field effect transistors on graphitized polymer surfaces

Phys. Status Solidi B 248, No. 2, 299–308 (2011) / DOI 10.1002/pssb.201046455 p s sb

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eature Article

asic solid state physics

Field effect transistors on graphitizedpolymer surfaces

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Y. Koval*,1, I. Lazareva1, P. Muller1, K. Muller2, K. Henkel2, and D. Friedrich2

1 Department of Physics, Universitat Erlangen-Nurnberg, Erwin-Rommel-Straße 1, 91058 Erlangen, Germany2 Lehrstuhl Angewandte Physik/Sensorik, Brandenburgische Technische Universitat Cottbus, Konrad-Wachsmann-Allee 1,

03046 Cottbus, Germany

Received 29 April 2010, revised 9 August 2010, accepted 19 August 2010

Published online 5 October 2010

Dedicated to Dieter Schmeißer on the occasion of his 60th birthday

Keywords conductivity, field effect transistor, graphitization, ion irradiation, mobility, polymers

* Corresponding author: e-mail [email protected], Phone: þ49 9131 8527408, Fax: þ49 9131 15249

Conducting properties of several polymers after low-energy ion

irradiation were investigated. The enhancement of conductance

induced by the ions is discussed in terms of graphitization. Field

effect transistors (FET) on the graphitized polymer surfaces

were studied. We found that the field effect mobility depends

on the conductivity of the graphitized surfaces according to

the power relation s�m0.82. Such behavior is typical for

disordered organic semiconductors with a variable range

hopping mechanism of conductance. In contrast, the graphitized

surfaces with a semimetallic type of conductance demonstrate a

high carrier mobility �1 cm2/Vs, which is almost independent

on the conductance. These semimetallic materials consist of

2 and 3 nm graphene patches and are characterized by a

significantly smaller disorder level. However, for a feasible

FET application the carrier concentration in the graphitized

surfaces must be reduced. Possibilities to improve the perform-

ance of the FETs are discussed.

� 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction During the last decades the demand toreplace traditional silicon-based semiconductor devices bylow-cost electronic components is permanently growing.Organic semiconductors as a possible alternative to siliconattracted a huge attention. However, in spite of a seriousprogress reached in the field of organic electronics, thedevice performance, and reliability, especially in ambientconditions, still have to be improved to be commerciallysuccessful. Another direction of an alternative electronicswas discovered since the first publication of fascinatingproperties of graphene [1]. A single layer of graphite with aremarkably high electron mobility at room temperature ofthe order of 15,000 cm2/Vs opens a lot of possibilities forfuture carbon based electronics.

In this article we discuss a perspective, which issomewhere in between organic semiconductors and gra-phene. These materials are graphitized polymers. Consistingmostly of carbon atoms, the graphitized polymers candemonstrate substantially different properties, which dependon the type of chemical bonds, microscopic structure,presence of long-range order, and many others. It is well

established that graphitization of polymers can be achievedby ion irradiation. High-energy ion implantation [2, 3] orlow-energy ion irradiation [4, 5] can convert differentpolymers into a carbon-rich material with disordered carbonclusters rich in p-conjugated bonds. Initially insulatingpolymers with room temperature conductivities smaller than10�15 S/cm demonstrate a substantial conductance after ionbombardment. Depending on the parameters of irradiation,the graphitized polymers can show different conductivitiesup to 200 S/cm [3, 5, 6]. The mechanism of conductance canbe changed from a variable range hopping (VRH) for lowconducting samples to a semi-metallic type of conductancefor highly conducting samples [3, 5, 6]. The last is typical fordisordered graphite.

High- or low-energy ion irradiation leads to similargraphitization results. However, low-energy ions (�1 keV)transform to a conducting state only a thin surface layer ofpolymers [4, 5, 7, 8]. This surface layer can be used for thechannel of thin film field effect transistors (FET). A seriousadvantage of graphtized polymers is their stability insolvents and to, e.g., electron irradiation. It allows to use in


300 Y. Koval et al.: Field effect transistors on graphitized polymer surfacesp

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device preparation standard microelectronics technologies(e.g., lithography) without any limitations [5, 8, 9].

Operation of FETs on polymers irradiated by ions wasrecently demonstrated for polymethylmethacrylate(PMMA) [10], and polyimide (PI) [8]. These first resultsshow that the characteristics of the FETs on graphitizedpolymers are rather similar to thin film transistors withorganic semiconductors. However, a systematic study ofcarrier concentration and mobility in the graphitizedpolymers is still missing. In this work we present our dataon electrical properties of the graphitized surfaces and theinfluence of the gate on their properties.

