- Email: [email protected]
Non-ohmic behaviour of iodine-doped polyacetylene
Solid State Communications, VoL 43, No. 11, pp. 857-861, 1 9 8 2 . Printed in Great Britain.
0038-1098/82/350857-05~03.00/0 Pergamon Press Ltd.
NON-OHMIC BEHAVIOUR OF IODINE-DOPED POLYACETYLENE A. Philipp, W. Mayr and K. Seeger Institut f0t Festk6rperphysik der Universitat Wien and Ludwig Boltzmann Institut fiir Festk6rperphysik, Wien, Austria
(Received 8 February 1982 by B. Miihlschlegel) We report on the temperature and electric field strength dependence of the conductivity of iodine-doped polyacetylene in the metallic regime. The experimental results are discussed in terms of Sheng model of fluctuation induced tunneling and characteristic dimensions of the tunneling zones between fibres are deduced from a fit between this theory and our experiments. 1. INTRODUCTION A LARGE VARIETY of organic semiconductors show superlinear non-Ohmic behaviour at high electric field strengths. The deviations from Ohm's law quite often can be explained by Joule heating of the crystal lattice [l]. The effect to be discussed here is not due to lattice heating because the nonlinearities observed occur already at low pulsed electric fields. The low mobilities of single carriers in these materials and the much more pronounced non.linearity in comparison to classical semiconductors indicate that one has to look for other mechanisms for an explanation of the non-Ohmic behaviour of quasi-one-dimensional conductors. For donoraccepter complexes such as TTF-TCNQ field depinning of charge density waves has been discussed as a mechanism for a field-dependent conductivity [2]. Recent measurements of the deviations from Ohm's law in AsFs- and iodine-doped (CH),, by a microwave harmonic mixing method gave rise to speculations that fluctuation-induced tunneling [3, 4] could be responsible for the observed nonlinearity [5, 6]. By measurements using pulsed electric fields absolute values of the deviations have been determined. The aim of this paper is to give a detailed report on results obtained with iodine-doped (CH)x in the metallic regime of which a short version has already been pubfished elsewhere [6]. Recent results by Epstein [7, 8] show somewhat different behaviour which possibly may be accounted to different sample preparation and doping procedures [9, 10]. A comparison of the results will be discussed. Our results show positive deviations from Ohm's law in the temperature range 4.2-200 K for iodine concentrations of 14% and 30%. A fit of Sheng's model of fluctuation-induced tunneling [3, 4] to our experimental results will be
857
presented. It will be shown that our temperature dependence of the low-field conductivity can be fitted. Also the model can explain the electric field dependence, supporting evidence for fluctuation-induced tunneling as the dominant transport mechanism in highly iodinedoped (CI-I)=. Sheng's calculations will be adapted to the low electric field strengths involved in our experiments. 2. EXPERIMENTAL TECHNIQUE Using techniques developed by Shirakawa et al. [11] and Ito et aL [12] (CH)x-f'timswere prepared at -- 78°C by polymerization of acetylene directly at the surface of a Ziegler-Natta catalyst. This is different from the usual procedure where polymerization takes place on the walls of a reaction vessel wetted with the catalyst. Our procedure assures an enhanced effectivity of subsequent washing with toluene. The trims obtained in this way have a density of 0.3 gcm -3. The side facing the catalyst is dull, while the other surface is shiny. Doping with iodine was performed by exposing the (CH)x-fiims in an evacuated pyrex.tube at 243 K to the vapor of iodine held at the same temperature until the desired iodine concentration was reached. The concentration was determined by weighing. Typical dimensions of the samples were 10 x 1 x 0.1 ram3 and 4-probe contacts were made using gold paint. In a glove box, the samples were encapsulated in small glass capillaries under dry argon atmosphere and never came into contact with air, although samples exposed a short time (10min) to air did not show different electrical behaviour in our experiments. The dependence of the current density / on the electric field strength E was measured using 1-5/~sec pulses and a repetition rate of 2 pps. Sample heating was ruled out by checking that a variation of the duty-cycle
858
NON-OHMIC BEHAVIOUR OF IODINE-DOPED POLYACETYLENE
Vol. 43, No. 11
010 21 K
(CHI~}=
~RT
T
102
005 101
x
e
•
/ 92K
1E
ol
02 I~K]
~3
Fig. 1. Resistivity p normalized to its room temperature value PaT vs. reciprocal temperature, o, (CI-Ho.14)=, exp. values; o a t = 68 fZ-I cm -1 . x, (CHlo s)x, exp. values; o a t = 320 f~-i em-l. ~ , fit of Sheng model [4].
(CHI014) x =56"o
S2K
l
.
/ /.
10
20 IV/crn]
3O
Fig. 3. Measured deviation Ao of the conductivity from the zero-field value Co vs. electric field strength E for (CHI0.3)x at 21 K (o), 37 K (x), 92 K (+), and 190 K (e). Full curves represent Sheng model [4].
25K
"
~
,E
- 0 9 2 ' ' ' 0
, , s=K
,x
013=.
•
.
