Temperature dependence of the electrical conductivity and Seebeckcoefficient of new poly(ester-syloxane)urethane elastomers in thin films

Mihaela Rusua, A. Stanciub, V. Bulacovschib, G.G. Rusua, Mihaela Bucescua, G.I. Rusua,*a‘Al. I.Cuza’ University, Faculty of Physics, Bd. Copou, 11, Iassy, R-6600 Romania

b‘P. Poni’ Institute of Macromolecular Chemistry, Aleea Grigore Ghica Voda, 41 A, Iassy, R-6600 Romania

Received 29 October 1997; accepted 12 March 1998

Abstract

The temperature dependences of the electrical conductivity and the Seebeck coefficient for some new poly(ester-syloxane)urethaneelastomers are studied. The measurements have been performed using thin films deposited from solution. It is found that the investigatedpolymers have semiconducting properties. Values of some semiconducting parameters of these films (activation energy of electricalconduction, charge carrier concentration, ratio of carrier mobilities) have been calculated. The correlations between some of theseparameters and the molecular structure of the respective polymers are discussed. 1998 Elsevier Science S.A. All rights reserved

Keywords:Polymers; Electrical properties and measurements; Semiconductors

1. Introduction

There have been extensive investigations on the electro-nic transport properties of organic semiconducting poly-mers [1–5]. A large number of papers have shown thatthe electrical and thermoelectrical properties of these mate-rials strongly depend on their macromolecular structures[1,3,6]. Consequently, it appears the possibility to synthe-tize the organic polymers with semiconducting propertiesexactly matched to the requirements of specific applicationssuch as semiconductor devices. In this connection, it isimportant to establish a correlation between the chemicalstructure of the organic semiconducting polymers and thevalues of some characteristic parameters (activation energy,mobility of charge carriers and more) which define theirsemiconducting properties.

In recent years, the electrical and dielectrical propertiesof organic polymers and the dependence of these propertieson the molecular structure of respective materials and onvarious external factors (temperature, intensity and fre-quency of applied electric field, radiation effect, etc.) hasbeen intensively studied. These investigations offer the pos-sibility to obtain very useful information about the mechan-

ism of electrical conduction in this important class oforganic compounds.

The mechanism of electron transfer in semiconductingorganic polymers having a complex molecular structure isin present far from being fully understood. Usually,obtained experimental results for different polymers havebeen interpreted in terms of various conduction mechan-isms, such as band conduction, variable-range hopping con-duction [3,6–10].

In a series of previous papers [11–13], we investigatedthe electrical and thermoelectrical properties for some neworganic polymers which showed typical semiconductingcharacteristics. By studying these properties, very usefulinformation has been obtained about the activation energyof electrical conduction, concentration and mobility of car-riers. We showed that at a higher temperature range themodel based on band gap representation could be suitablefor the study of electrical conduction mechanisms for alarge number of investigated polymers.

Polyurethanes are an important class of polymers havingthe presence of the urethane group (–NH–CO–O–) in com-mon in their molecular structure. Usually, this group isformed by reaction between isocyanate and hydroxylgroups. Polyurethane elastomers are characterized fromhigh reversible deformation, high abrasion and chemical

Thin Solid Films 326 (1998) 256–262

0040-6090/98/$19.00 1998 Elsevier Science S.A. All rights reservedPII S0040-6090(98)00570-7

* Corresponding author. Fax: +40 32 213330; e-mail: rusugxg@uaic.ro

resistance, blood and tissue compatibility, etc. [14,15]. Byvarying the type and the ratio of starting component duringprocessing it is possible to obtain polyurethane elastomerswith a various chemical structure and molecular weight[2,14,15].

In the present paper, the temperature dependence of theelectrical conductivity and Seebeck coefficient of somerecent synthesized poly(ester-siloxane)urethane elastomersin thin films has been studied. It was found that the respec-tive polymers have semiconducting characteristics.

