Suppression of Low-Frequency Electronic Noise in Polymer Nanowire

Oct 19, 2015 - Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, via Arnesano, I-73100 Lecce, Italy. ‡ Center for Biomole...
0 downloads 9 Views 3MB Size
Download PDF
Letter pubs.acs.org/NanoLett

Suppression of Low-Frequency Electronic Noise in Polymer Nanowire Field-Effect Transistors Francesca Lezzi,†,‡ Giorgio Ferrari,§ Cecilia Pennetta,†,⊥ and Dario Pisignano*,†,‡,¶ †

Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, via Arnesano, I-73100 Lecce, Italy Center for Biomolecular Nanotechnologies at UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano (LE), Italy § Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Via Colombo 81, I-20133 Milano, Italy ⊥ Istituto Nazionale di Fisica Nucleare (INFN), Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy ¶ Istituto Nanoscienze-CNR, Euromediterranean Center for Nanomaterial Modelling and Technology (ECMT), via Arnesano, I-73100 Lecce, Italy ‡

S Supporting Information *

ABSTRACT: The authors report on the reduction of lowfrequency noise in semiconductor polymer nanowires with respect to thin-films made of the same organic material. Flicker noise is experimentally investigated in polymer nanowires in the range of 10−105 Hz by means of field-effect transistor architectures. The noise in the devices is well described by the Hooge empirical model and exhibits an average Hooge constant, which describes the current power spectral density of fluctuations, suppressed by 1−2 orders of magnitude compared to thin-film devices. To explain the Hooge constant reduction, a resistor network model is developed, in which the organic semiconducting nanostructures or films are depicted through a two-dimensional network of resistors with a square-lattice structure, accounting for the different anisotropy and degree of structural disorder of the active nanowires and films. Results from modeling agree well with experimental findings. These results support enhanced structural order through size-confinement in organic nanostructures as effective route to improve the noise performance in polymer electronic devices. KEYWORDS: Polymer nanowires, soft nanolithography, field-effect transistors, low-frequency noise, noise in nanostructures

M

transistors (OFETs) based on conductive polymer nanowires for frequencies in the range of 10−105 Hz. The noise in the devices, working in accumulation regime in air conditions, is well described by the Hooge empirical model.3,10,11 Findings here reported involve various aspects: (i) the average Hooge constant, αH, describing the current power spectral density of fluctuations is suppressed by at least one order of magnitude with respect to reference thin-film devices based on the same active material and with identical preparation conditions in terms of process atmosphere, solution parameters, and electrode geometries, in agreement with the presence of a higher molecular order in the polymer fibers; (ii) the reduction of noise in the organic semiconductor relates with the corresponding increase of mobility and higher structural order, which are found upon miniaturization. Differently from crystalline inorganic materials, in which size reduction may lead to a higher amount of defects and to a relatively higher noise, the lateral spatial confinement in polymer nanowires leads to an enhanced molecular orientation, which in turn determines noise reduction. This suggests that the beneficial effects from

any solid-state electronic applications have been revolutionized due to the low-cost, solution-based processing and flexibility of organic semiconductors.1,2 However, many fundamental issues related to charge-carrier transport in conjugated materials are still not completely understood, especially in devices with strongly reduced dimensions. For instance, low-frequency noise3 is inherently and ubiquitously present in electronics, but the way it changes upon moving from bulk conducting organic materials to nanostructures is still poorly investigated. In fact, such flicker (1/f) noise becomes more and more significant in devices approaching nanoscale, thus being an important factor limiting performances. Furthermore, being very sensitive to variations of ambient conditions and to external contaminations, it can be also exploited as probe mechanism in sensing applications.4 For these reasons, studying the behavior of flicker noise in nanostructures such as polymer nanofibers 5 has both fundamental and technological interest. Polymer nanofibers, nanowires, and other nanostructures with similar lateral size confinement generally exhibit a chargecarrier mobility significantly enhanced with respect to thin films made of the same conjugated material6,7 due to a more ordered molecular arrangement.8,9 Here, we investigate the effect of the size confinement on the flicker noise in organic field-effect © XXXX American Chemical Society

Received: May 28, 2015 Revised: October 6, 2015

A

DOI: 10.1021/acs.nanolett.5b02103 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

Figure 1. (a) Scheme of the nanofiber device (features not in scale). The device processing includes the deposition of a droplet of dichlorobenzene P3HT solution, solvent-assisted soft lithography, and mold peeling-off. The textured surface underneath fibers indicates the dimethyldichlorosilane silica coverage. L: interelectrodes gap distance. W: corresponding width. (b) Nanofibers connecting S and D electrodes, imaged by confocal fluorescence microscopy. In this micrograph, the channel length is 18 μm. Excitation wavelength = 488 nm. Scale bar = 5 μm.

Figure 2. Output characteristics of OFETs based on (a) polymer nanofibers and (b) reference films. L = 12 μm. (c, d) Corresponding transfer characteristics IDS(VGS) (left vertical scale) and |IDS|1/2(VGS) (right vertical scale). Continuous lines are linear fits to data. VDS = −50 V.

