ELECTRONIC DEVICES | Energy | PHYSICS | CUET JEE | SELF STUDY | CBSE

 

PHYSICS  |  Class XII

Chapter 14

ELECTRONIC DEVICES

Semiconductor Electronics

Energy Bands  ◆  p-n Diode  ◆  Transistors  ◆  Logic Gates  ◆  Rectifiers

 

Introduction to Semiconductor Electronics

Semiconductor Electronics is the branch of physics and engineering that deals with the electrical properties of semiconductor materials and the devices made from them. The invention of the transistor in 1947 at Bell Laboratories by Bardeen, Brattain, and Shockley initiated the modern electronics revolution — fundamentally transforming communication, computing, medicine, transportation, and virtually every other area of human activity.

Today, billions of semiconductor devices are manufactured every year. A single modern microprocessor chip (smaller than your fingernail) contains over 50 billion transistors. Semiconductor devices are the backbone of smartphones, computers, satellites, medical equipment, electric vehicles, and renewable energy systems. Understanding their operating principles begins with understanding the band theory of solids.

 

1. Classification of Solids — Energy Band Theory

In isolated atoms, electrons occupy discrete energy levels. When a large number of atoms come together to form a solid, these discrete levels broaden into continuous energy bands due to the interaction between neighbouring atoms. The two most important bands are:

Valence Band (VB): The highest energy band that is completely or nearly completely filled with electrons at absolute zero temperature. These electrons are tightly bound to the atoms.

Conduction Band (CB): The energy band above the valence band. Electrons in this band are free to move throughout the solid and constitute the electric current.

Forbidden Energy Gap (Eg): The energy difference between the top of the valence band and the bottom of the conduction band. No electron can have an energy within this gap. The size of Eg determines whether a material is a conductor, semiconductor, or insulator.

 

Figure 1: Energy Band Diagrams — Conductor (overlapping bands), Semiconductor (small gap ~1 eV), Insulator (large gap > 5 eV)

Property	Conductor (Metal)	Semiconductor	Insulator
Energy Gap (Eg)	Zero (bands overlap)	~0.1 to ~3 eV	More than 5 eV
Examples	Cu, Al, Fe, Ag	Si (1.1 eV), Ge (0.7 eV)	Glass, Diamond (5.5 eV), Rubber
Conductivity	Very High (10⁶–10⁸ S/m)	Intermediate (10⁻⁶–10⁴ S/m)	Very Low (< 10⁻¹⁰ S/m)
Effect of Temperature	Conductivity decreases	Conductivity increases	No significant change
Conduction Mechanism	Free electrons (always present)	Electrons & holes (thermally generated)	None under normal conditions
Valence Band	Partially filled / overlapping	Completely filled at 0 K	Completely filled

 

1.1 Intrinsic Semiconductors

A pure semiconductor, without any impurity atoms added, is called an Intrinsic Semiconductor. At absolute zero (0 K), the valence band is completely filled and the conduction band is empty — so it behaves like an insulator. As temperature increases, some electrons gain enough thermal energy to jump across the forbidden gap into the conduction band, leaving behind vacancies called Holes in the valence band.

Hole: A hole is the absence of an electron in the valence band. It behaves like a positively charged particle with the same magnitude of charge as an electron (+e). In an electric field, holes move in the direction of the field (opposite to electrons).

In an intrinsic semiconductor: The number of electrons in the conduction band (nₑ) always equals the number of holes in the valence band (nₕ). That is, nₑ = nₕ = nᵢ (intrinsic carrier concentration).