2. Experimental details

2.1. Synthesis of polymers

2.1.1. MonomersThe polymers studied were synthesized using the follow-

ing monomers:a, q-Poly(dimethylsiloxane)diol (PDMS)with Mn = 2000 and Mn = 10 000, respectively, preparedand characterized by the method described in [16]; Poly(-ethyleneglicole adipate)diol (PEGA; Fibrex SA, Sa˘vinesti,Romania), and 1,4-buthanediol (BD; Aldrich); 4,4′-Diphe-nylmethane diisocyanate (MDI; Suprasec–ICI), 2,4-toluenediisocyanate (TDI; Riedel De Ha¨en), and 1,6-hexamethy-lene diisocyanate (HDI; Aldrich), purified by vacuum dis-tillation before use.

2.1.2. PolymerizationInvestigated poly(ester-siloxane)urethanes were synthe-

sized by melt polyaddition using prepolymer technique. Inorder to obtain high molecular weights it was necessary toknow the precise stoichiometric ratio (NCO:OH= 1:1). Theprepolymers, prepared from polyols and diisocyanates in thepresence of dibuthyltindilaurate (Bu2SnL2) at 80°C, werethen reacted with BD (chain extended) for 30 min, obtainingurethanic copolymers.

After preparation, all polymers were in the plate formhaving diameters of 200–300 mm and thickness 1 mm.

In order to complete the reaction, these plates were inaddition heated for 7 h at 60°C. Finally, the samples wereequilibrated for 7 days before testing.

Poly(ester-siloxane)urethane copolymers were obtainedby addition in two steps that might be illustrated as:

The substituents R1, R2, R3 and R4 are listed in Table 1.Chemical composition of flexible segments and soft seg-

ment concentrations are listed in Table 2.The preparation methods of investigated polymers and

some of their physical and chemical properties are describedin detail in Ref. [16].

2.2. Preparation of samples; study of the temperaturedependence of both electrical conductivity and Seebeckcoefficient

The electrical and thermoelectrical properties of the men-tioned polymers were investigated on samples of thin filmsdeposited from solution onto glass substrates. Dimethylfor-mamide was used as a solvent. Specific experimental con-ditions were chosen in order to obtain samples of a compactstructure and uniform thickness on sufficiently large areas ofthe substrate surface. The substrate temperature during thefilm deposition was kept at 320–330 K for slow evaporationof the solvent. Under these conditions, films adherent to thesubstrate were obtained.

The thickness,d, of polymer films was determined byFizeau’s method for fringes of equal thickness [17] usingan interferential microscope MII 4. The values obtained forinvestigated polymer films ranged between 0.15 and 0.80mm.

The temperature dependence of electrical conductivity(j) was studied using surface-type cells. Thin silver electro-des with thicknesses of 1.1–1.3mm were deposited onto thesubstrate by thermal evaporation under vacuum before thedeposition of polymer films. The interelectrode distance wasabout 5 mm.

For measurements ofj, static electric fields with intensity

Table 1

Chemical structure of the substituents R1, R2, R3, and R4

Substituents Chemical structure Symbols

R1 –[–(CH2)2–O–CO–(CH2)4–CO–O]n–(CH2)2–

PEGA

R2 –(CH3)2Si–[–O–(CH3)2Si]n PDMS–C6H4–CH2–C6H4– MDI

R3 –C6H3(CH3)– TDI–(CH2)6– HDI

R4 –(CH2)4– BD

Table 2

Molecular structure of investigated polymers

Polymer Chemical com-position (wt.%)*

Soft segment concentrations (wt.%)

PEGA PDMS10000 PDMS2000

P1 PEGA:MDI:BD 77.15 – –P2 PEGA:PDMS10000:

MDI:BD65.15 12.00 –

P3 PEGA:PDMS2000:MDI:BD

65.30 – 12.00

P4 PEGA:PDMS10000:TDI:BD

69.21 12.00 –

P5 PEGA:PDMS10000:HDI:BD

69.22 12.00 –

*All urethane copolymers contain about 1.5× 10−3 moles –NCO groupstransformed to –NH–COO– groups per gram product.

