Electrical conductivity of semiconductor pyropolymers in an alternating electrical field

1323

Electrical conductivity of semiconductor pyropolymers

9. Ye. MERKUSHEV, Usp. khimii 53: 583, 1984 10. Sintezy iodistykh otganicheskikh soyedinenii (Syntheses of Organo-lodine Compounds). (Eds. L. M. Yagupol'skii, A. N. Novikov and Ye. B. Merkushev) 88 pp., Tomsk, 1976 11. A. GORDON and R. FORD, Sputnik khimika (The Chemist's Companion). 541 pp., Moscow, 1983 12. I. GUVEN and T. WELL, Metody organicheskoi khimii (Methods in Organic Chemistry). Vol. 2, 1032 pp., Moscow, 1967 13. J. RABEC, Eksperimental'nye metody v khimii polimerov (Experimental Methods in Polymer Chemistry). Vol. 2, 479 pp., Moscow, 1983 14. T. AKIMOTO, Polimery spetsial'nogo naznacheniya (Special Purpose Polymers). (Eds. N. Isa and I. Tabusi) 204 0pp., Moscow, 1983 15. G. M. STEFANENKO, P. I. SIYANKO and Ye. B. MERKUSHEV, Vysokomol. soyed. B29: 181, 1987 (Not translated in Polymer Sci. U.S.S.R.)

PolymerScienceU.S.S.R. Vol. 31, No. 6, pp. 1323-1330,1989 Printed in Poland

0032-3950/89 $10.00+ .00 © 1990PergamonPress plc

ELECTRICAL CONDUCTIVITY OF SEMICONDUCTOR P Y R O P O L Y M E R S IN AN ALTERNATING ELECTRICAL FIELD* U. ABDURAKHMANOV,A. V. UMAROV, A. KH. ZAINUTDINOV

and M. A. MAGRUPOV Lenin Tashkent University

(Received 14 December 1987) The frequency dependence of the electrical conductivity of PAN-based semiconductor pyropolymers has been studied. With increase in frequency from 102 to 107 Hz electrical conductivity a increases as in most unordered s~stems ao~f. Analysis of the temperature dependence of electrical conductivity (in the interval 100-450 K) at fixed frequencies shows that in PAN-based semiconductor pyropolymers in the low temperature region th.eain contribution in the low temperature region the main ciontrbution to conductivity is made by the transitions of electrons between the regions of polyconjugation present in a c:rtain optimal energy band in the vicinity of the Fermi level and the in high temperature region between the regions of polyconjugation which are spatially the nearest neighbours. STUDY of the c o n d u c t i v i t y of heterogeneous polymeric systems, a typical representative o f which is p r o v i d e d by s e m i c o n d u c t o r p y r o p o l y m e r s in the a l t e r n a t i n g electrical field, is a powerful m e t h c d o f establishing the subtle aspects of the m e c h a n i s m o f charge tran.sfer in such systems. The frequency d e p e n d e n c e of c o n d u c t i v i t y of s e m i c o n d u c t o r p y r o p o l y m e r s is o f a p o w e r character of the type [1-5] a ccJ '~, * Vysokomol. soyed. A31: No. 6, 1208-1214, 1989.

(1)

1324

U; ABDURAKHMANOVet

at.

" "

:

with the exponent s~< 1. Most authors interpret this dependence within the model of jump conductivity in the binodal approximation regardless of the frequency range studied. In addition, in such systems to our knowledge no study has been made of the frequency depen.dence of a in the low temperature region when the temperature dependence of static co•.ductivity is described by a law with variable activational energy. The present paper deals with the frequency dependence of conductivity of PAN-based semiconductor pyropolymers over a wide temperature interval and analysis of the latter within the framework of the theory o f the frequency dependence of the conductivity o f unordered systems. As the main test object we used thermally treated powdery (grain diameter 0.5-1 /tm) PAN. Thermal treatment was applied in vacuo in the temperature range Tt = 200-600°C for 3 hr at each temperature with a 50°C step. Conductivity was measured under a pressure ~0"35 GPa in a fixed pressure chamber [6] and in vacuo ~ 10-3 mm Hg. This allowed us by excluding contact phenomena between the particles of the powder to study the properties of the monolithic compound [7]. Measurement of a in the samples in the finterval from 102 to 104 Hz was by the bridge method andl at f = 5 × 104-1 x 107 Hz with use of an E9-4 Q-meter. Figure 1 presents the temperature dependence of a of pyro-PAN samples with Tt=450°C at different frequencies. Temperature dependence of a of such a kind for a constant electric field for PAN samples was observed in [8]. To analyse a(T) the authorc o f [8] used the technique of investigating the reduced activational energy of conductivity developed in [9, 10] where it is shown that if a ( T ) is described by the law ~ = g0 exp [ -

