518
21 Diodes
Table 21.1 Typical current densities for various semiconductor devices
Device
j (A/cm 2 )
Dark current of cooled CCD (T ∼ 200 K)
< 10 −12
Dark current of CCD at room temperature
10 −9
3.6 nm SiOx gate dielectric (at 1 V)
10 −9
Photocurrent of Si solar cell (at 1 sun)
0.04
1.5 nm SiOx gate dielectric (at 1 V)
1
4-junction solar cell (at 508 sun)
6.5
Threshold of QD laser diodes
10
LED in typical operation
10
Threshold of QW laser diodes
10 2
LED in high power operation
10 2
Threshold of VCSEL
10 3
High power III–V laser diode in cw operation
10 3 –10 4
High power III–V laser diode in pulsed operation
10 5
Resonant tunneling diode peak current
10 5
Power electronics transistors
10 5 –10 7
Semiconductor devices carry vastly different currents depending on their design and eventual application. In Table 21.1, an overview of typical current densities is provided as a guide through the
following chapters.
21.2 Metal-Semiconductor Contacts
The metal-semiconductor contact was investigated in 1874 by F. Braun (see Sect. 1.1). For metal sulfides, e.g. CuFeS 2 , he found nonohmic behavior. We remark here that we treat first metal-semiconductor
contacts with rectifying properties. Later it becomes understandable that metal-semiconductor contacts can also be used as ohmic contacts, i.e. contacts with a very small contact resistance. Rectifying
metal-semiconductor contacts are also called Schottky diodes. A very important variation are metalinsulator-semiconductor diodes for which an insulator, mostly an oxide, is sandwiched between the
metal and the semiconductor. Such diodes are treated in Sect. 21.3. An early treatment on ‘crystal
rectifiers’ can be found in [1680]. Reviews on Schottky diodes can be found in [1681–1687].
21.2.1 Band Diagram in Equilibrium
The metal and the semiconductor have generally different positions of the Fermi levels relative to the
vacuum level. When the metal is in contact with the semiconductor, charges will flow in such a way that
in thermodynamic equilibrium the Fermi level is constant throughout the structure.
3 In the following
we treat two limiting cases: The contact of a metal with a semiconductor without any surface states
(Schottky-Mott model) and a contact where the semiconductor has a very high density of surface states
(Bardeen model).
3 This situation is similar to the heterostructure interface (Sect. 12.3.4), with the metal, however, having a very short
screening length.
21 Diodes
Table 21.1 Typical current densities for various semiconductor devices
Device
j (A/cm 2 )
Dark current of cooled CCD (T ∼ 200 K)
< 10 −12
Dark current of CCD at room temperature
10 −9
3.6 nm SiOx gate dielectric (at 1 V)
10 −9
Photocurrent of Si solar cell (at 1 sun)
0.04
1.5 nm SiOx gate dielectric (at 1 V)
1
4-junction solar cell (at 508 sun)
6.5
Threshold of QD laser diodes
10
LED in typical operation
10
Threshold of QW laser diodes
10 2
LED in high power operation
10 2
Threshold of VCSEL
10 3
High power III–V laser diode in cw operation
10 3 –10 4
High power III–V laser diode in pulsed operation
10 5
Resonant tunneling diode peak current
10 5
Power electronics transistors
10 5 –10 7
Semiconductor devices carry vastly different currents depending on their design and eventual application. In Table 21.1, an overview of typical current densities is provided as a guide through the
following chapters.
21.2 Metal-Semiconductor Contacts
The metal-semiconductor contact was investigated in 1874 by F. Braun (see Sect. 1.1). For metal sulfides, e.g. CuFeS 2 , he found nonohmic behavior. We remark here that we treat first metal-semiconductor
contacts with rectifying properties. Later it becomes understandable that metal-semiconductor contacts can also be used as ohmic contacts, i.e. contacts with a very small contact resistance. Rectifying
metal-semiconductor contacts are also called Schottky diodes. A very important variation are metalinsulator-semiconductor diodes for which an insulator, mostly an oxide, is sandwiched between the
metal and the semiconductor. Such diodes are treated in Sect. 21.3. An early treatment on ‘crystal
rectifiers’ can be found in [1680]. Reviews on Schottky diodes can be found in [1681–1687].
21.2.1 Band Diagram in Equilibrium
The metal and the semiconductor have generally different positions of the Fermi levels relative to the
vacuum level. When the metal is in contact with the semiconductor, charges will flow in such a way that
in thermodynamic equilibrium the Fermi level is constant throughout the structure.
3 In the following
we treat two limiting cases: The contact of a metal with a semiconductor without any surface states
(Schottky-Mott model) and a contact where the semiconductor has a very high density of surface states
(Bardeen model).
3 This situation is similar to the heterostructure interface (Sect. 12.3.4), with the metal, however, having a very short
screening length.