"
•
" 1
+
15SK
10" ,,,
÷
• -OC'. 0
'
' 20
'
, ~.0
. . . . 60 [V/oral 80
E
(CH I o 3 ) ~
p 100
Fig. 2. Measured deviation Ao of the conductivity from the zero-field value Oo vs. electric field strength E for (CHIo.z4)= at 4.2 K (o), 25 K (it), 62 K (x), and 155 K (+). Full curves represent Sheng model [4].
.
I 0 ";
(CHI0 ~) x
Sheng fit
x
by a factor of at least 10 had no influence on the measured pulse heights. Furthermore, t h e / - E charac. teristics were tested for reproducibility to assure that no significant temperature variations occured during the measurements. 3. EXPERIMENTAL RESULTS Figure 1 shows the temperature dependence of the remtivity normalized to its room temperature value for two samples with an iodine concentration of 14% and 30%, respectively. At 300K conductivities of 68 ~2-~ cm -~ for the lower and 320 f2- t c m -~ for the higher doped sample were obtained by four-probe measurements. Figures 2 and 3 show the normalized change of conductivity with electric field strength for samples
%
. . . .
so
. . . .
' 100
.
T[ . K .]
.
.
. . 150
Fig. 4. Nonlinearity coefficient ~ vs. temperature in (CHIo.3) = (it, x) and (CHIo.14)x (A). Dashed curve represents Sheng model [4]; the full curve serves as a guide line to the eye. with 14% and 30% iodine concentration at different temperatures. The experimental results were fitted with an expression of the f o r m / = oo(E + jSE3), where co is the conductivity at zero field and ~ the non-linearity coefficient, following the least mean square deviation principle. Using this fit, a phenomenological parameter 0 for the quantitative description of the non.linearity is obtained.
Vol. 43, No. 11
NON-OHMIC BEHAVIOUR OF IODINE-DOPED POLYACETYLENE
The temperature dependence of the coefficient/~ is shown in Fig. 4 for samples with the two iodine concentrations. In both cases ~ has its highest value of about 1-2 × 10-4 cm2 V-2 at 4.2K and decreases with increasing temperature. For (CHIo.~4)x the nonlinearity was too small to be observed at temperatures above 160 K and for (CHIo.3)= above 200K. 4. DISCUSSION Optical [13] and thermopower [10] experiments indicate a metallic nature of highly iodine-doped polyacetylene while d.c. and low-frequency a.c. transport measurements indicate semiconducting behaviour. Scanning electron micrographs [9, 12, 14, 15] show that (CH)= has a "Brillopad"like structure. Moreover nonuniformity of doping even at higher dopant concentrations is supported by X-ray [ 1 6 ] , electron energy loss [17] and optical absorption experiments [18]. This structure implies that electric transport is not limited by the re~tance of the fibrils but by the transition of electrons either between fibrils or between isolated wellconducting regions which might exist because of the inhomogeneity of doping. Recently a model for transport in inhomogeneous conductors has been developed by Sheng [3, 4] which is based on fluctuation-induced tunneling of carriers between the well-conducting regions. An excellent agreement between his theory and the temperature dependence of the conductivity of highly iodine-doped polyacetylene has already been pointed out by Shen8 [4] and by Seeger et aL [6]. By Park et aL [10] this has been confirmed for the case of AsFs doping. Figure 1 shows a fit of Sheng's theory to our experimental results of ohmic conductivity for samples doped with 14% and 30% iodine. The theory contains 3 undetermined parameters: the temperature To above which the fluctuation-induced contn"oution dominates the temperature independent contribution to tunneling; T~ which is proportional to the activation energy in the high.temperature regime, where the conductivity shows an activated behaviour; the parameter X governing the amount of image-force correction to the barrier between the conducting regions. The set of parameters for the smallest deviation between the theoretical curve and the experimental data can be defined unambiguously. Nevertheless it is not possible to determine the barrier height, Vo, the shape, the width w, and the cross-sectional area A on the basis of these data without making an assump. tion about one of these values as done by Park et al. [10]. Moreover Park et al. use a simplified Sheng model [3] which disregards the barrier shape at all. For an unequivocal determination of the barrier parameters, the nonlinearity of the current voltage
859
reiation ~redicted by Sheng's model [4] has been compared with the experimental values. This fit has been carried out using the same set of values, To, T~, and ~, obtained for each sample as described above and with Eo, the electric field where the barriers vanish, and ice, the field-independent prefactor in the expression for the fluctuation-induced tunneling current as additional parameters. As can be seen in Figs. 2 and 3 there is good agreement between the experimental and the theoretical deviations from Ohm's law over the whole investigated temperature range although the fit has been accomplisbed for a single temperature only and the so. obtained parameters E0 and ]0o remained unchanged in the subsequent calculations of the ]'-E dependence for the other temperature values. However, in order to take into account also the rela. tively small electric field strengths applied in our experiments, Sheng's calculations [4] had to be modified in so far as the flow of electrons counter to the externally applied field had to be taken into consideration. This has been done by subtracting from the expression for the tunneling conductivity
Jtt = } [ SoJ(EA + ET)P(F'T) dF'T +
s:A/(EA-- ET)P(~T) ~ T ] ,
a term 1
T S~A/(ET--EA)P(ET)
dET
where P(ET) is the fluctuation probability function, E T the thermal fluctuation field, EA the applied field, and i ]H the tunneling current (notation by Sbeng). This term makes ]'u = 0 for EA = 0 and has been neglected by Sheng for his case of large field strengths EA . At low field strengths EA the probability for ET > EA becomes quite important so that this term is no more ne~liT'ble. The parameters used in the conductivity vs. temperature and in the current-voltage fits are summarized in Table 1 as well as the barrier height and the tunneling zone characteristics. The barrier-height Vo in our iodinedoped samples is comparable to the one found by Park eral. [10] in [CH(AsF$)~] x and showsthe same trend of decreasing with increasing doping concentration. In contrast, the barrier width w for iodine doping turns out to be much larger than in the AsFs-doped samples. This difference can originate from - the deliberate choice of the cross-sectional area A of the barriers by Park etaL [10]. - our use of Sheng's more ref'med model taking into account an image-force corrected potential [4] and the electron flow counter to the applied field,
