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Wei Xie, Feilong Liu, Sha Shi, P. Paul Ruden, and C. Daniel Frisbie* Electrolyte gating has recently become a powerful technique to induce ultrahigh surface charge densities (1013 cm−2 to 1015 cm−2) in a variety of semiconductor materials in fieldeffect transistor (FET) geometry, forming the so-called electric double layer transistors (EDLTs).[1–4] With the application of a gate voltage, electrolyte ions migrate to the gate/electrolyte and semiconductor/electrolyte interfaces, forming two nanometer thick electric double layers (EDLs). The gate electric field is effectively screened across the bulk of the electrolyte layer and only persists at the EDLs. Consequently, a large capacitance on the order of 1–10 μF/cm2 is achieved, resulting in a high-density charge accumulation in the semiconductor channel.[5] Such field-induced high charge densities have facilitated observations of novel transport phenomena in physics-rich correlated electron materials, such as the insulator-to-metal transition in ZnO[6] and superconductivity in SrTiO3[7] near sheet charge densities of 1014 cm−2. For all these cases, charge densities can be systematically tuned by the gate voltage over a broad range within the same device, allowing stable and reversible transition between different electronic phases. The electrolyte gating technique also provides valuable opportunities to probe charge transport in organic semiconductor single crystals in the high-density regime, which previously was only accessed by tedious and irreversible chemical doping approaches.[8] In fact, most of the novel transport behavior in organic semiconductors, such as metallic transport and superconductivity, occur at sheet charge densities above 1013 cm−2.[9,10] Despite the increasing interest in tuning electronic phase transitions in electrolyte-gated organic semiconductors, the role of free carrier density on electrical properties is not as well understood as it is in more conventional electronic materials. In particular, significant charge carrier correlations can be anticipated in these materials because they are characterized by low permittivity (low charge screening) and relatively narrow bandwidths. Besides, the presence of bulky electrolyte ions in the vicinity (∼1 nm) of charge carriers at the
W. Xie, Prof. C. D. Frisbie Department of Chemical Engineering and Materials Science University of Minnesota 421 Washington Ave SE Minneapolis, MN 55455, USA E-mail: [email protected] F. Liu, S. Shi, Prof. P. P. Ruden Department of Electrical and Computer Engineering University of Minnesota 200 Union St. SE Minneapolis, MN 55455, USA
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semiconductor/electrolyte interface can introduce a large Coulombic effect that in turn influences the charge transport. One recent experimental observation possibly reflecting such effects was that in electrolyte-gated polymer films[11,12] and small-molecule single crystals,[13,14] the channel conductivity showed a significant peak as a function of increasing charge density, rather than a monotonic dependence as in organic transistors gated with conventional dielectrics.[15] The generality of this unusual conductivity peak among a wide category of organic semiconductors prompts us to perform systematic experimental and theoretical investigations. In this communication, we expand our previous work[13] in understanding the transport mechanism associated with the conductivity peak in ionic-liquid (IL) gated rubrene singlecrystal EDLTs. By extending the gate-induced surface charge density up to 6 × 1013 cm−2, which corresponds to 1/3 hole per rubrene molecule in one molecular layer, we observe two pronounced channel conductivity peaks reproducibly at densities corresponding to 0.11 holes/rubrene and 0.27 holes/rubrene. The validity of the conductivity peaks has been confirmed by various control measurements. Considering the strong interactions between holes and negatively charged ions at the rubrene/ IL interface, holes in the rubrene channel are viewed as moving in a potential landscape where hole density dependent trapping occurs. A two-channel conduction model is thus introduced, ascribing the first and second conductivity peaks to the transport of holes over the “free” sites and “trapped” sites, respectively. This model is based on and extensively extends our previous work for the first conductivity peak in rubrene EDLTs.[13] Our work is also a significant step forward in understanding the puzzling charge-density dependent conductivity behavior in organic semiconductor based EDLTs. Rubrene EDLTs were fabricated following previously established procedures.[16] An air-gap transistor was first made by laminating a rubrene crystal on a pre-patterned poly(dimethylsiloxane) (PDMS) substrate, and a small drop of IL was subsequently injected into the channel by capillarity filling up the entire space of air-gap, forming a rubrene EDLT (Figure 1a). Critical to the success of this study, which involves device operation at large gate bias for an extended period of time, was a careful selection of IL composition (we use [1-butyl-1-methyl pyrrolidinium][tris(pentafluoroethyl)trifluorophosphate], or [P14][FAP], molecular structure shown in Figure 1b) as well as operating the device at lower temperatures slightly above the freezing point of the liquid (around 230 K).[14] Consequently, a larger gate-voltage window for the EDLT was achieved, allowing hole accumulation up to (6–7) × 1013 cm−2 (ca. 0.33 holes/rubrene) before device failure, as identified by the gate displacement current measurement.[14,17,18] The pure capacitor-like characteristic of the displacement current[14]
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Charge Density Dependent Two-Channel Conduction in Organic Electric Double Layer Transistors (EDLTs)
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Figure 1. a) Cross-sectional device structure of a rubrene EDLT gated with IL. b) Molecular structure of rubrene and [P14][FAP]. c) (left axis, filled circles) sheet conductance σs as a function of gate voltage VG over three consecutive sweeps for a rubrene EDLT gated with [P14][FAP] taken at 225 K. Both forward and reverse sweeps are shown. The sweep rate is 50 mV/s; (right axis, open circles) hole density p as a function of VG, determined from gate displacement current. d,e) Hole mobility μ (d) and gate current IG (e) versus VG for the same device. Device dimensions: W = 250 μm, L = 300 μm. The gap is 5 μm in depth.
