21.2 Metal-Semiconductor Contacts
543
Fig. 21.26 Current density
from the beginning
(≈ 100 µs) of a pulsed
experiment versus applied
field (applied voltage
divided by sample
thickness) for 50 µm thick
CdS crystal between
indium-tipped electrodes.
The dashed line shows a
V 2 -dependence. Adapted
from [1748]
and for j (and E 0 = V 0 /L) therefore the Mott-Gurney law
13
j =
9
8
μ μ
L 3 V
2
0 =
9
8
μ μ
L
E
2
0 .
(21.76)
A quantum theory of space-charge limited current has been put forward in [1747]. For small voltages,
Ohm’s law j ∝ V 0 is valid.
The j ∝ V
2 -dependence has been first observed for CdS [1748, 1749]. In order to avoid the
effect of injected charge being trapped, pulsed measurements are applied [1748]; in this case, the
V
2 -dependence is well fulfilled (trap-free SCLC) (Fig. 21.26) while the steady-state current would be
many orders of magnitude smaller. In [1750], an investigation of crystalline silicon and also a theory
for bipolar transport can be found. Equation (21.76) can also serve to determine the mobility if the
conditions for space-charge limited current are fulfilled. Modifications are necessary in the presence
of traps as discussed in [1751] for the case of amorphous silicon.
21.2.7 Metal Contacts to Organic Semiconductors
Also, for organic semiconductors the metal contact plays a vital role, either for carrier injection or for
manipulation of the space-charge region. The position of the Fermi level has been determined for various
organic semiconductors as shown in Fig. 21.27. These data have been obtained from measurements on
metal-semiconductor-metal structures (MSM, see also Sect. 22.3.5) as shown in Fig. 21.28a. The thin
(50 nm) organic layer is fully depleted, thus the built-in field inside the semiconductor is constant. The
built-in field is measured by applying an external dc bias and finding the external potential at which the
electroabsorption signal vanishes. Figure 21.28b shows the measured electroabsorption signal /T
(relative change of transmission T ) and the optical density of an MEH-PPV film as a function of photon
energy for an Al/MEH-PPV/Al structure. The exciton absorption peak is found at 2.25 eV. The bias at
which the built-in field vanishes can then be determined for various other metals in metal/MEH-PPV/Al
structures. Figure 21.27 summarizes such results for various metals and three organic semiconductors.
The plot of the Fermi level position versus the metal work function (Fig. 21.28d,e) shows that the
metals investigated do not introduce interface states in the single-particle gap that pin the Schottky
13 For transport in vacuum where the electron motion is accelerated, j ∝ V
3/2
0
was found earlier, [1745, 1746]
543
Fig. 21.26 Current density
from the beginning
(≈ 100 µs) of a pulsed
experiment versus applied
field (applied voltage
divided by sample
thickness) for 50 µm thick
CdS crystal between
indium-tipped electrodes.
The dashed line shows a
V 2 -dependence. Adapted
from [1748]
and for j (and E 0 = V 0 /L) therefore the Mott-Gurney law
13
j =
9
8
μ μ
L 3 V
2
0 =
9
8
μ μ
L
E
2
0 .
(21.76)
A quantum theory of space-charge limited current has been put forward in [1747]. For small voltages,
Ohm’s law j ∝ V 0 is valid.
The j ∝ V
2 -dependence has been first observed for CdS [1748, 1749]. In order to avoid the
effect of injected charge being trapped, pulsed measurements are applied [1748]; in this case, the
V
2 -dependence is well fulfilled (trap-free SCLC) (Fig. 21.26) while the steady-state current would be
many orders of magnitude smaller. In [1750], an investigation of crystalline silicon and also a theory
for bipolar transport can be found. Equation (21.76) can also serve to determine the mobility if the
conditions for space-charge limited current are fulfilled. Modifications are necessary in the presence
of traps as discussed in [1751] for the case of amorphous silicon.
21.2.7 Metal Contacts to Organic Semiconductors
Also, for organic semiconductors the metal contact plays a vital role, either for carrier injection or for
manipulation of the space-charge region. The position of the Fermi level has been determined for various
organic semiconductors as shown in Fig. 21.27. These data have been obtained from measurements on
metal-semiconductor-metal structures (MSM, see also Sect. 22.3.5) as shown in Fig. 21.28a. The thin
(50 nm) organic layer is fully depleted, thus the built-in field inside the semiconductor is constant. The
built-in field is measured by applying an external dc bias and finding the external potential at which the
electroabsorption signal vanishes. Figure 21.28b shows the measured electroabsorption signal /T
(relative change of transmission T ) and the optical density of an MEH-PPV film as a function of photon
energy for an Al/MEH-PPV/Al structure. The exciton absorption peak is found at 2.25 eV. The bias at
which the built-in field vanishes can then be determined for various other metals in metal/MEH-PPV/Al
structures. Figure 21.27 summarizes such results for various metals and three organic semiconductors.
The plot of the Fermi level position versus the metal work function (Fig. 21.28d,e) shows that the
metals investigated do not introduce interface states in the single-particle gap that pin the Schottky
13 For transport in vacuum where the electron motion is accelerated, j ∝ V
3/2
0
was found earlier, [1745, 1746]