(To/rY]

x may be determined by using the equation log w = A - x log T w=

1 3 log o-

A=eonst

(3)

T 3(T-~) ' It is in practice convenient to determine the reduced activational energy of conductivity w=c31og a/Olog T [10]. As may be seen from Fig. 2 in the interval of temperatures 100--450 K and frequencies studied like a ( T ) for a constant field [8] there are three characteristic regions of the temperature dependence of a: high- (I) and low- (III) temperature separated by a transitional region II. At low temperatures ( T < Tv to the left of curve c) linear dependence of log w on log T applies corresponding to the exponential law a ( T ) with variable activation energy of the type (2) with x g 0 . 5 ,~ exp [ -

( T o / T ) a/2]

(4)

In the high temperature region T > Tg, to the right of curve a), we also find linear dependence of log w on log T corresponding to the exponential law a(T) with constant activation energy Ae with x ~ l aocexp - ~

Electrical conductivity of semiconductor pyropolymers

1325

~og~[~-Vr4

-3

logw :

c

\a

22

2.#

08

0.4

-7 I

2

6

I0

2.0

(lJ/r), K"

2.6 /o~ "r rs~"7

Fio. 1 FIG. 2 FIG. 1. Temperature dependence of the electrical conductivity of a PAN sample thermally treated at Tt = 450 °. Here and in Fig. 2 frequency of alternating fielg 10~ (1), 103 (2), 104 (3), 105 (4), 106 (5) and l07 (6) Hz. F'm. 2. Reduced activation energy of the conductivity of the PAN sample thermally treated at T,=450°C. •

4

.

Similar temperature dependences of tr have also been observed forbther thermally

treated PAN samples. Thus, ia semiconductor pyro-PANs in thb.low te~aperature region the main contribfition to a is made by the electron transifions between the regions of polyconjugatio n present in a certain optimal energy band in the vici~.!ty of the Fermi level and in the high temPerature region between the regiorts of polyconjugation, spatially the nearest neighbOurs. •,

-S.O~ I

e

__

I ....

,

[

e 1oeeC,;

Fla. 3. Dependence of the electrical conductivity on the frequency of the alternating field for the P A N sample thermally treated at different temperatures. Here and in Fig. 4 T..=300 (1), 350 (2), 450 (3) and 550 (4)°C. l'-4'-Theoretical calculations from formula (6)•

1326

U. ABDURAKHMANOVetal.

•

High temperature region T > T s. Figure 3 presents the frequency dependence of cr

for a series of thermally treated PAN samples. With increase in f t h e r e is rise in a and a is of a power character. The values of the exponent s in formula (1) were determined by differentiating the curves of the dependence of log ~r on logf. As may be seen from Fig. 4 in the f interval studied the dependence of s on l o g f h a s three regions with different frequency dependences of a: region I (to the left of curve a), region II (region f bounded by the curves a and b) and region III (to the right of curve b). For f < f v (to the left of curve a) there is a region of linear dependence of s on logf. With increase in T, of the sample the value of s decreases and the boundary of region I shifts to highf. For high f > f c (to the right of curve b) a region is seen where the value s ~ 1 also does not depend o n f a n d with increase in Tt of the sample the boundary of region III also shifts to high f. The regions I and III are separated by a certain transitional frequency region II. Similarly we treated the data on the dependence of a(f) of a number of studies [2-4] for pyropolymers based on PE, PAN and anthracene. In all these polymers the characteristic regions of the frequency dependences of s are identiacl. The analysis made of the dependence of s on l o g f (Fig. 4) within the theory of the frequency dependence of conductivity of unordered systems [11-13] taking into account the physical model of the structure and process of formation of semiconductor pyros 1.0