 

Intrinsic Carrier Concentration

nₑ = nₕ = nᵢ  ∝  T^(3/2) × exp(−Eg/2kT)

 

Mass Action Law

nₑ × nₕ  =  nᵢ²   (always constant at given T)

 

1.2 Extrinsic Semiconductors (Doped Semiconductors)

The electrical conductivity of a semiconductor can be dramatically increased and controlled by adding a tiny amount of a specific impurity — a process called Doping. The doped semiconductor is called an Extrinsic Semiconductor. There are two types:

Property	n-type Semiconductor	p-type Semiconductor
Dopant (Impurity)	Pentavalent atoms (5 valence electrons): Phosphorus (P), Arsenic (As), Antimony (Sb)	Trivalent atoms (3 valence electrons): Boron (B), Aluminium (Al), Indium (In), Gallium (Ga)
Donor/Acceptor	Donor impurity — donates one extra electron to conduction band	Acceptor impurity — accepts one electron from valence band, creates hole
Majority Carriers	Electrons (nₑ >> nₕ)	Holes (nₕ >> nₑ)
Minority Carriers	Holes	Electrons
Fermi Level	Shifts closer to conduction band	Shifts closer to valence band
Net Charge	Electrically neutral overall	Electrically neutral overall

 

Important: Even in a doped semiconductor, the mass action law nₑ × nₕ = nᵢ² still holds. So if we increase electrons (n-type), the hole concentration decreases proportionally.

 

2. p-n Junction Diode

A p-n junction is formed when a p-type semiconductor and an n-type semiconductor are joined together — either by doping a single crystal differently on two sides, or by other fabrication methods. The p-n junction is the fundamental building block of virtually all semiconductor devices.

Figure 2: p-n Junction Diode — Holes (p-side) and electrons (n-side) diffuse across the junction, creating a depletion region with a built-in electric field.

2.1 Formation of the Depletion Region

When p-type and n-type materials are joined, the following sequence of events occurs:

◆        Diffusion: Holes from the p-side diffuse across the junction to the n-side (high concentration to low), and electrons from the n-side diffuse to the p-side.

◆        Ionisation: As holes leave the p-side near the junction, they expose negatively charged acceptor ions. As electrons leave the n-side, they expose positively charged donor ions. These immobile ions create a layer of space charge near the junction.

◆        Depletion Region: The region near the junction — depleted of free charge carriers (holes and electrons) — is called the Depletion Region or Space Charge Region. Its width is typically 0.5–1 µm.

◆        Built-in Electric Field (E): The exposed positive ions (n-side) and negative ions (p-side) create an electric field pointing from n to p across the depletion region. This field opposes further diffusion — creating an equilibrium.

◆        Built-in Potential (V₀): The electric field creates a potential barrier (contact potential or built-in potential V₀) across the junction — about 0.7 V for silicon and 0.3 V for germanium.

 

Built-in Potential Barrier

V₀  ≈  0.7 V (Silicon)     V₀  ≈  0.3 V (Germanium)

 

2.2 Forward Bias and Reverse Bias

Figure 3: Forward Bias — positive terminal to p-side, depletion narrows, large current flows. Reverse Bias — positive terminal to n-side, depletion widens, tiny current flows.

Aspect	Forward Bias	Reverse Bias
Connection	Positive terminal of battery to p-side; Negative to n-side	Positive terminal to n-side; Negative to p-side
Effect on Depletion Region	Depletion region narrows and eventually vanishes	Depletion region widens
Effect on Barrier	Barrier potential decreases	Barrier potential increases
Current Flow	Large forward current (milliamperes to amperes)	Very small reverse saturation current (microamperes)
Carriers	Majority carriers flow across junction	Only minority carriers cause tiny leakage current
Resistance	Very low resistance	Very high resistance

 

2.3 I-V Characteristics

Figure 4: I-V Characteristics of p-n Diode — Forward: exponential current rise after knee voltage; Reverse: near-zero current until breakdown voltage Vbr.

Diode Current (Shockley Equation)

I  =  I₀ [ exp(eV/ηkT) − 1 ]

 

Here I₀ = reverse saturation current (nA range), e = electron charge, V = applied voltage, η = ideality factor (1 for Ge, 2 for Si), k = Boltzmann constant, T = absolute temperature. The knee voltage (threshold voltage) is ~0.7 V for Si and ~0.3 V for Ge. Below this, current is negligible; beyond it, current rises sharply.

 

3. Junction Diode as a Rectifier

A rectifier converts alternating current (AC) into direct current (DC). Since a p-n diode conducts only in forward bias, it can be used to allow only one half (or both halves) of an AC signal to pass through. This is the most common application of p-n junction diodes in power electronics.

