21.2 Metal-Semiconductor Contacts
533
(a)
AgO /ZnO
x
FB f
FB
n
(b)
AgO /ZnO
x
FB f
-1
1000/T (K )
-1
s,f
2
- 2- 2
s
2
- 2- 2
Fig. 21.14 Temperature dependent behavior of an AgO x /ZnO Schottky diode. a I –V -characteristics. Inset depicts
extracted parameters, ideality factor n, barrier height F B and flatband barrier height F f
B (21.54). b Richardson plots for
the extracted barrier height and the calculated flatband barrier height with linear fit. Adapted from [1713]
Ideality Factor
If the Schottky (image force) effect, i.e. the change of barrier height with bias voltage, is considered,
the semilogarithmic slope of the forward I –V characteristic is no longer V
−1
0
= e/kT but can be
expressed as V
−1
0
= e/nkT , n being a dimensionless parameter termed the ideality factor,
9
j = j s
exp
e V
n kT
− 1
.
(21.51)
n is given by
n =
1 −
1
e
∂ F B
∂ V
−1
≈ 1 +
1
e
∂ F B
∂ V
.
(21.52)
The ideality factor due to the image force effect n if (using (21.27) and the image force barrier lowering
if,0
B at zero bias) [1680] is
n if = 1 +
if,0
B
4 e V bi
= 1 +
x m
w 0
.
(21.53)
Typical values are smaller than 1.03. For GaAs and N D = 10
17 cm
−3 , n = 1.02. With regard to V 0 and
its temperature dependence, we refer also to Fig. 21.17 and the related discussion.
In Fig. 21.14a the temperature dependence of the I –V -characteristic of an almost ideal ZnO Schottky
diode [1713] is depicted. The extracted barrier height is almost independent of temperature as it
should be. Also the ideality factor is rather small (about 1.1) and also independent of temperature.
The Richardson plot Fig. 21.14b according to (21.50) for this diode is a straight line. The extracted
constant A
∗
= (10 ± 6) A cm
−2 K
−2 is reasonably close to the theoretical value of 32 A cm
−2 K
−2
(using m
∗
= 0.32).
In order to gain a barrier height independent from non-idealities, in [1714] the flatband barrier
height F
f
B is discussed which is calculated from the diode parameters via
F
f
B = n F B − (n − 1)
kT
e
ln
N C
N D
,
(21.54)
9 Obviously n = 1 for the ideal characteristic (21.48). Otherwise n ≥ 1.
533
(a)
AgO /ZnO
x
FB f
FB
n
(b)
AgO /ZnO
x
FB f
-1
1000/T (K )
-1
s,f
2
- 2- 2
s
2
- 2- 2
Fig. 21.14 Temperature dependent behavior of an AgO x /ZnO Schottky diode. a I –V -characteristics. Inset depicts
extracted parameters, ideality factor n, barrier height F B and flatband barrier height F f
B (21.54). b Richardson plots for
the extracted barrier height and the calculated flatband barrier height with linear fit. Adapted from [1713]
Ideality Factor
If the Schottky (image force) effect, i.e. the change of barrier height with bias voltage, is considered,
the semilogarithmic slope of the forward I –V characteristic is no longer V
−1
0
= e/kT but can be
expressed as V
−1
0
= e/nkT , n being a dimensionless parameter termed the ideality factor,
9
j = j s
exp
e V
n kT
− 1
.
(21.51)
n is given by
n =
1 −
1
e
∂ F B
∂ V
−1
≈ 1 +
1
e
∂ F B
∂ V
.
(21.52)
The ideality factor due to the image force effect n if (using (21.27) and the image force barrier lowering
if,0
B at zero bias) [1680] is
n if = 1 +
if,0
B
4 e V bi
= 1 +
x m
w 0
.
(21.53)
Typical values are smaller than 1.03. For GaAs and N D = 10
17 cm
−3 , n = 1.02. With regard to V 0 and
its temperature dependence, we refer also to Fig. 21.17 and the related discussion.
In Fig. 21.14a the temperature dependence of the I –V -characteristic of an almost ideal ZnO Schottky
diode [1713] is depicted. The extracted barrier height is almost independent of temperature as it
should be. Also the ideality factor is rather small (about 1.1) and also independent of temperature.
The Richardson plot Fig. 21.14b according to (21.50) for this diode is a straight line. The extracted
constant A
∗
= (10 ± 6) A cm
−2 K
−2 is reasonably close to the theoretical value of 32 A cm
−2 K
−2
(using m
∗
= 0.32).
In order to gain a barrier height independent from non-idealities, in [1714] the flatband barrier
height F
f
B is discussed which is calculated from the diode parameters via
F
f
B = n F B − (n − 1)
kT
e
ln
N C
N D
,
(21.54)
9 Obviously n = 1 for the ideal characteristic (21.48). Otherwise n ≥ 1.