Page 141 - Organic Electronics in Sensors and Biotechnology

118 Cha pte r F o u r

should not alter its electronic properties during the measurement, which
takes ~1 min. Especially when the DUT is biased during measurement,
it might experience electric stress leading to an ambiguous IS. When
biasing a device, the measurement of the impedance has to be quasi-
static; i.e., the EC at each frequency must have sufficient time to complete
all charging and discharging processes. It will be shown that for certain
ECs, which are typical of organic electronic devices, the related time con-
stants can be high enough to limit the measurement speed.
The impedance is a measure of the electric resistance of AC cir-
cuits. It is a complex value with a magnitude and phase which are
both measurable. An ohmic resistor does not alter the phase whereas
an ideal capacitor has a phase φ of −90° and an ideal inductor has a
phase φ of +90°. Combinations of these basic elements have a phase
value in between depending on the dominant element. At low fre-
quencies capacitive elements dominate because their impedance Z is
C
inversely proportional to the frequency f. For inductive elements it is
the opposite since their impedance Z is proportional to the frequency.
L
The impedance of ohmic elements Z is frequency-independent and
R
identical to the ohmic resistance R.
Although each of these three basic impedance elements have
individually a constant phase over the whole frequency range, com-
binations of these will show a characteristic frequency–dependent
total phase. Thus it is surprising that the impedance spectrum of
some organic devices shows constant phase between −90 and 0° over
a large frequency range. For that reason we will provide a closer look
at a class of impedance elements known from electrochemistry, the
constant-phase elements (CPEs).
CPEs are impedance elements with a frequency-independent
1
constant phase between −90 and 0°. One example is the Young element
whose characteristics suit well the properties of an organic semicon-
ductor. A Young element is a parallel circuit of an ideal capacitance
and a resistor with an exponential spatial dependence. According to
2
Rammelt and Schiller, its impedance Z is described by
y
−1
p 1 + iωτexp( p )
Z = ln (4.1)
y ω + iωτ
iC 1
y
with τ = R() C R() = ρ() δ and p = δ /d
0
0
0
y
where δ = characteristic penetration depth
p = relative penetration depth
d = thickness of capacitor
τ = Young time constant
The relative penetration depth p describes into which depth of the
capacitor the conductive layer extends. A value of p = 0.05 indicates
that at 5% of the capacitor thickness d the conductivity has decreased