3.1 Half-Wave Rectifier

A half-wave rectifier uses a single diode. During the positive half-cycle of AC input, the diode is forward biased and conducts — allowing current through the load resistor RL. During the negative half-cycle, the diode is reverse biased and does not conduct — no current flows. The output is a pulsating DC that exists only for half the time.

DC Output Voltage (Half-Wave)

V_dc  =  V_m / π  ≈  0.318 V_m

 

Ripple Factor (Half-Wave)

γ  =  1.21   (very high — lots of AC ripple)

 

Efficiency (Half-Wave)

η  =  40.6%   (theoretical maximum)

 

3.2 Full-Wave Rectifier

A full-wave rectifier utilises both halves of the AC cycle. It comes in two configurations:

Centre-Tap Full-Wave Rectifier: Uses two diodes and a centre-tapped transformer. One diode conducts during positive half-cycle, the other during negative half-cycle. Both produce current in the same direction through RL.

Bridge Rectifier: Uses four diodes arranged in a bridge configuration. No centre-tap transformer needed. During positive half-cycle, diodes D1 and D3 conduct; during negative half-cycle, D2 and D4 conduct. The output is always in the same direction — full-wave rectified DC.

 

DC Output Voltage (Full-Wave)

V_dc  =  2V_m / π  ≈  0.636 V_m

 

Ripple Factor (Full-Wave)

γ  =  0.48   (much lower than half-wave)

 

Efficiency (Full-Wave)

η  =  81.2%   (theoretical maximum)

 

3.3 Filter and Voltage Regulator

The pulsating DC output of a rectifier contains AC ripple components. A filter (typically a large capacitor C in parallel with the load, or an LC filter) smooths the output by charging when the rectified voltage is high and discharging slowly through the load when it drops. A Zener diode connected in reverse bias across the output acts as a voltage regulator — maintaining a constant output voltage despite variations in input or load.

Zener Diode Voltage Regulation

V_out  =  V_Z  (Zener breakdown voltage, constant)

 

 

4. Special Purpose Diodes

Diode	Principle / Key Feature	Symbol / Operation	Main Application
Zener Diode	Operates in reverse breakdown region. Breakdown voltage (Vz) is sharp and stable.	Reverse biased; Vz = fixed voltage (2.4 V to 200 V typical)	Voltage regulation, reference voltage, overvoltage protection
LED (Light Emitting Diode)	In forward bias, electrons recombine with holes at junction, releasing energy as photons (light).	Forward biased; colour depends on semiconductor material (band gap)	Display indicators, streetlights, optical communication (IR LED), smartphones
Photodiode	Reverse biased; incident photons generate electron-hole pairs, increasing reverse current.	Reverse biased; current proportional to light intensity	Light detectors, optical fibre receivers, solar cells, CCD cameras
Solar Cell	p-n junction converts light (photons) directly into electrical energy without any bias voltage.	No external bias; photovoltaic effect; V ~ 0.5–0.6 V	Solar panels, calculators, satellites, power generation

 

LED Colours and Materials: GaAs → Infrared (IR). GaAsP → Red/Orange. GaP → Green/Yellow. GaN → Blue/Violet/White. The energy gap Eg determines the photon energy and hence the colour: E = hν = hc/λ. Higher Eg → shorter wavelength → blue/violet light.

 

Solar Cell Efficiency: The theoretical maximum efficiency (Shockley-Queisser limit) for a single-junction solar cell is about 33%. Practical silicon solar cells achieve 15–22%. Multi-junction cells (GaInP/GaAs/Ge) can exceed 40%.

 

5. Bipolar Junction Transistors (BJT)

A Bipolar Junction Transistor (BJT) is a three-terminal semiconductor device consisting of two p-n junctions connected back to back. It can amplify electrical signals and act as a switch. The transistor was invented in 1947 and is arguably the most important invention of the 20th century — enabling the entire digital revolution.