257M. Rusu et al. / Thin Solid Films 326 (1998) 256–262

lower then 102 V/cm were used. Under these conditions,non-ohmic effects were not noticed [17,18]. The experimen-tal arrangement used for the study of temperature depen-dence of the electrical conductivity is presented in detail in[19–21].

The temperature dependence of Seebeck coefficient wasstudied by using sonde electrodes.

It is known [22–24] that the Seebeck voltage is given by:

DV =aDT (1)

wherea is the Seebeck coefficient.In our experiments the temperature differenceDT = T2 −

T1 was chosen as 10–15 K anda corresponds to the tem-peratureT = (T1 + T2)/2. The sonde electrodes were heatedat different temperatures,T1 andT2, respectively, by meansof two special heaters. Their temperature was measured bytwo iron-constantan thermocouples.

The Seebeck voltage has been determined by a standardDC-potentiometric method [22,23].

3. Results and discussion

In our previous papers, for a large number of organicpolymers, we found that at higher temperature ranges(350 K , T , 550 K) the temperature dependence of theelectrical conductivity (j) may be described by the expo-nential law [6,23,24]:

j =j0exp( −DE=2kT) (2)

whereDE denotes the thermal activation energy of electri-cal conduction,j0 represents a parameter depending on thesemiconductor nature, andk is Boltzmann’s constant.

In this paper we supposed that an exponential increase ofj with temperature is also possible for our investigatedsamples.

The transport properties of thin semiconducting filmsstrongly depend on their structure (grain size and shape aswell as the characteristics of the contact between them,structural defects, etc.) and purity (nature and concentrationof the impurities, adsorbed and absorbed gases, etc.) [17–21].

Heating of the film may modify these structural charac-teristics and consequently, the transport properties of therespective film (e.g. electrical conductivity) may vary too.Therefore, the study of the temperature dependence of theelectrical conductivity during the heat treatment may pro-vide information on the processes taking place in the films.Consequently, for a large number of samples the shapes oflnj = f(103/T) curves during heat treatment (consisting ofseveral successive heatings and coolings within a certaintemperature range) were examined.

The typical curves obtained are illustrated in Figs. 1 and 2for two of the polymers studied. The respective sampleswere submitted to two successive heatings and coolingswithin temperature range 300–550 K.

A slow decrease of electrical conductivity is observedduring the first heating within the lower temperature range(300 K , T , 360 K). This is due to the elimination of theadsorbed and/or absorbed gases, solvent molecules andother accidental impurities introduced during the polymersynthesis and preparation of thin-film samples. It is knownthat these factors strongly influence the electrical propertiesof organic semiconductors in thin films [6,11–13,19,20].Other changes in the film structure may also occur.

In the range of higher temperatures (T . 360 K), thelnj = f(103/T) curves show an exponential dependence ofelectrical conductivity on temperature.

After 2–4 series of successive heatings and coolings, thetemperature dependence of the electrical conductivitybecomes reversible. This fact indicated the stabilization ofthe film structure in the respective temperature range. InFig. 3 the lnj = f(103/T) curves for the heat-treated samplesare illustrated.

It can be observed that these dependences present twosections. In the first section, with a smaller slope, the extrin-sic conduction prevails, the electrical conductivity beingdetermined in principal by residual impurities [24]. A sec-ond section, with larger slope, corresponds to an intrinsicconduction of the studied polymers. The intrinsic conduc-tion domain begins at a certain temperature (Tc), character-istic for every sample. During the heat treatment, the valuesof (Tc) shift to the range of the lower temperatures, factwhich indicates a reduction in the concentration of impuri-ties in the respective sample. A similar behaviour has beenalso observed for other organic semiconductors in thin films[19–21].

TheTc values were found to depend on the polymer nat-ure (Table 3).

