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High electric field effect on the conductivity of iodine-doped polacetylene
4854
Synthetic Metals, 55-57 (1993) 4854--4859
HIGH ELECTRIC FIELD E F F E C T ON THE CONDUCTIVITY OF IODINE-DOPED POLYACETYLENE
Y. NOGAMI, M. YAMASHITA, H. KANEKO and T. ISHIGURO Department of Physics, Kyoto University, Kyoto 606-01 (Japan) J. T S U K A M O T O and A. TAKAHASHI Polymers Research Laboratories, Toray Industries Inc., Otsu 520 (Japan)
ABSTRACT The conductivities of iodine-doped new polyacetylenes with room-temperature values of 7.7 × 103 S/cm and 2.6 × 104 S/cm were measured as a function of applied electric field in the temperature range of 77 K to 4.2 K. It is shown that the behavior deviated obviously from the Sheng model which has been widely adopted in explaining temperature dependence for conventional polyacetylene with lower conductivity.
INTRODUCTION Recently developed highly conducting polyacetylene (HCPA) has exhibited new features on the properties of doped polyacetylenes [1]. It showed a conductivity reaching ]05 S / c m at room temperature which appoached the level of Cu. The metallic behavior was maintained down to very low temperature [1, 2]. The mass density of undoped polyacetylene film reached to 1.1 g/cm a which was in the same level with theoretical one, whereas that of conventional polyacetylene has stayed in the level of 0.4 g / c m a. All these features have promoted us to reexamine the physical properties of doped polyacetylene. We present here the study of non-ohmic behaviors of iodine-doped HCPA. Similar studies were carried out previously for conventional polyacetylenes with room-temperature conductivities of - 0.1 S/cm [3], 3 S/cm [4] and 68 S/cm and 320 S/cm [5]. It was concluded that the results of the high electric field study were consistent with the Sheng model [6, 7] based on the fluctuation-induced tunneling between metallic strand. It is interesting to check the applicability of the model to the newly developed polyacetylene.
EXPERIMENTAL The synthesis and resultant structural properties are reported elsewhere [1]. We studied the polyacetylene samples doped up to a saturation level where the concentration can be expressed as y -- 0.27 ~ 0.29 for (CHI~)~. The conductivities of two samples A 0379-6779/93/$6.00
© 1993- Elsevier Sequoia. All rights reserved
4855
and C adopted here were 7.7 x 10a and 2.6 x 104 S/era, respectively. High electric voltage pulses of 2.5/~sec width were applied with duration of a few Hz. Currents were monitored by crip-on-type ac current probe. Voltage pulse across potential electrodes was observed with use of a differential amplifier. The high field experiments were carried out at several temperatures in the range of 4.2 K to 77 K. The normalized conductivity deviation from zero field value as a function of temperature is shown in Fig. 1 and Fig. 2, where Acr(E~t) denotes -- ~r(0) and ~r(EA) represents the conductivity at externally applied electric field EA. The temperature dependences of the conductivity ~(T) in the ohmic region are also shown.
Aty(EA)/o(O)
o(EA)
During the high field experiments we found that the conductivity increased gradually with elapsed time due to heating, typically 10 % increase in 1.0 #sec at 4.2 K. In this case the conductivity extrapolated to the instance of field application was adopted as the observed. The increment was diminished drastically with increase of measuring temperature and with decrease of applied field. The results shown in Fig. 1 and Fig. 2 are summarized as follows. (1) The conductivity increased with applied electric field. This was obvious at 4.2 K: the increment of the conductivity reached 47 7¢ at 69 V/cm for sample A and 197 % at 97 V/era for sample C. The field dependence was enhanced for sample with less conductivity. With increase of temperature T, the non-ohmic behavior is suppressed and the field dependence became faint at 77 K in the field range less than 80
V/cm.
(2) There was no remarkable threshold field for the non-ohmic behavior. The conductivity increases gradually with E A. Generally speaking, these features are rather consistent with the reported results for conventional doped polyacetylenes [5]. Then we tried to fit our data by the formula given by Sheng [7], which has been accepted as useful device in explaining temperature dependence of doped polymers. ANALYSIS After Sheng [7] tunneling current expression j(e) at electric field e across a potential barrier between metallic strands is represented by
j(e) = j0(e)exp (TI~(e)) To ((0) = jl(e)
fore 1
(1)
E/Eo
where c = is renomalized electric field, E0 is the field when the potential barrier height become zero, To and T1 are parameters with dimension of temperature and ~(e) is a expression appearing in transmission coefficients calculated by WKB method. Considering an externally applied field eA and a fluctuation-induced field ~T, the total current across a potential barrier is written as
4856
5O 40 o ID
30
\
%
ra4.
