Band gap
As a band gap ( English band gap ) and band gap or forbidden zone that is energetic distance between the valence band and conduction band of a solid , respectively. Its electrical and optical properties are largely determined by the size of the band gap. The size of the band gap is usually given in electron volts (eV).
material | Art | Energy in eV | |
---|---|---|---|
0 K | 300 K | ||
elements | |||
C (as diamond ) | indirectly | 5.4 | 5.46-5.6 |
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 | |
In x Ga 1-x N | directly | 0.7-3.37 | |
GaN | directly | 3.37 | |
GaP 3C | indirectly | 2.26 | |
GaSb | directly | 0.81 | 0.69 |
GaAs | directly | 1.52 | 1.42 |
Al x Ga 1-x As | x <0.4 direct, x> 0.4 indirect |
1.42-2.16 | |
AlAs | indirectly | 2.16 | |
As B | indirectly | 1.65 | 1.58 |
AlN | directly | 6.2 | |
BN | 5.8 | ||
II-VI compounds | |||
TiO 2 | 3.03 | 3.2 | |
ZnO | directly | 3,436 | 3.37 |
ZnS | 3.56 | ||
ZnSe | directly | 2.70 | |
CdS | 2.42 | ||
CdSe | 1.74 | ||
CdTe | 1.45 |
origin
According to the band model , bound states of the electrons are only permitted at certain intervals on the energy scale, the bands . There may (but need not) be energetically forbidden areas 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 still completely occupied by electrons (valence band, VBM) and the next higher band (conduction band, CBM) is of decisive importance. Therefore, the band gap always refers to 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.
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 made. 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 from 0.1 to ≈ 4 eV .
- Insulators have a band gap greater than 4 eV.
Optical properties
The ability of a solid to the light absorption is subject to the condition, the photon energy by means of excitation of electrons to take. Since no electrons can be excited in the forbidden area between the valence and conduction bands, the energy of a photon must exceed the energy of the band gap
otherwise the photon cannot be absorbed.
The energy of a photon is coupled to the frequency ( Ny ) of the electromagnetic radiation via the formula
with Planck's quantum of action
If a solid has a band gap, it is transparent to radiation below a certain frequency / above a certain wavelength (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):
- Metals can not be transparent.
- Transparent solids are mostly insulators . But there are also electrically conductive materials with a comparatively high degree of transmission , e.g. B. transparent, electrically conductive oxides .
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 .
Types (with band structure diagram)
Direct band gap
In the diagram, the minimum of the conduction band lies directly above the maximum of the valence band;
therein is the wave vector , which in photons is proportional to their vectorial momentum :
with Planck's reduced quantum of action
With 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. Therefore, the change is where the momentum transfer of the photon is neglected because of its comparatively small size.
Application examples: light emitting diode
Indirect band gap
In the case of an indirect band gap, the minimum of the conduction band is shifted in relation to the maximum of the valence band on the -axis; H. the smallest distance between the bands is offset. The absorption of a photon is only possible with a direct band gap; with an indirect band gap, an additional quasi-pulse ( ) 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, where the material shows weaker absorption.
The best-known semiconductor, silicon , has an indirect band transition.
Temperature dependence
The energy of the band gap decreases with increasing temperature for many materials first quadratically, then linearly, starting from a maximum value at . For some materials that crystallize in a diamond structure , the band gap can also increase with increasing temperature. The dependence can be phenomenologically u. a. describe with the Varshni formula:
with the Debye temperature
The Varshni parameters can be specified for different semiconductors:
semiconductor |
E g (T = 0K) (eV) |
(10 −4 eV / K) |
(K) |
source |
---|---|---|---|---|
Si | 1.170 | 4.73 | 636 | |
Ge | 0.744 | 4,774 | 235 | |
GaAs | 1.515 | 5.405 | 204 | |
GaN | 3.4 | 9.09 | 830 | |
AlN | 6.2 | 17.99 | 1462 | |
InN | 0.7 | 2.45 | 624 |
This temperature behavior is mainly due to the relative shift in position of the valence and conduction band due to the temperature dependence of the electron- phonon interactions. A second effect that u. a. in the case of diamond leads to a negative , the displacement is due to the thermal expansion of the lattice. In certain areas, this can become non-linear and also negative, whereby negative can be explained.
Applications
There are applications above all in optics (including different colored semiconductor lasers ) and in all areas of electrical engineering . A. exploits the semiconductor or insulator properties of the systems and their great variability (e.g. through alloying ). The systems with a band gap also include the so-called topological insulators , which have been in effect since around 2010 and in which (almost) superconducting surface currents occur in addition to the internal states that carry no current .
See also
- Band structure
- Schrödinger equation
- Band Gap Reference
- Solar cell
- III-V compound semiconductors # Calculation of the ternary band transition energies
- Wide band gap semiconductors
literature
- Charles Kittel : Introduction to Solid State Physics. 14th edition, Oldenbourg, 2005, ISBN 3-486-57723-9 (German translation).
- Charles Kittel: Introduction to Solid State Physics. John Wiley and Sons, 1995, 7th edition, ISBN 0-471-11181-3 .
Web links
Individual evidence
- ↑ Jerry L. Hudgins: Wide and narrow band gap semiconductors for power electronics: A new valuation. In: Journal of Electronic Materials, June 2003, Volume 32, Issue 6. Springer , December 17, 2002, pp. 471–477 , accessed on August 13, 2017 .
- ^ A b A. F. Holleman , E. Wiberg , N. Wiberg : Textbook of Inorganic Chemistry . 101st edition. Walter de Gruyter, Berlin 1995, ISBN 3-11-012641-9 , p. 1313.
- ^ A b Y. P. Varshni: Temperature dependence of the energy gap in semiconductors . In: Physica . tape 34 , no. 1 , p. 149-154 , doi : 10.1016 / 0031-8914 (67) 90062-6 .
- ^ A b Hans-Günther Wagemann, Heinz Eschrich: Solar radiation and semiconductor properties, solar cell concepts and tasks . Vieweg + Teubner Verlag, 2007, ISBN 3-8351-0168-4 , p. 75 .
- ↑ a b c Barbara Monika Neubert: GaInN / GaN LEDs on semipolar side facets using selective epitaxy produced GaN strips . Cuvillier Verlag, 2008, ISBN 978-3-86727-764-8 , pp. 10 .