ARTICLE IN PRESS
Organic Electronics xxx (2006) xxx–xxx
www.elsevier.com/locate/orgel
Polymeric electronic oscillators based on bistable
conductance devices
José A. Freire a, Guilherme A. Dal Moro a, Rogério Toniolo
Ivo A. Hümmelgen a,*, Carlos A. Ferreira b
b
a
a
Departamento de Fı́sica, Universidade Federal do Paraná, Caixa Postal 19044, 81531-990 Curitiba, PR, Brazil
LAPOL/PPGEM, Universidade Federal do Rio Grande do Sul, Caixa Postal 15010, 91501-970 Porto Alegre, RS, Brazil
Received 20 March 2006; received in revised form 3 May 2006; accepted 4 May 2006
Abstract
We show electrical oscillatory behavior in simple circuits using poly(1,5-diaminonaphthalene)-based volatile switches
and determine the analytical expression for the oscillation period, as well as the minimum allowed oscillation period as
a function of oscillator capacitance, series resistance, the switch resistance in the ON- and OFF-states and switch critical
voltages for the ON–OFF and OFF–ON transitions.
Ó 2006 Elsevier B.V. All rights reserved.
PACS: 84.30.Ng; 81.05.Hd; 85.30.De
Keywords: Organic switches; Organic oscillators; Bistable conductance
1. Introduction
In the last years several organic materials presenting an abrupt switching of electrical resistance [1–14]
that can be controlled through the applied voltage
[5–8,10] were observed. In some of these devices an
OFF-state (highly resistive) remains until a voltage
(V) above a critical value (Vcrit) is applied to the
device. For V > Vcrit, the device resistance is reduced
by up to six orders of magnitude [4,5,7,8,10]. In some
of the reported devices [4,5,7] this ON-state condition remains so long as the applied voltage is main-
*
Corresponding author. Fax: +55 413613645.
E-mail address: iah@fisica.ufpr.br (I.A. Hümmelgen).
tained above a lower limit-value (Vhold) and for
V < Vhold, the OFF value is restituted. The phenomenon is reversible, the ON–OFF transition is fast and
Vcrit and Vhold were observed to be proportional to
the material layer thickness, so that these parameters
can be controlled [5,7].
The ON–OFF transition has been attributed to
different mechanisms. It was explained as originated
by different conductivities presented by the organic
material at different charge states [8,15] with a
possible contribution of conformational changes
of the molecules under high electric fields [16] (the
electronic density of states is highly sensitive to
molecular conformation). In some cases, the effect
was attributed to charge traps in the organic layer
of the device [17–19] or even to nanoparticles
1566-1199/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.orgel.2006.05.001
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J.A. Freire et al. / Organic Electronics xxx (2006) xxx–xxx
intentionally introduced [20] or accidentally precipitated inside the organic semiconductor film during
metal electrode evaporation [21].
Some years ago the use of these switches for
organic memories has been proposed [5]. The potential application in organic memory devices [22–28]
increased the interest concerning these switches,
motivated by the perception that existing technologies are inadequate in one or more memory operating parameters [20]. Apart from this major research
effort, quite simple organic oscillators were also
demonstrated using bistable volatile conductance
switching devices [29].
In this article, we demonstrate the construction
of an oscillator based on an organic switch. To
exemplify it, we use poly(1,5-diaminonaphthalene),
PDAN, whose electrical switching properties are
essentially similar to previously reported poly(5amino 1-naphthol) switches [4]. The molecular
structure of PDAN is shown in Fig. 1. The construction of the oscillator is similar to a previously
reported oscillator based on a poly(5-amino 1-naphthol) [29]. It uses, besides the organic switch, a
capacitor and a resistor (see Fig. 2). In this article
we obtain the theoretical expression for the frequency of the oscillator constructed in this manner
and we discuss the requirements for the organic
switch for successful construction of oscillators,
particularly emphasizing the requirements for building high frequency oscillators.
2. Experimental
The switching device was constructed by evaporating a 200 nm thick Ag film on glass substrate.
In the sequence the film was scratched using a tungsten tip with 17.15 g load. The scratch produces a
well-defined 27 lm wide gap in the Ag film, as
can be seen in Fig. 3. The PDAN, whose synthesis
is reported elsewhere [30,31], was deposited in the
gap region by dropping a 10 mg/ml PDAN:DMF
solution (DMF: N-N 0 -dimethylformamide). After
Fig. 2. Oscillator circuit composed by a PDAN-switch, a resistor
R and a capacitor C. The applied voltage e is supplied by a
voltage source.
Fig. 3. (a) Schematic lateral view of the PDAN-switching
devices. (b) Optical micrograph of the area of the Ag film
containing the scratch, observed through the glass substrate
(bottom view).
deposition the samples were dried for 2 h at room
temperature in flowing nitrogen, leading to a
1500 nm thick film. This planar geometry was chosen to minimize the capacitance of the switch, which
would be higher in a sandwich structure, and to
reduce shorts probability due to the high roughness
of the deposited PDAN films.
