Semiconductors are materials whose resistivity lies between that of conductors and insulators at room temperature: ρ = 10⁻⁴ ÷ 10⁷ Ω·m.
Silicon (Si) is the most widely used material in semiconductor devices. Its low material cost, relatively simple processing, wide operating temperature range, and the ability to produce wafers with diameters as large as 300 mm (12 in) make it the best among competing materials.
Germanium (Ge) was the first semiconductor material to be used, but its thermal sensitivity made it inferior to silicon. Today, germanium is alloyed with silicon for use in very high-speed Si/Ge devices.
Gallium arsenide (GaAs) is also widely used in high-speed devices, but producing large wafers is difficult.
A semiconductor in which every lattice point contains atoms of only one type of element is called an intrinsic semiconductor (or pure semiconductor), denoted by the subscript i (Intrinsic).
Charge carriers in an intrinsic semiconductor:
The charge carriers in a semiconductor are free electrons in the conduction band and holes in the valence band.
Consider the crystal structure of germanium or silicon represented in two dimensions as Figure below: Both germanium (Ge) and silicon (Si) have 4 valence electrons in their outermost shell. In the crystal lattice, each Ge (or Si) atom contributes its 4 valence electrons to form covalent bonds with the 4 valence electrons of 4 neighboring atoms so that every atom attains a valence of 4.
The nucleus of a Ge (or Si) atom carries a charge of +4. Therefore, the valence electrons in covalent bonds are strongly bound to the nucleus. As a result, although there are 4 valence electrons available, the crystal has low electrical conductivity. At 0 K, the ideal structure shown in Figure below is approximately correct, and the semiconductor behaves like an insulator.
If the temperature of the crystal is increased, thermal energy raises the energy of some electrons and breaks some covalent bonds. The electrons from the broken bonds become free and can move easily through the crystal lattice under the influence of an electric field. At the sites of the broken covalent bonds, holes are created. In terms of energy, it can be said that thermal energy increases the energy of electrons in the valence band.
When this energy exceeds the bandgap energy (0.7 eV for Ge and 1.12 eV for Si), electrons can cross the bandgap into the conduction band, leaving behind holes (empty energy states) in the valence band. It can be observed that the number of electrons in the conduction band is equal to the number of holes in the valence band.
If we denote n as the electron density in the conduction band and p as the hole density in the valence band, then:
n=p=ni
where ni is the intrinsic carrier concentration.
It has been proven that:
Suppose we dope pure silicon with group-V (group-15) elements of the periodic table such as arsenic (As), phosphorus (P), or antimony (Sb). Because the atomic radius of As is close to that of Si, it can substitute for a Si atom in the crystal lattice. Four of As’s electrons bond with the four neighboring Si atoms to form four covalent bonds, leaving one extra electron. At low temperature, all electrons in the covalent bonds have energies in the valence band, whereas the extra electrons from As that do not participate in bonding have an energy ED within the band gap, located about 0.05 eV below the conduction band edge.
Instead of doping pure silicon with a group-V element, we dope it with group-III elements such as indium (In), gallium (Ga), or aluminum (Al). Since the atomic radius of In is close to that of Si, it can substitute for a Si atom in the crystal lattice. Three electrons of the In atom bond with three neighboring Si atoms to form three covalent bonds, while one electron of Si remains in the valence band without forming a bond with indium. Between this In and Si, there exists an empty energy state with energy EA lying within the band gap, located about 0.08 eV above the valence band edge.
We can also dope pure silicon with both donor atoms and acceptor atoms to obtain a compound semiconductor.