corroborates the fact that hole accumulation is achieved via two-dimensional electrostatic field-effect, and ion penetration into rubrene does not occur. This is further supported by the preservation of the rubrene crystal structure before and after IL gating.[16] The transfer curve is shown in Figure 1c, where the four-terminal sheet conductance σs is plotted as a funcΔL I D tion of the gate voltage VG (σ s = W , where W is the channel ΔV width, ΔL and ΔV are, respectively, the distance and voltage difference between two voltage-sensing probes, and ID is the drain current). As VG is swept forward towards large negative values, the channel conductivity (used interchangeably with sheet conductance σs) exhibits two pronounced peaks which not only appear robust and repeatable over multiple VG sweeps, but are also reproducible when VG is swept backward. The hysteresis loop during a VG-sweep cycle is likely due to the slow ion motion at low temperatures, and can be negligibly small at elevated temperatures.[14] Looking only at the forward sweeps in over 20 rubrene EDLTs, we find the first conductivity peak
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occurs at hole density p = (2.0 ± 0.2) × 1013 cm−2 (ca. 0.11 holes/ rubrene) and the second peak at p = (5.2 ± 0.5) × 1013 cm−2 (ca. 0.27 holes/rubrene). The effective hole mobility μ (=σs/ep, where e is the elemental charge) shows a non-monotonic VG-dependence as well in Figure 1d, with a maximum mobility reaching 2–3 cm2 V−1 s−1. Compared with the value at the first peak, the hole mobility at the second peak is significantly smaller, typically below 1 cm2 V−1 s−1. The gate current IG, shown in Figure 1e, is orders of magnitude smaller than ID (not explicitly shown), and is monotonically dependent on VG without any peaks, indicating the electrochemical reaction of the IL during the device operation is negligible. To the best of our knowledge, these unusual conductivity and mobility behaviors at hole densities beyond 1013 cm−2 in rubrene EDLTs have not been observed in any OFETs gated with conventional dielectrics,[15,19,20] or inorganic EDLTs gated with electrolytes.[6] In separate work,[21] we have also investigated the coupling of channel conductivity peaks with the gate-to-channel capacitance
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reflecting the occurrence of a negative differential transconductance (NDT) (i.e., ID decreases with increasing VG). A transition from PDT to NDT therefore confirms the presence of the conductivity peak. Likewise, the second conductivity peak is confirmed by the same 180° shift in θ at larger VG (Figure S2b). To summarize the experimental results, we observe two robust and reproducible conductivity peaks as a function of VG in rubrene EDLTs at hole densities above 1013 cm−2. We have carefully excluded other possible contributions to the conductivity peaks, such as the electrochemical reaction of the IL, ion penetration into rubrene, interfacial EDL rearrangement, Joule heating and contact effects. Additionally, on the basis of the calculated band structure for bulk rubrene crystals,[30] we view multiband transport as unlikely in the structures examined. We therefore conclude the conductivity behavior is related to the transport properties of rubrene in the presence of ions at the interface. As indicated by our previous work on the first conductivity peak, a key consideration in these EDLT devices (compared to devices gated with conventional dielectrics) is the role played by discrete ions at the rubrene-IL interface.[13] Due to the low dielectric constant (εr ≈ 3) and narrow bandwidth (ca. 0.5 eV) of rubrene, a strong interaction of negatively charged anions in the IL with the positively charged holes at the rubrene surface is anticipated, resulting in trapping of holes. This important concept, as elaborated in the following, provides baseline guidance for understanding the charge transport in any EDLTs based on organic semiconductors at high charge densities. We assume that the positive and negative ions in the ILs (no solvent) are strongly correlated by their mutual Coulomb interactions. In equilibrium, as the overall IL is charge-neutral, the minimization of the Coulomb energy leads to a checkerboard arrangement of oppositely charged ions in each monolayer (Figure 2) (more discussion of the ion arrangements is presented in Section 4 in the Supporting Information). The application of VG leads to a rearrangement of the ions at both EDL interfaces. When a negative voltage VG is applied to the rubrene/IL interface, some positive ions are replaced by the same number of negative ions. If we assume that the number of substituted ions per unit area is N, to maintain charge neutrality, 2N holes in the semiconductor are introduced to the interface forming a conduction channel. Due to their Coulombic interaction with the ions, holes close to the interface see an electrostatic potential profile that is determined primarily by the first monolayer of the ions in the liquid. The N extra negative ions form “anion clusters” with their nearest neighbors of negative ions (Figure 2). Due to their greater Coulomb attraction, a hole that enters in close proximity to the cluster is likely to be “trapped”. The density of trapped holes is denoted by Pt. On the other hand, holes moving over the rest of unclustered negative ion sites are considered “free”, with a density of Pf. The charge neutrality requirement yields: Pf + Pt = 2N