2 Experimental details Experiments were carriedout with five different polymers: polymethylmethacrylate,polyimide, nylon, novolak, and polyethylene terephthalate(PET). The chemical structure of these polymers is shown inFig. 1. A solution of PMMA with molecular weight of 950 Kin chlorobenzene (supplied by All Resist GmbH) was used toobtain PMMA films. For PI films, we used solutions ofpyromellitic dianhydride co-4,40-oxydianiline from Sigma–Aldrich. For novolak, we used a conventional photoresistAZ5214e from Microchemicals GmbH. This photoresistcontains some amount of light sensitive components, whichwe believe do not contribute significantly to our results.Nylon 6 in pellets was supplied by Sigma–Aldrich. PET foilswere supplied by Leonhard Kurz GmbH. Sapphire sub-strates, which are known to show no conductivity after low-energy ion bombardment, were used. PMMA, PI, andAZ5214e were spun to the substrate from the liquid

Figure 1 Chemical structure of (a) PMMA, (b) novolak, (c) PI,(d) nylon, and (e) PET.


solutions, whereas nylon and PET were deposited byimmersion of the substrates into a melt. After coating, thesamples with PMMA, AZ5214, nylon, and PET were bakedon a conventional hot plate at 170, 110, 130, and 120 8C for 5,1, 5, and 5 min, respectively. PI samples were baked invacuum at 380 8C for 2 h to complete the reaction ofimidization.

The thickness of the films was between 300 and 1000 nm.Ion irradiation was performed in a setup for ion-beametching equipped with a Kaufman-type ion gun. All of ourexperiments were carried out with Arþ ions with energiesfrom 200 to 1500 eV. The dose of irradiation was between5� 1016 and 1018 ions/cm2. Beam current density was0.5 mA/cm2 resulting in irradiation times of less than10 min. During ion bombardment, the temperature of thesamples was maintained at a constant level between �150and 400 8C.

In-plane conductance was measured on bar-shapedstructures. The bars were prepared using different tech-niques. Several samples were patterned by reactive oxygenetching of the polymer films masked by a narrow piece of Sipressed against the films. Novolak films were patterned bystandard UV lithography. PI bars were prepared by oxygenplasma etching via a negative electron resist mask, whichwas obtained by a standard e-beam lithography technique.After ion irradiation, the contacts to the bars were depositedby thermal evaporation of Cr through a shadow mask.

Polyimide was used both for transport measurements andinvestigation of electric field effects. In order to reduce thedistance between electrodes the contacts to the bars wereproduced by electron-beam lithography, thermal evapor-ation of Cr/Au, and lift-off. The last technique allows todecrease the distance between the electrodes to 1–5mm. Atypical polymer structure with contacts for 4-point measure-ments is shown in Fig. 2e.

Field effect transistors we prepared in top-gate geome-try. Two different gate insulators were used: PI andpoly(vinylidene fluoride/trifluoroethylene) [P(VDF–TrFE)]. The last material is a ferroelectric polymer, whichallows to reach a significantly higher field effect. In the caseof PI insulator, a thin �0.5–1mm PI film was deposited byspin coating on the bar with contacts similar to the one shownin Fig. 2e. After baking with parameters described above forPI films, the gate electrodes were prepared by electron-beamlithography, thermal evaporation of Ag and lift-off.

The second type of FET structure with [P(VDF–TrFE)]gate insulator was prepared as described below. The[P(VDF–TrFE)] layer was spin-coated on the PI bar withcontacts from a specially prepared solution of [P(VDF–TrFE)] 70:30 (Solvey Solexis, Inc.). [P(VDF–TrFE)]powder of 1.35 g was dissolved in 15 ml of 2-butanone.Then the obtained solution was mixed with methoxypropy-lacetate (AZ EBR solvent) in a ratio of 1:2. The thickness of asingle spin-coated layer was �60 nm. To obtain thickerlayers, spin coating was performed several times withintermediate baking on a hot plate at 140 8C for 3 min. Afterthe last coating, the samples were baked at 140 8C for 2 h for

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Figure 2 (online color at: www.pss-b.com) Preparation of agraphitized polymer bar with contacts: (a) polymer film deposition;(b) bar patterning; (c) ion irradiation; (d) Cr/Au contact deposition;and (e) SEM micrograph of a structure ready for transportmeasurements.

improving the crystal structure of [P(VDF–TrFE)] film [11].In the next step, a film of Ag was deposited, and the gateelectrodes were patterned by electron-beam lithography andion-beam etching. Schematically, the preparation steps and aSEM micrograph of typical FET structure are shown inFig. 3.

Figure 3 (online color at: www.pss-b.com) Schematic view ofa PI transistor structure: (a) deposition of the gate insulator;(b) preparation of the top gate electrode; (c) SEM micrograph ofthe FET structure ready for measurements.