Polymer nanofibers can be produced by a variety of methods including electrospinning12 and soft lithography,7 leading to an improvement of device behavior compared to OFETs based on thin films. The devices for this study are realized by a solventassisted micromolding method on a bottom-contact architecture as schematized in Figure 1, panel a. OFETs are fabricated with a n-doped Si substrate as common gate electrode, a 100 nm-thick thermally grown SiO2 dielectric, and lithographically defined Cr/Au electrodes as source (S) and drain (D). In measured devices, the electrode width (W) and the channel length (L) are varied from 100 μm to about 3 mm, and from 6−25 μm, respectively. Dimethyldichlorosilane is deposited prior to nanowires to improve the semiconductor/dielectrics

enhanced structural order and higher coherence, induced by transversal confinement, on low-frequency noise prevails over noise-enhancing effects inherently related to miniaturization and to surface noise; (iii) results are well explained by a resistor network model, in which the organic semiconducting nanostructures or films are depicted through a two-dimensional network of resistors with a square-lattice structure; describing the conductive structures as networks in which perimetral conductive domains surround electrically insulated regions due to paracrystalline disorder, assuming that each element of the network may fluctuate independently, and taking into account effects from nonideal contacts, the model is entirely general and it can be applied to a wide number of different nanosystems. B

DOI: 10.1021/acs.nanolett.5b02103 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters interface. Following release of a 1 μL droplet of a 0.2 mM dichlorobenzene solution of regioregular P3HT onto the devices, nanostructured elastomeric molds are positioned on top, with features along the D−S gap, until complete solvent evaporation. The resulting conductive fibers connect source and drain, show a diameter around 300 nm, and are arranged in an array with period of 1 μm, as imaged by confocal microscopy (Figure 1b). For sake of comparison, P3HT thin film OFETs are realized by spin-coating (1000 rpm for 60 s) the same solution with identical electrodes (L = 6 and 12 μm), dielectric coatings, and active medium thickness. By grazing-incidence wide-angle X-ray scattering measurements, this class of nanowires has been found to exhibit a preferential edge-on orientation of P3HT molecules, with a well-defined lamellar structure and interbackbone separation, a = (1.67 ± 0.03) nm along the (100)-direction perpendicular to the substrate, and πstacking occurring along the (010)-direction parallel to the substrate with stacking distance b = (0.38 ± 0.02) nm.7 This supramolecular organization is similar to those typically observed in films with high regioregularity;13 however, an enhanced orientation of the P3HT molecules has been found upon increasing the resolution of the lateral spatial confinement.7 OFET characterization is performed in ambient conditions using a Keithley semiconductor parameter analyzer (4200SCS). The source−drain current (IDS) dependence on the source−drain voltage (VDS) highlights in all the devices the typical p-type behavior of P3HT-based OFETs, working in accumulation mode (Figure 2a,b). In nanowire devices, we cannot observe a complete current saturation at high VDS. Related to this, VTH has positive values (9 and 4 V for nanofiber and thin-film OFET, respectively), which suggest the presence of intrinsic accumulated holes in the conduction channel. A lack of well-defined saturation or slight positive VTH values are frequently found in p-type organic transistors due to residual processing impurities, acceptor-traps at the dielectric−polymer interface, or extrinsic doping.14−17 On the other hand, significant processing impurities have been associated with a relative decrease of the mobility measured in P3HT,18,19 which is not observed in our nanowires compared to films. The corresponding transfer characteristics, I DS (V GS ) and |IDS|1/2(VGS) curves (for VDS = −50 V) for fiber and thin-film devices are shown in Figure 2, panels c and d, respectively. The field-effect mobility, μ, is determined by the device characteristics, IDS = (Z/2L)Cμ(VGS − VTH)2,20 where C is the gate dielectric capacitance per unit area (∼34 nF cm−2), and Z is the effective channel width, which in nanofiber-OFETs is given by the width of each single nanostructure times the number of D− S connecting fibers (for films, Z = W). Devices based on nanowires exhibit a quite stable value of the mobility, μ = 10−2 cm2 V−1 s−1, corresponding to an electrical conductivity (σ) of 2 × 10−2 S m−1. Thin-film OFETs show instead μ, which is strongly variable in the range of 2 × (10−5−10−3) cm2 V−1 s−1 (i.e., σ = 3 × 10−6−10−3 S m−1). In the linear regime, we find typical mobilities of 6 × 10−3 cm2 V−1 s−1 and 2 × 10−5 cm2 V−1 s−1 for fibers and films, respectively. An important aspect to be clarified is the influence of the contact resistance on both the device characteristics and the low-frequency noise.21,22 The role of the resistance at the contacts can be especially relevant for relatively large current values when channel opening corresponds to decreased OFET channel resistance. Indeed, the usual gradual channel approximation can be extended by taking into account contact