860
NON-OHMIC BEHAVIOUR OF IODINE-DOPED POLYACETYLENE
Vol. 43, No. 11
Table 1. Parameters used for fitting the Sheng model [4] to our experimental results and tunnel~unction characteristics
(CHIo.14)= (CHIo.a)x
0.052 0.12
To [K]
T1 [K]
/oo [Acre -2]
Eo [Vcm -l ]
Fo [meV]
w [A]
,4 [A2]
14.5 27.5
175 52.75
1440 5000
428 56
5.32 3.90
119 54
i .4 x 106 3.6 x 107
differences in sample preparation and/or doping leading to a somewhat different morphology of the samples. -
In fact, the cross-sectional area ,4 as deduced from our current voltage fit implies fiber diameters of the order of 1000 A if one assumes all the fibers to cross at right angles. Actually Shirakawa [19] and very recently Epstein [15] report on electron micrographs showing fibers with quite large diameters. Furthermore, a distri. bution of fiber-crossing angles should be considered. In addition one should not disregard the fact that the obtained parameters are those of a tunneling zone idealized by a model-capacitor and thereby might not render the real physical dimensions. Nevertheless, the values of the tunneling zone parameters indicate that the fluctuation.induced tunneling takes place between fibers rather than between (CH)x chains. Tunneling between regions of inhomogeneous doping may be ruled out, for the experimental evidence mentioned before shows that at such high dopant-concentrations doping may be nonuniform [15-17] but not at such an extent that isolated metallic islands exist [20]. The increase of the tunneling zone cross-section ,4 and the decrease of the barrier width w with increasing dopant concentration agrees qualitatively with results showing a swelling of (CH)= fibers upon doping with iodine [14, 15]. Nevertheless, our samples show a behaviour very distinct from that investigated by Epstein et al. [7, 8] with regard to their electrical properties: (1) Room-temperature conductivities are much
higher. (2) A critical field for the onset of non.ohmic behaviour does not exist. (3) Deviations from Ohm's law were much lower and do not show a logarithmic dependence on the electric field strength. The origin for the different behaviour is not known. We can only speculate that it is due to differences in (CH)x-ffim preparation and doping procedure. This argument is supported by the fact that Epstein et al. [7, 8] fred different temperature dependences of the conductivity even in samples cut from the same doped film which differs moreover from the dependence measured on our samples, showing obviously the tremendous influence of disorder in polyacetylene. However, our
results were reproducible even on samples cut from different films. Measurements of the conductivity up to 9 GHz have shown that the frequency-dependence in highly iodine-doped polyacetylene is negligible at room temperature [7]. This has been used as an argument [7, 8] a~Ainst fluctuation-induced tunneling in (CHIy)= with reference to the effective-medium theory of Springett [21 ] which predicts a ~" cok in metal-dielectric composites where co is the frequency and k a constant depending on the composites' parameters. If one assumes localized electronic states, a lack of frequency dependence would imply a fast transfer rate between these states. Furthermore, the small deviations from Ohm's law that can be observed have to be taken as evidence against large barriers for electrons. We would like to point out that these arguments do not rule out the applicability of Sheng's model to doped (CH)~ for two reasons: (1) It is a crucial point that the electronic states in the well-conducting regions are assumed to be not localized as localization would inhibit the formation of voltage fluctuations. (2) The barrier height is on the order of some meV, so that already at temperatures well below room temperature the thermal energy of the electrons surmounts the barrier height and fluctuation induced tunneling becomes unimportant. Therefore the application of Sheng's model does not implicate a frequency dependence of the conductivity at high temperatures for highly doped polyacetylene. Actually it has been found recently [22] that in undoped and in ammonia-doped polyacetylene conductivity begins to show frequency dependence below approx. 245 K, while it is frequency independent at room temperature like in iodine-doped (CH),, [7]. At lower temperatures the a.c. conductivity oac is proportional to coo.6,where co is the frequency. It is therefore tempting to speculate about the conductivity of (CHly)x being frequency dependent, too, at low temperatures, as one might expect from Sheng's model [3, 4], though the frequency dependence should be rather weak because of the low barrier heights associated with fast transfer rates. On the other hand, Epstein's et al. [7, 8] tentative
Vol. 43, No. 11
NON-OHMIC BEHAVIOUR OF IODINE-DOPED POLYACETYLENE
explanation of the non.ohmic behavi0tir based on 2-D conduction in an anulus at the surface of the (CH)x fibers seems to be hardly compatible with the relatively high temperatures [23, 24] up to which nonlinearities can be observed and with the observation that the fibers are swelling during doping, indicating that the dopant does not adhere at the surface only, but enters into the fibers. In summary, we have shown that the conductivity depending on temperature as web as on the electric field strength for iodine-doped polyacetylene in the metallic regime can be described by fluctuation-induced tunneling even at low electric field strengths ff Sheng's calcuLations are refined as described above. The tunneling zone parameters obtained by a fit of this model to our experimental results indicate that tunneling takes place between the fibers of the material which swell upon doping [14, 15]. Finally, a comparison of our observatiom of the electric field dependence of the conductivity with those obtained by Epstein et al. [7, 8] shows a discrepancy which perhaps may be due to different sample preparation and/or doping procedure. Acknowledgements - This work was partly sponsored by Volkswagen-Sfiftung and the "Fonds zur F6rdenm 8 der wissenschaftlichen Forschung'.
