Semiconductors – energy bands, doping and the p–n junction
PhysicsElectricity & CircuitsAges 17–18
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Compare the energy band diagrams of a conductor (copper), a semiconductor (silicon, band gap 1.12 eV) and an insulator (diamond, 5.5 eV), and change the temperature to see the number of conduction electrons and the conductivity of silicon rise steeply while those of copper fall. The Doping screen adds phosphorus (donor, n-type) or boron (acceptor, p-type) to a silicon lattice: change the doping level and temperature and read the electron density n, the hole density p, the product n·p = nᵢ², the Fermi level and the conductivity. The p–n junction screen shows diffusion forming the depletion layer and a barrier of about 0.7 V, which narrows in forward bias and widens in reverse bias, linked to the diode I–V curve.
Lesson: Band theory of solids: conductors, semiconductors and insulators; n-type and p-type semiconductors and the p–n junction
What it shows
In a solid, electrons can only have energies inside allowed bands. In a metal the bands overlap, so there are always many free electrons. In silicon a gap of 1.12 eV separates the full valence band from the empty conduction band; heat lifts a few electrons across it and leaves holes, so conductivity rises steeply with temperature. Phosphorus atoms give extra electrons (n-type), boron atoms take electrons and leave holes (p-type), and n·p stays equal to nᵢ². Joining p and n makes a depletion layer with a barrier of about 0.7 V. The model treats every dopant atom as ionised.
How to use
On Energy bands, move Temperature T and compare copper, silicon and diamond and the conductivity graph. On Doping, choose a Dopant and its Doping level and watch the lattice, the band diagram and the n and p graph; press Record to add a row. On p–n junction, press Join p and n, then move Bias voltage V between reverse and forward bias and read the depletion width, the barrier and the current.
Parameters you can change
- Screen Energy bands, Doping silicon, p–n junction
- Temperature T 200–600 K
- Dopant None (pure), Phosphorus (n-type), Boron (p-type)
- Doping level (log₁₀ of atoms per cm³) 13–18
- Bias voltage V (positive: forward bias) -5–0.7 V
Questions to explore
- Why does the resistivity of silicon fall sharply when it is heated, while that of copper rises?
- Why does adding more phosphorus to silicon reduce the number of holes?
- Why does reverse bias widen the depletion layer and let almost no current flow?