resistances at the source (RS) and at the drain (RD), which are in series with the impedance provided by the OFET channel.23 The contact resistance is tailored by various factors including the work function, cleaning, and clustering conditions of metal at the electrode−organic interface.24 As a consequence, in the linear regime, the total resistance, RON, is given by23,25,26 RON = (∂VDS/∂IDS)|VVGS = RCH + RS + RD, where the channel DS ≈ −10 V resistance, RCH, is L/[ZCμ(VGS − VTH)]. For instance, for the device characteristics shown in Figure 2, RON ranges from 103 to 105 kΩ (calculated at VDS ≅ −10 V and VGS ≅ −15 V). The corresponding calculation for the contact resistance (RS + RD) according to the transfer line method [RON × Z = R̃ CH + (RS + RD) × Z, where R̃ CH is directly proportional to L according to the expressions above]25 might lead to negative values, indicating that RCH is dominant over RS + RD as recently found in top-contact transistors based on CdSe nanocrystals.27 This result is expected for organic transistors with L values in the scale of micrometers, while the relative contribution of the contact resistance typically becomes relevant only for very short (100 nm-scale) channels.26 However, electrode processing and wire bonding procedures must also be taken into account in this respect. We will come back to issues related to contacts, to better assess a possible effect on the noise characteristics, in the following. Noise measurements are performed by coupling the Keithley instrument with a custom spectrum analyzer, and reducing the instrumental noise by the cross-correlation technique 28 allowing both thermal noise and flicker noise to be explored and frequencies up to 105 Hz to be reached. Figure 3, panel a shows the typical current noise power spectral density of nanowire OFETs with a channel length of 6 μm. The noise spectra are shown in correspondence of different drain current values by changing the drain−source voltage VDS applied to the transistor from 0 V to −15 V and by a constant gate−source voltage (VGS = 0 V). At the equilibrium condition, the measured noise is in agreement with the calculated thermal noise produced by the drain−source channel resistance. Upon increasing the drain−source current, IDS, the spectra show an excess noise that follows a 1/f frequency dependence. Indeed, for all the 10 fiber OFETs measured, the exponent β of the 1/fβ dependence is found to be between 1.0 and 1.1, which is a noise behavior similar to that observed in thin-film devices.29,30 According to the empirical Hooge formula,3,10,11 the 1/f noise spectral density of homogeneous samples is given by SI I

2

=

αH Nf

(1)

where I is the current, N is the total number of free charge carriers in the sample, and αH is the Hooge’s parameter. In the linear regime, N can be estimated by the relation eN ≅ (VGS − VTH)LZC, that is, N is about 108 and 109 for nanowires and films, respectively. The corresponding carrier surface density is of the order of 1012 cm−2 for both samples, which allows us to rule out a significant influence of the carrier density on the noise characteristics. Fluctuations can be instead due to volume noise source mechanisms (highlighted by the superlinear dependence of SI on IDS)29 affecting carrier transport at the boundaries between domains with different conductivity in the conducting layers. In the case of transistors operating in linear regime, the previous equation can be conveniently written, using directly measurable quantities, as30 C

DOI: 10.1021/acs.nanolett.5b02103 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

VDS·IDS, which when found to be constant for devices of various length, clearly highlights that the noise is dominated by the channel, with minor contributions possibly associated with fluctuations of the contact resistance (full details are reported in the Supporting Information). For some devices, particularly where miniaturized (W = 100 μm) electrodes are used that need wire bonding to be performed onto pads very close to the conductive medium, eventual spurious effects at electrode− organics contacts cannot be ruled out. The following analysis of experimental data will be limited to devices with channeldominated noise. The average value of the Hooge parameter, αH, extracted by the measurements using eq 2, for these devices ranges between 1.2 and 4.6 (inset of Figure 3b). These values are comparable to values found in nanometric pentacene layers32 and in singlelayer MoS2 under ambient conditions,33 although they are still higher than values in carbon nanotube transistors by 1−3 orders of magnitude.34 Noise measurements on thin-film OFETs based on the same material and similar preparation conditions might allow one to discriminate the effect of a more ordered molecular arrangement such as that imposed by the nanofiber structure. We find that the nanostructured polymer material clearly exhibits a reduction of the average Hooge parameter, by more than one order of magnitude, with respect to thin-films. The intensity of low-frequency noise is associated with scattering centers constituting independent microscopic sources of noise;3,10,11 fluctuations are generally averaged upon increasing the size of a semiconducting material, which leads to a lower relative contribution compared to electrical signals. Consequently, in inorganic, crystalline materials the signal-tonoise ratio might decrease for strongly miniaturized components, related to the concomitant intensified role of defects and possibly decreased mobility. Our measurements suggest that in P3HT nanowires, these effects are overcome by the reduction of the scattering centers due to the higher structural order. In addition, the suppression of the Hooge constant found in nanowires is such to compensate and to dominate over eventual noise-enhancing effects related to impurities. To rationalize this behavior, we develop a resistor network model, describing a nanofiber or a thin film as a twodimensional network of resistors with square-lattice structure, rectangular shape, and overall resistance R. Each elementary resistor (rn) is associated with a nanoscopic conductive domain in the fiber and lines an electrically insulated grain, due to paracrystalline disorder,35 as schematized in Figure 4, panel a. The network is made by NL and NW grains in the length and width directions, respectively, corresponding to a total number of resistors NT = 2NLNW + NL − NW = NH + NV, where NH = NL(NW + 1), and NV = NW(NL − 1) are the total numbers of horizontal and vertical resistors, respectively. The anisotropy of the structure and the structural disorder are accounted for by taking different ranges of values for the resistances of the horizontal (rH,l) and vertical (rV,l) resistors in Figure 4, panel a, namely rH,l ∈[rH,a, rH,b] and rV,l ∈[rV,a, rV,b], where rV,a < rV,b < rH,a < rH,b (i.e., rH,a ≈ 10 rV,a, and rH,b ≈ 10 rV,b). In numerical simulations, each elementary resistance takes a random value in the corresponding intervals. By extending the model for 1/f noise introduced by Gingl et al.36 and Pennetta et al.,37 we assume that each resistor (n) fluctuates independently of each other: rn(t) = rk,l + δrk,l(t), where k = H and l = 1,..,NH, or k = V and l = 1,..,NV for horizontal or vertical resistors, respectively. The variance of the resistance fluctuations for the n-th resistor is Δn ≡ = ≡ Δk,l, where ΔH,l ∈[ΔH,a, ΔH,b]