6. 7. 8.
.
10. 11. 12.
13. 14. 15. 16. 17. 18.
REFERENCES 1. 2.
3. 4. 5.
See, eg. K. Seeger, Solid State Commun. 19,245 (1976). See, e.g.H. Kahlert, Solid State Commun. 17, 1161 (1975); M.J. Cohen, P.R. Newman & A.J. Heeger, Phys. Rev. Lett. 37, 1500 (1975); MJ. Cohen & A.J. Heeger,Phys. Rev. BI6, 688 (1977). P. Sheng, E.K. Sichel & J.l. GRtleman, Phys. Rev. Lett. 40, 1197 (1978). P. Sheng, Phys. Rev. B21, 2180 (1980). For a review see: H. Kahlert, Physics of Nonlinear Transport in Semiconductors, p. 479. Plenum Press, New York-London (1980).
19. 20. 21. 22. 23. 24.
861
~:~:Seeger,W. Mayr, A. Philipp & W. R6ss, Chemica Seripta 17, 129 (1981). A.J. Epstein, H.W. Gibson, P.M. Chaikin, W.G. Clark & G. Griiner, Chemica Scripta 17,135 (1981). A.J. Epstein, H.W. Gibson, PaM. Chaikin, W.G. Clark & G. Gr0ner, Phys. Rev. Lett. 45, 1730 (1980). W. Deits, P. Cukor, M. Rubner & H. Jopson, J. Electronic Materials 10, 683 (1981). Y.W. Park, AJ. Heeger, M.A. Druy & A.G. MaeDiarmid, J. Chem. Phys. 73,946 (1980). See, e.g.H. Shirakawa & S. Ikeda, Polymer d. 2, 231 (1971); H. Shirakawa, T. Ito & S. Ikeda, Makromolek. Chem. 179, 1565 (1978). See, e.g.T. Ito, H. Shirakawa & S. Ikeda, J. Polymer Sci. Polymer Chem. Ed. 12, 11 (1974); T. Ito, H. Shirakawa & S. Ikeda, J. Polymer Sci. Polymer Chem. Ed. 13, 1943 (1975). CX. Chiang & C.R. Fincher, Phys. Rev. Lett. 39, 1098 (1977). H. Rommelmann, R. Fernquist, H.W. Gibson, A.J. Epstein, M.A. Druy & T. Woerner (preprint). A3. Epstein, H. Rommelmann, R. Femquist, H.W. Gibson, M.A. Druy & T. Woerner (preprint). P. Robin, J.P. Pouget, R. Comes, A.J. Epstein & H.W. Gibson (to be published). J.J. Ritsko, E.J. Mele, A.J. Heeger, A.G. MacDiarmid & M. Ozak~,Phys. Rev. Lett. 44, 1351 (1980). C.R. Fincher, Jr., D.L. Peebles, A.J. Heeger, M.A. Druy, Y. Matsumura, A.G. MacDiamid, H. Shirakawa & S. Ikeda, Solid State Commun. 27, 489 (1978). H. Shirakawa & S. Ikeda, Synth. Metals 1,175 (1980). K. Mortensen, M.L.W. Thewalt, Y. Tomldewicz, T.C. Clarke & G.B. Street, Phys. Rev. Lett. 45, 490 (1980). B.E. Springett, Phys. Rev. Lett. 31, 1463 (1973). A.J. Epstein, H. Rommelmann, M. Abkowitz & H.W. Gibson, Phys. Rev. Lett. 47, 1549 (1981). P.W. Anderson, E. Abrahams & V. Rarnakrishnan, Phys. Rev. Lett. 43,718 (1979). G.J. Dolan & D.D. Osheroff, Phys. Rev. Lett. 43, 721 (1979).