b\ S

O.B

0.8

0"2

o.z I

2

4

B In f[Hz]

e

4

6 lo9 f[,zj

Fro. 4 FIc. 5 FIG. 4. Degree of s in formula (1) of the PAN sample as a function of the frequency of the alternating field. FIG. 5. Degree of s in formula (1) of the PAN sample thermally treated at T,=450°C as a function of the frequency of the alternating field. Temperature of measurement 100 (1), 200 (2), 300 (3) and 400 (4) K. polymers [14] shows that for low f < f v in the thermally treated PAN samples the character of the dependence of cr o n f m a y be described by a multiplet model, i.e. the electron in the time of the half-period of the vibration of the external field has time to perform many jumps between the regions of polyconjugation. In other words, it moves within a certain region the size of which decreases with rise in frequency [12]. To check on this conclusion the experimental results for a were compared with the calculated

Electrical conductivity of semiconductor pyropolymers

1327

described by the formula tr = a'-~-12 In

s'2

,

(6)

where f2 is the dimensionless magnitude derived from the multipled model [11 ]. A characteristic feature of the onset of the regime of multiplet jumps is rise in the exponent s with frequency which tends to unity by the law [11] s = 1 - 2/ln 12

(7)

For s = 0 in equation (7) I2 equals e 2, then from formula (6)

(8)

afo'~tT~e

where aro is the value of the conductivity of the sample for fo; )Co is the frequency corresponding to the value s = 0 at which the multiplet region begins. The value offo is determined by extrapolating the straight line part of the dependence of s on log f for s ~ 0 (Fig. 4). The closeness of the experimental results of conductivity with the calculated for f f c in the time of the half period of the vibration of the external field, the electron does not have time to jump t> 3 times between the regions of polyconjugation and, consequently, the transition within one pair becomes more probable. As is known [11, 15] transitions within the pairs in the high frequency region may occur both with the participation of phonons and without them. In the first case which is called relaxational the energy required for the transition of the electron within a pair is of the order kT and in the second non-phonon case this energy is equal to a quantum of the field hco. On relaxational absorption the distance between the localized states within the pair r is determined from the condition [15] that the frequency of the field is of the order of the frequency transitions within the pair vphexp(-2r/a) where vph is the characteristic phonort frequency of the order 1012 sec -1. From this follows a

Yph

r=---In - - , 2 o~ where a is the radius of the localized state. Absorption of such a kind was first considered in [16] where for the case of an impure zone of a weakly doped semiconductor the formula 7r 3 O"= - - e 2 k T o 2 ( e ) aoJr 4

6

was derived.

(10)

1328

U . ABDURAKHMANOV et al.

A similar dependence of a on f associated with relaxational absorption often used to describe ¢r of amorphous semiconductors was derived by Austin and Mott [15, 17] 7~4

a =-- e2kTg2(e) mar 4

(11)

24

More precise calculations ill] show that in the region f when the paired model is applicable a ofunordered systems is described by the expression

o=--~-256rc2e2kTg2(s)amr411L+-~e22_# s3 I'~

#~J#2(~) -]

(12)

it is close to the function a ~ f . As may be seen from Fig. 4 in the region f>fc (to the right of curve b) the value s,,~ 1.0. The activational energy of conductivity determined from the angle of slope, log a against 103/T with increase in f diminishes and at f>fc it is a magnitude of the order kT. From these results it may be concluded that the dependence of a on f of semiconductor pyro-PANs at f > f c may be described by the paired model with the participation of a phonon. Because of the difficulties in calculating the density of the localized states g(e) from formula (12) the formula (11) is used to evaluate g(e). For the calculations ofg(e) from formulae (10) and (11) it is usual for unordered substances to take the value a as ~ 2 - 15 x 10 -t° m [3, 17]. As may be seen from Table 1 with increase in Tt of the sample the values of g(~) ca!culated for f = 106nz, T=290 K and a = 1 × 10 -9 m and the number of localized states N, calculated from the formula N=g(e)Ae, increase but the investigations of the voltage-current characteristics for determining the magnitude a in semiconductor 'pyro-PANs show that with change in Tt of the sample the magnitude a changes. I1" for the calculations from formula (11) the values of a determined from the voltage-current characteristic (Table 1) are substituted the magnitude N with TABLE 1. ]DEPENDENCE OF THE PARAMETERS ,q(~), Z~6, N AND a ON THE TEMPERATURJE OF THERMAL TREATMENT Tt OF THE P A N