Three Terminals: (1) Emitter (E) — heavily doped, emits majority carriers. (2) Base (B) — very thin and lightly doped, controls carrier flow. (3) Collector (C) — moderately doped, collects majority carriers from emitter.

Two Types: NPN (n-type emitter and collector, p-type base) and PNP (p-type emitter and collector, n-type base). NPN transistors are more common because electrons have higher mobility than holes.

 

Figure 5: NPN Transistor Structure — Thin lightly-doped p-type base between two n-type regions. Common Emitter (CE) configuration used as signal amplifier.

5.1 Working of an NPN Transistor

In normal operation (active region), the Emitter-Base (EB) junction is forward biased and the Collector-Base (CB) junction is reverse biased.

◆        The forward-biased EB junction injects a large number of electrons from the heavily-doped n-type emitter into the thin p-type base.

◆        Because the base is very thin (a few micrometres) and lightly doped, most of these injected electrons (about 95–99%) diffuse across the base and are swept into the collector by the reverse-biased CB junction's electric field.

◆        Only a tiny fraction (1–5%) of electrons recombine with holes in the base, constituting the small base current IB.

◆        Result: A small change in base current (IB) controls a large change in collector current (IC). This is the amplification mechanism.

 

Current Relationship

I_E  =  I_C  +  I_B    (Kirchhoff's Current Law)

 

Current Gain (β or hFE)

β  =  I_C / I_B      (common emitter; β = 20 to 500)

 

Current Gain (α)

α  =  I_C / I_E      (common base; α < 1, typically 0.95–0.99)

 

Relation between α and β

β  =  α / (1 − α)     and     α  =  β / (β + 1)

 

5.2 Transistor Configurations

Configuration	Input	Output	Current Gain	Voltage Gain	Use
Common Base (CB)	Emitter	Collector	α < 1	High	RF amplifiers, high-frequency applications
Common Emitter (CE)	Base	Collector	β = 20–500	High	Most common — audio amplifiers, switching
Common Collector (CC)	Base	Emitter	≈ β+1	< 1 (≈1)	Impedance matching, buffer amplifier

 

5.3 Transistor as an Amplifier (CE Configuration)

In the CE configuration, a small AC signal (Vin) applied at the base is amplified and appears as a larger signal (Vout) at the collector — with a 180° phase reversal (inverted output). The transistor amplifier has a DC bias (Q-point) set so it operates in the active region for the full swing of the input signal.

Voltage Gain (CE Amplifier)

Av  =  −β × (R_C / R_in)   (negative sign = 180° phase shift)

 

Power Gain

Ap  =  β² × (R_C / R_in)  =  Av × Ai

 

5.4 Transistor as a Switch

A transistor operates as a switch when it is driven between Saturation (fully ON) and Cut-off (fully OFF) — never in the active (amplifier) region. This is the basis of digital electronics and logic gates.

◆        Cut-off Region: Both EB and CB junctions are reverse biased. IB ≈ 0, IC ≈ 0. Transistor is OFF (like an open switch).

◆        Saturation Region: Both EB and CB junctions are forward biased. IC is maximum (limited by external circuit). Transistor is ON (like a closed switch). VCE ≈ 0.2 V (VCEsat).

◆        Switching applications: Logic gates, NOT gates, flip-flops, counters, microprocessors — all use transistors as switches, switching billions of times per second in modern chips.

 

6. Digital Electronics and Logic Gates

Digital electronics deals with signals that have only two discrete levels: HIGH (logic 1, typically +5 V or +3.3 V) and LOW (logic 0, typically 0 V). Boolean algebra, developed by George Boole, is the mathematical framework for digital logic. Logic gates are the basic building blocks of all digital circuits.

Figure 6: Basic Logic Gates — AND, OR, NOT, NAND with symbols, truth tables, and Boolean expressions. All complex digital circuits are built from these gates.