0038-1098/82/350857-05~03.00/0 Pergamon Press Ltd.
NON-OHMIC BEHAVIOUR OF IODINE-DOPED POLYACETYLENE A. Philipp, W. Mayr and K. Seeger Institut f0t Festk6rperphysik der Universitat Wien and Ludwig Boltzmann Institut fiir Festk6rperphysik, Wien, Austria
(Received 8 February 1982 by B. Miihlschlegel) We report on the temperature and electric field strength dependence of the conductivity of iodine-doped polyacetylene in the metallic regime. The experimental results are discussed in terms of Sheng model of fluctuation induced tunneling and characteristic dimensions of the tunneling zones between fibres are deduced from a fit between this theory and our experiments. 1. INTRODUCTION A LARGE VARIETY of organic semiconductors show superlinear non-Ohmic behaviour at high electric field strengths. The deviations from Ohm's law quite often can be explained by Joule heating of the crystal lattice [l]. The effect to be discussed here is not due to lattice heating because the nonlinearities observed occur already at low pulsed electric fields. The low mobilities of single carriers in these materials and the much more pronounced non.linearity in comparison to classical semiconductors indicate that one has to look for other mechanisms for an explanation of the non-Ohmic behaviour of quasi-one-dimensional conductors. For donoraccepter complexes such as TTF-TCNQ field depinning of charge density waves has been discussed as a mechanism for a field-dependent conductivity [2]. Recent measurements of the deviations from Ohm's law in AsFs- and iodine-doped (CH),, by a microwave harmonic mixing method gave rise to speculations that fluctuation-induced tunneling [3, 4] could be responsible for the observed nonlinearity [5, 6]. By measurements using pulsed electric fields absolute values of the deviations have been determined. The aim of this paper is to give a detailed report on results obtained with iodine-doped (CH)x in the metallic regime of which a short version has already been pubfished elsewhere [6]. Recent results by Epstein [7, 8] show somewhat different behaviour which possibly may be accounted to different sample preparation and doping procedures [9, 10]. A comparison of the results will be discussed. Our results show positive deviations from Ohm's law in the temperature range 4.2-200 K for iodine concentrations of 14% and 30%. A fit of Sheng's model of fluctuation-induced tunneling [3, 4] to our experimental results will be
857
presented. It will be shown that our temperature dependence of the low-field conductivity can be fitted. Also the model can explain the electric field dependence, supporting evidence for fluctuation-induced tunneling as the dominant transport mechanism in highly iodinedoped (CI-I)=. Sheng's calculations will be adapted to the low electric field strengths involved in our experiments. 2. EXPERIMENTAL TECHNIQUE Using techniques developed by Shirakawa et al. [11] and Ito et aL [12] (CH)x-f'timswere prepared at -- 78°C by polymerization of acetylene directly at the surface of a Ziegler-Natta catalyst. This is different from the usual procedure where polymerization takes place on the walls of a reaction vessel wetted with the catalyst. Our procedure assures an enhanced effectivity of subsequent washing with toluene. The trims obtained in this way have a density of 0.3 gcm -3. The side facing the catalyst is dull, while the other surface is shiny. Doping with iodine was performed by exposing the (CH)x-fiims in an evacuated pyrex.tube at 243 K to the vapor of iodine held at the same temperature until the desired iodine concentration was reached. The concentration was determined by weighing. Typical dimensions of the samples were 10 x 1 x 0.1 ram3 and 4-probe contacts were made using gold paint. In a glove box, the samples were encapsulated in small glass capillaries under dry argon atmosphere and never came into contact with air, although samples exposed a short time (10min) to air did not show different electrical behaviour in our experiments. The dependence of the current density / on the electric field strength E was measured using 1-5/~sec pulses and a repetition rate of 2 pps. Sample heating was ruled out by checking that a variation of the duty-cycle
858
NON-OHMIC BEHAVIOUR OF IODINE-DOPED POLYACETYLENE
Vol. 43, No. 11
010 21 K
(CHI~}=
~RT
T
102
005 101
x
e
•
/ 92K
1E
ol
02 I~K]
~3
Fig. 1. Resistivity p normalized to its room temperature value PaT vs. reciprocal temperature, o, (CI-Ho.14)=, exp. values; o a t = 68 fZ-I cm -1 . x, (CHlo s)x, exp. values; o a t = 320 f~-i em-l. ~ , fit of Sheng model [4].
(CHI014) x =56"o
S2K
l
.
/ /.
10
20 IV/crn]
3O
Fig. 3. Measured deviation Ao of the conductivity from the zero-field value Co vs. electric field strength E for (CHI0.3)x at 21 K (o), 37 K (x), 92 K (+), and 190 K (e). Full curves represent Sheng model [4].
25K
"
~
,E
- 0 9 2 ' ' ' 0
, , s=K
,x
013=.
•
.