Within the higher temperature range (T . Tc), the slopesof the lnj = f(103/T) curves were not modified significantlyas a result of the heat treatment.

Fig. 1. Temperature dependence of the electrical conductivity during heattreatment for polymer P3.

258 M. Rusu et al. / Thin Solid Films 326 (1998) 256–262

Based on the Eq. (2), the values of activation energy ofelectrical conduction (DE), were calculated fromlnj = f(103/T) curves within the intrinsic domain. Valuesobtained for the studied polymers are listed in Table 3.The values of other characteristic parameters of respectivesamples are also indicated in Table 3.

The semiconducting properties of the studied polymersare determined by their specific molecular structure whichaffords an extended conjugation of the electrons. The mole-cular structure of these polymers (numbers ofp electrons,the character of the end group, etc.) significantly influencesthe values of activation energy,DE.

The polymers P1, P2 and P3 showed the lowest activationenergy and highest electrical conductivity. This fact mightbe explained by the presence in their molecular structure ofMDI segments, which have a great number of double bonds,and one methylene group (–CH2–). Effects of incorporating(–CH2–) group (bridge) into the structure of some polymershave been studied by different authors [25–29]. Accordingto Dulov et al. [25], the decrease in activation energy for thepolymers having methylene bridges is due to an increase ofthe flexibility of the polymer chain. This is leading to acloser packing of the molecules and consequently to aneasier energy transfer and electron interaction between indi-vidual chains. Using X-ray data, Bonart et al. [27–29] stu-died the packing of chains in segmented polyurethanescontaining MDI and BD segments. They also found thatthe presence of methylene groups determines an increaseof the flexibility of the polymers chain. These results arein good agreement with our data concerning semiconduct-ing properties of the investigated polymers.

The Seebeck coefficient,a, in the temperature range of320–450 K for a series of thin polymeric films has been alsoinvestigated. By studying the temperature dependence ofthis coefficient, some new information on the nature

mechanism of electrical conduction may be obtained. Fig.4 shows the typical dependencesa = f(103/T) for investi-gated polymers.

The charge carriers (in finite semiconductors, under theinfluence of temperature gradients) diffuse from the hot endto the cold end and the polarity of Seebeck voltage (DV)depends upon the sign of the respective carriers [22–24].When the charge carriers are holes, the hot end comes nega-tive and the cold end positive, and the Seebeck coefficient ispositive. For our investigated samples the polarity of theSeebeck voltage shows that the polymers under studymight be considered as p-type semiconductors.

Within the intrinsic domain (T . Tc), the Seebeck coeffi-cient decreases with increasing temperature.

The aspect of the obtained dependences lnj = f(103/T)anda = f(103/T) suggests that a model based on band gaprepresentation could be suitable for study of electron trans-fer mechanism through investigated samples.

In this connection, the values of some characteristic para-meters of investigated samples have been estimated basedon respective dependences.

The carrier concentration within intrinsic domain wascalculated from the formula [6,24]:

n=p=ni =2(2pkT)3=2h−3(me × mh)3=4exp( −DE=2kT) (3)

wheren andme, p andmh are the concentrations and effec-tive masses of the electrons and holes respectively,h isPlanck’s constant andk is Boltzmann’s constant. The effec-tive masses of the charge carriers have been determinedfrom the static current-voltage characteristic of thin filmssandwich structures of the metal/organic polymer/metaltype. The method used has been similar to that describedin [18,30,31].

The ratio of the carrier mobilities,b, has been determinedusing the temperature dependence of the Seebeck coeffi-cient.

Fig. 2. Temperature dependence of the electrical conductivity during heattreatment for polymer P5.

Fig. 3. Temperature dependence of the electrical conductivity for heat-treated samples.

