doPhysics · Modern Physics
Semiconductors and the p-n Junction
Energy bands in solids, and why a semiconductor conducts better when hot. Electrons and holes, n-type and p-type doping and the mass action law. The p-n junction, its depletion layer and barrier, the diode in forward and reverse bias, and the rectifiers, filters, clippers and clampers built from it.
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Why this chapter
Why this chapter exists
Every phone, charger and solar lamp is built on one material, silicon, and one structure, the p-n junction. Pure silicon barely conducts. A trace of phosphorus or boron, one atom in millions, makes it conduct a hundred thousand times better, with either negative or positive carriers. Join the two kinds in one crystal and you get a diode, a one-way valve for current. This chapter builds that valve from the band picture of a solid. It ends with the circuits that turn the alternating mains into the steady current a phone battery needs.
You will learn
By the end of this chapter you will
- Explain how energy bands form in a solid, and sort solids into metals, semiconductors and insulators by their band gap.
- Explain why the resistance of a semiconductor falls when it is heated, while that of a metal rises.
- Describe electrons and holes, make n-type and p-type silicon by doping, and use the mass action law \(n_e n_h = n_i^2\) and the conductivity \(\sigma = e(n_e\mu_e + n_h\mu_h)\).
- Explain how diffusion and drift form the depletion layer and the barrier potential of a p-n junction.
- Describe forward and reverse bias, read a diode's I-V curve, find its dynamic resistance, and solve circuits with the ideal and the 0.7 V models.
- Explain half-wave, centre-tap and bridge rectifiers, find their output peak, frequency and average, and explain how a capacitor filter reduces the ripple.
- Find the output of a clipper and of a clamper for a sine-wave input.
Before you begin
Before you begin
From the chapter on the Bohr atom, you should know that an electron in an atom has only certain energies, a ladder of levels. From the chapter on photons, you should know the electron volt and that a photon of wavelength \(\lambda\) carries \(hc/\lambda\). From the chapter on oscillations, you should know a sine wave, its period and its frequency. What the chapter needs about potential difference, Ohm's law and the rms value of the mains is stated where it is first used.
Lessons
1
Energy Bands: Conductors, Insulators, Semiconductors
In a crystal the sharp levels of single atoms spread into bands. The gap between the valence band and the conduction band decides whether a solid is a metal, a semiconductor or an insulator, and why heat helps a semiconductor conduct.
Energy bands in a solidBand gap classifies solidsSemiconductors conduct better when hot
2
Electrons, Holes and Doping
A broken bond gives a free electron and a hole, a vacancy that moves like a positive charge. A few donor or acceptor atoms make n-type or p-type silicon, and the mass action law fixes the number of the other carrier.
Electrons and holesN type and p typeThe mass action law
3
The p-n Junction
Where p-type meets n-type silicon, electrons and holes diffuse across and recombine. They leave a depletion layer of fixed ions, whose field sets up a barrier of about 0.7 V in silicon. The layer stops growing when drift balances diffusion.
Diffusion and the depletion layerThe barrier potentialDrift balances diffusion
4
Forward and Reverse Bias: the Diode Curve
A battery that lowers the barrier lets a large current through the junction; one that raises it lets through almost nothing. The diode's I-V curve, its knee voltage and dynamic resistance, and two simple models for solving circuits with diodes.
Forward biasReverse biasThe diode characteristicSolving circuits with diodes
5
Rectifiers and the Filter
A diode that conducts one way turns the alternating mains into current in one direction. The half-wave rectifier, the centre-tap and bridge full-wave rectifiers, their output frequency and peak, and the capacitor that smooths the pulses into nearly steady DC.
Half wave rectifierFull wave rectifierThe capacitor filter
6
Clippers and Clampers
A diode and a battery can cut a wave off at a chosen level, and a diode and a capacitor can lift the whole wave without changing its shape. Clippers, clampers and how to find their output step by step.
Clipping a waveClamping a wave
Read in order. The small labels are the topics of each lesson. They take your colour as you answer the checks.
0%The Workbook
Questions to solve on paper, marked by you.
Glossary
The key words of this chapter, with the meaning this chapter gives them.
- acceptor
- A trivalent impurity atom, such as boron, aluminium or indium. It takes an electron from a bond, leaving a hole, and becomes a fixed negative ion.
- band gap
- The energy range between the valence band and the conduction band, written \(E_g\), in which no electron can be. Silicon 1.1 eV, germanium 0.7 eV, diamond 5.4 eV.