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peaks in the same rubrene EDLT structure, but this is beyond the scope of the current discussion. Compared with prior work on electrolyte-gated rubrene transistors,[22–26] our current work described here employs a larger VG window (due to the appropriate IL selection and low temperature operation) and therefore, a much larger hole density. The successful achievement of large hole densities leads directly to our observation of two robust conductivity peaks. A series of control experiments were performed to confirm the validity of the conductivity peaks (Section 1 in the Supporting Information). One was to employ a four-terminal architecture to correct for contact resistance and to extract the sheet conductance, which is already included in Figure 1c. In Figure S1a in the Supporting Information, the contact resistance Rc is displayed together with the channel resistance Rch in the VG sweep. The result shows that Rc is typically a fraction of, or on the same order of magnitude as, Rch, as is generally observed in other electrolyte-gated organic transistors.[24,27] The non-monotonic VG-dependence of Rc is more likely related to the non-monotonic VG-dependence of hole mobility (in Figure 1d), as Rc was found to be inversely proportional to carrier mobility in organic transistors.[28,29] Besides the [P14][FAP] liquid that generally contributed to higher mobility and better device stability, rubrene EDLTs were also gated with other types of ILs, in which two conductivity peaks were likewise observed for similar hole densities (Figure S1b). In addition, the two conductivity peaks (with the same peak height) reproducibly appeared regardless of the VG sweep rate (Figure S1c), implying that the rubrene channel conduction is not affected by the ion motion and/or EDL rearrangement at the interface, both of which are strongly time-dependent. Finally, ID–VG and IG–VG were recorded at various temperatures (Figure S1d), where the peaks were robust at temperatures (245 K and 225 K) above IL melting points, whereas when the IL became frozen at 212 K, ID remained constant with no peaks and could not be modulated by VG anymore. This result clearly confirms that the two conductivity peaks are not associated with two different states of the IL, when a local Joule heating effect may induce solid-toliquid transitions that may cause two current levels. In addition, a lock-in setup was developed to examine the phase response between the drain current ID and VG as a function of hole densities, especially around the peak regions (Section 2 in the Supporting Information). In this method, a small AC oscillation (100 mV) was superimposed on the slowly swept DC voltage VG applied to the gate contact. The oscillation frequency was set at or below 10 Hz to minimize the gate displacement current. A fixed DC voltage VD was applied to the drain contact (typically −0.1 V). The drain current response ID (essentially equal to the source current IS), which includes the AC component, was measured. The phase angle θ between ID and VG, which is directly related to the sign of the differential transconductance, ∂(ID)/∂(VG), was also measured as a function of VG. As shown in Figure S2b in the Supporting Information, θ starts from 90° when the device is OFF (purely capacitive) and changes to almost 0° once the device is turned on, indicating that a conducting channel is formed. θ = 0° also indicates a positive differential transconductance (PDT), which is the case before the first conductivity peak. Interestingly, θ shifts sharply from 0° to almost 180° immediately after the first peak,
(1)
The positive ion sites are inaccessible to holes because of the Coulomb repulsion. Therefore, the potential landscape at the semiconductor/electrolyte interface exhibits a (random) muffin-tin type structure (this is consistent with our previous
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Figure 2. Schematic cartoon of hole transport in the vicinity of first ion layer of IL at the rubrene/IL interface. A trap site is composed of an anion clustered with its four neighboring anions, with shared cations at the boundary. Hole conduction occurs mainly between neighboring free sites and between neighboring trap sites, as indicated by the red arrows in the picture.