6.1 Basic Logic Gates — Truth Tables and Boolean Expressions

Gate	Boolean Expression	A=0,B=0	A=0,B=1	A=1,B=0	A=1,B=1
AND	Y = A · B	0	0	0	1
OR	Y = A + B	0	1	1	1
NOT	Y = A'  (NOT A)	1	—	—	0
NAND	Y = (A·B)'	1	1	1	0
NOR	Y = (A+B)'	1	0	0	0
XOR	Y = A ⊕ B	0	1	1	0
XNOR	Y = (A ⊕ B)'	1	0	0	1

 

6.2 Universal Gates — NAND and NOR

NAND and NOR gates are called Universal Gates because any other logic gate (AND, OR, NOT, XOR, XNOR) can be constructed using only NAND gates, or only NOR gates. This is extremely valuable in IC chip manufacturing — a single type of gate can implement any digital function.

Implementing Basic Gates from NAND Gates Only

NOT from NAND:  Connect both inputs of NAND together → A NAND A = (A·A)' = A'  ✓ AND from NAND:  NOT (NAND) → A·B = ((A·B)')' — use NAND then invert output with another NAND  ✓ OR from NAND:   Use De Morgan's theorem: A+B = (A'·B')' — invert each input, then NAND  ✓ NOR from NAND:  AND the inverted inputs, then NAND again  ✓ All digital chips (including Intel/AMD processors) are built using primarily NAND or NOR gate logic.

 

6.3 De Morgan's Theorems

De Morgan's Theorems are the most important identities in Boolean algebra for logic design. They state how to distribute a NOT operation over AND and OR:

De Morgan's First Theorem

(A · B)'  =  A'  +  B'    (NAND = OR of NOTs)

 

De Morgan's Second Theorem

(A + B)'  =  A' · B'    (NOR = AND of NOTs)

 

6.4 Boolean Algebra — Key Laws

Law / Identity	Expression 1	Expression 2
Identity Law	A + 0 = A	A · 1 = A
Null Law	A + 1 = 1	A · 0 = 0
Idempotent Law	A + A = A	A · A = A
Complement Law	A + A' = 1	A · A' = 0
Double Negation	(A')' = A	(same both sides)
Commutative Law	A+B = B+A	A·B = B·A
Associative Law	(A+B)+C = A+(B+C)	(A·B)·C = A·(B·C)
Distributive Law	A·(B+C) = A·B+A·C	A+(B·C) = (A+B)·(A+C)
De Morgan 1	(A·B)' = A'+B'	NAND = OR of NOTs
De Morgan 2	(A+B)' = A'·B'	NOR = AND of NOTs

 

 

7. Integrated Circuits (IC) — Brief Overview

An Integrated Circuit (IC) is a miniaturised electronic circuit that contains thousands to billions of transistors, diodes, resistors, and capacitors — all fabricated on a single chip of semiconductor (usually silicon), typically a few millimetres square. ICs were invented independently by Jack Kilby (Texas Instruments, 1958) and Robert Noyce (Fairchild Semiconductor, 1959). Kilby received the Nobel Prize in Physics in 2000.

IC Scale	Abbreviation	Number of Components	Examples
Small Scale Integration	SSI	< 100	Basic logic gates (7400 series)
Medium Scale Integration	MSI	100 – 1,000	Multiplexers, decoders, adders
Large Scale Integration	LSI	1,000 – 100,000	8-bit microprocessors (Intel 8080)
Very Large Scale Integration	VLSI	100,000 – 10 million	Modern CPUs, GPUs, microcontrollers
Ultra Large Scale Integration	ULSI	> 10 million	Modern processors (50 billion transistors per chip)

 

The transistor count in chips has been doubling roughly every two years since the 1960s — a trend known as Moore's Law, observed by Intel co-founder Gordon Moore. Modern chips (Apple M4, AMD Ryzen 9000, Qualcomm Snapdragon) use 3 nm to 5 nm process nodes — meaning transistors smaller than 10 silicon atoms wide.