"
•
" 1
+
15SK
10" ,,,
÷
• -OC'. 0
'
' 20
'
, ~.0
. . . . 60 [V/oral 80
E
(CH I o 3 ) ~
p 100
Fig. 2. Measured deviation Ao of the conductivity from the zero-field value Oo vs. electric field strength E for (CHIo.z4)= at 4.2 K (o), 25 K (it), 62 K (x), and 155 K (+). Full curves represent Sheng model [4].
.
I 0 ";
(CHI0 ~) x
Sheng fit
x
by a factor of at least 10 had no influence on the measured pulse heights. Furthermore, t h e / - E charac. teristics were tested for reproducibility to assure that no significant temperature variations occured during the measurements. 3. EXPERIMENTAL RESULTS Figure 1 shows the temperature dependence of the remtivity normalized to its room temperature value for two samples with an iodine concentration of 14% and 30%, respectively. At 300K conductivities of 68 ~2-~ cm -~ for the lower and 320 f2- t c m -~ for the higher doped sample were obtained by four-probe measurements. Figures 2 and 3 show the normalized change of conductivity with electric field strength for samples
%
. . . .
so
. . . .
' 100
.
T[ . K .]
.
.
. . 150
Fig. 4. Nonlinearity coefficient ~ vs. temperature in (CHIo.3) = (it, x) and (CHIo.14)x (A). Dashed curve represents Sheng model [4]; the full curve serves as a guide line to the eye. with 14% and 30% iodine concentration at different temperatures. The experimental results were fitted with an expression of the f o r m / = oo(E + jSE3), where co is the conductivity at zero field and ~ the non-linearity coefficient, following the least mean square deviation principle. Using this fit, a phenomenological parameter 0 for the quantitative description of the non.linearity is obtained.
Vol. 43, No. 11
NON-OHMIC BEHAVIOUR OF IODINE-DOPED POLYACETYLENE
The temperature dependence of the coefficient/~ is shown in Fig. 4 for samples with the two iodine concentrations. In both cases ~ has its highest value of about 1-2 × 10-4 cm2 V-2 at 4.2K and decreases with increasing temperature. For (CHIo.~4)x the nonlinearity was too small to be observed at temperatures above 160 K and for (CHIo.3)= above 200K. 4. DISCUSSION Optical [13] and thermopower [10] experiments indicate a metallic nature of highly iodine-doped polyacetylene while d.c. and low-frequency a.c. transport measurements indicate semiconducting behaviour. Scanning electron micrographs [9, 12, 14, 15] show that (CH)= has a "Brillopad"like structure. Moreover nonuniformity of doping even at higher dopant concentrations is supported by X-ray [ 1 6 ] , electron energy loss [17] and optical absorption experiments [18]. This structure implies that electric transport is not limited by the re~tance of the fibrils but by the transition of electrons either between fibrils or between isolated wellconducting regions which might exist because of the inhomogeneity of doping. Recently a model for transport in inhomogeneous conductors has been developed by Sheng [3, 4] which is based on fluctuation-induced tunneling of carriers between the well-conducting regions. An excellent agreement between his theory and the temperature dependence of the conductivity of highly iodine-doped polyacetylene has already been pointed out by Shen8 [4] and by Seeger et aL [6]. By Park et aL [10] this has been confirmed for the case of AsFs doping. Figure 1 shows a fit of Sheng's theory to our experimental results of ohmic conductivity for samples doped with 14% and 30% iodine. The theory contains 3 undetermined parameters: the temperature To above which the fluctuation-induced contn"oution dominates the temperature independent contribution to tunneling; T~ which is proportional to the activation energy in the high.temperature regime, where the conductivity shows an activated behaviour; the parameter X governing the amount of image-force correction to the barrier between the conducting regions. The set of parameters for the smallest deviation between the theoretical curve and the experimental data can be defined unambiguously. Nevertheless it is not possible to determine the barrier height, Vo, the shape, the width w, and the cross-sectional area A on the basis of these data without making an assump. tion about one of these values as done by Park et al. [10]. Moreover Park et al. use a simplified Sheng model [3] which disregards the barrier shape at all. For an unequivocal determination of the barrier parameters, the nonlinearity of the current voltage
859
reiation ~redicted by Sheng's model [4] has been compared with the experimental values. This fit has been carried out using the same set of values, To, T~, and ~, obtained for each sample as described above and with Eo, the electric field where the barriers vanish, and ice, the field-independent prefactor in the expression for the fluctuation-induced tunneling current as additional parameters. As can be seen in Figs. 2 and 3 there is good agreement between the experimental and the theoretical deviations from Ohm's law over the whole investigated temperature range although the fit has been accomplisbed for a single temperature only and the so. obtained parameters E0 and ]0o remained unchanged in the subsequent calculations of the ]'-E dependence for the other temperature values. However, in order to take into account also the rela. tively small electric field strengths applied in our experiments, Sheng's calculations [4] had to be modified in so far as the flow of electrons counter to the externally applied field had to be taken into consideration. This has been done by subtracting from the expression for the tunneling conductivity
Jtt = } [ SoJ(EA + ET)P(F'T) dF'T +
s:A/(EA-- ET)P(~T) ~ T ] ,
a term 1
T S~A/(ET--EA)P(ET)
dET
where P(ET) is the fluctuation probability function, E T the thermal fluctuation field, EA the applied field, and i ]H the tunneling current (notation by Sbeng). This term makes ]'u = 0 for EA = 0 and has been neglected by Sheng for his case of large field strengths EA . At low field strengths EA the probability for ET > EA becomes quite important so that this term is no more ne~liT'ble. The parameters used in the conductivity vs. temperature and in the current-voltage fits are summarized in Table 1 as well as the barrier height and the tunneling zone characteristics. The barrier-height Vo in our iodinedoped samples is comparable to the one found by Park eral. [10] in [CH(AsF$)~] x and showsthe same trend of decreasing with increasing doping concentration. In contrast, the barrier width w for iodine doping turns out to be much larger than in the AsFs-doped samples. This difference can originate from - the deliberate choice of the cross-sectional area A of the barriers by Park etaL [10]. - our use of Sheng's more ref'med model taking into account an image-force corrected potential [4] and the electron flow counter to the applied field,
