What this chapter is about
This chapter introduces the physics of semiconductors and how they are used to build electronic devices. You move from passive components like resistors to active devices that can amplify signals and switch currents on and off. Understanding semiconductors is essential because nearly every modern electronic system—from mobile phones to computers—relies on semiconductor devices.
You begin by classifying solids into conductors, insulators and semiconductors based on their energy band structure. You then study intrinsic and extrinsic semiconductors, learning how adding impurities (doping) creates n-type and p-type materials. The heart of the chapter is the p-n junction diode: how it forms, how it behaves under forward and reverse bias, and its applications in rectification. You also meet special-purpose diodes (Zener diode, LED, photodiode) and the bipolar junction transistor, which can amplify signals and act as a switch in digital logic circuits.
After studying this chapter you should be able to explain conduction in semiconductors, draw and interpret the I–V characteristic of a diode, analyse half-wave and full-wave rectifier circuits, describe transistor action, and recognise basic logic gates.
Key ideas
- Energy bands in solids: In a crystal, atomic energy levels spread into bands. The valence band holds electrons that are bound; the conduction band holds electrons free to carry current. The energy gap Eg between them determines whether a material is a conductor (no gap or overlapping bands), semiconductor (small gap, about 1 eV) or insulator (large gap, several eV).
- Intrinsic and extrinsic semiconductors: Pure silicon or germanium at 0 K has a full valence band and empty conduction band, so it does not conduct. At room temperature, thermal energy excites some electrons across the gap, creating electron–hole pairs. Doping with pentavalent atoms (P, As) gives extra electrons (n-type); doping with trivalent atoms (B, Al) creates extra holes (p-type).
- p-n junction formation: When p-type and n-type materials are joined, electrons diffuse into the p-side and holes into the n-side, leaving behind fixed ions. This creates a depletion region with a built-in potential barrier (about 0.7 V for Si, 0.3 V for Ge) that opposes further diffusion.
- Biasing a diode: Forward bias (p connected to positive terminal) reduces the barrier, allowing current to flow easily. Reverse bias widens the depletion region, and only a tiny reverse saturation current flows until breakdown occurs.
- Rectification: A diode converts alternating current to direct current. A half-wave rectifier uses one diode and conducts only during one half-cycle. A full-wave rectifier (centre-tapped transformer or bridge arrangement) conducts during both half-cycles, giving smoother output.
- Zener diode: Designed to operate in reverse breakdown at a well-defined Zener voltage Vz. Used as a voltage regulator because current through it can vary while voltage across it stays nearly constant.
- Transistor basics: A bipolar junction transistor (BJT) has three doped regions—emitter, base and collector—forming either n-p-n or p-n-p structures. The thin, lightly doped base allows most carriers from the emitter to reach the collector. In the active region, a small base current controls a much larger collector current, giving current amplification.
- Logic gates: Electronic circuits that perform Boolean operations. Basic gates are AND, OR and NOT. Combinations like NAND and NOR are universal gates because any logic function can be built from them.
Formulas and facts to remember
1. Conductivity of a semiconductor: σ = e (neμe + nhμh), where ne and nh are electron and hole concentrations, μe and μh are their mobilities, and e is the electronic charge.
2. Mass-action law (at thermal equilibrium): ne × nh = ni², where ni is the intrinsic carrier concentration.
3. Diode current (ideal): I = I0 [exp(eV / kT) − 1], where I0 is the reverse saturation current, V is the applied voltage, k is Boltzmann's constant and T is absolute temperature.
4. Knee voltage: Approximately 0.7 V for silicon diodes, 0.3 V for germanium diodes.
5. Current gain of a transistor (common-emitter): β = Ic / Ib, typically 20–500.
6. Relation between α and β: β = α / (1 − α), where α = Ic / Ie is the common-base current gain (slightly less than 1).
7. Zener regulation: The Zener diode maintains nearly constant output voltage Vz across a load even if input voltage or load current varies, provided it stays in the breakdown region.
8. Logic gate truth tables: NOT inverts (0→1, 1→0); AND gives 1 only when all inputs are 1; OR gives 1 when at least one input is 1; NAND and NOR are complements of AND and OR.
Worked examples
### Example 1: Carrier concentrations in doped silicon
A silicon crystal is doped with phosphorus atoms at a concentration of 1 × 10¹⁷ atoms per cm³. The intrinsic carrier concentration ni at room temperature is 1.5 × 10¹⁰ per cm³. Find the electron and hole concentrations in the doped material.
Solution
Phosphorus is pentavalent, so it donates electrons. In n-type silicon the electron concentration ne ≈ donor concentration = 1 × 10¹⁷ cm⁻³.
Using the mass-action law: nh = ni² / ne = (1.5 × 10¹⁰)² / (1 × 10¹⁷) = 2.25 × 10²⁰ / 10¹⁷ = 2.25 × 10³ cm⁻³.
So electrons are the majority carriers (10¹⁷ cm⁻³) and holes are the minority carriers (about 2250 cm⁻³).
### Example 2: Half-wave rectifier output
An AC source of peak voltage 12 V is connected to a silicon diode and a 1 kΩ resistor in series. Estimate the peak current through the resistor and the average (DC) voltage across it.
Solution
The diode drops about 0.7 V when conducting. Peak voltage across the resistor = 12 − 0.7 = 11.3 V.
Peak current = 11.3 V / 1000 Ω = 11.3 mA.
For a half-wave rectifier the average output voltage = Vpeak / π = 11.3 / 3.14 ≈ 3.6 V.
### Example 3: Transistor current gain
In a transistor circuit operating in the active region, the base current is 40 μA and the collector current is 4 mA. Calculate the current gain β and the emitter current.
Solution
β = Ic / Ib = 4 × 10⁻³ / 40 × 10⁻⁶ = 100.
Emitter current Ie = Ic + Ib = 4 mA + 0.04 mA = 4.04 mA.
Common mistakes
- Thinking holes are positive particles that move → Holes are missing electrons; what moves is actually a neighbouring electron filling the vacancy, giving the appearance of positive charge moving.
- Forgetting the diode voltage drop and using the full source voltage in rectifier calculations → Always subtract about 0.7 V (Si) per conducting diode.
- Confusing forward and reverse bias → Forward bias means p-side at higher potential than n-side; reverse bias is the opposite.
- Treating β as constant for all conditions → β varies with temperature and operating point; use the value given for the specific condition.
- Mixing up n-type and p-type majority carriers → In n-type, electrons are majority; in p-type, holes are majority.
Quick revision
- Semiconductors have a small energy gap (about 1 eV); doping creates n-type (excess electrons) or p-type (excess holes).
- A p-n junction in forward bias conducts readily; in reverse bias it blocks current until breakdown.
- Rectifiers convert AC to pulsating DC; half-wave uses one diode, full-wave uses two or four.
- Zener diode operates in controlled breakdown and regulates voltage.
- In a transistor, a small base current controls a large collector current; β = Ic / Ib.
- NAND and NOR are universal gates; any logic circuit can be built from them.