259M. Rusu et al. / Thin Solid Films 326 (1998) 256–262

For a non-degenerated semiconductor within the intrinsicconduction domain, the temperature dependence of the See-beck coefficient is described by relationship [19–21,24]:

a = −ke

⋅b−1b+1

52

−s

� �+

DE2kT

� �(4)

whereb is the ratio of the carrier mobilities (b = me/mh), e isthe electron charge, ands is a parameter which depends onthe nature of the predominant scattering mechanism in theinvestigated sample. Within the intrinsic conductiondomain, the scattering on the lattice vibrations is predomi-nant ands = 1/2 [6,19,24].

Based on Eq. (4) the ratio of carrier mobility was deter-mined using the expression [19–24]:

b=DE=2 ⋅ D(1=T) − lel ⋅ Da

DE=2 ⋅ D(1=T) + lel ⋅ Da(5)

In Eq. (5), Da is the variation of the Seebeck coefficientcorresponding to a determined variationD(1/T) of the tem-perature. The relationship is deduced by supposing that inthe respective temperature range, the values ofs do notdepend on the temperature. The values ofD(1/T) and Da

have been estimated from the curvesa = f(103/T) presentedin Fig. 4.

The values obtained forb are shown in Table 4 and othercharacteristic parameters were calculated for investigatedsamples.

It can be observed that the values ofb are lower thanunity.

Theb values smaller than one have been also reported forseveral inorganic (Se, PbSe, PbTe [32,33]) and organic(anthrancene, pyrene, methylciclohexane [6,34]) semicon-ductors.

For explanation of these results, Callen [35] has proposeda model based on band structure representation. Accordingto this model the conduction band of these materials consistsof two overlapping bands. The forbidden energy gapbetween the lower conduction band and valence band isDE. When the electrons are excited from the valence band

at smaller temperature, they occupy mainly the lower con-duction band in which their mobility is larger than that ofthe holes. As the temperature increases, the concentration ofelectrons excited into upper conduction band increases. Themobility in this upper conduction band is smaller than thatof the holes. Consequently, the ratio of carrier mobilities issmaller than one (b , 1) and the Seebeck coefficient of therespective material is positive.

For molecular crystals, Damask and Dienes [34] shownthat the values ofb smaller than one are in the reasonableagreement with band theory calculations [36,37].

Using the values ofni and b listed in Table 4 the holemobility was calculated according to the formula[23,24,32]:

mh =ji

ni × e(b+1)(6)

whereji denotes electrical conductivity in intrinsic domaincalculated from the dependence lnj = f(103/T).

Table 3

Values of some characteristic parameters* of investigated samples

Polymer Sample d (mm) DT (K) jc (Q−1cm−1) jT (Q−1cm−1) Tc (K) DE (eV)

P1 P1/05A 0.15 300–530 2.50× 10−8 3.75× 10−8 345 1.30P2 P2/21A 0.18 300–530 1.25× 10−9 5.16× 10−9 360 1.34P2 P2/21B 0.66 300–525 3.40× 10−9 7.56× 10−9 365 1.35P3 P3/24A 0.15 300–520 5.60× 10−8 8.34× 10−8 350 1.22P3 P3/24B 0.31 300–525 4.14× 10−8 8.4 × 10−8 345 1.23P4 P4/29A 0.21 300–520 1.12× 10−9 4.56× 10−9 365 142P4 P4/29B 0.48 300–520 2.52× 10−9 5.60× 10−9 365 1.40P5 P5/43A 0.24 300–525 1.25× 10−8 2.27× 10−8 360 1.48P5 P5/43B 0.27 300–525 5.62× 10−9 6.84× 10−9 355 1.50

*d, film thickness;DT, temperature range in which the heat treatment of the sample was performed;jc, electrical conductivity at room temperature beforeheat treatment;jT, electrical conductivity at room temperature after heat treatment;Tc, characteristic temperature for heat-treated sample;DE, activationenergy of electrical conduction.

Fig. 4. Temperature dependence of the Seebeck coefficient.