860
NON-OHMIC BEHAVIOUR OF IODINE-DOPED POLYACETYLENE
Vol. 43, No. 11
Table 1. Parameters used for fitting the Sheng model [4] to our experimental results and tunnel~unction characteristics
(CHIo.14)= (CHIo.a)x
0.052 0.12
To [K]
T1 [K]
/oo [Acre -2]
Eo [Vcm -l ]
Fo [meV]
w [A]
,4 [A2]
14.5 27.5
175 52.75
1440 5000
428 56
5.32 3.90
119 54
i .4 x 106 3.6 x 107
differences in sample preparation and/or doping leading to a somewhat different morphology of the samples. -
In fact, the cross-sectional area ,4 as deduced from our current voltage fit implies fiber diameters of the order of 1000 A if one assumes all the fibers to cross at right angles. Actually Shirakawa [19] and very recently Epstein [15] report on electron micrographs showing fibers with quite large diameters. Furthermore, a distri. bution of fiber-crossing angles should be considered. In addition one should not disregard the fact that the obtained parameters are those of a tunneling zone idealized by a model-capacitor and thereby might not render the real physical dimensions. Nevertheless, the values of the tunneling zone parameters indicate that the fluctuation.induced tunneling takes place between fibers rather than between (CH)x chains. Tunneling between regions of inhomogeneous doping may be ruled out, for the experimental evidence mentioned before shows that at such high dopant-concentrations doping may be nonuniform [15-17] but not at such an extent that isolated metallic islands exist [20]. The increase of the tunneling zone cross-section ,4 and the decrease of the barrier width w with increasing dopant concentration agrees qualitatively with results showing a swelling of (CH)= fibers upon doping with iodine [14, 15]. Nevertheless, our samples show a behaviour very distinct from that investigated by Epstein et al. [7, 8] with regard to their electrical properties: (1) Room-temperature conductivities are much
higher. (2) A critical field for the onset of non.ohmic behaviour does not exist. (3) Deviations from Ohm's law were much lower and do not show a logarithmic dependence on the electric field strength. The origin for the different behaviour is not known. We can only speculate that it is due to differences in (CH)x-ffim preparation and doping procedure. This argument is supported by the fact that Epstein et al. [7, 8] fred different temperature dependences of the conductivity even in samples cut from the same doped film which differs moreover from the dependence measured on our samples, showing obviously the tremendous influence of disorder in polyacetylene. However, our
results were reproducible even on samples cut from different films. Measurements of the conductivity up to 9 GHz have shown that the frequency-dependence in highly iodine-doped polyacetylene is negligible at room temperature [7]. This has been used as an argument [7, 8] a~Ainst fluctuation-induced tunneling in (CHIy)= with reference to the effective-medium theory of Springett [21 ] which predicts a ~" cok in metal-dielectric composites where co is the frequency and k a constant depending on the composites' parameters. If one assumes localized electronic states, a lack of frequency dependence would imply a fast transfer rate between these states. Furthermore, the small deviations from Ohm's law that can be observed have to be taken as evidence against large barriers for electrons. We would like to point out that these arguments do not rule out the applicability of Sheng's model to doped (CH)~ for two reasons: (1) It is a crucial point that the electronic states in the well-conducting regions are assumed to be not localized as localization would inhibit the formation of voltage fluctuations. (2) The barrier height is on the order of some meV, so that already at temperatures well below room temperature the thermal energy of the electrons surmounts the barrier height and fluctuation induced tunneling becomes unimportant. Therefore the application of Sheng's model does not implicate a frequency dependence of the conductivity at high temperatures for highly doped polyacetylene. Actually it has been found recently [22] that in undoped and in ammonia-doped polyacetylene conductivity begins to show frequency dependence below approx. 245 K, while it is frequency independent at room temperature like in iodine-doped (CH),, [7]. At lower temperatures the a.c. conductivity oac is proportional to coo.6,where co is the frequency. It is therefore tempting to speculate about the conductivity of (CHly)x being frequency dependent, too, at low temperatures, as one might expect from Sheng's model [3, 4], though the frequency dependence should be rather weak because of the low barrier heights associated with fast transfer rates. On the other hand, Epstein's et al. [7, 8] tentative
Vol. 43, No. 11
NON-OHMIC BEHAVIOUR OF IODINE-DOPED POLYACETYLENE
explanation of the non.ohmic behavi0tir based on 2-D conduction in an anulus at the surface of the (CH)x fibers seems to be hardly compatible with the relatively high temperatures [23, 24] up to which nonlinearities can be observed and with the observation that the fibers are swelling during doping, indicating that the dopant does not adhere at the surface only, but enters into the fibers. In summary, we have shown that the conductivity depending on temperature as web as on the electric field strength for iodine-doped polyacetylene in the metallic regime can be described by fluctuation-induced tunneling even at low electric field strengths ff Sheng's calcuLations are refined as described above. The tunneling zone parameters obtained by a fit of this model to our experimental results indicate that tunneling takes place between the fibers of the material which swell upon doping [14, 15]. Finally, a comparison of our observatiom of the electric field dependence of the conductivity with those obtained by Epstein et al. [7, 8] shows a discrepancy which perhaps may be due to different sample preparation and/or doping procedure. Acknowledgements - This work was partly sponsored by Volkswagen-Sfiftung and the "Fonds zur F6rdenm 8 der wissenschaftlichen Forschung'.