work for the first peak where the charge-neutral (unpaired) sites are a combination of the same number of positive and negative ions.[13] We assume that double occupancy of any anion sites is suppressed by the holes’ mutual Coulomb repulsion. At steady state, capture and emission of holes from the traps have to balance. If the total number of ions per unit area is M, and the capture (emission) rate is proportional to the amounts of free (trapped) holes and the unoccupied trap (free) sites, the following relationship is obtained:
M −γN cPf (2N − Pt ) = ePt ⎛⎜ − Pf ⎞⎟ τ ⎝ ⎠
(2)
where 1/τ is the fraction of ion sites accessible to holes in the absence of traps, γ/τ characterizes the number of such sites included in each trap, and γ is the spatial extent of the trap in terms of total number of cations and anions in the trap. Generally the values of γ and τ depend on the specific ion arrangement near the semiconductor/electrolyte interface. In the absence of specific information, a square lattice is assumed (Figure 2). For this case, τ is equal to 2 as only 1/2 of the ions (negatively charged) are accessible to holes, and γ/τ equals 4, assuming that the trap extends over nearest neighbor sites (γ = 8). The 2N term on the left-hand side indicates that each trap can accommodate two holes. c and e are the capture and emission kinetic coefficients. By detailed balance their ratio, F = e/c = exp(−ΔE/kT), is determined by the energy difference ΔE between the free and trap levels. Normalizing Equation 2 by M, a simple quadratic equation is obtained:
⎡ ⎛ 1 − nγ ⎞ ⎤ 2Fn(1 − nγ ) + 2n ⎟ ⎥ − p f2 (1 − F ) + p f ⎢F ⎜ =0 τ τ ⎝ ⎠⎦ ⎣
(3)
The lower case letters denote normalized densities (e.g., n = N/M). The normalized free hole concentration pf from 2530
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Equation 3, and the fraction of free holes to the total holes, are plotted as a function of the total hole concentration, p = 2N (proportional to the gate voltage VG), in Figure 3a and 3b, respectively. Results are shown for different emission/capture ratios, F. At small hole concentration (small VG), the trap density is small and the number of free sites is large, hence pf increases with p because an increase of gate voltage induces more holes to the interface. At large enough hole concentration (large VG), the trap density becomes significant and a further increase of the gate voltage brings more negative ions to the interface, which reduces the fraction of free sites and leads to a decrease of pf. When F increases, the emission of holes from trap to free states becomes easier and hence pf becomes larger. These results, consistent with our previous study,[13] imply that carrier localization is inevitable at high charge densities due to a strong correlation between holes and anions at the rubrene/ IL interface. Transport in this system involves hole transitions between free sites, between trap sites, and between traps and free sites. The system is mapped onto a two-dimensional square lattice and is treated as a bond percolation problem.[31] At equilibrium, no additional ions are present, and this lattice has M/τ nodes (per unit area). When N ions are exchanged, the lattice has M/τ – N(γ/τ) free nodes and N trap nodes. The fraction of normalized trap concentration is: ft =
n 1 ⎛γ ⎞ − n ⎜ − 1⎟ τ ⎝τ ⎠
(4)
A bond that describes the hole transport from free to free sites has the probability of bf = (1 −ft)2. Similarly, the bond fraction for the hole transport between trap sites is bt = ft2, and the bond fraction between a trap and a free site is btf = 2ft(1 −ft). The overall hole transition rate within each type of bond network is
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Figure 3. a,b) Free hole density pf (a) and fractions of free holes and trapped holes relative to the total holes (for F = 0.1) (b), as a function of the total hole concentration p, calculated from Equation 3. The hole densities pf and p are normalized with respect to the total areal density of ions, M. In panel (a), results are shown for different F values: F = 0.1 (solid line), F = 0.01 (dashed line), F = 0.001 (dash-dotted line).
proportional to the transition rate through a single bond, the densities of holes in the network where the transition starts, and the density of available sites in the network where the transition ends. The obtained overall transition rate is subsequently transformed into an equivalent “bond strength” for the specific network. The effective hole transition rate combining all three types of bonds is calculated analytically using an effective medium approximation (EMA), which replaces the random distribution of different types of bonds by a single effective bond that is the same for the whole lattice. The macroscopic properties of the system calculated from EMA are approximately the same with the results from Monte Carlo simulation.[32,33] The details are shown in Section 3 in the Supporting Information. Once the effective transition rate wm is determined, the channel conductivity in the semiconductor is given by:[34] g bm =
e2 w kT m
(5)
The calculated channel conductivity is displayed in Figure 4 for different emission/capture ratios, F. Two pronounced peaks are clearly accounted for by the proposed theory, in good agreement with our experimental observations. The first peak is attributed to the conduction of free holes. When the magnitude of VG is small, the density of trap sites is below the percolation threshold, therefore holes can only travel in the rubrene channel via free sites. As the magnitude of VG increases, the conductivity initially increases because pf increases, and
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Figure 4. Channel conductivity (arbitrary units, evaluated in effective medium approximation) as a function of the total hole concentration p (normalized with respect to the total areal density of ions, M). The total hole density is proportional to VG in rubrene EDLTs. Two peaks in the conductivity are observed. Results are shown for different F values: F = 0.1 (solid line), F = 0.01 (dashed line), F = 0.001 (dash-dotted line).
