21.2 Metal-Semiconductor Contacts
539
Fig. 21.20 Calculated
conditions for thermionic
field (‘TF’), field (‘F’) and
thermionic (‘TE’) emission
in a Au/GaAs Schottky
diode as a function of
temperature and doping
concentration. Adapted
from [1684]
12
10
8
6
4
2
0
10
16
10
17
10
18
10
15
kT (meV)
N (cm )
D
-3
Au/GaAs
F
TE
TF
validity of the two regimes is shown in Fig. 21.20 for Au/GaAs Schottky diodes as a function of doping
concentration (n-type) and temperature.
Tunneling through the image-charge effect rounded triangular Schottky barrier is discussed in detail
in [1733]. In the field-emission regime the forward current is given by [1684]
j = j s exp
eV
E 00
,
(21.64)
with the characteristic energy parameter E 00 given by
E 00 =
e
2
N D
m ∗ s
.
(21.65)
The saturation current is
j s ∝ exp
−
F Bn
E 00
.
(21.66)
In Fig. 21.21, the forward characteristic of a highly doped Au/Si is shown. The experimental value of
E 00 = 29 meV agrees well with the theoretical expectation of E 00 = 29.5 meV. Note that at T = 77 K
kT = 7 meV, thus thermionic emission is excluded for the diode current.
In the reverse direction the I –V characteristic under field emission is given by [1684]
j =
4π e m
∗
h 3
E
2
00
e (V bi − V )
F Bn
exp
−
2 F
3/2
Bn
3E 00
√
e(V bi − V )
.
(21.67)
From Fig. 21.21b, a barrier height of 0.79 eV is deduced.
In the TF-emission regime the current-voltage characteristic is given by
j = j s exp
eV
E 0
,
(21.68)
with
E 0 = E 00 coth
E 00
kT
,
(21.69)
where E 00 is given by (21.65). The energy for maximum TF emission E m is given by E m = e(V bi −
V )/ cosh
2
(E 00 /kT ). The coth-dependence of E 0 is shown in Fig. 21.22 for an Au/GaAs diode.
539
Fig. 21.20 Calculated
conditions for thermionic
field (‘TF’), field (‘F’) and
thermionic (‘TE’) emission
in a Au/GaAs Schottky
diode as a function of
temperature and doping
concentration. Adapted
from [1684]
12
10
8
6
4
2
0
10
16
10
17
10
18
10
15
kT (meV)
N (cm )
D
-3
Au/GaAs
F
TE
TF
validity of the two regimes is shown in Fig. 21.20 for Au/GaAs Schottky diodes as a function of doping
concentration (n-type) and temperature.
Tunneling through the image-charge effect rounded triangular Schottky barrier is discussed in detail
in [1733]. In the field-emission regime the forward current is given by [1684]
j = j s exp
eV
E 00
,
(21.64)
with the characteristic energy parameter E 00 given by
E 00 =
e
2
N D
m ∗ s
.
(21.65)
The saturation current is
j s ∝ exp
−
F Bn
E 00
.
(21.66)
In Fig. 21.21, the forward characteristic of a highly doped Au/Si is shown. The experimental value of
E 00 = 29 meV agrees well with the theoretical expectation of E 00 = 29.5 meV. Note that at T = 77 K
kT = 7 meV, thus thermionic emission is excluded for the diode current.
In the reverse direction the I –V characteristic under field emission is given by [1684]
j =
4π e m
∗
h 3
E
2
00
e (V bi − V )
F Bn
exp
−
2 F
3/2
Bn
3E 00
√
e(V bi − V )
.
(21.67)
From Fig. 21.21b, a barrier height of 0.79 eV is deduced.
In the TF-emission regime the current-voltage characteristic is given by
j = j s exp
eV
E 0
,
(21.68)
with
E 0 = E 00 coth
E 00
kT
,
(21.69)
where E 00 is given by (21.65). The energy for maximum TF emission E m is given by E m = e(V bi −
V )/ cosh
2
(E 00 /kT ). The coth-dependence of E 0 is shown in Fig. 21.22 for an Au/GaAs diode.