6. 7. 8.
.
10. 11. 12.
13. 14. 15. 16. 17. 18.
REFERENCES 1. 2.
3. 4. 5.
See, eg. K. Seeger, Solid State Commun. 19,245 (1976). See, e.g.H. Kahlert, Solid State Commun. 17, 1161 (1975); M.J. Cohen, P.R. Newman & A.J. Heeger, Phys. Rev. Lett. 37, 1500 (1975); MJ. Cohen & A.J. Heeger,Phys. Rev. BI6, 688 (1977). P. Sheng, E.K. Sichel & J.l. GRtleman, Phys. Rev. Lett. 40, 1197 (1978). P. Sheng, Phys. Rev. B21, 2180 (1980). For a review see: H. Kahlert, Physics of Nonlinear Transport in Semiconductors, p. 479. Plenum Press, New York-London (1980).
19. 20. 21. 22. 23. 24.
861
~:~:Seeger,W. Mayr, A. Philipp & W. R6ss, Chemica Seripta 17, 129 (1981). A.J. Epstein, H.W. Gibson, P.M. Chaikin, W.G. Clark & G. Griiner, Chemica Scripta 17,135 (1981). A.J. Epstein, H.W. Gibson, PaM. Chaikin, W.G. Clark & G. Gr0ner, Phys. Rev. Lett. 45, 1730 (1980). W. Deits, P. Cukor, M. Rubner & H. Jopson, J. Electronic Materials 10, 683 (1981). Y.W. Park, AJ. Heeger, M.A. Druy & A.G. MaeDiarmid, J. Chem. Phys. 73,946 (1980). See, e.g.H. Shirakawa & S. Ikeda, Polymer d. 2, 231 (1971); H. Shirakawa, T. Ito & S. Ikeda, Makromolek. Chem. 179, 1565 (1978). See, e.g.T. Ito, H. Shirakawa & S. Ikeda, J. Polymer Sci. Polymer Chem. Ed. 12, 11 (1974); T. Ito, H. Shirakawa & S. Ikeda, J. Polymer Sci. Polymer Chem. Ed. 13, 1943 (1975). CX. Chiang & C.R. Fincher, Phys. Rev. Lett. 39, 1098 (1977). H. Rommelmann, R. Fernquist, H.W. Gibson, A.J. Epstein, M.A. Druy & T. Woerner (preprint). A3. Epstein, H. Rommelmann, R. Femquist, H.W. Gibson, M.A. Druy & T. Woerner (preprint). P. Robin, J.P. Pouget, R. Comes, A.J. Epstein & H.W. Gibson (to be published). J.J. Ritsko, E.J. Mele, A.J. Heeger, A.G. MacDiarmid & M. Ozak~,Phys. Rev. Lett. 44, 1351 (1980). C.R. Fincher, Jr., D.L. Peebles, A.J. Heeger, M.A. Druy, Y. Matsumura, A.G. MacDiamid, H. Shirakawa & S. Ikeda, Solid State Commun. 27, 489 (1978). H. Shirakawa & S. Ikeda, Synth. Metals 1,175 (1980). K. Mortensen, M.L.W. Thewalt, Y. Tomldewicz, T.C. Clarke & G.B. Street, Phys. Rev. Lett. 45, 490 (1980). B.E. Springett, Phys. Rev. Lett. 31, 1463 (1973). A.J. Epstein, H. Rommelmann, M. Abkowitz & H.W. Gibson, Phys. Rev. Lett. 47, 1549 (1981). P.W. Anderson, E. Abrahams & V. Rarnakrishnan, Phys. Rev. Lett. 43,718 (1979). G.J. Dolan & D.D. Osheroff, Phys. Rev. Lett. 43, 721 (1979).