Fig. 1. Structure of poly(1,5-diaminonaphthalene). If the polymer is totally reduced y = 1 and if it totally oxidized y = 0.
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The oscillator was constructed associating the
switching device with a capacitor of capacitance C
and a series resistance R as shown in Fig. 2. A voltage source was used to apply a voltage e to the circuit and the voltage drop in the series resistor was
recorded with an oscilloscope.
3. Results
3
film-forming properties of the material, which presents high roughness after deposition. But such a
high dispersion was reported even in case of devices
produced under much more refined conditions [20].
The plot of the current through the series resistor
versus time of an oscillator constructed using
R = 101 MX, C = 10 nF is presented in Fig. 5, demonstrating the oscillating behavior. For this oscillator, the frequency is f = 0.77 Hz.
3.1. Switch and oscillator
3.2. Theoretical analysis of the oscillator
The electrical characteristic of switching devices
presenting bistable conductivity is presented in
Fig. 4(a). In these devices the OFF-state (highly
resistive) remains until a voltage V above a critical
value Vcrit is applied to the device. For V > Vcrit,
the device resistance is rapidly reduced and this
ON-state condition remains so long as the applied
voltage is maintained above a lower limit-value
Vhold. For V < Vhold, the OFF value is restituted
and the cycle can be repeated. A relatively high dispersion of Vcrit and Vhold values is observed in a set
of devices with nominally identical characteristics.
We attribute this problem, in part, to the bad
Consider a switch, with characteristics like those
presented in Fig. 4(b), used in a circuit like that of
Fig. 2. In order to obtain an analytical solution,
the switch resistance is assumed to be constant,
independent of the potential applied to the switch
device, both in the OFF-state (Roff) and in the
ON-state (Ron). Denoting by I the current that
passes through R and I 0 the current that passes
through the switch of resistance r (which can be
either Ron or Roff), one has
e ¼ RI þ rI 0 :
ð1Þ
0
The relationship between I and I is obtained from
¼ rI 0 , where dQ
¼ I I 0 and Q is the charge in
dt
0
the capacitor. It follows that I I 0 ¼ rC dIdt . This
equation has as solution
Z t
Iðt0 Þ 0
0
dt ;
I 0 ðtÞ ¼ I 00 et=rC þ
eðtt Þ=rC
ð2Þ
rC
0
Q
C
where I 00 is fixed by the initial condition. The resulting integro-differential equation for I(t) reads:
Z
1 t ðtt0 Þ=rC 0 0
0 t=rC
þ
e
Iðt Þdt :
ð3Þ
e ¼ RI þ rI 0 e
C 0
Fig. 4. (a) Electrical characteristics of a planar Ag/PDAN/Ag
bistable conductance switch. (b) The electrical characteristics of
the model for the switch that was used in the theoretical analysis.
Fig. 5. Current as a function of time in a resistor R = 101 MX of
an oscillator constructed with C = 10 nF, e = 100 V.
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The solution of this equation is
e
r
e
0
þ
I 0 expðt=sÞ;
IðtÞ ¼
Rþr R Rþr
ð4Þ
where s = rRC/(r + R) is the characteristic time.
The corresponding expression for I 0 (t) is
e
e
0
0
þ I0 I ðtÞ ¼
expðt=sÞ:
ð5Þ
Rþr
Rþr
These expressions assume that the switch resistance
r does not change in the time interval between t = 0
and t. In the case of a switch four currents are of relevance, see Fig. 4(b):
V hold
V crit
V hold
I 01 ¼
< I 02 ¼
and I 03 ¼
< I 04
Roff
Roff
Ron
V crit
¼
:
ð6Þ
Ron
Two characteristic times appear in the current
expressions:
Ron R
Roff R
son ¼
C < soff ¼
C:
ð7Þ
Ron þ R
Roff þ R
If I 0 starts out at I 01 (the switch operating with resistance Roff), it will increase its value only if
e
V hold
>
:
R þ Roff
Roff
ð8Þ
Moreover, I 0 will reach the value I 02 only if
e
V crit
<
:
R þ Roff
Roff
ð9Þ
When I 0 reaches the value I 02 the switch resistance
drops to Ron and the current I 0 becomes I 04 . I 0 will
then decrease from I 04 only if
e
V crit
<
:
R þ Ron
Ron
ð10Þ
Moreover, I 0 will reach the value I 03 only if
e
V hold
<
:
R þ Ron
Ron
ð11Þ
When I 0 reaches the value I 03 the switch resistance
changes back to Roff and the current I 0 becomes
I 01 , thus completing the cycle.These four conditions
can be summarized as
e
e
< V hold < V crit <
:
ð12Þ
1 þ ðR=Ron Þ
1 þ ðR=Roff Þ
The time needed for the current I 0 to change from I 01
to I 02 (the OFF part of the cycle) is
e V hold ð1 þ R=Roff Þ
toff ¼ soff ln
ð13Þ
e V crit ð1 þ R=Roff Þ
and the time needed for the current I 0 to change
from I 04 to I 03 (the ON part of the cycle) is
V crit ð1 þ R=Ron Þ e
ton ¼ son ln
:
ð14Þ
V hold ð1 þ R=Ron Þ e
Finally, the oscillation period is given by
Ron RC
V crit ð1 þ R=Ron Þ e
T ¼
ln
Ron þ R
V hold ð1 þ R=Ron Þ e
Roff RC
e V hold ð1 þ R=Roff Þ
þ
ln
:
Roff þ R
e V crit ð1 þ R=Roff Þ
ð15Þ
4. Discussion
It can be seen from Eq. (12) that a proper selection
of e and R is necessary in order to obtain current
oscillations. The condition involves four switch
parameters, which are not necessarily dependent on
each other. The condition Vhold < Vcrit is observed
whenever conductance bistability occurs, by definition. In some cases investigated using switching
devices in a sandwich structure [5,7] Vcrit and Vhold
were observed to be proportional to the material
layer thickness, so that these parameters can, at least
in these cases, be controlled. Still, from Eq. (12), it
can be seen that in order to allow for a significant difference between Vcrit and Vhold, which would result in
a more reliable device operation, a significant difference between Ron and Roff is desirable.