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Transport measurements were carried out with aKeithley 6517A electrometer and Keithley 6431 SourceMeter. A Source-Meter Keithley 238 was used for the gatevoltage.

3 Graphitization of polymer surfaces by low-energy ion irradiation After ion irradiation all polymersdemonstrate a substantial enhancement of conductance. Theconductance increases with the energy of ions Eion and thetemperature of the samples during ion irradiation Tirr. TheRT sheet conductance of all measured samples is shown inFig. 4. We found that the parameters of ion irradiation Eion

and Tirr can be combined into one universal variableC¼ TirrþaEion, where a is a parameter. If the irradiationtemperature Tirr is in 8C and the ion energies Eion have unitsof eV’s, all points collapse into one curve with the parametera¼ 0.22 [5]. By changing the energy of ions and thetemperature of irradiation the conductance was varied bynearly 10 orders of magnitude up to >2� 10�4 S. It isremarkable that we observed no influence of the chemicalstructure of the pristine polymers onto their conductanceafter ion irradiation.

The temperature dependence of conductance for theirradiated PMMA, PI, nylon, and novolak was measuredbetween RT and 4.2 K. The conductance of all samplesdecreases with cooling. However, the samples with higherconductance at RT show a substantially weaker s(T)dependence. In Fig. 5 we show the conductance versustemperature plots for 5 PI samples irradiated at differenttemperatures. We found that the temperature dependence ofconductance of the samples with an RT sheet conductancesmaller than �10�5 S follows an exponential law

Figusheeiablin 8C

s ¼ s0exp �ðT0=TÞxð Þ: (1)

The stretched exponent (1) is a signature of a VRHmechanism of conductance observed in different materialsincluding organic semiconductors [12, 13]. The power x is

re 4 (online color at: www.pss-b.com) Room temperaturet conductance of irradiated polymers versus the universal var-

e C¼ Tirrþ 0.22Eion, where Tirr is the irradiation temperatureand Eion is the ion energy in eV.



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Figure 5 (online color at: www.pss-b.com) Temperature depend-ence of conductance of PI irradiated with 1018 Arþ ions/cm2 at 1 keVand different irradiation temperatures. The arrows show the mech-anism of conductance of the corresponding samples. The sampleswith the highest conductance show semi-metallic behavior. On theright-hand side we show our interpretation of the conductancemechanism.

equal to ½ for the samples irradiated in conditions when thevariable C is smaller than �380. At higher values of C thepower x changes non-monotonically from 1/2 to >1/2 andthen to �1/4. We interpret our result as a transition from theCoulomb gap VRH regime to Mott’s VRH via anintermediate regime with x> 1/2. The last regime was alsoobserved in different systems. For example, a power of 0.74was found for ion implanted p-phenylenebenzobisoxazole[6], x¼ 0.75 was observed for ultrathin quench-condensedmetal films [14]. Here we emphasize that the power>1/2 wasobserved as an intermediate power between Coulomb gapGVRH and Mott’s VRH. The high conducting samples(C> 550, sRT> 10�5 S) show a semi-metallic behavior:their s(T) is weaker than exponential at least at temperaturesabove 4.2 K. For comparison with literature data theconductivity of the graphitized layers can be estimatedassuming the thickness of the conducting layer to be�10 nm.Apparently, this value is overestimated [4, 5, 7], whichmeans that the conductivity of the semimetallic samples is atleast 200 S/cm (see Fig. 4).

4 Analysis of graphitization processes Enhance-ment of polymer conductance after ion irradiation is awell-known phenomenon studied in details for the case ofhigh-energy ion implantation (see, e.g., review [2] andreferences therein). Comparing the conducting properties ofour samples with literature data of ion implanted polymers,we conclude that, independent on the ion energy, thegraphitization processes under ion irradiation are similar.For example, the polymers modified by ion implantationalso follow the Coulomb gap VRH law of conductance forlow-conducting samples and show a semi-metallic behaviorfor highly conducting samples [3]. However, differentconductances for high-energy ions are achieved by thechange of the fluence of implantation. This is different fromlow-energy ions where the energy of ions and thetemperature of irradiation are also important parameters.


During high-energy ion irradiation the chemical struc-ture of polymers is gradually destroyed with ion fluencemostly due to inelastic collisions of ions with polymer atoms.Small volatile molecules of CO, H2, CHx, and others areproduced as a result of destruction [2], diffuse to the surface,and desorb. The polymers convert to carbon-rich materialwith disordered carbon clusters rich in p-conjugated bonds.Transport in the modified polymers takes place by hoppingbetween carbon clusters. Typically, the conductance obeys aCoulomb gap VRH law (1) with x¼ 1/2 up to at least RT [3,15, 16]. Polymers after ion implantation are characterized bya high concentration of unpaired spins (>1020 cm�3) [3].Similar to amorphous a-C:H films, high spin concentrationcan be attributed to subnanometer size sp2 clusters [17].