subsequently decreases because the increasing density of traps blocks the percolation path through free sites. The second peak is contributed by the conduction of trapped holes. As the magnitude of VG further increases beyond the complete obstruction of free sites, the percolation path through trap sites starts to form and the conductivity again increases. Eventually the conductivity decreases because most of the trap sites are filled and few sites are unoccupied as needed for hole transitions. The non-zero conductivity in the region between the two peaks is due to the free-to-trap and trap-to-free transitions. However, this transition is relatively weak since the free-to-free and trapto-trap transitions correspond to resonant processes but the former processes do not. The range of the hole concentration involving the two peaks predicted by the model depends on the specific arrangement of ions (i.e., the values of τ and γ). Our model is also applicable to traps with different energetic depths, namely, either shallow or deep traps, since the conductivity peaks are qualitatively the same for different F values. It is noteworthy that the two-channel conduction is more of a strong coupling effect between the holes in the rubrene and anions in the IL, rather than being dependent on any specific properties of rubrene itself. As a result, we expect this peak behavior of conductivity to be a general phenomenon in EDLTs based on low dielectric constant and narrow bandwidth semiconductors. However, we note also that in the system explored here the areal densities of IL molecules and organic semiconductor molecules are very similar. In summary, a charge transport model is proposed to explain the experimentally observed and unusual conductivity peaks as a function of hole densities above 1013 cm−2 in IL-gated rubrene EDLTs. We attribute the results to hole conduction in a free-site channel at low hole density, and in a trap-site channel at large hole density. Charge-carrier trapping arising from the strong interaction between holes and negatively charged ions is the
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key concept for understanding the transport behavior in these unconventional transistors. The experimental and theoretical results suggest that in order to overcome the conductivity peak and further enhance the conductivity, the electrical potential landscape at the rubrene/IL interface has to be smoothed. This can possibly be achieved by the use of semiconductor crystals with larger dielectric constant, or perhaps by enlarging the anion and/or cation radius to reduce the Coulombic interaction with holes. Our work is important to the current research community exploring novel transport phenomena in organic semiconductors through electrolyte gating.
Experimental Section Crystal Growth: The source materials of rubrene were purchased from Sigma–Aldrich (sublimed grade) (Milwaukee, US). Rubrene crystals were grown by horizontal physical vapor transport.[35] Thick crystals (>10 μm in thickness) were selected for subsequent device fabrication. Device Fabrication: Air-gap polydimethylsiloxane (PDMS) (Sylgard 184, Ellsworth Adhesives) substrates with pre-patterned souce/drain/ gate contacts were fabricated using previously establish procedures.[36] The metal contacts were 3/20 nm Cr/Au (evaporation rate 0.1 nm/s) deposited in a CHA e-beam evaporator. The depth of the air-gap was 5 μm, measured by a KLA-Tencor P-16 surface profiler. Crystals were laminated across the source and drain contacts forming so-called air-gap transistors at first, and the EDLTs were fabricated by injecting a drop of ionic liquid (IL) (all in high purity grade 99.9%, purchased from EMD Chemicals, USA) into the channel and filling up the entire air-gap through capillarity. The liquids were dried before use in a vacuum oven at 70 °C for three days and were kept in a N2-filled glovebox afterwards to minimize the water contamination. Electrical Measurement: Rubrene EDLTs were characterized in a Desert Cryogenics (Lakeshore, Inc) vacuum probe station in a N2-filled glovebox with Keithley 236 and 6517 electrometers using homemade LabVIEW programs for control. In the four-probe measurement, two 10 μm-wide voltage-sensing probes were connected with high-impedance Keithley 6517 electrometers. The low-temperature measurement employed a Lakeshore 331 temperature controller. The lock-in measurement used an EG&G 7260 Lock-In Amplifier (typical AC oscillation was 100 mV). All the measurements were carried out in the dark and in vacuum at a pressure of
Wei Xie, Feilong Liu, Sha Shi, P. Paul Ruden, and C. Daniel Frisbie* Electrolyte gating has recently become a powerful technique to induce ultrahigh surface charge densities (1013 cm−2 to 1015 cm−2) in a variety of semiconductor materials in fieldeffect transistor (FET) geometry, forming the so-called electric double layer transistors (EDLTs).[1–4] With the application of a gate voltage, electrolyte ions migrate to the gate/electrolyte and semiconductor/electrolyte interfaces, forming two nanometer thick electric double layers (EDLs). The gate electric field is effectively screened across the bulk of the electrolyte layer and only persists at the EDLs. Consequently, a large capacitance on the order of 1–10 μF/cm2 is achieved, resulting in a high-density charge accumulation in the semiconductor channel.