I
2K
a IOK • 20K
x i
•f t
O3)
-
12 E
/
-
(a)
/
20
6
,,m
ID <~ 1 0 0
I I.l I I I I i i 20 4 0
EA
60
0__] ~ i i I I I i
80 i 0 0
0
20 4 0
60
T
(K)
(V/cm)
80
Fig. 1. (a) Applied field EA dependence of normalized conductivity deviation from zero field value A*(EA)/,r(O) for sample A as a function of temperature. (b) Temperature dependence of ~r(T). Solid lines are the calculated corresponding to the observed (see text).
J(CA) =
+
(T1)'{f0"(~') / TI~T ~'~ deTjO(eA +Er)exp[--Te ,
f
deTjl(eA + CT)exp -(
ex
To
((o)
]
E
-- T--~I( 2
(2) r(eA)=l--eAforeA_
for eA > 1
where exp(-~-e~) denotes the fluctuation probability at temperature T. The last term in eq. (2) which represents the flow of electrons by thermally induced field counter to applied field, was neglected by Sheng for the case of large field strength [7]. However, during numerical calcuiation we found that even at not-so-small field as 20 V/era, this term is not negligible as pointed out by Philipp at. al. [5]. Then the field dependent conductivity ~r(EA) is given as
rr(EA) = J(eA)/EA
(3)
where EA = eAEo is macroscopic external field. By differentiating eq. (1), Sheng gave the conductivity at low field as
(4)
4857
200
3.0
( x l O 3)
o4. 2K • 10K 20K
0
••/ /
O77K• • //
i00
\
•/
(a)
1
[
•
/
<3 0 0
] I L I I I I L N 20 40 60 80 I00 EA (V//c m)
I I I I I I I I O 20 40 60 80
T
(K)
Fig. 2. (a) Applied field EA dependence of nomalized conductivity deviation from zero field value Ao(Ea)/o'(O) for sample C as a function of temperature. (b) Temperature dependence of ~r(T). Solid lines are the calculated corresponding to the obseved (see text). where
~(fT) is the
differential conduetivities given by
1 dj(c) = Eo(e)exp ( T1 ((e)'~ fore < 1
z(4 -So
-
= Y;q(j
for e > 1.
The definite expression of j ( J , ((e), E(c) are given in Ref.7 as eqs. 25(a-d), 17(b), 26(a-d), respectively. We examined appropriate parameter sets in the range of 0.002 < A < 0.2, 1 < To _< 100 K, 1.01 _< T1/To <_ 10 and 20 _< E0 < 600 V/era, where A governs shape and height of potential barrier through image force correction [8]. The procedures of searching appropriate parameter sets were following. 1. Parameter sets (A, To and T1/To) to fit ¢(T) were searched with a criterion that calculated ratio ~r(77 K)/(r(4.2 K) after eq. (4) was in the range of 0.9 to 1.10 times of the observed ratio. 2. For the parameter sets searched in the above procedure, we choosed residual parameter E0 so that the calculated ratio ~r(Ea ma~:)/o'(Ea ,ni,~) at. 4.2 K after eq. (3) fell in the range of 0.9 to 1.10 times of the observed, where Ea ma: and EA ,~i,~ are the maximum and the minimum fields used for the observation. 3. Then we checked the degrees of fitting of the calculated to the observed for ~r(Ea) at various temperatures. The parameter sets passing the prodedure 1 were depicted in Fig. 3. The best fit examples of the calculated conductivity were shown in Fig. 1 and Fig. 2. The used parameters were A = 0.03, T0=5 K, 771=7.5 K and E0=60 V/cm for sample A, whereas A = 0.03, To = 25 K, T1 = 110 K and E0=290 V/cm for sample C. Obviously the trends of the field dependences were different for the observed and the calculated. The
4858
10
•
(D
•
::
-: •:.•
• o • m ~
\
ooo • o•
I
I
11
e e o
5
0 0
A=0
•o
l
•
•
...
