522
21 Diodes
(a)
1.5
1.0
0
F (eV)
Bn
W (eV)
m
3.0
4.0
5.0
0.5
GaP
GaAs
Si
CdS
S=1
S=0
Ge
(b)
10
1.0
0.1
E -E (meV)
C
F
E (meV)
g
0.1
1.0
10
InSb
InP
Ge
GaSb
Si
GaAs AlSb
BP
AlAs
GaP
SiC
C
BN
(c)
Fig. 21.5 a Experimental Schottky barrier heights F Bn versus metal work function W m for various metal-semiconductor
junctions as labeled. Dashed lines are guides to the eye, dash-dotted lines indicate dependencies for the surface index
(21.6) S = 1 and S = 0. Data from [1690, 1691]. b E C − E F at the metal-semiconductor interface versus the band
gap E g for Au Schottky contacts on various semiconductors. The dashed line represents E C − E F = 2E g /3. Data from
[1692]. cSurface index S versus the electronegativity difference between the species of compound semiconductors.
Dashed line is a guide to the eye. Data from [1691, 1693]
The surface index is defined as
S =
∂ F Bn
∂ W m
.
(21.6)
From the present consideration (21.3), the same semiconductor with metals of varying work function
should result in S = 1.
Band Diagram in the Presence of Surface States
Experimental data shown in Fig. 21.5a, however, show a different behavior with smaller slope. For
GaAs, e.g., the barrier height is almost independent of the metal work function. Thus, a different model
is needed for realistic Schottky diodes. A rule of thumb for the dominantly covalent semiconductors
is that for n-type material the barrier height is 2/3 of the band gap and for p-type material 1/3 of
the band gap, such that E C − E F ≈ 2E g /3 (Fig. 21.5b). Only for ionic semiconductors S ≈ 1 holds
(Fig. 21.5c) [1694].
If the semiconductor has a large density of states at its surface ( 10
12 cm
−2 ), there is a space-charge
region already without the metal [1695]. Surface traps are filled up to the Fermi level (Fig. 21.6a). The
size of the band bending in the semiconductor will be denoted as F Bn since it will turn out below as
the Schottky barrier height. If the density of surface states is very high, the charge carriers moving
21 Diodes
(a)
1.5
1.0
0
F (eV)
Bn
W (eV)
m
3.0
4.0
5.0
0.5
GaP
GaAs
Si
CdS
S=1
S=0
Ge
(b)
10
1.0
0.1
E -E (meV)
C
F
E (meV)
g
0.1
1.0
10
InSb
InP
Ge
GaSb
Si
GaAs AlSb
BP
AlAs
GaP
SiC
C
BN
(c)
Fig. 21.5 a Experimental Schottky barrier heights F Bn versus metal work function W m for various metal-semiconductor
junctions as labeled. Dashed lines are guides to the eye, dash-dotted lines indicate dependencies for the surface index
(21.6) S = 1 and S = 0. Data from [1690, 1691]. b E C − E F at the metal-semiconductor interface versus the band
gap E g for Au Schottky contacts on various semiconductors. The dashed line represents E C − E F = 2E g /3. Data from
[1692]. cSurface index S versus the electronegativity difference between the species of compound semiconductors.
Dashed line is a guide to the eye. Data from [1691, 1693]
The surface index is defined as
S =
∂ F Bn
∂ W m
.
(21.6)
From the present consideration (21.3), the same semiconductor with metals of varying work function
should result in S = 1.
Band Diagram in the Presence of Surface States
Experimental data shown in Fig. 21.5a, however, show a different behavior with smaller slope. For
GaAs, e.g., the barrier height is almost independent of the metal work function. Thus, a different model
is needed for realistic Schottky diodes. A rule of thumb for the dominantly covalent semiconductors
is that for n-type material the barrier height is 2/3 of the band gap and for p-type material 1/3 of
the band gap, such that E C − E F ≈ 2E g /3 (Fig. 21.5b). Only for ionic semiconductors S ≈ 1 holds
(Fig. 21.5c) [1694].
If the semiconductor has a large density of states at its surface ( 10
12 cm
−2 ), there is a space-charge
region already without the metal [1695]. Surface traps are filled up to the Fermi level (Fig. 21.6a). The
size of the band bending in the semiconductor will be denoted as F Bn since it will turn out below as
the Schottky barrier height. If the density of surface states is very high, the charge carriers moving