260 M. Rusu et al. / Thin Solid Films 326 (1998) 256–262

At temperatureT = 400 K, the calculated values of holemobility ranged between 10 and 50 cm2/Vs. These valuesare larger than common values for organic compounds[1,6].

The mechanism of electrical conduction in investigatedsamples cannot be easily explained. In general, the values ofcoefficients of transport phenomena strongly depend onsample morphology. The polyurethane-elastomer morphol-ogy is determined by variable hard segment (MDI/BD)concentration [38]. A lamellar, cylindrical or rod-like struc-ture has been observed in polyurethanes having a differenthard-segment weight fraction [39,40]. According to Cella[41], solid-state structure of segmented polyurethane elas-tomers can include crystalline domains and junctionsbetween crystalline lamellae and non-crystalline hard seg-ments. In thin films, the crystalline domains predominate.Heat treatment causes an increase in the number of suchdomains. The lamellae become larger and more ordered.Taking into account these structural characteristics, thetransport of charge carriers in the heat-treated thin filmsamples may be relieved. Consequently, the larger valuesof the carrier mobilities obtained in our paper may bejustified.

4. Conclusion

The synthesis of five new poly(ester-syloxane)urethaneelestomers were described and the temperature dependenceof the electrical conductivity (and Seebeck coefficient,a,for respective polymers were studied. The measurementshave been performed using the thin-film samples. Investi-gated polymers show typical semiconducting properties.The aspect of lnj = f(103/T) and a = f(103/T) curves canlead to the conclusion that the band-conduction model couldbe used as a ‘macroscopic’ model for explaining the carriertransfer mechanism through the investigated samples. Thevalues of some characteristic parameters (thermal activationenergy of electrical conduction, carrier concentrations, ratioof carrier mobilities) of studied polymers have been deter-mined based on these dependences. Some correlationsbetween semiconducting properties and molecular structureof the polymers are established.

References

[1] J. Mort, D.M. Pai, Electronic Properties of Polymers, Wiley Inter-science Publication, New York, 1982.

[2] J.L. Bredas, R.R. Chance (eds.), Conjugated Polymer Materials:Opportunities in Electronics, Optoelectronics and Molecular Electro-nics, Kluwer Academic Press, Dordrecht, 1990.

[3] D.E. Katon, Organic Semiconducting Polymers, Marcel Dekker,New York, 1968, p. 87.

[4] M. Kuzmani, M. Mehring, S. Roth (eds.), Electronic Propertiesof Polymers and Related Compounds, Springer-Verlag, Berlin, 1995.

[5] V.S. Malnikov, Fotoprovodimosti Polymerov, Izd. Himija, Sankt,Petersburg, 1990.

[6] F. Gutman, L.E. Lyons. Organic Semiconductors, Wiley, New York,1967.

[7] H. Laurs, G. Heiland, Thin Solid Films 149 (1987) 129.[8] K. Tanaka, S. Nishio, Y. Matsuura, T. Yamabe, J. Appl. Phys. 73

(10) (1993) 5017.[9] V.V.R. Narasimha Rao, T. Subba Rao, N. Narsing, Das. J. Phys.

Chem. Solids 47 (1) (1986) 33.[10] N. Venugopal Reddy, B. Subba Rao, V.V.R. Narasimha Rao, Mater.

Lett. 13 (1992) 147.[11] M. Spiratos, G.I. Rusu, A. Airinei, A. Ciobanu, Angew. Makromol.

Chem. 107 (1982) 33.[12] M. Spiratos, A. Airinei, G.I. Rusu, J. Macromol. Sci. Chem. A28

(1989) 1415.[13] G.I. Rusu, H. Oleinek, I. Zugra˘vescu, Macromol. Chem. 175 (1974)

1651.[14] Z.S. Petrovicˇ, J. Ferguson, Prog. Polym. Sci. 16 (1991) 695.[15] C. Hepbeke (ed.), Polyurethane Elastomers, Applied Science Pub-

lishers, London, 1978.[16] A. Stanciu, C. Ciobanu, G. Stoica, V. Bulacovschi, Bull. Inst. Poly-

teh. Iassy, XLI(XLV), 1–4, II, (1995) 107.[17] K.L. Chopra, Thin Film Phenomena, McGraw-Hill, New York, 1969,

p. 102.[18] G.I. Rusu, Appl. Surf. Sci. 65/66 (1993) 381.[19] M. Rusu, V. Sunel, I. Caplanus, C. Soldea, G.I. Rusu, Mol. Cryst.