[5] Such field-induced high charge densities have facilitated observations of novel transport phenomena in physics-rich correlated electron materials, such as the insulator-to-metal transition in ZnO[6] and superconductivity in SrTiO3[7] near sheet charge densities of 1014 cm−2. For all these cases, charge densities can be systematically tuned by the gate voltage over a broad range within the same device, allowing stable and reversible transition between different electronic phases. The electrolyte gating technique also provides valuable opportunities to probe charge transport in organic semiconductor single crystals in the high-density regime, which previously was only accessed by tedious and irreversible chemical doping approaches.[8] In fact, most of the novel transport behavior in organic semiconductors, such as metallic transport and superconductivity, occur at sheet charge densities above 1013 cm−2.[9,10] Despite the increasing interest in tuning electronic phase transitions in electrolyte-gated organic semiconductors, the role of free carrier density on electrical properties is not as well understood as it is in more conventional electronic materials. In particular, significant charge carrier correlations can be anticipated in these materials because they are characterized by low permittivity (low charge screening) and relatively narrow bandwidths. Besides, the presence of bulky electrolyte ions in the vicinity (∼1 nm) of charge carriers at the
W. Xie, Prof. C. D. Frisbie Department of Chemical Engineering and Materials Science University of Minnesota 421 Washington Ave SE Minneapolis, MN 55455, USA E-mail: [email protected] F. Liu, S. Shi, Prof. P. P. Ruden Department of Electrical and Computer Engineering University of Minnesota 200 Union St. SE Minneapolis, MN 55455, USA
DOI: 10.1002/adma.201304946
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semiconductor/electrolyte interface can introduce a large Coulombic effect that in turn influences the charge transport. One recent experimental observation possibly reflecting such effects was that in electrolyte-gated polymer films[11,12] and small-molecule single crystals,[13,14] the channel conductivity showed a significant peak as a function of increasing charge density, rather than a monotonic dependence as in organic transistors gated with conventional dielectrics.[15] The generality of this unusual conductivity peak among a wide category of organic semiconductors prompts us to perform systematic experimental and theoretical investigations. In this communication, we expand our previous work[13] in understanding the transport mechanism associated with the conductivity peak in ionic-liquid (IL) gated rubrene singlecrystal EDLTs. By extending the gate-induced surface charge density up to 6 × 1013 cm−2, which corresponds to 1/3 hole per rubrene molecule in one molecular layer, we observe two pronounced channel conductivity peaks reproducibly at densities corresponding to 0.11 holes/rubrene and 0.27 holes/rubrene. The validity of the conductivity peaks has been confirmed by various control measurements. Considering the strong interactions between holes and negatively charged ions at the rubrene/ IL interface, holes in the rubrene channel are viewed as moving in a potential landscape where hole density dependent trapping occurs. A two-channel conduction model is thus introduced, ascribing the first and second conductivity peaks to the transport of holes over the “free” sites and “trapped” sites, respectively. This model is based on and extensively extends our previous work for the first conductivity peak in rubrene EDLTs.[13] Our work is also a significant step forward in understanding the puzzling charge-density dependent conductivity behavior in organic semiconductor based EDLTs. Rubrene EDLTs were fabricated following previously established procedures.[16] An air-gap transistor was first made by laminating a rubrene crystal on a pre-patterned poly(dimethylsiloxane) (PDMS) substrate, and a small drop of IL was subsequently injected into the channel by capillarity filling up the entire space of air-gap, forming a rubrene EDLT (Figure 1a). Critical to the success of this study, which involves device operation at large gate bias for an extended period of time, was a careful selection of IL composition (we use [1-butyl-1-methyl pyrrolidinium][tris(pentafluoroethyl)trifluorophosphate], or [P14][FAP], molecular structure shown in Figure 1b) as well as operating the device at lower temperatures slightly above the freezing point of the liquid (around 230 K).[14] Consequently, a larger gate-voltage window for the EDLT was achieved, allowing hole accumulation up to (6–7) × 1013 cm−2 (ca. 0.33 holes/rubrene) before device failure, as identified by the gate displacement current measurement.[14,17,18] The pure capacitor-like characteristic of the displacement current[14]
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Figure 1. a) Cross-sectional device structure of a rubrene EDLT gated with IL. b) Molecular structure of rubrene and [P14][FAP]. c) (left axis, filled circles) sheet conductance σs as a function of gate voltage VG over three consecutive sweeps for a rubrene EDLT gated with [P14][FAP] taken at 225 K. Both forward and reverse sweeps are shown. The sweep rate is 50 mV/s; (right axis, open circles) hole density p as a function of VG, determined from gate displacement current. d,e) Hole mobility μ (d) and gate current IG (e) versus VG for the same device. Device dimensions: W = 250 μm, L = 300 μm. The gap is 5 μm in depth.
