Electronic Material Properties - und Geowissenschaften ...

∆ = 0
−
exhibiting dominance of space charge effects at low barriers. At low voltages
up to 0.1 V all I-V-characteristics show an Ohmic-like j ≈ V dependence. This Ohmic
regime is followed by an exponential increase of the current density with the voltage
up to the built-in voltage VBI = 0.81 eV corresponding to the difference in the workfunctions
of the electrodes. This increase can be attributed to a diffusive charge
carrier transport against the weakened electric field in the organic material. If a high
injection barrier is present, the following current-density increase is also exponential
due to the barrier modification by the electric field at the interface. After all, when the
injection barrier at the injecting electrode falls below ∆ crit the calcium contact can
supply more charge carriers than the bulk of the organic semiconductor can
transport. That is why all the I-V-characteristics end up in the space charge limited
regime.
In the case of high injection barriers the approximate analytic consideration results in
the I-V-characteristic of the system which reads
⎛ eV ⎞
− exp⎜−
⎟ −1
V + V ⎛ ∆ ⎞
BI
eff
exp⎜
⎟ ⎝ kT
j = −eµ
⎠
s N
⎜
−
⎟
, (2)
L ⎝ kT ⎠ ⎛ e(
V + VBI
) ⎞
exp⎜−
⎟ −1
⎝ kT ⎠
where µ s is the mobility of electrons in the insulator and the modified barrier equals
−
−
∆eff
= ∆ + eε lTFFs
( −L
/ 2)
. The agreement of this formula with numerical calculations is
perfect for reverse and forward bias until the space charge effects become dominant.
Fig. 1: I-V-characteristics for an organic layer with thickness L = 100 nm contacted with a
calcium electrode at x = -L/2 and a magnesium electrode at x = L/2. The injection barrier of
the calcium electrode is varied from 0 eV to 0.4 eV with an increment of 0.1 eV.
Finally, the presented model is capable of describing a metal/insulator/metal device
in the injection limited as well as in the space charge limited regime and reveals
conditions of the crossover from one regime to another.
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