What does the band gap diagram mean



As Band gap (engl. band gap) or. forbidden zone the energetic distance between the valence band and the conduction band of a solid is called. Its electrical and optical properties are largely determined by the size of the band gap.

material Art Energy in eV
0 K 300 K
elements
diamond indirectly 5,4 5,46–6,4
Si indirectly 1,17 1,12
Ge indirectly 0,75 0,67
Se directly 1,74
IV-IV connections
SiC 3C indirectly 2,36
SiC 4H indirectly 3,28
SiC 6H indirectly 3,03
III-V connections
InP directly 1,42 1,27
InAs directly 0,43 0,355
InSb directly 0,23 0,17
InN directly 0,7
InxGa1-xN directly 0,7–3,37
GaN directly 3,37
GaP 3C indirectly 2,26
GaSb directly 0,81 0,69
GaAs directly 1,52 1,43
AlxGa1-xAs x 1,42–2,16
AlAs indirectly 2,16
As B indirectly 1,65 1,58
AlN 6,2
II-VI compounds
TiO2 3,03 3,2
ZnO directly 3,436 3,37
ZnS 3,56
CdS 2,42
CdSe 1,74
CdTe 1,45

origin

According to the ribbon model, bound electronic states are only permitted at certain intervals on the energy scale, the Ribbons. Areas that are energetically forbidden can (but do not have to) lie between the bands. Each of these areas represents a gap between the bands, but for the physical properties of a solid only the possible gap between the highest band that is completely occupied by electrons (valence band) and the next higher band (conduction band) is of decisive importance. Therefore is with the The band gap always means the one between the valence and conduction bands.

The occurrence of a band gap in some materials can be understood quantum mechanically through the behavior of the electrons in the periodic potential of a crystal structure. This Model of the quasi-free electrons provides the theoretical basis for the ribbon model.

The size of the band gap is usually given in electron volts (eV). If the valence band overlaps the conduction band, no band gap occurs. If the valence band is not completely occupied with electrons, the upper unfilled area takes over the function of the conduction band, consequently there is no band gap here either. In these cases, infinitesimal amounts of energy are sufficient to excite an electron.

Effects

Electric conductivity

Only excited electrons in the conduction band can move practically freely through a solid and contribute to electrical conductivity. At finite temperatures there are always some electrons in the conduction band due to thermal excitation, but their number varies greatly with the size of the band gap. On the basis of this, the classification according to conductors, semiconductors and insulators is carried out. The exact limits are not clear, but the following limit values ​​can be used as a rule of thumb:

  • Conductors do not have a band gap.
  • Semiconductors have a band gap in the range of 0-3 eV.
  • Insulators have a band gap greater than 3 eV.

Optical properties

The ability of a solid to absorb light is linked to the condition that it absorbs the photon energy by exciting electrons. Since no electrons can be excited in the forbidden area between the valence and conduction bands, the energy of a photon must exceed that of the band gap - otherwise the photon cannot be absorbed.

The energy of a photon is about the formula E. = Hν coupled to the frequency ν (Ny) of the electromagnetic radiation. If a solid has a band gap, it is therefore transparent for radiation up to a certain frequency (in general, this statement is not entirely correct, as there are other ways of absorbing the photon energy). The following rules can be derived specifically for the permeability of visible light (photon energies around ~ 2 eV):

  1. Metals cannot be transparent
  2. Transparent materials are insulators

Since the absorption of a photon is linked to the excitation of an electron from the valence to the conduction band, there is a connection with the electrical conductivity. In particular, the electrical resistance of a semiconductor decreases with increasing light intensity, which z. B. can be used with brightness sensors, see also under photo line.

species

 

Indirect band gap

The minimum is opposite the maximum on the k-Axis shifted. In the case of a direct transition from the valence band to the conduction band, the smallest distance between the bands is directly above the maximum of the valence band. In the case of an indirect transition, it is offset.

The absorption of a photon is only effectively possible with a direct band gap, with an indirect band gap an additional quasi-pulse (k) must be involved, whereby a suitable phonon is generated or destroyed. This process with one photon alone is much less likely due to the low momentum of the light, the material shows weaker absorption there.

Direct band gap

The minimum of the conduction band is in E.(k) Diagram directly above the maximum of the valence band.

In the case of a direct transition from valence band to conduction band, the smallest distance between the bands is directly above the maximum of the valence band.

Application examples: light emitting diode

See also

literature

  • Charles Kittel, Introduction to solid state physics (German translation), Oldenbourg 2005, 14th edition, ISBN 3486577239
  • Charles Kittel, Introduction to Solid State Physics, John Wiley and Sons 1995, 7th edition, ISBN 0471111813

Categories: Solid State Physics | Spectroscopy