corroborates the fact that hole accumulation is achieved via two-dimensional electrostatic field-effect, and ion penetration into rubrene does not occur. This is further supported by the preservation of the rubrene crystal structure before and after IL gating.[16] The transfer curve is shown in Figure 1c, where the four-terminal sheet conductance σs is plotted as a funcΔL I D tion of the gate voltage VG (σ s = W , where W is the channel ΔV width, ΔL and ΔV are, respectively, the distance and voltage difference between two voltage-sensing probes, and ID is the drain current). As VG is swept forward towards large negative values, the channel conductivity (used interchangeably with sheet conductance σs) exhibits two pronounced peaks which not only appear robust and repeatable over multiple VG sweeps, but are also reproducible when VG is swept backward. The hysteresis loop during a VG-sweep cycle is likely due to the slow ion motion at low temperatures, and can be negligibly small at elevated temperatures.[14] Looking only at the forward sweeps in over 20 rubrene EDLTs, we find the first conductivity peak
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occurs at hole density p = (2.0 ± 0.2) × 1013 cm−2 (ca. 0.11 holes/ rubrene) and the second peak at p = (5.2 ± 0.5) × 1013 cm−2 (ca. 0.27 holes/rubrene). The effective hole mobility μ (=σs/ep, where e is the elemental charge) shows a non-monotonic VG-dependence as well in Figure 1d, with a maximum mobility reaching 2–3 cm2 V−1 s−1. Compared with the value at the first peak, the hole mobility at the second peak is significantly smaller, typically below 1 cm2 V−1 s−1. The gate current IG, shown in Figure 1e, is orders of magnitude smaller than ID (not explicitly shown), and is monotonically dependent on VG without any peaks, indicating the electrochemical reaction of the IL during the device operation is negligible. To the best of our knowledge, these unusual conductivity and mobility behaviors at hole densities beyond 1013 cm−2 in rubrene EDLTs have not been observed in any OFETs gated with conventional dielectrics,[15,19,20] or inorganic EDLTs gated with electrolytes.[6] In separate work,[21] we have also investigated the coupling of channel conductivity peaks with the gate-to-channel capacitance
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reflecting the occurrence of a negative differential transconductance (NDT) (i.e., ID decreases with increasing VG). A transition from PDT to NDT therefore confirms the presence of the conductivity peak. Likewise, the second conductivity peak is confirmed by the same 180° shift in θ at larger VG (Figure S2b). To summarize the experimental results, we observe two robust and reproducible conductivity peaks as a function of VG in rubrene EDLTs at hole densities above 1013 cm−2. We have carefully excluded other possible contributions to the conductivity peaks, such as the electrochemical reaction of the IL, ion penetration into rubrene, interfacial EDL rearrangement, Joule heating and contact effects. Additionally, on the basis of the calculated band structure for bulk rubrene crystals,[30] we view multiband transport as unlikely in the structures examined. We therefore conclude the conductivity behavior is related to the transport properties of rubrene in the presence of ions at the interface. As indicated by our previous work on the first conductivity peak, a key consideration in these EDLT devices (compared to devices gated with conventional dielectrics) is the role played by discrete ions at the rubrene-IL interface.[13] Due to the low dielectric constant (εr ≈ 3) and narrow bandwidth (ca. 0.5 eV) of rubrene, a strong interaction of negatively charged anions in the IL with the positively charged holes at the rubrene surface is anticipated, resulting in trapping of holes. This important concept, as elaborated in the following, provides baseline guidance for understanding the charge transport in any EDLTs based on organic semiconductors at high charge densities. We assume that the positive and negative ions in the ILs (no solvent) are strongly correlated by their mutual Coulomb interactions. In equilibrium, as the overall IL is charge-neutral, the minimization of the Coulomb energy leads to a checkerboard arrangement of oppositely charged ions in each monolayer (Figure 2) (more discussion of the ion arrangements is presented in Section 4 in the Supporting Information). The application of VG leads to a rearrangement of the ions at both EDL interfaces. When a negative voltage VG is applied to the rubrene/IL interface, some positive ions are replaced by the same number of negative ions. If we assume that the number of substituted ions per unit area is N, to maintain charge neutrality, 2N holes in the semiconductor are introduced to the interface forming a conduction channel. Due to their Coulombic interaction with the ions, holes close to the interface see an electrostatic potential profile that is determined primarily by the first monolayer of the ions in the liquid. The N extra negative ions form “anion clusters” with their nearest neighbors of negative ions (Figure 2). Due to their greater Coulomb attraction, a hole that enters in close proximity to the cluster is likely to be “trapped”. The density of trapped holes is denoted by Pt. On the other hand, holes moving over the rest of unclustered negative ion sites are considered “free”, with a density of Pf. The charge neutrality requirement yields: Pf + Pt = 2N