g(e) × 10-2s, Tt°C

300 350 450 550

eV71/m a

2.6 6-4 19'0 44.0

I [ I

de × 102, eV 10.0 8-5 6"0 4'0

Nx 10-24,

a x 101°,

m -3

m

2.6 5"5 11'0 17.0

5"2 10.0 27.0 71"4

SAMPLE

g(8) x 10-24, I- Nx lO-2a,. eV-1/m a

134"0 64'0 15"0 3'2

'

m -a

134.0 54.0 9.0 1.3

rise in Tt decreases. These results at first sight appear untrue, i.e. it would seem that with rise in Tt of the sample the value N ought to increase. But in [18, 19] it was demonstrated that on formation of semiconductor pyro-PAN there is clustering of the regions of polyconjugation leading to fall in the value of N with increase in It. The complex of frequency-temperature investigations of a of PAN samples in the high temperature region for f < f o revealed a further phen.omenon, so-called frequencycompensation. The essence of the effect first explained by Vidadi [20] is that increase

Electrical c o n d u c t i v i t y o f s e m i c o n d u c t o r p y r o p o l y m e r s

1329

irt a with rise in f through fall in the value of the activational energy of conductivity is compensated by fall in the prexponential multiplier in tbrmula (5). The existence of a single point of intersection of the .high temperature portions of the cmwes or(T) (Fig. 1) for f < f t means that the frequency compensation effects is fulfilled. From the investigations of the freque~.cy-compensation effect it may be concluded that this effect is observed for frequencies when the frequency dependence of a of the PAN samples is described within the multiplet model. Low temperature region T Tg) the analytical expressions (6) ap.d (11) are inapplicable here since ia ob:aining these expressions it ,was considered that the length of the jump of the electron between localized states is constant. References [21, 22] on the basis of the multiplet model give a calculation formula for a(f) of unordered systems when the temperature dependence of static conductivity is described by the law (2). It has the form a(~o, T)oco~(r) exp [ - p ( ~°)P l ,

(13)

s (T) = 1 - [ln (tot0) + 2.4 In -~° + ( ~ - f ] -~

(14)

where

If the density of the localized states around the Fermi level decreases by the law g(c) oz(c-e,F) 2 [23] then p=½. The expression (16) applies with the coodition [21] B>>I, w,here

/

(,5)

Here ro-,~10-12; #=~-(7+fl); ~' and flare standard critical indices [23] equal resFcctively to 1.7 and 0.4. As may be seen from Table 2 condition (15) is well fulfilled for the PAN samples in the temperature region T< To. This shows that the calculation formula (13) may be used to describe tr of pyro-PAN for T< To and f
TREATED THERMALLY AT T t = 4 5 0 ° C

J; H z

To X 10 -2, K

1 x10 2 1 x 10 a I x 10 4 1 x l0 s

430 300 200 160

B f o r T, K 100 883-7 181.3 57.5 86.4

[i !i

150

200

12.6 5.0 2'3 5"2

0"90 0'50 0"38 0'93

1330

U. ABDURAKHMANOVet at.

N o w , let us c o n s i d e r the b e h a v i o u r o f cr o f the p y r o - P A N s a m p l e s at T < To a n d

f > f c . A s m a y be seen f r o m Fig. 2, f o r f > f c the d e p e n d e n c e o f a o n T i s n o t a c t i v a t i o n a l b u t in the t e m p e r a t u r e region b o u n d e d b y the curve b c o n d u c t i v i t y d e p e n d s o n t e m p e r a t u r e in. the f o r m u l a a o o T - m . Thus, in the low t e m p e r a t u r e region for f > f c w h e n a is d e s c r i b e d by the p a i r e d m o d e l with the p a r t i c i p a t i o n o f a p h o n o n the t e m p e r a t u r e d e p e n d e n c e o f a o f the P A N s a m p l e s is e x p r e s s e d b y a p o w e r law.