The oscillator frequency is inversely proportional
to the value of C, so that this is the simplest frequency control parameter. In what regards the
switching device characteristics, the values Ron and
Roff are the most important factors determining
the frequency.
In Fig. 6 the oscillation period T is shown as a
function of e and R. For the circuit to operate as
an oscillator, e must be in the range
V crit ð1 þ R=Roff Þ < e < V hold ð1 þ R=Ron Þ:
ð16Þ
This inequality has a solution only if the switch
parameters are such that (Vcrit/Roff) < (Vhold/Ron),
which is equivalent to I 02 < I 03 , see Fig. 4(b). This
condition is easily attained since, for a representative resistance ratio Roff/Ron 103 and Vcrit/
Vhold 2. The contour lines shown in the figure correspond to a particular case where Roff/Ron = 20
and Vcrit/Vhold = 5, although these are not typical
switch parameters they make the structure of the
contour lines more visible. For any parameter values, the oscillator period is infinite along the straight
borders and smaller periods are found as one moves
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5
Vhold 2), Tmin 3RonC, so that using capacitances of the order of a few pF, frequencies larger
than radio frequency identification low frequency
band (130 kHz) should be possible. It must be
pointed out, however, that this analysis assumes
instantaneous switching, ignoring peculiarities of
the switching process characteristic times related
to, for example, modification of molecular conformation, modification of molecular charge state,
charge emission and capture by traps, etc., which
may also be limiting factors.
5. Conclusion
Fig. 6. The period T as a function of e and R according to Eq.
(15). The switch parameters were taken to be such that Roff/
Ron = 20 and Vcrit/Vhold = 5. Five contour lines are displayed.
Along the borderlines, where e is at the boundary of the range
shown in Eq. (16), the period is infinite. As one moves away from
the borderlines, towards larger values of R and e, the period
decreases monotonically towards the Tmin of Eq. (18).
away from the borderlines towards larger values of
R and e.
By changing the value of e, for a fixed R, one can
obtain all periods between infinity and a minimum
period, Tmin. The minimum period expression, as a
function of R, is
Ron RC
T min ðRÞ ¼
Ron þ R
ðV crit =V hold Þð1 þ R=Ron Þ ð1 þ R=Roff Þ
ln
ðV hold =V crit Þð1 þ R=Ron Þ ð1 þ R=Roff Þ
Roff RC
þ
Roff þ R
ð1 þ R=Ron Þ ðV hold =V crit Þð1 þ R=Roff Þ
ln
: ð17Þ
ð1 þ R=Ron Þ ðV crit =V hold Þð1 þ R=Roff Þ
In the limit R Roff, Tmin(R) converges to
ðV crit =V hold Þ ðRon =Roff Þ
T min ! ðRon CÞ ln
ðV hold =V crit Þ ðRon =Roff Þ
þ ðRoff CÞ
ðRoff =Ron Þ ðV hold =V crit Þ
ln
:
ðRoff =Ron Þ ðV crit =V hold Þ
ð18Þ
This period is the smallest period that can be
obtained with a given set of switch parameters,
Ron, Roff, Vcrit and Vhold, and a capacitance C.
If, for example, the values mentioned above after
Eq. (16), are used (Roff/Ron 103 and Vcrit/
In summary, we reported the construction of oscillators using poly(1,5-diaminonaphthalene)-based
switches and determined the analytical expression
for the oscillation period, as well as the minimum
allowed oscillation period (corresponding to a
maximum frequency) as a function of oscillator components: capacitance, series resistance, switch resistance in the ON- and OFF-states and switch critical
voltages for the ON–OFF and OFF–ON transition.
The theoretical results show that in principle, it is
possible to produce oscillators operating at higher
frequencies, provided that stable materials with
appropriate characteristics can be found.
Acknowledgements
The authors thank CNPq, Renami and Instituto
do Milênio IM2C for research grants.
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