Figure 3. (a) Current noise spectral density in a nanofiber OFET. L = 6 μm. The gate−source voltage is fixed at 0 V, and the drain-source voltage ranges from 0 V to −15 V. The dashed line indicates the 1/f slope. Current values, from top to bottom, are 15.7, 7.8, 3.7, 1.8, 0.8, 0.4, 0.2, 0.1 μA, 53, 26, 13, and 0 nA. The gray region at high frequency indicates the instrumental noise. (b) Normalized noise level at 1 kHz for a set of devices with different channel lengths. The dashed line indicates the slope of VDS·IDS predicted by the Hooge formula. Exemplary curves are shown for devices with L = 6 μm (squares), 12 μm (circles, downward triangles), 25 μm (diamonds, leftward triangles). Inset: comparison of the Hooge parameter, αH, for OFETs based on conductive nanofibers or thin-films. The squares are the mean values for each length at VDS·IDS = 100 nW, and the error bars here span from the minimum to the maximum value estimated.

SI =

eμαH fL2

VDSIDS

(2)

where e indicates the electronic charge. This equation is independent of the channel width, allowing a simpler comparison of transistors with different geometry. In Figure 3, panel b, we show the measured noise level at 1 kHz, normalized by the square of the device length as a function of the power VDS·IDS. The curves have a constant slope ranging from 0.87 to 1 for more than five decades in good agreement with the Hooge formula. The slope lower than the ideal value of 1 could be related to mobility dependence on the applied voltage.30 In addition, to better assess a possible influence of the contact resistance on the ultimate 1/f noise characteristics, we also consider the L-dependence of noise, which allows one to distinguish contributions coming from the channel and the contact regions.31 Indeed, the overall noise behavior can be seen as the superposition of effects from two uncorrelated sources as (SRCH + SRC)/(RCH + RS + RD)2, where the noises from the device channel (SRCH) and the contacts (SRC) are separately indicated.27 To this aim, we plot the powernormalized SI L2 quantity at a constant power dissipation D

DOI: 10.1021/acs.nanolett.5b02103 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

Figure 4. (a) 2D network model by fluctuating resistors with NL = 80 and NW = 8. Here, the external bias, V, is applied to the network through electrical contacts realized by perfectly conducting bars at the left and right terminations of the network. The different colors show the different resistance values (23 levels): the third box of the color-bar (starting from the left) corresponds to rn = 104 Ω, while the last box (at the right) to rn > 2.5 × 105 Ω. The coherence region (10 × 10) is visible in the central part of the network. (b) Modeled frequency dependence of SI/I2 for films. Overall network resistance, from top to bottom: R = 188.6, 197.2, 195.7, and 199.4 MΩ, respectively, with NT = 5 × 103, 2 × 104, 4.5 × 104, and 8 × 104. V = 20 V, I ≅ 100 nA. Dashed lines are the best-fit with a power-law of slope β. The values of β and αH are also reported for each curve. Dotted lines are guides with −1 slope. Inset: SI/I2 versus NT in a double-log plot; the solid line is the best-fit with a power-law. (c) Same as panel b for nanofibers. From top to bottom: R = 1.18, 1.46, 2.37, and 2.96 MΩ, respectively, with NT ≅ 1.3 × 103, 1.7 × 103, 2.7 × 103, and 3.4 × 103. V = 20 V, I ≅ 6.7−16.9 μA. Inset: corresponding SI/I2 versus NT log−log plot for nanofibers. Simulation parameters: rH,a = 105 Ω, rV,a = 104 Ω, ΔH,a = 6 × 109 Ω2, ΔV,a = 106 Ω2, with rH,b film > rH,b fiber = 2.5 × 105 Ω, rV,b f ilm > rV,b fiber = 2.5 × 104 Ω, ΔH,b film > ΔH,b fiber = 6 × 1011 Ω2, ΔV,b film > ΔV,b fiber = 107 Ω2. Moreover, the size of the coherence region for fibers is Lc = 0.5L, Wc = W, while for films, Lc = Wc ≈ L/25. (d) Schematic illustrations of results. For fibers (right), fluctuations are lower than in films (left), as indicated by the lower contrast in the textured pattern in the picture, due to an increase in size of the coherence regions and a narrower distribution of rk,l and Δk,l. These effects lead to a reduction of αH.