Liq. Cryst. 289 (1996) 289.[20] V. Sunel, G.I. Rusu, G.G. Rusu, L. Leontie, C. S¸oldea, Prog. Org.

Coat. 26 (1995) 53.[21] V. Sunel, M. Rusu, I. Ca˘planus, G.I. Rusu, Appl. Surf. Sci. 65/66

(1993) 371.[22] Metody Izmerenija Kharakteristik Termoelektricheskih Materialov i

Preobrazovatelei, Izd. Nauka, Moskva, 1974.[23] G.I. Rusu, Semiconductori Organici, Ed. Tehnica˘, Bucures¸ti, 1982.[24] R. Smith, Semiconductors, Cambridge University Press, London,

1980.[25] A.A. Dulov, A.A. Slinkin, B.I. Liogonski, A.M. Rubinstein, Dokl.

Akad. Nauk SSSR 143 (1962) 1355.[26] A.A. Berlin, B.I. Liogonski, V.P. Parini, J. Polymer Sci. 55 (1961)

675.[27] R. Bonart, J. Macromol. Sci. Phys. B2 (1) (1968) 115.[28] R. Bonart, L. Morbitzer, G. Hentze, J. Macromol. Sci. Phys. B3 (2)

(1962) 337.[29] R. Bonart, Angew. Makromolek. Chem. 58/59 (1979) 259.[30] C.M. Vodenicharov, Phys. Stat. Sol. (a) 29 (1975) 223.[31] C.M. Vodenicharov, Phys. Stat. Sol. (a) 28 (1975) 263.[32] E.H. Putley, The Hall Effect and Semiconductor Physics, Dover

Publications, New York, 1960, p. 212, 237.[33] D.M. Fedik, M.A. Galushak, L.I. Mejilovskaya, Fizika i Technolo-

giya Poluprovodnikovih Plionok, Visha Shkola, Lvov, 1988.[34] A.C. Damask, G.J. Dienes, Comments Solid State Phys. 11 (1969)

64.[35] H.B. Callen, J. Chem. Phys. 22 (1954) 518.[36] L. Friedman, Phys. Rev. 133 (1964) A1668.[37] O.H. Le Blanc Jr., J. Chem. Phys. 39 (1963) 2395.

Table 4

Values of characteristic parameters* for investigated samples

Polymer Sample d (mm) me/m0 ni (cm−3) b

P1 P1/05C 0.55 0.85 1.93× 1011 0.95P2 P2/21C 0.52 0.90 1.20× 1011 0.95P3 P3/24C 0.68 0.82 3.73× 1010 0.90P4 P4/29C 0.48 0.90 5.00× 1010 0.85P5 P5/43C 0.73 0.93 1.25× 109 0.95

*d, film thickness;me, effective mass of charge carriers;m0, free electronmass;ni, carrier concentration atT = 400°K; b, ratio of carrier mobilities.

261M. Rusu et al. / Thin Solid Films 326 (1998) 256–262

[38] G. Oertel (ed.), Polyurethane Handbook, Hanser Publishers, Munich,1985.

[39] C. Li, S.L. Cooper, Polymer 31 (1990) 3.

[40] C. Li, C.L. Goodman, R.M. Albrecht, C.L. Cooper, Macromolecules21 (1988) 2367.

[41] J.R. Cella, J. Polym. Sci. 42 (1973) 727.

262 M. Rusu et al. / Thin Solid Films 326 (1998) 256–262