A=0
Sample
C
. . . . . .• . •
I
I
25
•
I
• • • • • • •
I
I
I
• •
I
I
o • •
° •
I
I
I
50 TO (K)
Fig. 3. Plots of parameters To versus sample C.
03
° •
• •
• •
• •
• •
I
I
I
I
I
75
T1/To, satisfying the
criterion 1 as function of A for
observed was extended almost linearly in the measured field region whereas the latter grew with higher rate with increase of the field. We noticed that large To and T1 were inappropriate for highly conductive sample A, even if they satisfied criterions 1 and 2. For example, if TI exceeded 30 K, the upswinging behavior of the field dependence was enhanced. Furthermore, the calculated Ao'(EA) at 10 K became more than 1.4 times larger than the observed Ao'(EA). The characteristics appeared almost always for sample A with larger value of To and T1, and were rather insensitive to A and E0. This situation condradicted to rather large T1 for highly conducting polyacetylenes with conductivity of the order of 10 5 S/cm on fitting of (r(T) by eq. (4) [9, 10].
DISCUSSION For the HCPA the metallic strands are considered to be formed more ideally compared to the conventional polyacetylene with less conductivity. From the viewpoint of the Sheng model where the conductivity is assumed to be infinite within metallic strands, this situation is favorable and the resistivity of the conducting polymer is determined by the barrier across the metallic strands. However, the failure of the fitting by the Sheng model indicates that this assumption is inappropriate to explain the behavior of the t/CPA. For samples doped to the saturation level the contents of the charge carriers are considered to be in the same level for both the HCPA and the heavily doped conventional polyacetylene, irrespective of the remarkable difference in the conductivity. This is evidenced by the magnitude and the temperature dependences of thermoelectric power. The difference in the conductivity seems to be ascribed to the degrees of disorders, which may bring about barriers and trapping centers for charge carriers throughout samples. In terms of the Sheng model, the high conductivity is realized by diminishing the effects of barriers. However, it is important to consider the temperature dependence of the conductivity of metallic strands in itself for the HCPA .
4859
The field dependence and the temperature dependence were enhanced with decrease of the conductivity or with increase of defects. This indicates that these dependences are not due to intrinsic nature of HCPA, but due to extrinsic origin represented by imperfections in polymer. Each sample decreases its conductivity by successive agings and systematic study of the aging effect indicates that the temperature dependence of the fully aged sample is represented more properly by anisotropic variable range hopping model rather than the Sheng model [11]. Finally, we rule out the sliding motion of the charge density waves specific to quasi one-dimensional conductors [12] as a cause of the non-ohmic behavior, since any threshold was not observed in the field dependence of the conductivity. This is supported by the observation that the non-ohmic behavior was enhanced with increase of the imperfections in the conjugating polymer. On the other hand rather perfect low-dimensional conductors are required to observe the effect of the sliding motion. ACKNOWLEDGEMENT This work was supported by a Grant for International Joint Research Project from the NEDO, Japan. REFERENCES 1. J. Tsukamoto, A. Takahashi and K. Kawasaki, Jpn. J. Appl. Phys. 29,125 (1990). 2. Y. Nogami, H. Kaneko, H. Ito, T. Ishiguro, T. Sasaki, N. Toyota, A. Takahashi and J. Tsukamoto, Phys. Rev. B 43, 11829 (1991). 3. K. Mortensen, M. L. W. Thewalt and Y. Tomkiewicz, Phys. Rev. Lett. 45, 490 (1980). 4. A. J. Epstein, H. W. Gibson, P. M. Chaikin, W. G. Clark and G. Griiner, Phys. Rev. Lett. 45, 1730 (1980). 5. A. Philipp, W. Mayr and K. Seeger, Solid State Commun. 43,857 (1982). 6. P. Sheng, E. K. Sichel and J. I. Gittleman, Phys. Rev. Left. 40, 1197 (1978). 7. P. Sheng, Phys. Rev. B 21, 2180 (1980). 8. J. G. Simmons, J. Appl. Phys. 34, 1793 (1963). 9. Th. Schimmel, G. Denninger, W. Riess, J. Volt, M. Schwoever, W. Schoepe and H. Naarmann, Synth. Metals, 28, Dll (1989). 10. G. Paasch, G. Lehmann and L. Wuckel, Synth. Metals. 37, 23 (1990). 11. H. Kaneko, T. Ishiguro, J. Tsukamoto and A. Takahashi, these Proceedings. 12. G. Grfiner, Rev. Mod. Phys. 60, 1129 (1988).