and ΔV,l ∈[ΔV,a, ΔV,b]. According to the Cohn’s theorem,38,39 the network resistance can be written as NT

R=

⎛ i ⎞2 I

∑ rn⎜⎝ n ⎟⎠ n=1

The measured 1/f noise in the frequency range of 10 Hz−100 kHz can be modeled assuming a correlation time τ n hyperbolically distributed41 between 10−6 s and 1 s and randomly associated with each resistor. In the case of nanofibers, the strong confinement in the directions perpendicular to the longitudinal fiber axis leads to an increased structural coherence.42 This can be modeled by assuming coherence regions Ωc of length, Lc, and width, Wc, characterized by the conditions: rH,l = rH,a, rV,l = rV,a, ΔH,l = ΔH,a, ΔV,l = ΔV,a, and τn = τMAX for all the resistors n within Ωc (Figure 4a). For films (NW ≈ NL) with a relatively higher degree of structural disorder as expressed by smaller coherence regions and by broader distributions of rk,l and Δk,l, this leads to the total current relative spectral density shown in Figure 4, panel b (the local currents, in, of eq 4 are calculated by solving the Kirchhoff’s loop equations).43 A well-behaved 1/f noise is obtained, scaling with the overall size of the film and with αH ≅ 100−120. Now, by comparing a film modeled by 200 × 200 domains (i.e., with NT ≅ 8 × 104) with a fiber with 8 × 200 domains (NT ≅ 3.4 × 103), one finds analogous values of SI/I2 (Figure 4c), which immediately leads to αH values that are lower by about two orders of magnitude in fiber devices. For nanofibers, one obtains αH ≅ 1−2, in very good agreement with experimental results. A schematic summarizing these results is shown in Figure 4, panel d. In addition, one should notice that the dependence of SI/I2 is not exactly inversely proportional to NT (slopes 0.96 and 0.94 for the straight lines in the insets of Figure 4, panels b and c, which show the best-fit with a power-

(3)

where in is the local current through the nth elementary resistor, and I is the total current flowing in the fiber. On the other hand, by the virtual-power (Tellegen’s) theorem,38,40 the spectral density of the current fluctuations of a two-terminal network, in the linear regime and under constant voltage conditions, can be written as S I (f ) I2

=

S R (f ) R2

N

=

∑n =T 1 sn(f )in 4 2

⎡⎣∑nN=T 1 rnin 2⎤⎦

(4)

where sn( f) is the spectral density of the local resistance noise associated with the fluctuations of the resistor n. Then, by using the above expression for the current spectral density, we are generalizing the model to the case of a completely disordered network by releasing the conditions assumed in the previous works.36,37 Finally, the fluctuation of each elementary resistor is characterized by a correlation time, τn, with a Lorentzian spectrum: sn(f ) =

4⟨(Δrn)2 ⟩τn 1 + (2πτnf )2

(5) E

DOI: 10.1021/acs.nanolett.5b02103 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters law on a double log scale). This finding can be attributed to the effect of the coherence region and consequent charge delocalization improving transport properties. Besides the realization of nanowires and of other systems where confined geometries enhance molecular ordering, other methods for improving the structural coherence may involve annealing conductive polymers at high temperatures and under controlled atmosphere.30 In addition, distributions of rk,l and Δk,l varying along the “vertical” direction of Figure 4, panel a and possibly asymmetric with respect to the longitudinal axis of the network are well-suited to estimate the impact on the noise behavior of local bending of a nanowire, or of inhomogeneous degrees of regioregularity and charge delocalization in its different crosssectional regions (Figure S3 in the Supporting Information). Finally, we introduce a model to study the effects related to nonideal contacts, that is, to electrodes with not negligible resistance and resistance noise as discussed earlier. The modeling of nonideal contacts is detailed in the Supporting Information. In this case, the network of elementary, regular resistors associated with the conductive organic materials is added with extra elementary, contact resistors, as schematized in Figure 5, panel a. Two kinds of contact resistors are introduced.

