breakdown.

7. Applications of Junction Diode

• Rectifier: Converts Alternating Current (AC) to Direct Current (DC).
  • Half-Wave Rectifier: Uses one diode. Conducts only during one half-cycle of the AC input. Output is pulsating DC. Low efficiency. High ripple factor.
  • Full-Wave Rectifier: Uses two (centre-tap) or four (bridge) diodes. Conducts during both half-cycles of the AC input. Output is pulsating DC with higher frequency. Higher efficiency than half-wave. Lower ripple factor.
• Filter Circuits: Used to smoothen the pulsating DC output of a rectifier. A common filter is a capacitor connected in parallel with the load resistor. The capacitor charges during peaks and discharges slowly through the load, reducing fluctuations (ripple).
• Zener Diode: A specially designed diode that operates in the reverse breakdown region without being damaged.
  • Heavily doped p and n sides, resulting in a thin depletion region and low breakdown voltage (Zener voltage, V<0xE1><0xB5><0x8B>).
  • Breakdown mechanism is primarily Zener breakdown (field emission) at low voltages and Avalanche breakdown (carrier multiplication) at higher voltages.
  • Application: Voltage Regulator: Maintains a constant output voltage across the load, even if the input voltage or load current changes, provided the input voltage is greater than V<0xE1><0xB5><0x8B>. It is connected in reverse bias parallel to the load.

8. Optoelectronic Junction Devices

• Devices where charge carriers are generated by photons or light is emitted during carrier recombination.
  • Photodiode:
    • Operates in reverse bias.
    • When light falls on the junction, electron-hole pairs are generated in or near the depletion region.
    • These carriers are swept across the junction by the reverse bias field, causing an increase in the reverse current.
    • Reverse current is proportional to the intensity of incident light.
    • Uses: Light detection, optical communication, counters, smoke detectors.
  • Light Emitting Diode (LED):
    • Operates in forward bias.
    • Made from compound semiconductors (like GaAs, GaP, GaAsP) where energy released during electron-hole recombination is emitted as photons (light).
    • The colour of light depends on the semiconductor material and its band gap energy (E<0xE1><0xB5><0x8A> = hν).
    • Advantages: Low voltage operation, fast action, long life, rugged, efficient.
    • Uses: Indicator lamps, displays, optical communication, remote controls.
  • Solar Cell (Photovoltaic Cell):
    • A p-n junction that generates emf when solar radiation falls on it (photovoltaic effect). No external bias is applied.
    • Light generates e-h pairs near the junction.
    • The junction field separates electrons (to n-side) and holes (to p-side), creating a potential difference (photovoltage).
    • When connected to a load, a current flows.
    • Uses: Power supply for satellites, calculators, street lighting, remote areas. Materials: Si, GaAs, CdTe.

9. Junction Transistor

• A semiconductor device with three regions (Emitter, Base, Collector) forming two p-n junctions back-to-back. Used for amplification and switching.
• Types:
  • n-p-n: A thin p-type base sandwiched between two n-type regions (emitter and collector).
  • p-n-p: A thin n-type base sandwiched between two p-type regions (emitter and collector).
• Regions:
  • Emitter (E): Heavily doped. Supplies majority carriers.
  • Base (B): Very thin and lightly doped. Controls the flow of carriers.
  • Collector (C): Moderately doped and largest in size. Collects majority carriers.
• Biasing (for active/amplifying mode):
  • Emitter-Base (EB) junction: Forward biased.
  • Collector-Base (CB) junction: Reverse biased.
• Working (n-p-n example): Electrons from the heavily doped emitter are injected into the thin, lightly doped base (due to forward bias). Most of these electrons pass through the base into the collector region (due to reverse bias attraction by the collector), forming the collector current (I<0xE1><0xB5><0x84>). A small fraction recombines with holes in the base, forming the base current (I<0xE1><0xB5><0x83>).
  • Emitter Current (I<0xE1><0xB5><0x87>) = Base Current (I<0xE1><0xB5><0x83>) + Collector Current (I<0xE1><0xB5><0x84>) => I<0xE1><0xB5><0x87> = I<0xE1><0xB5><0x83> + I<0xE1><0xB5><0x84>.
• Transistor Configurations: Common Base (CB), Common Emitter (CE), Common Collector (CC). CE is most widely used for voltage amplification.
• Transistor as an Amplifier (CE Configuration):
  • Input signal applied between base and emitter. Output taken across collector and emitter.
  • Current Gain:
    • DC Current Gain (β<0xE1><0xB5><0x85><0xE1><0xB5><0x84>): β<0xE1><0xB5><0x85><0xE1><0xB5><0x84> = I<0xE1><0xB5><0x84> / I<0xE1><0xB5><0x83> (Typically 20-500)
    • AC Current Gain (β<0xE1><0xB5><0x82><0xE1><0xB5><0x84>): β<0xE1><0xB5><0x82><0xE1><0xB5><0x84> = (ΔI<0xE1><0xB5><0x84> / ΔI<0xE1><0xB5><0x83>) at constant V<0xE1><0xB5><0x84><0xE1><0xB5><0x87>
  • Voltage Gain (A<0xE1><0xB5><0x9B>): A<0xE1><0xB5><0x9B> = V<0xE1><0xB5><0x90><0xE1><0xB5><0x98><0xE1><0xB5><0x9C> / V<0xE1><0xB5><0x8A><0xE1><0xB5><0x8B> = β<0xE1><0xB5><0x82><0xE1><0xB5><0x84> * (R<0xE1><0xB5><0x90><0xE1><0xB5><0x98><0xE1><0xB5><0x9C> / R<0xE1><0xB5><0x8A><0xE1><0xB5><0x8B>) (where R<0xE1><0xB5><0x90><0xE1><0xB5><0x98><0xE1><0xB5><0x9C> is output/load resistance, R<0xE1><0xB5><0x8A><0xE1><0xB5><0x8B> is input resistance).
  • Power Gain (A<0xE1><0xB5><0x9D>): A<0xE1><0xB5><0x9D> = A<0xE1><0xB5><0x9B> * β<0xE1><0xB5><0x82><0xE1><0xB5><0x84>
  • In CE amplifier, the output voltage is 180° out of phase with the input voltage.
• Transistor as a Switch:
  • Cut-off Region: Input voltage is low/zero. Both junctions are effectively reverse biased (or zero biased). I<0xE1><0xB5><0x84> ≈ 0. Transistor is OFF.
  • Saturation Region: Input voltage is high. Both junctions become forward biased. I<0xE1><0xB5><0x84> reaches its maximum value, determined by the supply voltage and load resistance. Transistor is ON.