As it was shown in Refs. [3, 6], at high fluences ofimplantation the conductance has a weak temperaturedependence, and the material is approaching properties ofdisordered graphite. Highly conducting samples are charac-terized by a high carrier concentration [18]. This is attributedto growth of p-conjugated islands, which can overlapproviding conduction without tunneling.

Low-energy ion irradiation provides modification ofonly a thin surface layer [4, 5, 7]. Similar to ion implantation,in the early stages of irradiation a lot of gaseous products areformed. As a consequence, in the early stages, the etchingrate of polymers is rather high [19]. At higher irradiationfluences, a thin carbonized layer is formed on the surface ofpolymers. The thickness of this layer is of the order of thepenetration depth of the ions. This carbonized surface layer isbeing permanently sputtered, and, in contrast to ionimplantation, the depth of sputtering is comparable withthe penetration depth of ions. Increasing the fluence ofirradiation further, a steady-state regime of etching isachieved. In this state the surface layer is permanentlysputtered, and ions penetrate deeper into the polymerunderneath the carbonized layer. There, ions invoke thedestruction processes, which results in growth of thecarbonized layer from beneath of the surface. Formation ofthe carbonized layer under low-energy ion irradiation wasrecently simulated by molecular dynamics [20]. The authorsshowed that the surface of different polymers can becarbonized and the carbonized layer in the steady-stateregime does not change preserving its properties indepen-dently on the ion fluence.

This is an important difference to ion implantation,where the ions penetrate so deep that decrease of the filmthickness due to sputtering can be neglected. For ionimplantation the increase of the ion fluence always leads toaccumulation of the radiation induced changes. By low-energy ions, the sputtering rate of the carbonized surfacelayer limits the density of the energy, which ions can depositinto the surface layer. Influence of the sputtering on thedistribution of the deposited energy in the surface layer wasdiscussed in Ref. [4]. It was shown that in the steady-stateregime the maximum of the deposited energy lies on thesurface and can be estimated by a simple formulam¼ j�Eion/n, where j is the ion flux, and n is the sputtering

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Figure 6 (online color at: www.pss-b.com) Scanning tunnelingmicroscopy images of PI films after ion irradiation. Parameters ofArþ irradiation: energy: 1000 eV, irradiation temperature: 350 8C,and dose: 1018 cm�2. (a) 9� 9 nm2 image of several islands with aregular atomic structure; (b) 3� 3 nm2 image of one of these islands;(c) the same as (b), but with an overlay of graphite lattice; and(d) Fourier transform of image (b).

rate of the carbonized layer. Estimation of the total density ofthe deposited energy including the energy losses in elasticand inelastic collisions gives the value �4� 104 eV/nm3,which only slightly depends on the energy of ions. Thesteady-state regime is achieved at fluences of the order of1017 ion/cm2. In our experiments the fluences of ionirradiation varied for different samples between 5� 1016

and 1018 ion/cm2, and we did not observe any influence of theirradiation dose on the conducting properties of polymers. Itconfirms that the steady-state regime of polymer etching wasachieved for all our samples.

The next important difference of low-energy ionirradiation with high-energy ion implantation is a contri-bution of elastic and inelastic collisions in the deposited byions energy. In ion implantation, electronic losses dominate,and above a threshold value of 14 eV/nm, ions effectivelygraphitize polymers [3]. In low-energy ion irradiationelectronic stopping power of Arþ in carbon is higher thanthis threshold value and is equal to �32 eV/nm for 250 eV,and �79 eV/nm for 1500 eV ions. However, the ions losetheir energy mostly in nuclear interactions, and contributionof elastic interactions to the destruction of polymer structurecannot be neglected. A simple estimation shows that eachatom suffers at least 10 displacements from its positionbefore being sputtered.

This means that the destruction of polymer structure inthe surface layer is provided mostly by elastic displacementsof atoms. However, the final structure of the surface layer isstrongly determined by processes leading to bonding of thedisplaced atoms. Comelli et al. [21] showed that differentamorphous a-C and a-C:H films after Arþ irradiation create atwo phase structure consisting of a graphite-like network anda random matrix. The graphite-like regions contain con-jugated odd- and even-membered rings without long-rangeorder. These regions can play the role of a precursor of thebigger area graphite/graphene patches.