total resistance RT, is different from R (Figure S4). Figure 5, panel b displays the resulting, ensemble-averaged values of the Hooge parameter as a function of the resistance rh,c for several values of Δh,c and for the prototypical (8 × 100) network considered in Figure 4, panel c. Interestingly, our simulations show that (i) mainly varies for rh,c above the threshold value rV,a (the smallest elementary resistance composing the regular network associated with the nanofiber), (ii) the value at low rh,c depends weakly on the variance describing the contact resistor fluctuations, at least when Δh,c < ΔH,b (the highest variance of the fluctuating resistors composing the regular network), and (iii) a decrease, unexpected at first sight, is found for at high rh,c values. This result can be rationalized by considering that the value of rh,c strongly affects the distribution of local currents. In particular, an increase of rh,c leads to sharper distributions of local currents in inside the network (Figure S5), which consequently explains the reduction of at the higher values of the contact resistance38,39 (see Supporting Information for details). Hence, these findings further highlight the interplay of conductive polymer nanofibers and of device geometrical and material characteristics in leading to noisereducing effects. Conclusions. In summary, we have presented noise measurements of organic polymer nanofibers, finding a significant suppression of noise compared to more disordered film structures, as expressed by the Hooge constant. We have developed a model based on resistor networks, rationalizing results on 1/f noise in nanofibers, and highlighting the role of structural coherence on the noise behavior in the organic system. These results confirm that αH is related to the degree of material structural order, with higher values of αH being associated with poorly ordered materials.33,44 Contact noise can be also taken into account and found to lead to decreased device αH for large elementary resistances at the electrode− nanowire interface. The enhanced molecular orientation and structural order resulting from size-confinement in nanostructures are consequently effective in improving the noise performance of organic FETs, in contrast to devices based on crystalline materials where a reduction of the size could affect the defects percentage and consequently increase the flicker noise.11 These findings are significant for the fundamental understanding of the transport properties of organic semiconductors, as well as due to the reduced noise levels, for technological applications45,46 in the fields of enhanced chemical sensors and bioelectronics.

Figure 5. (a) Schematic representation of a 3 × 5 resistor network in contact with two lateral nonideal electrodes: each electrode here is made by three vertical resistors rv,c and four horizontal resistors rh,c. (b) Value of the Hooge parameter, , averaged over 20 devices (networks 8 × 100) with nonideal contacts, as a function of rh,c. The different curves correspond to values of the contact variance, Δh,c, ranging from 108−1013 Ω2. Other parameters are the same as in Figure 4, panel c.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b02103. Additional technical details on the dependence of noise on the geometrical parameters of nanofiber-based OFETs and on the developed model (PDF)

“Horizontal” resistors, rh,c, are collinear with the nanofiber longitudinal axis and describe the effect of the disordered and high-resistivity regions at the interface between the metal and the fiber. “Vertical” resistors, rv,c,, are associated with the resistivity of the metallic region (rv,c ≪ rh,c). To account for the noise due to the contacts, we assume that contact resistors fluctuate with variances Δh,c ≡ and Δv,c ≡ , respectively, Δv,c ≪ Δh,c for good quality electrodes. Thus, at the simplest level of modelization, the presence of nonideal contacts implies two further parameters, rh,c and Δh,c. The overall device is simulated by such enhanced network whose

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

F.L. and G.F. contributed equally to this work. Notes

The authors declare no competing financial interest. F

DOI: 10.1021/acs.nanolett.5b02103 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

