536
21 Diodes
(a)
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
j (Acm )
d
-2
0.0
0.2
0.4
0.6
0.8
10 -7
10 -6
10 -5
10 -4
10 -3
j (Acm )
d
-2
-3
-2
-1
0
1
T=293K
Pd/ZnO
T=
293K
210K
(b)
(c)
1.2
1.4
1.6
1.8
2.0
n
200
250
T (K)
-0.55
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
1/n-1
3.0
3.5
4.0
4.5
5.0
1/T (1000/K)
Fig. 21.16 a Forward I –V characteristic of Pd/ZnO Schottky diodes for various temperatures. Diode temperatures
are 210, 220, 230, 240, 250, 260, 270, and 293 K. The inset shows the current density versus voltage for 293 K on a
semilogarithmic scale. b Effective barrier height F
j
Bn versus the inverse temperature. The solid line is a linear fit according
to (21.57) yielding the standard deviation σ F = 0.13 eV and the mean barrier height ¯
F Bn = 1.1 eV. (c) Plot of 1/n − 1
versus the inverse temperature. The solid line is a linear fit of the data yielding the voltage deformation coefficients
ρ 2 = −0.025 and ρ 3 = −0.028 eV. The inset shows the experimentally determined n factors and the n factors calculated
from (21.59) using the voltage-deformation coefficients obtained from the linear fit (dashed line). Adapted from [1724]
Correlation of Barrier Height and Ideality Factor
Diffusion Theory
In diffusion theory the current density is considered in the presence of a carrier-density and electricfield gradient. In the Boltzmann approximation the electron current is given by (8.60a). In stationary
equilibrium the current density is constant, i.e. independent of x. Assuming that the carrier density has
its equilibrium values at x = 0 and x = w, we find after integration and using (21.8)
j = −e μ n N C E m exp
−
F Bn
kT
exp (βV ) − 1
(21.61)
= j s
exp (βV ) − 1
.
Therefore, also in this case the ideal diode characteristic is obtained, however, with a different saturation
current. The ideality factor in diffusion theory is n = 1.06 (for F Bn 15 kT ) [1684].
21 Diodes
(a)
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
j (Acm )
d
-2
0.0
0.2
0.4
0.6
0.8
10 -7
10 -6
10 -5
10 -4
10 -3
j (Acm )
d
-2
-3
-2
-1
0
1
T=293K
Pd/ZnO
T=
293K
210K
(b)
(c)
1.2
1.4
1.6
1.8
2.0
n
200
250
T (K)
-0.55
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
1/n-1
3.0
3.5
4.0
4.5
5.0
1/T (1000/K)
Fig. 21.16 a Forward I –V characteristic of Pd/ZnO Schottky diodes for various temperatures. Diode temperatures
are 210, 220, 230, 240, 250, 260, 270, and 293 K. The inset shows the current density versus voltage for 293 K on a
semilogarithmic scale. b Effective barrier height F
j
Bn versus the inverse temperature. The solid line is a linear fit according
to (21.57) yielding the standard deviation σ F = 0.13 eV and the mean barrier height ¯
F Bn = 1.1 eV. (c) Plot of 1/n − 1
versus the inverse temperature. The solid line is a linear fit of the data yielding the voltage deformation coefficients
ρ 2 = −0.025 and ρ 3 = −0.028 eV. The inset shows the experimentally determined n factors and the n factors calculated
from (21.59) using the voltage-deformation coefficients obtained from the linear fit (dashed line). Adapted from [1724]
Correlation of Barrier Height and Ideality Factor
Diffusion Theory
In diffusion theory the current density is considered in the presence of a carrier-density and electricfield gradient. In the Boltzmann approximation the electron current is given by (8.60a). In stationary
equilibrium the current density is constant, i.e. independent of x. Assuming that the carrier density has
its equilibrium values at x = 0 and x = w, we find after integration and using (21.8)
j = −e μ n N C E m exp
−
F Bn
kT
exp (βV ) − 1
(21.61)
= j s
exp (βV ) − 1
.
Therefore, also in this case the ideal diode characteristic is obtained, however, with a different saturation
current. The ideality factor in diffusion theory is n = 1.06 (for F Bn 15 kT ) [1684].