In our experiments, higher temperature of the samplesduring ion irradiation causes enhancement of the displacedcarbon atoms mobility. These atoms have better chances tojoin the graphite-like regions leading to the growth ofnanometer area graphite/graphene islands. Indeed, recently,we proved the formation of 1–3 nm regular regions, whichhave the structure of graphite. Typical scanning tunnelingmicroscopy micrographs of the highly conducting graphi-tized PI surface are presented in Fig. 6. The measurementswere performed in a constant current mode. A peak-to-peakheight amplitude is near 0.9 nm for the largest area image(Fig. 6a). On the larger scale 1� 1mm2 the roughness ischaracterized by 3–5 nm peak-to-peak amplitude.

Analogously to the effect of higher irradiation tempera-ture Tirr, the increase of the energy of Ar ions leads to higherconcentration of phonons in the cascade, which can beconsidered as the equivalent of local heating. Growth of thegraphite/graphene patches with the energy of ions andthe temperature of irradiation qualitatively explain theincrease of conductance and the transition from hopping tosemi-metallic conductance.

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The transition from VRH to semi-metallic conductancecan be interpreted as it is shown in Fig. 5. In thelow-conducting samples the graphitic structures are verysmall and have a high charging energy. They are separatedby the random matrix of carbon atoms, and the conductancetakes place by tunneling between the graphitic islands.The high charging energy suppress the density of statesaround the Fermi energy leading to Coulomb gap VRH. Inthe higher conducting surfaces the size of the graphiticislands increases leading to the Mott’s VRH, when thedensity of states is not influenced by charging. Theislands are still separated by the random matrix, andelectrons still tunnel between them. When the graphiticislands overlap so strongly that the current can flow throughthe sample without tunneling, we observe the semimetalstate.

5 NEXAFS study of the graphitized polyimidesurfaces The graphitization of PI by low-energy ionirradiation was investigated by Near Edge X-rayAbsorption Fine Structure (NEXAFS). The experimentswere done at the U49/2-PGM2 beam line at BESSY II, usingTEY (total electron yield) and TFY (total fluorescence yield)detection. Recording spectra around C1s, O1s, and N1sedges we detected substantial changes for the C1s and theN1s edge. The TFY and TEY spectra at the C1s edge beforeand after the Arþ modification at different temperatures areshown in Fig. 7a and b, respectively. Spectra of puregraphitic carbon and PI data taken from literature [22] areadditionally shown in these diagrams.



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Figure 7 C1s TFY (a) and TEY (b) signals of PI samples, before(Ref.) and after modification by Argon at room temperature (RT),350 8C, and 400 8C. Reference data taken from a graphite sample andfrom literature [22] are shown, too.

Figure 8 (online color at: www.pss-b.com) A series of Id–s curvesversusgatevoltageUg atdifferent temperatures forPI irradiatedwithArþ ions. Parameters of irradiation: (a) 1000 eV, RT, normalincidence; (b) 1000 eV, 390 8C, grazing angle 58 for the samplesTR05 and TR06, respectively. The arrows point to the minimum ofthe conductance. With decreasing temperature, the minimum shiftstoward Ug¼ 0.

The doublet peak at around 285 eV and the peak at289.4 eV are assigned to the p� resonance (C––C) of thePDMA (pyromellitimido) and ODA (oxydianiline) aromaticrings. The peak at 286.5 eV correspond to the C–N bondageof the aromatic ring of the ODA part of the PI molecule,while the sharp peak at 287.4 eV is attributed to the C––Obond. We observe that in the more bulk sensitive TFY mode(Fig. 7a) the emission characteristic of PI is maintained andthe difference to the graphite absorption spectra is visible. Inthe TEY spectra (Fig. 7b) of the not treated sample (indicatedas ‘‘Ref.’’ in Fig. 7) we observe all the peaks which occur alsoin the TFY spectra. When the temperature of the sampleduring Arþ irradiation is increased, the peaks associated tothe C–N and C––O bonds disappear.

This is consistent with the graphitization of the surfaceupon Arþ bombardment. We identify the characteristicabsorption band of graphitic carbon. The band is muchbroader in comparison with graphite, pointing to a strongdisorder in the graphitized films. Our spectra demonstratethat the graphitization is starting at around 300 8C. Thedifference is visible in particular for the more surfacesensitive TEY mode, because only the surface is graphitized.

6 Field effect transistors with polyimide gateinsulators The basic geometry of the FET structure isshown in Fig. 3 The distance between source and drainelectrodes was approximately 5mm. The width of thechannel was 5–10mm. We used PI films of 0.5 and 1mmthickness for the gate insulator. The area capacitance of thegate was 4.4 and 2.2� 10�9 F/cm2, correspondingly. Thegate voltage varied in the range � 80 V. The maximumsurface charge density induced by the gate voltage was 1–2� 10�12 cm�2. The current between the gate and the sourcewas controlled during FET operation. The leakage currentwas always significantly smaller than source–drain currentand never exceeded 1 pA. Later we will show that theinduced charge density is rather small compared to thecarrier density in the graphtized films. This explains a limitedinfluence of the gate voltage on the channel conductance,especially for highly conducting samples.