■

(20) Dimitrakopoulos, C. D.; Malenfant, P. R. L. Organic Thin Film Transistors for Large Area Electronics. Adv. Mater. 2002, 14, 99−117. (21) Reza, S.; Bosman, G.; Saif Islam, M.; Kamins, T. I.; Sharma, S.; Stanley Williams, R. Noise in Silicon Nanowires. IEEE Trans. Nanotechnol. 2006, 5, 523−529. (22) Lin, Y. M.; Appenzeller, J.; Knoch, J.; Chen, Z.; Avouris, P. LowFrequency Current Fluctuations in Individual Semiconducting SingleWall Carbon Nanotubes. Nano Lett. 2006, 6, 930−936. (23) Hoppe, A.; Balster, T.; Muck, T.; Wagner, V. Scaling Limits and MHz Operation in Thiophene-Based Field-Effect Transistors. Phys. Status Solidi A 2008, 205, 612−625. (24) Bürgi, L.; Richards, T. J.; Friend, R. H.; Sirringhaus, H. Close Look at Charge Carrier Injection in Polymer Field-Effect Transistors. J. Appl. Phys. 2003, 94, 6129−6137. (25) Luan, S.; Neudeck, G. W. An Experimental Study of the Source/ Drain Parasitic Resistance Effects in Amorphous Silicon Thin Film Transistors. J. Appl. Phys. 1992, 72, 766−772. (26) Tu, D.; Pagliara, S.; Camposeo, A.; Potente, G.; Mele, E.; Cingolani, R.; Pisignano, D. Soft Nanolithography by Polymer Fibers. Adv. Funct. Mater. 2011, 21, 1140−1145. (27) Lai, Y.; Li, H.; Kim, D. K.; Diroll, B. T.; Murray, C. B.; Kagan, C. R. Low-Frequency (1/f) Noise in Nanocrystal Field-Effect Transistors. ACS Nano 2014, 8, 9664−9672. (28) Ferrari, G.; Sampietro, M. Correlation spectrum analyzer for direct measurement of device current noise. Rev. Sci. Instrum. 2002, 73, 2717−2723. (29) Martin, S.; Dodabalapur, A.; Bao, Z.; Crone, B.; Katz, H. E.; Li, W.; Passner, A.; Rogers, J. A. Flicker Noise Properties of Organic Thin-Film Transistors. J. Appl. Phys. 2000, 87, 3381−3385. (30) Deen, M.; Marinov, O.; Holdcroft, S.; Yu, J.; Woods, W. Lowfrequency noise in polymer transistors. IEEE Trans. Electron Devices 2001, 48, 1688−1695. (31) Lee, B.; Chen, Y.; Fu, D.; Yi, H. T.; Czelen, K.; Najafov, H.; Podzorov, V. Trap Healing and Ultralow-Noise Hall Effect at the Surface of Organic Semiconductors. Nat. Mater. 2013, 12, 1125−1129. (32) Conrad, B. R.; Cullen, W. G.; Yan, W.; Williams, E. D. Percolative Effects on Noise in Pentacene Transistors. Appl. Phys. Lett. 2007, 91, 242110. (33) Sangwan, V. K.; Arnold, H. N.; Jariwala, D.; Marks, T. J.; Lauhon, L. J.; Hersam, M. C. Low-Frequency Electronic Noise in Single-Layer MoS2 Transistors. Nano Lett. 2013, 13, 4351−4355. (34) Back, J. H.; Kim, S.; Mohammadi, S.; Shim, M. Low-Frequency Noise in Ambipolar Carbon Nanotube Transistors. Nano Lett. 2008, 8, 1090−1094. (35) Noriega, R.; Rivnay, J.; Vandewal, K.; Koch, F. P. V.; Stingelin, N.; Smith, P.; Toney, M. F.; Salleo, A. A general relationship between disorder, aggregation and charge transport in conjugated polymers. Nat. Mater. 2013, 12, 1038−1044. (36) Gingl, Z.; Pennetta, C.; Kiss, L. B.; Reggiani, L. Biased Percolation and Abrupt Failure of Electronic Devices. Semicond. Sci. Technol. 1996, 11, 1770−1775. (37) Pennetta, C.; Gingl, Z.; Kiss, L. B.; Reggiani, L. Biased Percolation and Electrical Breakdown. Semicond. Sci. Technol. 1997, 12, 1057−1063. (38) Rammal, R.; Tannous, C.; Breton, P.; Tremblay, A. M. S. Flicker (1/f) Noise in Percolation Networks: A New Hierarchy of Exponents. Phys. Rev. Lett. 1985, 54, 1718−1721. (39) Stauffer, D.; Aharony, A. Introduction to Percolation Theory; Taylor and Francis: London, 1991. (40) Spence, R. Linear Active Network; Wiley-Interscience: London, 1970. (41) Hooge, F. N.; Kleinpenning, T. G. M.; Vandamme, L. K. J. Experimental Studies on 1/f Noise. Rep. Prog. Phys. 1981, 44, 479− 532. (42) Shimomura, T.; Takahashi, T.; Ichimura, Y.; Nakagawa, S.; Noguchi, K.; Heike, S.; Hashizume, T. Relationship between Structural Coherence and Intrinsic Carrier Transport in an Isolated Poly(3hexylthiophene) Nanofiber. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 115314.

ACKNOWLEDGMENTS The authors acknowledge the financial support from the Italian Minister of University and Research through the FIRB RBFR08DJZI “Futuro in Ricerca” and from the Apulia Regional Projects Networks of Public Research Laboratories Wafitech (9) and M. I. T. T. (13). We also thank Prof. M. Sampietro for the helpful discussion.

