Concept 07 / 07Solid State
Electrical and Magnetic Properties of Solids: Band Theory, Semiconductors and Magnetism
Conductors, insulators and semiconductors explained by band theory, intrinsic semiconductors, n-type and p-type doping of silicon, 13-15 and 12-16 compound semiconductors and applications, and magnetic classes of solids: diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic and ferrimagnetic, with domain alignment and Curie temperature.
Electrical conductivity of solids ranges over about orders of magnitude: conductors ( to ), semiconductors ( to ) and insulators ( to ).
Band theory (see figure). In a solid, the atomic orbitals of many atoms combine into closely spaced molecular orbitals that form continuous bands. The highest filled band is the valence band; the band above it is the conduction band.
Metals (conductors): the valence band is partly filled or overlaps the conduction band, so electrons move freely under an applied field.
Insulators: a large forbidden gap separates a full valence band from an empty conduction band; electrons cannot jump it.
Semiconductors: the gap is small; at room temperature some electrons are thermally excited into the conduction band. Their conductivity increases with temperature (unlike metals, whose conductivity decreases as vibrations scatter electrons).
Intrinsic and extrinsic semiconductors. Pure silicon and germanium are intrinsic semiconductors with low conductivity. Doping with impurities increases conductivity enormously.
n-type: Si (group 14) doped with a group 15 element (P, As). Each dopant uses four electrons in bonding and has one extra electron, which becomes delocalised; the negative electrons carry current.
p-type: Si doped with a group 13 element (B, Al, Ga). Each dopant has only three valence electrons, leaving an electron vacancy, a hole; holes move as electrons from neighbouring bonds fill them, behaving as positive charge carriers.
Applications: a p-n junction acts as a rectifier (diode); transistors (npn and pnp) amplify and switch signals; solar cells are photodiodes that convert light to electrical energy.
Compound semiconductors: 13-15 compounds (InSb, AlP, GaAs; GaAs has a very fast response and is used in LEDs and solar cells) and 12-16 compounds (ZnS, CdS, CdSe, HgTe). Some transition metal oxides conduct like metals (, , ), while others (, , , ) show metallic or insulating behaviour depending on temperature.
Magnetic properties. Arise from the spin and orbital motion of electrons; each unpaired electron acts as a tiny magnet ().
Diamagnetic: all electrons paired; weakly repelled by a magnetic field (NaCl, , benzene, ).
Paramagnetic: unpaired electrons; weakly attracted; magnetism lost when the field is removed (, , , ).
Ferromagnetic: strongly attracted and can be permanently magnetised (Fe, Co, Ni, Gd, ). Unpaired spins align in domains; in a magnetic field all domains align in one direction and the order persists (permanent magnet).
Antiferromagnetic: domains align with equal numbers of opposite moments, cancelling to zero net moment (MnO).
Ferrimagnetic: moments aligned antiparallel in unequal numbers, giving a net moment (, ferrites such as and ).
On heating, ferromagnetic, antiferromagnetic and ferrimagnetic substances become paramagnetic, as thermal motion randomises the spins (above the Curie temperature for ferromagnets; becomes paramagnetic at ).
Key Takeaways:
- Band gap: overlap (metals), small (semiconductors), large (insulators).
- n-type: group 15 dopant, extra electrons; p-type: group 13 dopant, holes.
- Semiconductor conductivity rises with temperature; metal conductivity falls.
- Ferro: aligned domains; antiferro: cancelled; ferri: unequal antiparallel ().
- Pitfall: a p-type semiconductor is still electrically neutral overall; "p" refers to the positive charge carriers (holes), not a net charge.
Brain-Teaser 1: What type of semiconductor forms when (a) Ge is doped with In, (b) Si is doped with As, (c) Si is doped with B?
Solution: (a) In (group 13) in Ge (group 14): p-type. (b) As (group 15) in Si: n-type. (c) B (group 13) in Si: p-type.
Brain-Teaser 2: Classify as diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic or ferrimagnetic: , , MnO, , .
Solution: ferrimagnetic; ferromagnetic (used in audio tapes); MnO antiferromagnetic; diamagnetic (, ); paramagnetic.
Brain-Teaser 3: Why does the conductivity of silicon increase on heating while that of copper decreases?
Solution: In silicon, heat promotes more electrons across the small band gap into the conduction band, creating more charge carriers (electrons and holes), which outweighs the extra scattering. In copper the number of carriers is already large and fixed; heating only increases lattice vibrations that scatter the electrons, raising resistance.
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