Semiconductivity – Band Theory

In general, semiconductors are materials, inorganic or organic, which have the ability to control their conduction depending on chemical structure, temperature, illumination, and presence of dopants. The name semiconductor comes from the fact that these materials  have an electrical conductivity between that of a metal, like copper, gold, etc. and an insulator, such as glass. They have an energy gap less than 4eV (about 1eV). In solid-state physics, this energy gap or band gap is an energy range between valence band and conduction band where electron states are forbidden. In contrast to conductors, electrons in a semiconductor must obtain energy (e.g. from ionizing radiation) to cross the band gap and to reach the conduction band. Properties of semiconductors are determined by the energy gap between valence and conduction bands. To understand, what is semiconductor, we have to define these terms.

Properties of Semiconductors

To understand the difference between metals, semiconductors and electrical insulators, we have to define the following terms from solid-state physics:

  • Valence Band - Conduction Band - Band GapValence Band. In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level and thus determine the electrical conductivity of the solid. In electrical insulators and semiconductors, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature. For example, a silicon atom has fourteen electrons. In the ground state, they are arranged in the electron configuration [Ne]3s23p2. Of these, four are valence electrons, occupying the 3s orbital and two of the 3p orbitals. The distinction between the valence and conduction bands is meaningless in metals, because conduction occurs in one or more partially filled bands that take on the properties of both the valence and conduction bands.
  • Conduction Band. In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level and thus determine the electrical conductivity of the solid. In electrical insulators and semiconductors, the conduction band is the lowest range of vacant electronic states. On a graph of the electronic band structure of a material, the valence band is located below the Fermi level, while the conduction band is located above it. In semiconductors, electrons may reach the conduction band, when they are excited, for example, by ionizing radiation (i.e. they must obtain energy higher than Egap). For example, diamond is a wide-band gap semiconductor (Egap = 5.47 eV) with high potential as an electronic device material in many devices. On the other side, germanium has a small band gap energy (Egap = 0.67 eV), which requires to operate the detector at cryogenic temperatures. The distinction between the valence and conduction bands is meaningless in metals, because conduction occurs in one or more partially filled bands that take on the properties of both the valence and conduction bands.
  • Band Gap. In solid-state physics, the energy gap or the band gap is an energy range between valence band and conduction band where electron states are forbidden. In contrast to conductors, electrons in a semiconductor must obtain energy (e.g. from ionizing radiation) to cross the band gap and to reach the conduction band. Band gaps are naturally different for different materials. For example, diamond is a wide-band gap semiconductor (Egap = 5.47 eV) with high potential as an electronic device material in many devices. On the other side, germanium has a small band gap energy (Egap = 0.67 eV), which requires to operate the detector at cryogenic temperatures.
  • Fermi Level. The term “Fermi level” comes from Fermi-Dirac statistics, which describes a distribution of particles over energy states in systems consisting of fermions (electrons) that obey the Pauli exclusion principle. Since they cannot exist in identical energy states, Fermi level is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. The Fermi level is the surface of Fermi sea at absolute zero where no electrons will have enough energy to rise above the surface. In metals, the Fermi level lies in the hypothetical conduction band giving rise to free conduction electrons. In semiconductors the position of the Fermi level is within the band gap, approximately in the middle of the band gap.
  • extrinsic - doped semiconductor - p-type - acceptorElectron-hole Pair. In the semiconductor, free charge carriers are electrons and electron holes (electron-hole pairs). Electrons and holes are created by excitation of electron from valence band to the conduction band. An electron hole (often simply called a hole) is the lack of an electron at a position where one could exist in an atom or atomic lattice. It is one of the two types of charge carriers that are responsible for creating electric current in semiconducting materials. Since in a normal atom or crystal lattice the negative charge of the electrons is balanced by the positive charge of the atomic nuclei, the absence of an electron leaves a net positive charge at the hole’s location. Positively charged holes can move from atom to atom in semiconducting materials as electrons leave their positions. When an electron meets with a hole, they recombine and these free carriers effectively vanish. The recombination means an electron which has been excited from the valence band to the conduction band falls back to the empty state in the valence band, known as the holes.

The conductivity of a semiconductor can be modeled in terms of the band theory of solids. The band model of a semiconductor suggests that at ordinary temperatures there is a finite possibility that electrons can reach the conduction band and contribute to electrical conduction. In the semiconductor, free charge carriers (electron-hole pairs) are created by excitation of electron from valence band to the conduction band. This excitation left a hole in the valence band which behaves as positive charge and an electron-hole pair is created. Holes can sometimes be confusing as they are not physical particles in the way that electrons are, rather they are the absence of an electron in an atom. Holes can move from atom to atom in semiconducting materials as electrons leave their positions.

References:

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See above:

Properties of Semiconductors