Synthetic Metals, 55-57 (1993) 4854--4859
HIGH ELECTRIC FIELD E F F E C T ON THE CONDUCTIVITY OF IODINE-DOPED POLYACETYLENE
Y. NOGAMI, M. YAMASHITA, H. KANEKO and T. ISHIGURO Department of Physics, Kyoto University, Kyoto 606-01 (Japan) J. T S U K A M O T O and A. TAKAHASHI Polymers Research Laboratories, Toray Industries Inc., Otsu 520 (Japan)
ABSTRACT The conductivities of iodine-doped new polyacetylenes with room-temperature values of 7.7 × 103 S/cm and 2.6 × 104 S/cm were measured as a function of applied electric field in the temperature range of 77 K to 4.2 K. It is shown that the behavior deviated obviously from the Sheng model which has been widely adopted in explaining temperature dependence for conventional polyacetylene with lower conductivity.
INTRODUCTION Recently developed highly conducting polyacetylene (HCPA) has exhibited new features on the properties of doped polyacetylenes [1]. It showed a conductivity reaching ]05 S / c m at room temperature which appoached the level of Cu. The metallic behavior was maintained down to very low temperature [1, 2]. The mass density of undoped polyacetylene film reached to 1.1 g/cm a which was in the same level with theoretical one, whereas that of conventional polyacetylene has stayed in the level of 0.4 g / c m a. All these features have promoted us to reexamine the physical properties of doped polyacetylene. We present here the study of non-ohmic behaviors of iodine-doped HCPA. Similar studies were carried out previously for conventional polyacetylenes with room-temperature conductivities of - 0.1 S/cm [3], 3 S/cm [4] and 68 S/cm and 320 S/cm [5]. It was concluded that the results of the high electric field study were consistent with the Sheng model [6, 7] based on the fluctuation-induced tunneling between metallic strand. It is interesting to check the applicability of the model to the newly developed polyacetylene.
EXPERIMENTAL The synthesis and resultant structural properties are reported elsewhere [1]. We studied the polyacetylene samples doped up to a saturation level where the concentration can be expressed as y -- 0.27 ~ 0.29 for (CHI~)~. The conductivities of two samples A 0379-6779/93/$6.00
© 1993- Elsevier Sequoia. All rights reserved
4855
and C adopted here were 7.7 x 10a and 2.6 x 104 S/era, respectively. High electric voltage pulses of 2.5/~sec width were applied with duration of a few Hz. Currents were monitored by crip-on-type ac current probe. Voltage pulse across potential electrodes was observed with use of a differential amplifier. The high field experiments were carried out at several temperatures in the range of 4.2 K to 77 K. The normalized conductivity deviation from zero field value as a function of temperature is shown in Fig. 1 and Fig. 2, where Acr(E~t) denotes -- ~r(0) and ~r(EA) represents the conductivity at externally applied electric field EA. The temperature dependences of the conductivity ~(T) in the ohmic region are also shown.
Aty(EA)/o(O)
o(EA)
During the high field experiments we found that the conductivity increased gradually with elapsed time due to heating, typically 10 % increase in 1.0 #sec at 4.2 K. In this case the conductivity extrapolated to the instance of field application was adopted as the observed. The increment was diminished drastically with increase of measuring temperature and with decrease of applied field. The results shown in Fig. 1 and Fig. 2 are summarized as follows. (1) The conductivity increased with applied electric field. This was obvious at 4.2 K: the increment of the conductivity reached 47 7¢ at 69 V/cm for sample A and 197 % at 97 V/era for sample C. The field dependence was enhanced for sample with less conductivity. With increase of temperature T, the non-ohmic behavior is suppressed and the field dependence became faint at 77 K in the field range less than 80
V/cm.
(2) There was no remarkable threshold field for the non-ohmic behavior. The conductivity increases gradually with E A. Generally speaking, these features are rather consistent with the reported results for conventional doped polyacetylenes [5]. Then we tried to fit our data by the formula given by Sheng [7], which has been accepted as useful device in explaining temperature dependence of doped polymers. ANALYSIS After Sheng [7] tunneling current expression j(e) at electric field e across a potential barrier between metallic strands is represented by
j(e) = j0(e)exp (TI~(e)) To ((0) = jl(e)
fore
(1)
E/Eo
where c = is renomalized electric field, E0 is the field when the potential barrier height become zero, To and T1 are parameters with dimension of temperature and ~(e) is a expression appearing in transmission coefficients calculated by WKB method. Considering an externally applied field eA and a fluctuation-induced field ~T, the total current across a potential barrier is written as
4856
5O 40 o ID
30
\
%
ra4.
