- Conductivity Definition: The conductivity of a semiconductor is defined as its ability to conduct electricity, which is moderate due to its intermediate free electron concentration.
- Role of Electrons and Holes: In semiconductors, both free electrons and holes act as charge carriers, enabling electrical conduction.
- Temperature Effects: Conductivity of semiconductors increases with temperature because higher temperatures generate more free electrons and holes.
- Energy for Bond Breaking: The energy needed to break covalent bonds in semiconductors, releasing electrons and creating holes, is crucial for understanding their conductivity.
- Applications of Conductivity: The temperature sensitivity of semiconductors is useful for creating devices like thermistors that measure temperature changes
Conductivity of a semiconductor is set by how many free carriers it has. Metals (conductors) have a high free-electron density and therefore a high conductance (and a low resistance). Insulators have very few free electrons. A semiconductor sits between those two densities, so its conductivity sits between a metal and an insulator.
That is why a semiconductor conducts moderately. Valence electrons sit in covalent bonds between neighbouring atoms, not free as in a metal. Germanium and silicon are the usual elemental semiconductors. Their crystals repeat a tetrahedral unit cell.
A germanium atom has 32 electrons around its nucleus.
Each germanium atom uses four valence electrons to form covalent bonds with four neighbours, so the lattice is tetravalent. The ion core then behaves as a charge of +4 electronic charges. Those valence electrons hold one atom to the next.
Those valence electrons stay bound, so a perfect germanium crystal is a poor conductor at low temperature. At absolute zero an intrinsic semiconductor acts as an insulator because no free carriers are present.
At room temperature (300oK) some covalent bonds break, free electrons appear and the crystal can carry a small current.
Older textbooks put the energy to break a covalent bond at about 0.72 eV in germanium and 1.1 eV in silicon at room temperature. Present 300 K gaps are about 0.66 eV (Ge) and 1.12 eV (Si). When a bond breaks, one electron leaves and a vacant site, a hole, remains.
In a semiconductor that hole also carries current. Hole current is a successive hop of valence electrons into the vacant site, not the free-electron drift of a metal.
An incomplete bond is a hole. A valence electron from a neighbouring bond can occupy that hole more easily than an electron from a distant atoms, and it then leaves a new hole behind.
That hop repeats, so the hole appears to move opposite to the electrons. The crystal then conducts by two charge carriers: free electrons and holes.
A hole moving one way is the same event as a valence electron moving the other way. A negative charge moving backward is equivalent to a positive charge moving forward.
Hole motion therefore carries a positive charge through the crystal. In an ideal intrinsic crystal, the number of holes created per unit time equals the number of electrons freed in that time.
If temperature rises, the electron-hole pair generation rate rises. If temperature falls, recombination reduces the number of pairs.
Each generated pair adds two carriers: a negative electron and a positive hole.
Let hole mobility in the crystal be μh and electron mobility in the same crystal be μe. Holes and electrons drift in opposite directions. Electrons drift opposite to the applied electric field. The hole drift current density is
The electron drift current density is
Hole drift and electron drift both give current in the same conventional direction, the hole-drift direction. The two densities add:
Where n is the free-electron concentration, p is the hole concentration and σ is the Conductivity of Semiconductor.
If the semiconductor is ideally pure, n = p = ni. A rise in temperature raises that carrier density, so conductivity rises. For a pure or intrinsic semiconductor the usual relation is
Where T is the temperature on the kelvin scale.
That expression grows exponentially with T. Older textbooks quote a rise of about 6% per degree C for germanium carrier density near room temperature.
The same older rule of thumb is about 8% per degree C for silicon, which is a plausible room-temperature slope for ni(T). Germanium with a 0.66 eV gap is closer to 5% per kelvin. Device leakage therefore rises quickly with temperature, so operating limits must be kept.
The same temperature dependence is used on purpose in temperature transducers. Those parts are thermistors.