The FETs were operated in non-saturated regime whenthe voltage applied between source and drain was below�10 V, which is smaller than the gate voltage by one order


of magnitude. The dependence of Is–d versus the gate voltageUg for two samples are presented in Fig. 8. The graphitizationwas produced by Arþ irradiation with parametersEion¼ 1000 eV, Tirr¼ 20 8C for sample TR05, andEion¼ 1000 eV, Tirr¼ 390 8C for sample TR06. The lastsample was irradiated at a grazing angle �58. We show Is–d

(Ug) dependencies measured at different temperatures.The source–drain current is normalized by Is–d(Ug¼ 0).The temperature dependence of conductance s at Ug¼ 0for the corresponding samples is shown in Fig. 9.Both samples follow an exponential dependence (1).For the low-conducting sample TR05 the power is x¼ 1/2,which we attribute to Coulomb gap VRH. The higherconducting sample TR06 shows an intermediate powerof x¼ 0.85.

Is–d(Ug) measured at room temperature shows a typicalbehavior for p-type channel: at the negative Ug theconductance increases and at positive Ug the conductancedecreases. However, at lower temperatures, it becomesobvious that the FETs demonstrate ambipolar behavior. Theminimum of the channel conductance shifts to lower Ug, andat low enough temperature the minimum of conductance isobserved at Ug¼ 0.

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Figure 9 (online color at: www.pss-b.com) Conductance versustemperature for two PI samples: (a) TR05; (b) TR06. For parametersof ion irradiation see Fig. 8.

Figure 10 (onlinecolorat:www.pss-b.com)Temperaturedepend-ence of the field effect mobility of three PI samples. TR04 wasirradiated by 1250 eV Arþ ions at 380 8C at normal incidence. Forparameters of irradiation of the samples TR05 and TR06 see Fig. 8.

For the non-saturated regime the source–drain currentcan be analyzed by the formula [23]

www

Is-d ¼ �mciW

LðUg�UthÞUs�d�

U2s�d

2

� �;

where ci is the insulator capacitance per unit area, Uth thethreshold voltage, m the mobility of charge carriers, and Wand L are the width and the length of the channel,respectively. The transconductance is

gm ¼ @Is�d

@Ug

:

Then the field effect mobility as a function of gate bias is

m ¼ gmd

ere0Us�d

L

W;

where er and d are permitivity and thickness of the gateinsulator, respectively.

The field effect mobilities were determined at negativeUg for four different samples. We plot them versus 1/T inFig. 10. The mobility of the semi-metallic sample TR07 isalmost temperature independent. The lower conductingsamples demonstrate a thermally activated behavior andfollow the Arrhenius equation. As an exception, in the hightemperature region the higher conducting sample TR06shows a deviation from the activation behavior: the field

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effect mobility is nearly temperature independent similar tothe semi-metallic sample.

The activation energies Eam for the mobilities deter-mined from the slopes of m(1/T) curves are: �170, 94, and19 meV for TR04, TR05, and TR06, respectively. The fieldeffect mobility and conductance of the samples obeydifferent temperature dependencies. Indeed, the low-con-ducting samples TR04 and TR05 show Coulomb gap VRH(1) with x¼ 1/2 (see, e.g., Fig. 9a). The higher conductingsample TR06 follows the law (1) with x¼ 0.85 (Fig. 9b).That is, the activation energy of conductance is temperaturedependent in contrast to the activation energy of themobility, which does not change with temperature. Arational conclusion would be that the strong deviation fromthe Arrhenius law points to a significant contribution of someadditional parameters on the conductance except of thecarrier mobility.

The activation energies of conductance Eas found fromthe plots s(1/T) for 200 K are: 250, 130, and 28 meV forTR04, TR05, and TR06, respectively. It can be clearly seenthat Eas is systematically higher than Eam. We think that themain reason for the observed difference in the activationenergies is the temperature dependence of the carrierconcentration. On the other hand, the contribution of themobility to the conductance is dominating for these samplesbecause Eam is always near 70% of the Eas.