Translated by A. CROZY REFERENCES

1. L. I. BOGUSLAVSKII and L. S. STIL'BANS, Vysokomol. soyed. 6: 1802, 1964 (Translated in Polymer Sci. U.S.S.R. 6: 10, 1996, 1964) 2. N. A. BAKH, A. V. VANNIKOV and A. D. GRISHINA, Elektroprovodnost' i pa(amagnetizm polimernykh poluprovodnikov (Electrical Conductivity and Paramagnetism of Polymeric Semiconductors). 136 pp., Moscow, 1971 3. J. C. GUINTINI, D. JULLIEN, I. V. ZANCHETTA, F. CARMONA and P. DELHAES, J. Non-Crystal. Solids 30: 87, 1978 4. J. L. JACQUEMIN, A. ARDALAN and G. BORDURE, Ibid. 28: 249, 1978 5. U. ABDURAKHMANOV, Authols Abstr. Dissert. Cand. Phys. Math. Sci. {in Russian) 19 pp., LPI im M. I. Kalinina, Leningrad, 1981 6. A. V. UMAROV, U. ABDURAKHMANOV, A. R. FAIZIYEV and M. A. MAGRUPOV, Pribl. i tekhnikh, eksp., 1, 206, 1986 7. M. A. MAGRUPOV and U. ABDURAKHMANOV, Vysokomol. soyed. B21: 731, 1979 (Not translated in Polymer Sci. U.S.S.R.) 8. U. ABDURAKHMANOV, A.G. ZABRODSKII, M. A. MAGRUPOV and A. V. UMAROV, Fizika tverdogo tela 28: 3680, 1986 9. A. G. ZABRODSKII, Fizika i tekhnika poluprovodnikov 11: 595, 1977 10. A. G. ZABRODSKII and K. N. ZINOV'EVA, Zh. eksp. teot. fiz. 86:727 1984 11. V. V. BRYKSlN, Fizika tverdogo tela 22: 2441, 1980 12. V. V. BRYKSIN, M. N. D'YAKONOV, V. M. MUZHDABA and S. D. KHANIN, Ibid. 23: 1516, 1981 13. I. V. KLYAUKINA and I. S. SHLIMAK, Fizika i tekhnika poluprovodnikov 12: 134, 1978 14. M. A. MAGRUPOV, Dissert. Doct. Phys. Math. Sci. (in Russian} 465 pp. NIFKhI im L. Ya. Karpova, 1981 15. B. I. SHKLOVSKII and L. L. EFROS, Zh. eksp. teor. fiz. 81: 406, 1981 16. M. POLLAK and T. H. GEBALLY, Phys. Rev. 122: 1742, 1961 17. N. MOTT and E. DAVIS, Elektronnyve protsessy v nekristallicheskikh veshchestvakh (Electron Processes in Non-Crystalline Substances). 658 pp., Moscow, 1982 18. M. A. MAGRUPOV and U. ABDURAKHMANOV, Vysokomol. soyed. B23: 527, 1981 (Not translated in Polymer Sci. U.S.S.R.) 19. m. A. MAGRUPOV, Usp. khimii 50: 2106, 1981 20. Yu. A. VIDADI, Phys. Stat. Sol. (a) 61: k59, 1980 21. V. N. RUD'KO and I. I. FISHCF1UK, Fizika tverdogo tela 22: 1897, 1980 22. V. N. RUDKOV, Phys. Stat. Sol. (a) 110: klT, 1982 23. B. I. SHKLOVSKII and A. L. EFROS, Elektronnye svoistva legirovannykh poluprovodnikov (Electron Properties of Doped Semiconductols). 416 pp., Moscow, 1979