Energy bands: conductors, semiconductors and insulators
In a solid, atomic energy levels spread into valence and conduction bands. The energy gap Eg between them decides whether the solid is a conductor, semiconductor or insulator.
How energy bands form
In a single atom, electrons have sharp energy levels. In a crystal, atoms are only about 2 to 3 Å apart, so the outer electrons of neighbouring atoms affect one another. Each level then splits into a huge number of very close levels, which together form an energy band. The band holding the valence electrons is the valence band; at 0 K it is completely filled. The next higher band is the conduction band. Electrons in it are free to move and can carry current. The energy gap Eg between the two bands has no allowed levels.
Comparing the three classes of solids
| Property | Conductor (metal) | Semiconductor | Insulator |
|---|---|---|---|
| Band picture | Bands overlap or conduction band partly filled | Small gap, Eg < 3 eV | Large gap, Eg > 3 eV |
| Resistivity ρ (Ω m) | 10⁻² to 10⁻⁸ | 10⁻⁵ to 10⁶ | 10¹¹ to 10¹⁹ |
| Conductivity σ (S m⁻¹) | 10² to 10⁸ | 10⁵ to 10⁻⁶ | 10⁻¹¹ to 10⁻¹⁹ |
| Examples | Copper, aluminium, silver | Silicon, germanium, GaAs | Diamond, glass |
| When heated | Resistance increases | Resistance decreases | Stays a very poor conductor |
How to draw the three band diagrams
- Draw three panels side by side, each with an upward arrow labelled electron energy.
- Conductor: draw two rectangles that overlap; label them valence band and conduction band.
- Semiconductor: shade the lower valence band and leave a narrow gap labelled Eg < 3 eV. Draw an almost empty conduction band with a few dots for electrons at room temperature.
- Insulator: shaded valence band, a wide gap labelled Eg > 3 eV, and an empty conduction band.
- Write the name of each solid under its panel.
Types of semiconductor materials
- Elemental: silicon (Si) and germanium (Ge).
- Compound, inorganic: CdS, GaAs, CdSe, InP.
- Compound, organic: anthracene, doped phthalocyanines.
- Organic polymers: polypyrrole, polyaniline, polythiophene.
- Most devices today use Si, Ge and inorganic compound semiconductors.
Worked example: light that can cross the band gap
The band gap of silicon is 1.1 eV and of diamond is 5.4 eV. Find the longest wavelength of light that can lift an electron across each gap. (hc = 1240 eV nm)
- A photon can cross the gap only if its energy hc/λ ≥ Eg, so λmax = hc/Eg.
- Silicon: λmax = 1240 eV nm ÷ 1.1 eV ≈ 1130 nm (infrared). So all visible light (400 to 700 nm) can free electrons in silicon.
- Diamond: λmax = 1240 ÷ 5.4 ≈ 230 nm (ultraviolet). Visible light cannot cross the gap, so it passes through diamond.
Silicon: about 1130 nm; diamond: about 230 nm
Silicon solar panels on Indian rooftops and farms work because sunlight photons carry more than silicon's 1.1 eV gap and free electrons into the conduction band. Diamond, with a 5.4 eV gap, lets visible light pass, so it looks clear.
2 marks: “Draw the energy band diagrams of a conductor, a semiconductor and an insulator. Label the energy gap in each.” Conductor: overlapping bands. Semiconductor: small gap, Eg < 3 eV. Insulator: large gap, Eg > 3 eV. Label valence band, conduction band and Eg.
3 marks: “Distinguish between conductors, semiconductors and insulators on the basis of energy bands, and give the range of resistivity of each.” Conductors: bands overlap, ρ 10⁻² to 10⁻⁸ Ω m. Semiconductors: Eg < 3 eV, ρ 10⁻⁵ to 10⁶ Ω m. Insulators: Eg > 3 eV, ρ 10¹¹ to 10¹⁹ Ω m.
1 marks: “What is the order of the energy gap of an insulator?” More than about 3 eV (diamond: about 5.4 eV).
Zero, small, large: conductor no gap, semiconductor under 3 eV, insulator over 3 eV.