The semi-metallic sample deserves a special discussion.Firstly, the mobility in this case is temperature independentbetween 300 and 4.2 K. It means that in this sample theconductance exclusively depends on the carrier concen-tration, but not on the mobility as for the samples TR04-05.Secondly, the calculated absolute values of the field effectmobility are smaller than the values of m for the lowerconducting sample TR06 at high temperatures. We supposethat in the semi-metallic sample the carrier concentration isso high that the carriers effectively screen the electric field ofthe gate. In this case, the gate can change conductance only inthe very top part of the graphitized film close to the gateelectrode. The lower part of the graphitized film is not



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Figure 12 (online color at: www.pss-b.com) Id–s (red curve)and Ig–s (black curve) versus gate voltage Ug of the FET with[P(VDF–TrFE)] gate insulator. The arrows show the changeof Id–s and Ig–s depending on the direction of the Ug sweep. Thevoltage between the drain and source was Ud–s¼ 5 V.

influenced by the gate. As a consequence, the field effectmobility is strongly underestimated. In order to check themobility independently, we performed the Hall effectmeasurements. Indeed, we found that the Hall mobility is�1 cm2/Vs, which is even a little higher than the mobility inthe sample TR06.

7 Field effect transistors with [P(VDF–TRFE)]gate insulators The second polymer used for the gateinsulator was [P(VDF–TrFE)]. It is a ferroelectric material,which can be used, e.g., in ferroelectric FETs for non-volatilememory applications. Operation of FETs with [P(VDF–TrFE)] was recently demonstrated in several publications[24, 25]. Polarization of [P(VDF–TrFE)] can reach a value of8mC/cm2, which corresponds to �5� 1013 cm�2. Thissurface charge density is more than one order of magnitudehigher than the one we obtained with the PI gate insulator.

The polarization curve and current–voltage character-istic of a capacitor with [P(VDF–TrFE)] insulating layer of�0.75mm thickness are presented in Fig. 11. The peaks inthe current–voltage characteristic correspond to the changeof polarization direction. The coercive electric field of[P(VDF–TrFE)] is �0.4 MV/cm. The change of polarizationinduces a strong response in FET structures. In Fig. 12 wepresent a typical dependence of Is–d versusUg for graphitizedPI. The measurements were done at room temperature. Thegate voltage was changed according to the arrows in theplots. The current–voltage characteristic of the capacitorformed by the gate electrode and the channel of the FET isalso shown for comparison. These two curves confirm thatthe response of Is–d is the consequence of the polarizationchange in the [P(VDF–TrFE)] insulator. The FET demon-strates a clear hysteresis caused by the persistent polarizationin the [P(VDF–TrFE)] layer. If the gate voltage is well belowthe coercive voltage, the [P(VDF–TrFE)] layer can beconsidered as an insulator with er� 7. Operating the FeFETsat Ug below the coercive field we determined the field effectmobility for three different samples. The measurements were

Figure 11 (online color at: www.pss-b.com) Polarization curve(red) and current–voltage characteristic (black curve) of a capacitorwith [P(VDF–TrFE)] insulator. The current–voltage characteristicand the polarization curves correspond to the right and left axes,respectively.


performed at different temperatures similar to the FETs withthe PI gate insulator (see Section 6).

All mobilities obtained from the samples with PI and[P(VDF–TrFE)] insulator at different temperatures areshown in Fig. 13. We plot the mobilities versus sheetconductance of the samples at the corresponding tempera-tures. Apparently, all points collapse to the same curveindependently on the sample conductance and temperature.The dependence of the field effect mobility versusconductance follows the power law

Figucondgateonly

m � s0:82: (2)

The power law of mobility versus conductivity is wellknown in the literature. Several disordered organic semi-conductors demonstrate a similar behavior. The power 0.82found for the graphitized PI is rather close to the power 0.76reported previously for the different amorphous organicsemiconductors [26]. The conductance of the organic

re 13 (onlinecolorat:www.pss-b.com)MobilityversusSheetuctance for all transistor structures with PI and [P(VDF–TrFE)]insulator. The solid line is a linear fit to the data. In the fit,the data with s< 10�6 S were used.

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semiconductors was changed by doping. Here we show thatthe power law (2) is more universal. It holds independentlyon the way the conductance of the samples was changed: bydoping or by changing the temperature. Moreover, the typeof hopping does not influence the validity of the relation (2).For example, the Mott’s VRH was analyzed in Ref. [27]. Wefound the Coulomb gap VRH and hopping with x> 1/2. In allcases the rule (2) is fulfilled with rather high accuracy. Onlythe sample with semimetallic type of conductance (e.g.,highly conducting sample TR07) shows a strong deviationfrom (2). For semimetals, tunneling between the conductingclusters is not limiting the transport. The mobility isdetermined mostly by scattering on defects. This explains anearly temperature independent field effect mobility for thesemi-metallic sample. Using the general relation s¼ enmand the mobility data obtained earlier we calculated thecarrier concentration n. The surface area concentration wasdefined as N¼ n2/3. The dependence N versus sheetconductance s is presented in Fig. 14. The area concentrationalways increases with conductance. However, for the lowconducting surfaces this change is rather small in compari-son to the mobility change. On the contrary, the highconducting samples show that the conductance is mostly afunction of the carrier concentration.

