Why semiconductors?
Early electronics used vacuum tubes: bulky, power-hungry and fragile. Semiconductor devices are small, cheap, reliable and efficient, and they power everything from phones to satellites.
Classifying solids by conductivity
Type | Resistivity (Ω m) | Examples |
|---|---|---|
Metals | 10⁻² to 10⁻⁸ | copper, silver |
Semiconductors | 10⁻⁵ to 10⁶ | silicon, germanium, gallium arsenide |
Insulators | 10¹¹ to 10¹⁹ | glass, rubber |
Energy bands
In a solid, the energy levels of atoms spread into bands. The band of outermost electrons is the valence band; the next higher band is the conduction band. The gap between them is the energy gap Eg.
Metals: the bands overlap or the conduction band is partly filled. Electrons move freely.
Insulators: a large gap (Eg > 3 eV); no electrons reach the conduction band at room temperature.
Semiconductors: a small gap (Eg < 3 eV): about 1.1 eV for Si and 0.7 eV for Ge. At room temperature a few electrons jump across, so they conduct a little. Conductivity increases with temperature, unlike metals.
Intrinsic semiconductors
In pure silicon, each atom forms covalent bonds with four neighbours. Thermal energy breaks some bonds, freeing an electron and leaving a vacancy called a hole, which acts as a positive charge carrier.
In an intrinsic (pure) semiconductor, nₑ = nₕ = nᵢ: the number of free electrons equals the number of holes.
Extrinsic semiconductors (doping)
Adding a tiny amount of a suitable impurity (doping, about 1 part per million) greatly increases conductivity.
Type | Dopant | Example | Majority carriers | Minority carriers |
|---|---|---|---|---|
n-type | pentavalent (5 valence electrons): donor | arsenic, antimony, phosphorus | electrons | holes |
p-type | trivalent (3 valence electrons): acceptor | indium, boron, aluminium | holes | electrons |
In a pentavalent dopant, four electrons bond and the fifth is loosely held, easily freed. A trivalent dopant leaves one bond incomplete: a hole.
In both cases, the material as a whole is electrically neutral. At equilibrium, nₑ nₕ = nᵢ².
The p-n junction
When p-type and n-type regions are formed in one crystal:
Electrons diffuse from n to p and holes from p to n, because of the concentration difference.
This leaves a layer of fixed positive ions on the n-side and fixed negative ions on the p-side, a region empty of mobile carriers called the depletion region.
The ions create an electric field and a barrier potential (about 0.7 V for Si, 0.3 V for Ge) that opposes further diffusion. A drift current flows the other way, and equilibrium is reached.
The semiconductor diode
A p-n junction with metal contacts is a diode. Its symbol is an arrow (the p-side) pointing towards a bar (the n-side).
Forward bias: p-side to the positive terminal. The applied voltage opposes the barrier, the depletion layer narrows, and above the threshold (knee) voltage, current rises sharply. The diode conducts with low resistance.
Reverse bias: p-side to the negative terminal. The barrier increases, the depletion layer widens, and only a tiny reverse saturation current (microamperes) flows due to minority carriers. At a high enough reverse voltage, breakdown occurs and current rises suddenly.
So a diode allows current essentially in one direction only.
Rectifiers
A rectifier converts AC to DC.
Half-wave rectifier: one diode. It conducts only during the half-cycles when it is forward biased, so the output has every other half-cycle missing. The output frequency equals the input frequency (50 Hz).
Full-wave rectifier: two diodes with a centre-tapped transformer. One diode conducts in each half-cycle, so both halves are used. The output frequency is twice the input (100 Hz), and it is more efficient.
The output is pulsating DC. A capacitor filter across the output smooths the ripple.
Special-purpose diodes
Device | Bias | Use |
|---|---|---|
Zener diode | reverse, at breakdown | voltage regulator: the voltage across it stays constant even when the current changes |
Photodiode | reverse | detects light: the reverse current increases with light intensity |
LED | forward | emits light when electrons and holes recombine; colour depends on the band gap. Uses low power, long life, fast switching |
Solar cell | none (generates emf) | converts sunlight to electricity; a p-n junction with a large area. Silicon and GaAs are used |
Logic gates
Digital circuits work with two voltage levels: 1 (high) and 0 (low). A logic gate produces an output from one or more inputs according to a rule, shown by a truth table.
A | B | AND (A·B) | OR (A + B) | NAND | NOR |
|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 0 |
1 | 0 | 0 | 1 | 1 | 0 |
1 | 1 | 1 | 1 | 0 | 0 |
NOT gate: one input, output is the opposite (Ā).
AND: output 1 only if all inputs are 1.
OR: output 1 if any input is 1.
NAND = NOT AND; NOR = NOT OR.
NAND and NOR are universal gates: any other gate can be built using only NAND gates, or only NOR gates. For example, joining both inputs of a NAND gate together makes a NOT gate.
Summary
Semiconductors have a small energy gap; conductivity rises with temperature.
n-type (pentavalent dopant) has majority electrons; p-type (trivalent) has majority holes.
A p-n junction has a depletion region and barrier potential; it conducts in forward bias only.
Diodes rectify AC; Zener diodes regulate voltage; LEDs emit light; solar cells make electricity.
AND, OR, NOT, NAND, NOR follow truth tables; NAND and NOR are universal.