■

REFERENCES

(1) Sekitani, T.; Someya, T. Stretchable, Large-area Organic Electronics. Adv. Mater. 2010, 22, 2228−2246. (2) Wang, C.; Dong, H.; Hu, W.; Liu, Y.; Zhu, D. Semiconducting πConjugated Systems in Field-Effect Transistors: A Material Odyssey of Organic Electronics. Chem. Rev. 2012, 112, 2208−2267. (3) Dutta, P.; Horn, P. M. Low-Frequency Fluctuations in Solids: 1/f noise. Rev. Mod. Phys. 1981, 53, 497−516. (4) Rumyantsev, S.; Liu, G.; Shur, M. S.; Potyrailo, R. A.; Balandin, A. A. Selective Gas Sensing with a Single Pristine Graphene Transistor. Nano Lett. 2012, 12, 2294−2298. (5) Pisignano, D. Polymer Nanofibers; Royal Society of Chemistry: Cambridge, 2013. (6) Zheng, Z.; Yim, K. H.; Saifullah, M. S. M.; Welland, M. E.; Friend, R. H.; Kim, J. S.; Huck, W. T. S. Uniaxial Alignment of LiquidCrystalline Conjugated Polymers by Nanoconfinement. Nano Lett. 2007, 7, 987−992. (7) Mele, E.; Lezzi, F.; Polini, A.; Altamura, D.; Giannini, C.; Pisignano, D. Enhanced Charge-Carrier Mobility in Polymer Nanofibers Realized by Solvent-Resistant Soft Nanolithography. J. Mater. Chem. 2012, 22, 18051−18056. (8) Aryal, M.; Trivedi, K.; Hu, W. Nano-Confinement Induced Chain Alignment in Ordered P3HT Nanostructures Defined by Nanoimprint Lithography. ACS Nano 2009, 3, 3085−3090. (9) Hlaing, H.; Lu, X.; Hofmann, T.; Yager, K. G.; Black, C. T.; Ocko, B. M. Nanoimprint-Induced Molecular Orientation in Semiconducting Polymer Nanostructures. ACS Nano 2011, 5, 7532−7538. (10) Hooge, F. N. l/f Noise is no Surface Effect. Phys. Lett. A 1969, 29, 139−140. (11) Hooge, F. N. l/f Noise Sources. IEEE Trans. Electron Devices 1994, 41, 1926−1935. (12) Reneker, D. H.; Chun, I. Nanometre Diameter Fibres of Polymer, Produced by Electrospinning. Nanotechnology 1996, 7, 216− 223. (13) Sirringhaus, H.; Brown, P. J.; Friend, R. H.; Nielsen, M. M.; Bechgaard, K.; Langeveld-Voss, B. M. W.; Spiering, A. J. H.; Janssen, R. A. J.; Meijer, E. W.; Herwig, P.; et al. Two-Dimensional Charge Transport in Self-Organized, High-Mobility Conjugated Polymers. Nature 1999, 401, 685−688. (14) Liu, H.; Reccius, C. H.; Craighead, H. G. Single Electrospun Regioregular Poly(3-hexylthiophene) Nanofiber Field-Effect Transistor. Appl. Phys. Lett. 2005, 87, 253106. (15) Merlo, J. A.; Frisbie, C. D. Field Effect Transport and Trapping in Regioregular Polythiophene Nanofibers. J. Phys. Chem. B 2004, 108, 19169−16179. (16) Tu, D.; Pagliara, S.; Camposeo, A.; Persano, L.; Cingolani, R.; Pisignano, D. Single Light-Emitting Polymer Nanofiber Field-Effect Transistors. Nanoscale 2010, 2, 2217−2222. (17) Babel, A.; Li, D.; Xia, Y.; Jenekhe, S. A. Electrospun Nanofibers of Blends of Conjugated Polymers: Morphology, Optical Properties, and Field-Effect Transistors. Macromolecules 2005, 38, 4705−4711. (18) Abdou, M. S. A.; Orfino, F. P.; Son, Y.; Holdcroft, S. Interaction of Oxygen with Conjugated Polymers: Charge Transfer Complex Formation with Poly(3-alkylthiophenes). J. Am. Chem. Soc. 1997, 119, 4518−4524. (19) Hoshino, S.; Yoshida, M.; Uemura, S.; Kodzasa, T.; Takada, N.; Kamata, T.; Yase, K. Influence of Moisture on Device Characteristics of Polythiophene-based Field-Effect Transistors. J. Appl. Phys. 2004, 95, 5088−5093. G

DOI: 10.1021/acs.nanolett.5b02103 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters (43) Pennetta, C.; Alfinito, E.; Reggiani, L.; Fantini, F.; De Munari, I.; Scorzoni, A. A Biased Resistor Network Model for Electromigration Phenomena in Metallic Lines. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 70, 174305. (44) Jurchescu, O. D.; Hamadani, B. H.; Xiong, H. D.; Park, S. K.; Subramanian, S.; Zimmerman, N. M.; Anthony, J. E.; Jackson, T. N.; Gundlach, D. J. Correlation between Microstructure, Electronic Properties and Flicker Noise in Organic Thin Film Transistors. Appl. Phys. Lett. 2008, 92, 132103. (45) Torsi, L.; Farinola, G. M.; Marinelli, F.; Tanese, M. C.; Omar, O. H.; Valli, L.; Babudri, F.; Palmisano, F.; Zambonin, P. G.; Naso, F. A Sensitivity-Enhanced Field-Effect Chiral Sensor. Nat. Mater. 2008, 7, 412−417. (46) Cheng, Z.; Li, Q.; Li, Z.; Zhou, Q.; Fang, Y. Suspended Graphene Sensors with Improved Signal and Reduced Noise. Nano Lett. 2010, 10, 1864−1868.

H

DOI: 10.1021/acs.nanolett.5b02103 Nano Lett. XXXX, XXX, XXX−XXX