I
2K
a IOK • 20K
x i
•f t
O3)
-
12 E
/
-
(a)
/
20
6
,,m
ID <~ 1 0 0
I I.l I I I I i i 20 4 0
EA
60
0__] ~ i i I I I i
80 i 0 0
0
20 4 0
60
T
(K)
(V/cm)
80
Fig. 1. (a) Applied field EA dependence of normalized conductivity deviation from zero field value A*(EA)/,r(O) for sample A as a function of temperature. (b) Temperature dependence of ~r(T). Solid lines are the calculated corresponding to the observed (see text).
J(CA) =
+
(T1)'{f0"(~') / TI~T ~'~ deTjO(eA +Er)exp[--Te ,
f
deTjl(eA + CT)exp -(
ex
To
((o)
]
E
-- T--~I( 2
(2) r(eA)=l--eAforeA_
for eA > 1
where exp(-~-e~) denotes the fluctuation probability at temperature T. The last term in eq. (2) which represents the flow of electrons by thermally induced field counter to applied field, was neglected by Sheng for the case of large field strength [7]. However, during numerical calcuiation we found that even at not-so-small field as 20 V/era, this term is not negligible as pointed out by Philipp at. al. [5]. Then the field dependent conductivity ~r(EA) is given as
rr(EA) = J(eA)/EA
(3)
where EA = eAEo is macroscopic external field. By differentiating eq. (1), Sheng gave the conductivity at low field as
(4)
4857
200
3.0
( x l O 3)
o4. 2K • 10K 20K
0
••/ /
O77K• • //
i00
\
•/
(a)
1
[
•
/
<3 0 0
] I L I I I I L N 20 40 60 80 I00 EA (V//c m)
I I I I I I I I O 20 40 60 80
T
(K)
Fig. 2. (a) Applied field EA dependence of nomalized conductivity deviation from zero field value Ao(Ea)/o'(O) for sample C as a function of temperature. (b) Temperature dependence of ~r(T). Solid lines are the calculated corresponding to the obseved (see text). where
~(fT) is the
differential conduetivities given by
1 dj(c) = Eo(e)exp ( T1 ((e)'~ fore < 1
z(4 -So
-
= Y;q(j
for e > 1.
The definite expression of j ( J , ((e), E(c) are given in Ref.7 as eqs. 25(a-d), 17(b), 26(a-d), respectively. We examined appropriate parameter sets in the range of 0.002 < A < 0.2, 1 < To _< 100 K, 1.01 _< T1/To <_ 10 and 20 _< E0 < 600 V/era, where A governs shape and height of potential barrier through image force correction [8]. The procedures of searching appropriate parameter sets were following. 1. Parameter sets (A, To and T1/To) to fit ¢(T) were searched with a criterion that calculated ratio ~r(77 K)/(r(4.2 K) after eq. (4) was in the range of 0.9 to 1.10 times of the observed ratio. 2. For the parameter sets searched in the above procedure, we choosed residual parameter E0 so that the calculated ratio ~r(Ea ma~:)/o'(Ea ,ni,~) at. 4.2 K after eq. (3) fell in the range of 0.9 to 1.10 times of the observed, where Ea ma: and EA ,~i,~ are the maximum and the minimum fields used for the observation. 3. Then we checked the degrees of fitting of the calculated to the observed for ~r(Ea) at various temperatures. The parameter sets passing the prodedure 1 were depicted in Fig. 3. The best fit examples of the calculated conductivity were shown in Fig. 1 and Fig. 2. The used parameters were A = 0.03, T0=5 K, 771=7.5 K and E0=60 V/cm for sample A, whereas A = 0.03, To = 25 K, T1 = 110 K and E0=290 V/cm for sample C. Obviously the trends of the field dependences were different for the observed and the calculated. The
4858
10
•
(D
•
::
-: •:.•
• o • m ~
\
ooo • o•
I
I
11
e e o
5
0 0
A=0
•o
l
•
•
...
A=0
Sample
C
. . . . . .• . •
I
I
25
•
I
• • • • • • •
I
I
I
• •
I
I
o • •
° •
I
I
I
50 TO (K)
Fig. 3. Plots of parameters To versus sample C.
