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Intrinsic conduction (also intrinsic conduction ) referred to in the solid-state physics , the relatively low electrical conductivity un -doped (pure) semiconductor . Materials in which intrinsic conduction is the determining mechanism for the conductivity of electrical current are called intrinsic semiconductors (or intrinsic semiconductors ).

In contrast to this, the impurities in doped semiconductors (impurity conductors) lead to an increase in electrical conductivity, here the impurity conduction dominates .

description

Conduction mechanisms in doped and undoped semiconductors as a function of temperature

The electrical conductivity of materials is mainly determined by the availability of charge carriers and free energy levels in the energy bands , i.e. H. Empty as well as full energy bands do not allow charge transport.

At the absolute zero point (at 0 K ) there is not enough energy available to excite electrons into the conduction band or to the impurity level, which is why doped and undoped semiconductors do not differ here in terms of charge carrier density .

The available energy (e.g. phonons ) increases with increasing temperature , so that the probability of thermal excitation of an electron from the valence band to the conduction band also increases. In typical semiconductors such as germanium or silicon, the band gap energy is in the range from 0.5 to 3.5  eV and thus usually significantly higher than the distance between the valence or conduction band and the impurity level (0.01 to 0.5 eV) in doped semiconductors . As a result, the electrical conductivity increases through intrinsic conduction only at significantly higher temperatures than in the case of fault line conduction.

Intrinsic conductivity

A characterizing material constant can hardly be specified for the electrical conductivity of a semiconductor, since the conductivity can be changed by several orders of magnitude through contamination or doping of the semiconductor. With silicon, values ​​in the range 10 ⁰ … 10 ⁶  S / m are possible. For germanium with a degree of purity > 99.999%, the specific resistance at 20 ° C is given as 53000 μΩ · cm; this corresponds to a conductance of 1.9 · 10 ³  S / m. This value is three orders of magnitude higher than the value of the intrinsic or intrinsic conductivity calculated below . The same is reported for silicon. A representative constant of the semiconductor can only be given for a state that is independent of the degree of purity, that is the state of intrinsic conduction.

Data on intrinsic conductivity at 300 K

material	${\displaystyle n_{\mathrm {i} }}$ in ${\displaystyle {\tfrac {1}{{\text{cm}}^{3}}}}$	${\displaystyle b_{\mathrm {n} }}$ in ${\displaystyle \mathrm {\tfrac {cm^{2}}{Vs}} }$	${\displaystyle b_{\mathrm {p} }}$ in ${\displaystyle \mathrm {\tfrac {cm^{2}}{Vs}} }$	${\displaystyle \sigma _{\mathrm {i} }}$ in ${\displaystyle \mathrm {\tfrac {S}{m}} }$	source
Germanium	2.4the13	3600	1700	2.0
	2.4the13	3900	1900	2.2
	2.3e13	3900	1900	2.1
silicon	6th.8the10	1400	400	2.0e-3
	1.5e10	1350	850	0.5e-3
	1.5e10	1350	480	0.4the-3

For conductivity , not only the free electrons contribute, but also the remaining holes (holes) , each with its negative or positive charges, their mobilities ,  and their particle densities ,  . ${\displaystyle \sigma }$ ${\displaystyle b_{\mathrm {n} }}$ ${\displaystyle b_{\mathrm {p} }}$ ${\displaystyle n_{\mathrm {n} }}$ ${\displaystyle n_{\mathrm {p} }}$

With the elementary charge results ${\displaystyle e}$

${\displaystyle \sigma =e\,(n_{\mathrm {n} }\,b_{\mathrm {n} }+n_{\mathrm {p} }\,b_{\mathrm {p} })}$.

In the case of intrinsic conduction, the particle densities are the same size and equal to the intrinsic conduction density . This results in the intrinsic conductivity to ${\displaystyle n_{\mathrm {i} }=n_{\mathrm {p} }=n_{\mathrm {n} }}$

${\displaystyle \sigma _{\mathrm {i} }=e\,n_{\mathrm {i} }\,(b_{\mathrm {n} }+b_{\mathrm {p} })}$.

The data required and the results are in the attached table. The different information in different sources shows the difficulty in getting reliable data even for self-management.

The intrinsic conduction density should be seen in relation to the atomic density . With the table values ​​for 300 K is ${\displaystyle n_{\mathrm {A} }=4\ldots 5\cdot 10^{22}\,\mathrm {cm} ^{-3}}$

${\displaystyle n_{\mathrm {i} }/n_{\mathrm {A} }<10^{-9}}$for germanium and for silicon. ${\displaystyle <10^{-12}}$

This means that for the intrinsic state there may be at most one foreign atom for every 10 ⁹ germanium atoms.

The lowest impurity concentration that can be achieved in semiconductor single crystals today is 10 ¹²  cm ⁻³ . This means that intrinsically conductive germanium is possible at room temperature. In the case of silicon and technically used germanium with an impurity concentration of 10 ¹⁵ … 10 ¹⁸  cm ⁻³   , self-conduction is not possible at room temperature.

Individual evidence

1. ^ SM Sze: Physics of Semiconductor Devices . 2nd Edition. Wiley & Sons, 1981, ISBN 0-471-09837-X , pp. 21 (Newer editions do not contain an overview for germanium).
2. ↑ Konrad Reif (ed.): Bosch car electrics and car electronics: vehicle electrical systems, sensors and electronic systems. 6th edition, Vieweg + Teubner, 2011, ISBN 9783834899026 , p. 168
3. ↑ Brochure sheet Ge 99.999% see properties; accessed November 10, 2019
4. ↑ Henricus PJ Wijn, Peter Dullenkopf: Materials in electrical engineering: physical fundamentals of technical applications. Springer, 1967, ISBN 978-3-642-88698-0 , p. 59.
5. ^ ^{A b c} Franz Moeller (original), Hans Fricke, Heinrich Frohne, Paul Vaske: Fundamentals of electrical engineering. 17th edition, Springer, 1986, ISBN 3663121569 , p. 234.
6. ↑ ^{a b} Wilfried Plaßmann, Detlef Schulz (ed.): Handbook of electrical engineering: Fundamentals and applications for electrical engineers. 5th edition, Vieweg + Teubner, 2009, ISBN 978-3-8348-0470-9 , p. 231.
7. ↑ ^{a b c} Leonhard Stiny: Active electronic components: design, structure, mode of operation, properties and practical use. 4th edition, Springer-Vieweg, 2019, ISBN 978-3-658-24751-5 , p. 28.
8. ↑ Wilfried Plaßmann, Detlef Schulz (Hrsg.): Handbook of electrical engineering: Basics and applications for electrical engineers. 5th edition, Vieweg + Teubner, 2009, ISBN 978-3-8348-0470-9 , p. 225.
9. ↑ Eberhard Spenke: Electronic semiconductors: An introduction to the physics of rectifiers and transistors. Springer, 1955, p. 26 f, footnote 2.
10. ↑ Harald Ibach, Hans Lüth: Solid State Physics: Introduction to the Basics. 7th edition, Springer, 2009, ISBN 9783540857952 , p. 416
11. ↑ Reinhold Paul: Transistors: Physical Basics and Properties. Springer and Vieweg, 1965, p. 24 f.