Learning Objectives
- Understand energy band theory and classification of materials
- Learn about intrinsic and extrinsic semiconductors
- Study p-n junction diode characteristics and applications
- Understand transistor operation and its use as switch/amplifier
- Learn about logic gates and their truth tables
Key Concepts
Energy Band Theory
In solids, atomic energy levels split into bands due to interactions.
Valence band: Highest occupied band. Conduction band: Lowest unoccupied band.
Band gap (E_g): Energy gap between valence and conduction bands.
- Conductors: Overlapping bands or partially filled conduction band (E_g = 0).
- Insulators: Large band gap (E_g > 3 eV). Example: diamond (E_g = 5.47 eV).
- Semiconductors: Small band gap (E_g ≈ 1 eV). Si: 1.1 eV, Ge: 0.67 eV.
Intrinsic and Extrinsic Semiconductors
Intrinsic: Pure semiconductor. n_e = n_h = n_i. Conductivity increases with temperature.
Extrinsic (doped):
n-type: Doped with pentavalent impurity (P, As, Sb). Majority carriers: electrons. n_e >> n_h.
p-type: Doped with trivalent impurity (B, Al, Ga, In). Majority carriers: holes. n_h >> n_e.
In both types: n_e × n_h = n_i² (mass action law).
p-n Junction Diode
Formed by joining p-type and n-type semiconductors. A depletion region forms at the junction.
Forward bias: P connected to +, N to -. Barrier potential reduced, current flows easily. Barrier voltage: Si ≈ 0.7 V, Ge ≈ 0.3 V.
Reverse bias: P to -, N to +. Barrier increases, very small reverse saturation current flows.
V-I characteristics: Non-linear. Forward: exponential rise. Reverse: small constant current until breakdown.
Diode equation: I = I₀(e^(eV/kT) - 1)
Diode Applications
Half-wave rectifier: Uses one diode, output frequency = input frequency.
Full-wave rectifier: Uses two diodes (centre-tap) or four (bridge), output frequency = 2 × input frequency.
Zener diode: Operates in reverse breakdown for voltage regulation. V_Z remains constant.
LED: Emits light in forward bias. Used in displays, indicators.
Photodiode: Operates in reverse bias, current ∝ intensity of light. Used in light detectors.
Solar cell: Converts sunlight to electricity. Open-circuit voltage ~ 0.5-1 V.
Transistor
Three-terminal device: Emitter (E), Base (B), Collector (C). Two types: npn and pnp.
Configuration: Common emitter (CE), common base (CB), common collector (CC).
CE amplifier:
I_E = I_B + I_C
Current gain: β = I_C/I_B (typically 20-200). α = I_C/I_E. Relation: β = α/(1-α).
Voltage gain: A_v = β × R_L/R_in. Output is 180° out of phase with input.
Transistor as switch: Cutoff (off) when V_BE < 0.7 V; Saturation (on) when base current is sufficient.
Logic Gates
Basic gates: AND, OR, NOT. Universal gates: NAND, NOR.
- AND: Y = A·B (output 1 only if both inputs are 1)
- OR: Y = A+B (output 1 if any input is 1)
- NOT: Y = A̅ (output is complement of input)
- NAND: Y = (A·B)̅ (complement of AND). Universal gate.
- NOR: Y = (A+B)̅ (complement of OR). Universal gate.
- XOR: Y = A⊕B = A̅B + AB̅ (output 1 if inputs differ)
De Morgan's theorems: (A·B)̅ = A̅ + B̅; (A+B)̅ = A̅ · B̅
Summary
Semiconductors have small band gaps that allow controlled conductivity through doping. p-n junctions form the basis of diodes, which rectify AC to DC and have many applications (LED, photodiode, solar cell, Zener). Transistors amplify signals and act as switches, forming the basis of digital electronics. Logic gates perform Boolean operations and are the building blocks of computers.
Important Terms
- Band Gap: Energy difference between valence and conduction bands
- Doping: Adding impurities to change semiconductor properties
- Depletion Region: Charge-free region at p-n junction
- Forward Bias: Reduced barrier, easy current flow
- Reverse Bias: Increased barrier, minimal current
- Current Gain (β): Ratio of collector to base current in CE configuration
Quick Revision
- Band gap: Si = 1.1 eV, Ge = 0.67 eV; Conductor: 0, Insulator: > 3 eV
- n-type: pentavalent dopant (electrons majority); p-type: trivalent (holes majority)
- n_e × n_h = n_i²; Forward bias: Si 0.7V, Ge 0.3V
- β = I_C/I_B; α = I_C/I_E; β = α/(1-α)
- NAND and NOR are universal gates
- De Morgan: (A·B)̅ = A̅+B̅; (A+B)̅ = A̅·B̅