Chapter 7
Electronic Defect States
Über Halbleiter sollte man nicht arbeiten, das ist eine Schweinerei, wer weiß ob es
überhaupt Halbleiter gibt.
One should not work on semiconductors. They are a mess. Who knows whether
semiconductors even exist.
W. Pauli, 1931[554]
Abstract After the carrier statistics for intrinsic conduction and general doping principles, donors
and acceptors, compensation and high doping effects are treated in detail. The concept of quasi-Fermi
levels is introduced. Finally for deep levels and their thermodynamics general remarks and several
examples are given.
7.1 Introduction
One cm
3 of a semiconductor contains about 5 × 10
22 atoms. It is practically impossible to achieve
perfect purity. Typical low concentrations of impurity atoms are in the 10
12
− 10
13 cm
−3 regime. Such
a concentration corresponds to a purity of 10
−10 , corresponding to about one alien in the world’s
human population. In the beginning of semiconductor research the semiconductors were so impure
that the actual semiconducting properties could only be used inefficiently. Nowadays, thanks to large
improvements in high-purity chemistry, the most common semiconductors, in particular silicon, can be
made so pure that the residual impurity concentration plays no role in the physical properties. However,
the most important technological step for semiconductors is doping, the controlled incorporation of
impurities, in order to manage the semiconductor’s conductivity. Typical impurity concentrations used
in doping are 10
15
− 10
20 cm
−3 . A milestone in the understanding of doping and the spreading of
semiconductor technology was the 1950 textbook by Shockley [555].
7.2 Carrier Concentration
Generally, the density of electrons in the conduction band is given by
n =
∞
E C
D e (E) f e (E) dE ,
(7.1)
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_7
179
Electronic Defect States
Über Halbleiter sollte man nicht arbeiten, das ist eine Schweinerei, wer weiß ob es
überhaupt Halbleiter gibt.
One should not work on semiconductors. They are a mess. Who knows whether
semiconductors even exist.
W. Pauli, 1931[554]
Abstract After the carrier statistics for intrinsic conduction and general doping principles, donors
and acceptors, compensation and high doping effects are treated in detail. The concept of quasi-Fermi
levels is introduced. Finally for deep levels and their thermodynamics general remarks and several
examples are given.
7.1 Introduction
One cm
3 of a semiconductor contains about 5 × 10
22 atoms. It is practically impossible to achieve
perfect purity. Typical low concentrations of impurity atoms are in the 10
12
− 10
13 cm
−3 regime. Such
a concentration corresponds to a purity of 10
−10 , corresponding to about one alien in the world’s
human population. In the beginning of semiconductor research the semiconductors were so impure
that the actual semiconducting properties could only be used inefficiently. Nowadays, thanks to large
improvements in high-purity chemistry, the most common semiconductors, in particular silicon, can be
made so pure that the residual impurity concentration plays no role in the physical properties. However,
the most important technological step for semiconductors is doping, the controlled incorporation of
impurities, in order to manage the semiconductor’s conductivity. Typical impurity concentrations used
in doping are 10
15
− 10
20 cm
−3 . A milestone in the understanding of doping and the spreading of
semiconductor technology was the 1950 textbook by Shockley [555].
7.2 Carrier Concentration
Generally, the density of electrons in the conduction band is given by
n =
∞
E C
D e (E) f e (E) dE ,
(7.1)
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_7
179