03
° •
• •
• •
• •
• •
I
I
I
I
I
75
T1/To, satisfying the
criterion 1 as function of A for
observed was extended almost linearly in the measured field region whereas the latter grew with higher rate with increase of the field. We noticed that large To and T1 were inappropriate for highly conductive sample A, even if they satisfied criterions 1 and 2. For example, if TI exceeded 30 K, the upswinging behavior of the field dependence was enhanced. Furthermore, the calculated Ao'(EA) at 10 K became more than 1.4 times larger than the observed Ao'(EA). The characteristics appeared almost always for sample A with larger value of To and T1, and were rather insensitive to A and E0. This situation condradicted to rather large T1 for highly conducting polyacetylenes with conductivity of the order of 10 5 S/cm on fitting of (r(T) by eq. (4) [9, 10].
DISCUSSION For the HCPA the metallic strands are considered to be formed more ideally compared to the conventional polyacetylene with less conductivity. From the viewpoint of the Sheng model where the conductivity is assumed to be infinite within metallic strands, this situation is favorable and the resistivity of the conducting polymer is determined by the barrier across the metallic strands. However, the failure of the fitting by the Sheng model indicates that this assumption is inappropriate to explain the behavior of the t/CPA. For samples doped to the saturation level the contents of the charge carriers are considered to be in the same level for both the HCPA and the heavily doped conventional polyacetylene, irrespective of the remarkable difference in the conductivity. This is evidenced by the magnitude and the temperature dependences of thermoelectric power. The difference in the conductivity seems to be ascribed to the degrees of disorders, which may bring about barriers and trapping centers for charge carriers throughout samples. In terms of the Sheng model, the high conductivity is realized by diminishing the effects of barriers. However, it is important to consider the temperature dependence of the conductivity of metallic strands in itself for the HCPA .
4859
The field dependence and the temperature dependence were enhanced with decrease of the conductivity or with increase of defects. This indicates that these dependences are not due to intrinsic nature of HCPA, but due to extrinsic origin represented by imperfections in polymer. Each sample decreases its conductivity by successive agings and systematic study of the aging effect indicates that the temperature dependence of the fully aged sample is represented more properly by anisotropic variable range hopping model rather than the Sheng model [11]. Finally, we rule out the sliding motion of the charge density waves specific to quasi one-dimensional conductors [12] as a cause of the non-ohmic behavior, since any threshold was not observed in the field dependence of the conductivity. This is supported by the observation that the non-ohmic behavior was enhanced with increase of the imperfections in the conjugating polymer. On the other hand rather perfect low-dimensional conductors are required to observe the effect of the sliding motion. ACKNOWLEDGEMENT This work was supported by a Grant for International Joint Research Project from the NEDO, Japan. REFERENCES 1. J. Tsukamoto, A. Takahashi and K. Kawasaki, Jpn. J. Appl. Phys. 29,125 (1990). 2. Y. Nogami, H. Kaneko, H. Ito, T. Ishiguro, T. Sasaki, N. Toyota, A. Takahashi and J. Tsukamoto, Phys. Rev. B 43, 11829 (1991). 3. K. Mortensen, M. L. W. Thewalt and Y. Tomkiewicz, Phys. Rev. Lett. 45, 490 (1980). 4. A. J. Epstein, H. W. Gibson, P. M. Chaikin, W. G. Clark and G. Griiner, Phys. Rev. Lett. 45, 1730 (1980). 5. A. Philipp, W. Mayr and K. Seeger, Solid State Commun. 43,857 (1982). 6. P. Sheng, E. K. Sichel and J. I. Gittleman, Phys. Rev. Left. 40, 1197 (1978). 7. P. Sheng, Phys. Rev. B 21, 2180 (1980). 8. J. G. Simmons, J. Appl. Phys. 34, 1793 (1963). 9. Th. Schimmel, G. Denninger, W. Riess, J. Volt, M. Schwoever, W. Schoepe and H. Naarmann, Synth. Metals, 28, Dll (1989). 10. G. Paasch, G. Lehmann and L. Wuckel, Synth. Metals. 37, 23 (1990). 11. H. Kaneko, T. Ishiguro, J. Tsukamoto and A. Takahashi, these Proceedings. 12. G. Grfiner, Rev. Mod. Phys. 60, 1129 (1988).