Valence band

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The term valence band is part of the band model with which the electrical conductivity , especially those of the semiconductor , is explained. The valence band is generally the highest occupied electron energy band at absolute zero (temperature) or it is the bands whose electrons ( valence electrons ) contribute to the chemical bond.

Position of the valence band for different types of material

Explanations

As mentioned above, the valence band is the highest occupied energy band at absolute zero (temperature). In semiconductors and insulators , this band is completely occupied and separated from the next higher energy band ( conduction band ) by the so-called band gap . In the case of conductors - depending on the electron configuration of the element - the valence band can either be identical to the conduction band (e.g. in the case of sodium), or it can overlap with the next higher band (quasi the conduction band). As a result, the valence band in metals is only partially occupied.

In the case of a monovalent metal, each atom in the crystal compound contributes a valence electron to the bond (basic configuration 3s 1 ). The valence electrons, as the cause of the chemical bond , belong to the solid as a whole. In the case of sodium (monovalent metal), this creates the 3s band, the valence band of sodium; For the origin of the bands, see the band model . Since sodium only contributes one valence electron for the corresponding energy level and thus also to the corresponding energy band, only half of the 3s band is occupied (see Pauli principle ).

The situation is different with divalent metals such as magnesium . Magnesium has two valence electrons (basic configuration 3s 2 ), so it would be expected that its valence band is fully occupied and therefore an insulator. Due to the energetic superposition with the next higher energy band (also called the 2nd valence band, in the case of magnesium the 3p band) electrons can pass from the 1st to the 2nd valence band, so that both are only partially occupied; The electrons are not simply proportionately distributed, but are distributed depending on the density of states (see also band structure ). The situation is analogous in the case of aluminum (basic configuration 3s 2 3p 1 ), in which the 3-s band should be fully occupied and the 3-p band half-occupied. Due to the superposition of the energy bands, both bands are only partially occupied, as is the case with magnesium.

Valence band in the band model (potential well representation) using the example of magnesium

In the case of semiconductors and insulators, the described superposition of the valence band and the next higher (unoccupied) band does not exist. For example, silicon has four valence electrons (basic configuration 3s 2 3p 2 ). Similar to sodium, magnesium and aluminum, the two valence bands (3s and 3p bands) also overlap here. But since there is no overlap with the next higher band - the energy scheme of carbon can also be used for illustration - the valence band (here both valence bands are often simply combined) is completely occupied. The energetic gap between the valence band and the conduction band is called the band gap , a quantum-mechanically forbidden zone for electrons. Since there are no free energy levels in the valence band, silicon is  an insulator at absolute zero ( T = 0 K), because an external (small) electric field cannot transport valence electrons into the free conduction band. Since it is possible with increasing temperature or incidence of light that electrons can change into the conduction band, silicon is also called a semiconductor.

Significance in electrical conduction

Ground state and external electric field

Fully occupied bands cannot contribute to the conductivity, because when an external electric field is applied, electrons absorb energy from this field, they are raised to free higher energy terms in the band, and band bending occurs. Free energy states are necessary for electrons to move in the solid. If the band is fully occupied, the electrons cannot assume a higher energy level in the same band due to the energy supplied by the electric field. Since a change in the location of all electrons does not result in a net transport of electrical charge, a material with a fully occupied valence band is an insulator.

External energy supply

If, however, a thermal or photonic amount of energy is supplied to a semiconductor which is in the range of the band gap , many valence electrons are excited into the conduction band . These electrons in the conduction band can absorb energy from an electric field and make the material (together with the resulting defect electrons, i.e. “holes” in the valence band) conductive. This effect, which increases strongly with temperature, is known as intrinsic conduction , in the case of excitation by photons, as photoconduction . In contrast, there is the impurity conduction , which can be generated by introducing foreign atoms ( doping ) into the semiconductor.

Semiconductors and insulators differ only in the width of the band gap. In the case of the latter, this is so large ( E g  > 3 eV) that electrons can hardly overcome it by thermal excitation at room temperature and even at higher temperatures. Insulators only turn into conductors at (very) high temperatures or when a sufficiently high voltage is applied, although these are usually irreversibly destroyed in the process.

Individual evidence

  1. ↑ Energy Scheme of Carbon
  2. ^ Peter W. Atkins, Julio De Paula: Physical chemistry . John Wiley & Sons, 2013, ISBN 978-3-527-33247-2 , pp. 764,765 ( limited preview in Google Book Search [accessed February 1, 2017]).
  3. ↑ Hansgeorg Hofmann, Jürgen Spindler: Materials in electrical engineering: Fundamentals - structure - properties - testing - application - technology . Carl Hanser Verlag GmbH & Company KG, 2013, ISBN 978-3-446-43748-7 , p. 105 ( limited preview in Google Book Search [accessed February 1, 2017]).
  4. ^ Matthias Günther: Energy efficiency through renewable energies: possibilities, potentials, systems . Springer-Verlag, 2014, ISBN 978-3-658-06753-3 , pp. 70 ( limited preview in Google Book Search [accessed February 1, 2017]).
  5. ↑ Wilfried Plaßmann, Detlef Schulz: Handbook of electrical engineering: Basics and applications for electrical engineers . Springer-Verlag, 2013, ISBN 978-3-8348-2071-6 , pp. 202 ( limited preview in Google Book Search [accessed February 1, 2017]).