10. Digital Electronics and Logic Gates

• Analog Signal: Varies continuously with time.
• Digital Signal: Has only two discrete levels, usually represented as 0 (Low) and 1 (High).
• Logic Gates: Basic building blocks of digital circuits that perform logical operations based on Boolean algebra.
  • NOT Gate (Inverter): One input, one output. Output is the complement of the input. Y = A̅
  • OR Gate: Two or more inputs, one output. Output is HIGH (1) if any input is HIGH (1). Y = A + B
  • AND Gate: Two or more inputs, one output. Output is HIGH (1) only if all inputs are HIGH (1). Y = A . B
  • NAND Gate (NOT AND): Output is LOW (0) only if all inputs are HIGH (1). Y = (A . B)̅. It's a Universal Gate (can implement AND, OR, NOT).
  • NOR Gate (NOT OR): Output is HIGH (1) only if all inputs are LOW (0). Y = (A + B)̅. It's also a Universal Gate.
  • Know the symbols and truth tables for each gate.

11. Integrated Circuits (ICs)

• Complete electronic circuits (containing transistors, diodes, resistors, capacitors) fabricated on a single small chip of semiconductor material (usually Silicon).
• Classified based on the number of components/gates: SSI (Small Scale Integration), MSI (Medium), LSI (Large), VLSI (Very Large).

Multiple Choice Questions (MCQs)

1. In an n-type semiconductor, the majority charge carriers are:
   (a) Holes
   (b) Electrons
   (c) Protons
   (d) Both electrons and holes

2. The forbidden energy gap for Silicon (Si) at room temperature is approximately:
   (a) 0.3 eV
   (b) 0.7 eV
   (c) 1.1 eV
   (d) 5.0 eV

3. When a p-n junction diode is forward biased:
   (a) The depletion region width increases.
   (b) The potential barrier increases.
   (c) The resistance offered by the diode is high.
   (d) The majority carriers flow across the junction.

4. A Zener diode is primarily used as a:
   (a) Rectifier
   (b) Amplifier
   (c) Voltage regulator
   (d) Oscillator

5. Which of the following logic gates is known as a universal gate?
   (a) AND gate
   (b) OR gate
   (c) NOT gate
   (d) NAND gate

6. In a common emitter (CE) transistor amplifier, the output voltage is phase-shifted with respect to the input voltage by:
   (a) 0°
   (b) 90°
   (c) 180°
   (d) 270°

7. Doping a pure semiconductor with a trivalent impurity results in:
   (a) An n-type semiconductor
   (b) A p-type semiconductor
   (c) An intrinsic semiconductor
   (d) An insulator

8. A solar cell works on the principle of:
   (a) Photoconductive effect
   (b) Photovoltaic effect
   (c) Photoelectric effect
   (d) Thermoelectric effect

9. In a p-n-p transistor, the current consists mainly of:
   (a) Electrons
   (b) Holes
   (c) Positive ions
   (d) Negative ions

10. The process of converting AC into DC is called:
    (a) Amplification
    (b) Rectification
    (c) Oscillation
    (d) Modulation

Answer Key for MCQs:

1. (b)
2. (c)
3. (d)
4. (c)
5. (d) (NOR is also a universal gate)
6. (c)
7. (b)
8. (b)
9. (b)
10. (b)

Study these notes carefully, focusing on the definitions, principles, characteristics of devices, and their applications. Pay attention to the energy band diagrams and V-I characteristics. Good luck with your preparation!