- barrier potential
- The step in potential across the depletion layer, the n side higher, written \(V_0\): about 0.7 V for silicon and 0.3 V for germanium.
- clamper
- A circuit of a capacitor and a diode. It keeps the shape of a wave but shifts the whole wave up or down by a steady voltage.
- clipper
- A diode circuit that cuts off the part of a wave beyond a chosen level and passes the rest unchanged.
- conduction band
- The energy band just above the valence band. Electrons in it move freely through the crystal and carry current.
- depletion layer
- The thin region on both sides of a p-n junction that has lost its free carriers. It holds fixed ions, negative on the p side and positive on the n side.
- diffusion
- The spreading of carriers from where they are many to where they are few, by their random motion. Across a junction it gives a current from p to n.
- donor
- A pentavalent impurity atom, such as phosphorus, arsenic or antimony, that gives a free electron to the crystal and becomes a fixed positive ion.
- doping
- Adding a small, controlled number of impurity atoms to a semiconductor to change the number and kind of its carriers.
- drift
- The motion of carriers pushed by an electric field. Across a junction it carries minority carriers and gives a current from n to p.
- dynamic resistance
- The ratio \(r_d = \Delta V/\Delta I\) of a small change of voltage to the change of current it causes, at a point on a diode's characteristic.
- energy band
- A range of closely spaced allowed energies for the electrons in a solid. Each level of a single atom spreads into a band when the atoms form a crystal.
- extrinsic semiconductor
- A semiconductor doped with impurity atoms, so that one kind of carrier far outnumbers the other.
- forward bias
- A voltage applied with the p side positive, which lowers the barrier to \(V_0 - V\) and lets a large current flow.
- full-wave rectifier
- A rectifier that sends both halves of each cycle the same way through the load. It uses two diodes and a centre-tapped winding, or four diodes in a bridge. From 50 Hz mains it gives 100 pulses a second.
- half-wave rectifier
- A rectifier with one diode in series with the load, which passes only one half of each cycle. From 50 Hz mains it gives 50 pulses a second.
- hole
- The empty place left in a bond when an electron leaves it. It moves when a neighbouring bound electron hops in, and behaves like a carrier of charge \(+e\).
- ideal diode
- A model of a diode as a perfect switch. It is a closed switch with no voltage across it in forward bias, and an open switch in reverse bias.
- insulator
- A solid with a full valence band and a large band gap, several electron volts, so that almost no electron reaches the conduction band.
- intrinsic semiconductor
- A pure semiconductor, whose free electrons and holes come only in pairs, so that \(n_e = n_h = n_i\).
- knee voltage
- The forward voltage beyond which the current of a diode rises steeply: about 0.7 V for silicon and 0.3 V for germanium.
- majority carriers
- The more numerous kind of carrier in a doped semiconductor: electrons in n-type, holes in p-type.
- mass action law
- In thermal equilibrium the product of the electron and hole concentrations is fixed by the temperature: \(n_e n_h = n_i^2\).
- minority carriers
- The less numerous kind of carrier in a doped semiconductor: holes in n-type, electrons in p-type.
- mobility
- The drift speed of a carrier per unit electric field, written \(\mu\), in \(\text{m}^2/\text{V s}\). In silicon 0.135 for electrons and 0.048 for holes.
- n-type
- A semiconductor doped with donors, in which free electrons are the majority carriers.
- p-n junction
- A single crystal doped p-type on one side and n-type on the other, and the boundary between the two regions.
- p-type
- A semiconductor doped with acceptors, in which holes are the majority carriers.
- rectifier
- A circuit that turns alternating current into current in one direction.
- reverse bias
- A voltage applied with the p side negative, which raises the barrier to \(V_0 + V\) and lets only a tiny current flow.
- reverse saturation current
- The tiny current, about a microampere or less, carried across a reverse-biased junction by minority carriers. It hardly depends on the voltage and grows with temperature.
- ripple
- The part of a rectifier's output that still rises and falls, left on top of the steady DC.
- ripple factor
- The ratio of the varying part of a rectifier's output to its steady average: 1.21 for half-wave and 0.48 for full-wave, without a filter.
- rms value
- The steady value that would heat a resistor at the same rate as an alternating voltage or current. For a sine wave the peak is \(\sqrt{2}\) times the rms value.
- semiconductor
- A solid with a full valence band and a small band gap, about 1 eV. It is an insulator at 0 K, and conducts better the hotter it is.
- valence band
- The highest energy band filled by the valence electrons at 0 K. In a semiconductor its electrons are those locked in the bonds.