Carrier concentrations of the graphitized PI surfaces arehigher than 1012 cm�2 (see Fig. 14). In Section 6 wecalculated the maximum surface carrier concentrationinduced by the gate voltage, which is also of the order of1012 cm�2. This explains the small ON/OFF ratio of the FETswith PI gate insulator. The expected surface charge density inthe ferroelectric FETs with [P(VDF–TrFE)] insulator was�5� 1013 cm�2 atUg higher than the coercive voltage of the[P(VDF–TrFE)] film. According to the data in Fig. 14 such ahigh density of carriers should change the conductance of thechannel by several orders of magnitude. However, theobserved response was significantly weaker and has to beexplained.

In our estimation of the surface charge density inpolarized [P(VDF–TrFE)] film we relied on the highestpossible value �5� 1013 cm�2. However, recently it wasfound that the polarization of [P(VDF–TrFE)] in capacitors

Figure 14 (online color at: www.pss-b.com) Carrier concentra-tion versus conductivity for all transistor structures.

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and FeFETs is strongly reduced in the interface region. Wediscussed this effect in details in Ref. [8]. It was shown thatthe surface charge of the ferroelectric layer is screened by thecharge carriers injected into the subsurface layer of [P(VDF–TrFE)]. Due to this effect, which is often called the imprinteffect, ferroelectric properties in the interface regionbetween the [P(VDF–TrFE)] layer and gate/channel arecorrupted. The imprint effect reduces the surface density ofpolarization charges leading to a significantly weakerresponse of the FeFETs than expected. On the contrary,operated at Ug below the coercive voltage, the FETs with[P(VDF–TrFE)] insulator show results similar to the PIinsulator.

The relation (2) between carrier mobility and conduc-tivity in the FETs with graphitized PI rises a question typicalfor the device performance of disordered semiconductors.High mobilities are required to achieve reasonable switchingspeeds in logic circuits. By increasing the conductance,higher mobilities can be achieved. Then, however, the highcarrier concentration limits the ON/OFF ratio of FETs.

This dilemma can be resolved by using materials, whoseconductance is not limited by hopping. The semi-metallicbehavior found in the highly conducting graphitizedsurfaces is characterized by high mobilities. It is interestingto note that the mobility does not strongly depend on theconductance any more (see Fig. 13). The material consistsof 2 and 3 nm graphene patches as we showed by STM(see Fig. 6). The defects in these patches cause a highconcentration of carriers and lead to a strong carrierscattering. Increasing the size of the patches anddecreasing the number of defects, one can considerablyimprove the properties of the graphitized polymers for FETchannels.

8 Conclusions We showed that by low-energy ionirradiation the surface of different insulating polymers can begraphitized. The graphitization leads to a substantialconductance of the surface, which can reach 200 S/cm. Theconductivity increases with the energy of ions Eion and thesample temperature during irradiation Tirr. A universalscaling law between conductivity and irradiation parameterswas found. It was observed that the conductivity at roomtemperature and the mechanism of conductivity are stronglycorrelated. Less conducting samples show VRH conduc-tivity. Highly conducting surfaces demonstrate a semi-metallic behavior. Semi-metallic layers can be obtained atrather modest ion energy (�1000 eV) and irradiationtemperature Tirr (<400 8C). Under these conditions, thesurface of the polymers is transformed to a graphitized state:it consists of overlapping graphite islands with a diameter of1–3 nm.

The irradiated PI was used for the channel of field effecttransistor structures. Two different gate insulators were used:PI and the ferroelectric polymer [P(VDF–TrFE)]. Fieldeffect mobilities were determined. We found that themobility depends on the conductivity according to the powerrelation m� sy well known for organic semiconductors.



hys

ica ssp st

atu

s

solid

i b

We also showed that this universal relation holds indepen-dently on the way the conductance of the samples waschanged: by temperature, or by using different parameters ofirradiation. The power y¼ 0.82 obtained in our experimentsis rather close to the power of 0.76 found previously fororganic semiconductors.

For higher conductance the power relation between themobility and conductivity does not hold. In the semi-metallicregime the mobility can reach 1 cm2/Vs and does not dependon conductance. However, the carrier concentration is stilltoo high for feasible applications. To improve the perform-ance of the FETs with graphitized polymers, the size of thegraphene patches and the number of defects in the patchesmust be significantly improved.

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field effect transistors on graphitized polymer surfaces

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