Energy bands and electrical conduction Semiconductors are defined by their unique electric conductive behavior, somewhere between that of a conductor and an insulator. The differences between these materials can be understood in terms of the
quantum states for electrons, each of which may contain zero or one electron (by the
Pauli exclusion principle). These states are associated with the
electronic band structure of the material.
Electrical conductivity arises due to the presence of electrons in states that are
delocalized (extending through the material), however in order to transport electrons a state must be
partially filled, containing an electron only part of the time. If the state is always occupied with an electron, then it is inert, blocking the passage of other electrons via that state. The energies of these quantum states are critical since a state is partially filled only if its energy is near the
Fermi level (see
Fermi–Dirac statistics). High conductivity in material comes from it having many partially filled states and much state delocalization. Metals are good
electrical conductors and have many partially filled states with energies near their Fermi level.
Insulators, by contrast, have few partially filled states, their Fermi levels sit within
band gaps with few energy states to occupy. Importantly, an insulator can be made to conduct by increasing its temperature: heating provides energy to promote some electrons across the band gap, inducing partially filled states in both the band of states beneath the band gap (
valence band) and the band of states above the band gap (
conduction band). An (intrinsic) semiconductor has a band gap that is smaller than that of an insulator and at room temperature, significant numbers of electrons can be excited to cross the band gap. A pure semiconductor, however, is not very useful, as it is neither a very good insulator nor a very good conductor. However, one important feature of semiconductors (and some insulators, known as
semi-insulators) is that their conductivity can be increased and controlled by
doping with impurities and
gating with electric fields. Doping and gating move either the conduction or valence band much closer to the Fermi level and greatly increase the number of partially filled states. Some
wider-bandgap semiconductor materials are sometimes referred to as
semi-insulators. When undoped, these have electrical conductivity nearer to that of electrical insulators, however they can be doped (making them as useful as semiconductors). Semi-insulators find niche applications in micro-electronics, such as substrates for
HEMT. An example of a common semi-insulator is
gallium arsenide. Some materials, such as
titanium dioxide, can even be used as insulating materials for some applications, while being treated as wide-gap semiconductors for other applications.
Charge carriers (electrons and holes) The partial filling of the states at the bottom of the conduction band can be understood as adding electrons to that band. The electrons do not stay indefinitely (due to the natural thermal
recombination) but they can move around for some time. The actual concentration of electrons is typically very dilute, and so (unlike in metals) it is possible to think of the electrons in the conduction band of a semiconductor as a sort of classical
ideal gas, where the electrons fly around freely without being subject to the
Pauli exclusion principle. In most semiconductors, the conduction bands have a parabolic
dispersion relation, and so these electrons respond to forces (electric field, magnetic field, etc.) much as they would in a vacuum, though with a different
effective mass.
Doping array. Silicon based intrinsic semiconductor becomes extrinsic when impurities such as
Boron and
Antimony are introduced. The conductivity of semiconductors may easily be modified by introducing impurities into their
crystal lattice. The process of adding controlled impurities to a semiconductor is known as
doping. The amount of impurity, or dopant, added to an
intrinsic (pure) semiconductor varies its level of conductivity. Doped semiconductors are referred to as
extrinsic. By adding impurity to the pure semiconductors, the electrical conductivity may be varied by factors of thousands or millions. A 1 cm3 specimen of a metal or semiconductor has the order of 1022 atoms. In a metal, every atom donates at least one free electron for conduction, thus 1 cm3 of metal contains on the order of 1022 free electrons, whereas a 1 cm3 sample of pure germanium at 20°C contains about atoms, but only free electrons and holes. The addition of 0.001% of
arsenic (an impurity) donates an extra 1017 free electrons in the same volume and the electrical conductivity is increased by a factor of 10,000. The materials chosen as suitable dopants depend on the atomic properties of both the dopant and the material to be doped. In general, dopants that produce the desired controlled changes are classified as either electron
acceptors or
donors. Semiconductors doped with
donor impurities are called
n-type, while those doped with
acceptor impurities are known as
p-type. The n and p type designations indicate which charge carrier acts as the material's
majority carrier. The opposite carrier is called the
minority carrier, which exists due to thermal excitation at a much lower concentration compared to the majority carrier. For example, the pure semiconductor
silicon has four valence electrons that bond each silicon atom to its neighbors. In silicon, the most common dopants are
group III and
group V elements. Group III elements all contain three valence electrons, causing them to function as acceptors when used to dope silicon. When an acceptor atom replaces a silicon atom in the crystal, a vacant state (an electron "hole") is created, which can move around the lattice and function as a charge carrier. Group V elements have five valence electrons, which allows them to act as a donor; substitution of these atoms for silicon creates an extra free electron. Therefore, a silicon crystal doped with
boron creates a p-type semiconductor whereas one doped with
phosphorus results in an n-type material. During
manufacture, dopants can be diffused into the semiconductor body by contact with gaseous compounds of the desired element, or
ion implantation can be used to accurately position the doped regions.
Amorphous semiconductors Some materials, when rapidly cooled to a glassy amorphous state, have semiconducting properties. These include B,
Si, Ge, Se, and Te, and there are multiple theories to explain them. == Early history of semiconductors ==