 

8. Master Formula & Key Values Table

Formula / Quantity	Expression / Value	Notes
Mass Action Law	nₑ × nₕ = nᵢ²	Always holds, even in doped semiconductors
Built-in Voltage	V₀ ≈ 0.7 V (Si), 0.3 V (Ge)	Potential barrier at unbiased junction
Diode (Shockley Eq.)	I = I₀[exp(eV/ηkT) − 1]	I₀ = reverse saturation current
Transistor KCL	IE = IC + IB	Always valid for any BJT
Current Gain (β)	β = IC / IB = 20 to 500	Common-emitter; most useful parameter
Current Gain (α)	α = IC / IE < 1	Common-base; α ≈ 0.95 – 0.99
α−β Relation	β = α/(1−α);  α = β/(β+1)	Both are constants for a given transistor
CE Voltage Gain	Av = −β(RC/Rin)	Negative sign = 180° phase inversion
H-W Rectifier Vdc	Vdc = Vm/π ≈ 0.318 Vm	Vm = peak AC voltage; low efficiency
F-W Rectifier Vdc	Vdc = 2Vm/π ≈ 0.636 Vm	Full-wave; ripple factor = 0.48
LED Photon Energy	E = hν = hc/λ = Eg	Colour depends on semiconductor Eg
Ripple Factor (HW)	γ = 1.21	High ripple — needs filter
Ripple Factor (FW)	γ = 0.48	Lower ripple — more useful DC
Si Energy Gap	Eg = 1.1 eV	At room temperature (300 K)
Ge Energy Gap	Eg = 0.7 eV	Narrower gap → more thermally generated carriers
NAND Universal	NOT: A NAND A = A'	NAND can implement any logic function
De Morgan 1	(A·B)' = A' + B'	Fundamental Boolean identity
De Morgan 2	(A+B)' = A'·B'	Fundamental Boolean identity

 

 

9. Quick Revision — Key Points to Remember

Semiconductors & p-n Junction — Must Know

* Conductors: Eg = 0 (bands overlap). Semiconductors: Eg ~ 1 eV. Insulators: Eg > 5 eV. * Intrinsic: nₑ = nₕ = nᵢ. Extrinsic: n-type (electrons majority), p-type (holes majority). * Mass action law: nₑ × nₕ = nᵢ² (always holds at given temperature). * Depletion region: forms at junction due to diffusion; creates built-in field from n to p. * Forward bias (p+ n−): depletion narrows → large current. Knee voltage: 0.7 V (Si), 0.3 V (Ge). * Reverse bias (p− n+): depletion widens → tiny current (~µA). Breakdown at Vbr. * Zener diode: works in reverse breakdown; Vz is constant → used for voltage regulation. * LED: forward biased; E = hν = Eg → emits photons. Photodiode: reverse biased → current α light.

 

Transistors & Logic Gates — Must Know

* BJT: 3 terminals — Emitter (E, heavily doped), Base (B, very thin + lightly doped), Collector (C). * Active region: EB forward biased, CB reverse biased. IE = IC + IB; IC >> IB (β = IC/IB = 20-500). * CE config: most common; voltage gain Av = −βRC/Rin; 180° phase inversion in output. * Switch: Saturation (both junctions forward biased → ON). Cut-off (both reverse biased → OFF). * AND: Y=A·B (output 1 only if ALL inputs 1). OR: Y=A+B (output 1 if ANY input 1). * NOT: Y=A' (inverts input). NAND: Y=(A·B)' — Universal gate. NOR: Y=(A+B)' — Universal gate. * De Morgan: (A·B)' = A'+B' and (A+B)' = A'·B'. Essential for logic simplification. * Full-wave rectifier: Vdc = 2Vm/π. Ripple factor = 0.48. Efficiency = 81.2%.

 

Important Numerical Values

* Si: Eg = 1.1 eV; threshold voltage = 0.7 V. Ge: Eg = 0.7 eV; threshold voltage = 0.3 V. * Typical β values: 50–300 for NPN transistors. Typical α values: 0.95–0.99. * Reverse saturation current I₀ ~ nA (nanoamperes) at room temperature. * Photodiode: reverse biased, current increases with light intensity. * Solar cell: no external bias; photovoltaic effect; ~0.5 V per cell; efficiency 15–22% (Si). * Ripple factor: Half-wave = 1.21, Full-wave = 0.48. Lower is better.

 

— End of Chapter 14: Electronic Devices (Semiconductor Electronics) —