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peaks in the same rubrene EDLT structure, but this is beyond the scope of the current discussion. Compared with prior work on electrolyte-gated rubrene transistors,[22–26] our current work described here employs a larger VG window (due to the appropriate IL selection and low temperature operation) and therefore, a much larger hole density. The successful achievement of large hole densities leads directly to our observation of two robust conductivity peaks. A series of control experiments were performed to confirm the validity of the conductivity peaks (Section 1 in the Supporting Information). One was to employ a four-terminal architecture to correct for contact resistance and to extract the sheet conductance, which is already included in Figure 1c. In Figure S1a in the Supporting Information, the contact resistance Rc is displayed together with the channel resistance Rch in the VG sweep. The result shows that Rc is typically a fraction of, or on the same order of magnitude as, Rch, as is generally observed in other electrolyte-gated organic transistors.[24,27] The non-monotonic VG-dependence of Rc is more likely related to the non-monotonic VG-dependence of hole mobility (in Figure 1d), as Rc was found to be inversely proportional to carrier mobility in organic transistors.[28,29] Besides the [P14][FAP] liquid that generally contributed to higher mobility and better device stability, rubrene EDLTs were also gated with other types of ILs, in which two conductivity peaks were likewise observed for similar hole densities (Figure S1b). In addition, the two conductivity peaks (with the same peak height) reproducibly appeared regardless of the VG sweep rate (Figure S1c), implying that the rubrene channel conduction is not affected by the ion motion and/or EDL rearrangement at the interface, both of which are strongly time-dependent. Finally, ID–VG and IG–VG were recorded at various temperatures (Figure S1d), where the peaks were robust at temperatures (245 K and 225 K) above IL melting points, whereas when the IL became frozen at 212 K, ID remained constant with no peaks and could not be modulated by VG anymore. This result clearly confirms that the two conductivity peaks are not associated with two different states of the IL, when a local Joule heating effect may induce solid-toliquid transitions that may cause two current levels. In addition, a lock-in setup was developed to examine the phase response between the drain current ID and VG as a function of hole densities, especially around the peak regions (Section 2 in the Supporting Information). In this method, a small AC oscillation (100 mV) was superimposed on the slowly swept DC voltage VG applied to the gate contact. The oscillation frequency was set at or below 10 Hz to minimize the gate displacement current. A fixed DC voltage VD was applied to the drain contact (typically −0.1 V). The drain current response ID (essentially equal to the source current IS), which includes the AC component, was measured. The phase angle θ between ID and VG, which is directly related to the sign of the differential transconductance, ∂(ID)/∂(VG), was also measured as a function of VG. As shown in Figure S2b in the Supporting Information, θ starts from 90° when the device is OFF (purely capacitive) and changes to almost 0° once the device is turned on, indicating that a conducting channel is formed. θ = 0° also indicates a positive differential transconductance (PDT), which is the case before the first conductivity peak. Interestingly, θ shifts sharply from 0° to almost 180° immediately after the first peak,
(1)
The positive ion sites are inaccessible to holes because of the Coulomb repulsion. Therefore, the potential landscape at the semiconductor/electrolyte interface exhibits a (random) muffin-tin type structure (this is consistent with our previous
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Figure 2. Schematic cartoon of hole transport in the vicinity of first ion layer of IL at the rubrene/IL interface. A trap site is composed of an anion clustered with its four neighboring anions, with shared cations at the boundary. Hole conduction occurs mainly between neighboring free sites and between neighboring trap sites, as indicated by the red arrows in the picture.
work for the first peak where the charge-neutral (unpaired) sites are a combination of the same number of positive and negative ions.[13] We assume that double occupancy of any anion sites is suppressed by the holes’ mutual Coulomb repulsion. At steady state, capture and emission of holes from the traps have to balance. If the total number of ions per unit area is M, and the capture (emission) rate is proportional to the amounts of free (trapped) holes and the unoccupied trap (free) sites, the following relationship is obtained:
M −γN cPf (2N − Pt ) = ePt ⎛⎜ − Pf ⎞⎟ τ ⎝ ⎠
(2)
where 1/τ is the fraction of ion sites accessible to holes in the absence of traps, γ/τ characterizes the number of such sites included in each trap, and γ is the spatial extent of the trap in terms of total number of cations and anions in the trap. Generally the values of γ and τ depend on the specific ion arrangement near the semiconductor/electrolyte interface. In the absence of specific information, a square lattice is assumed (Figure 2). For this case, τ is equal to 2 as only 1/2 of the ions (negatively charged) are accessible to holes, and γ/τ equals 4, assuming that the trap extends over nearest neighbor sites (γ = 8). The 2N term on the left-hand side indicates that each trap can accommodate two holes. c and e are the capture and emission kinetic coefficients. By detailed balance their ratio, F = e/c = exp(−ΔE/kT), is determined by the energy difference ΔE between the free and trap levels. Normalizing Equation 2 by M, a simple quadratic equation is obtained:
⎡ ⎛ 1 − nγ ⎞ ⎤ 2Fn(1 − nγ ) + 2n ⎟ ⎥ − p f2 (1 − F ) + p f ⎢F ⎜ =0 τ τ ⎝ ⎠⎦ ⎣
(3)
The lower case letters denote normalized densities (e.g., n = N/M). The normalized free hole concentration pf from 2530
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Equation 3, and the fraction of free holes to the total holes, are plotted as a function of the total hole concentration, p = 2N (proportional to the gate voltage VG), in Figure 3a and 3b, respectively. Results are shown for different emission/capture ratios, F. At small hole concentration (small VG), the trap density is small and the number of free sites is large, hence pf increases with p because an increase of gate voltage induces more holes to the interface. At large enough hole concentration (large VG), the trap density becomes significant and a further increase of the gate voltage brings more negative ions to the interface, which reduces the fraction of free sites and leads to a decrease of pf. When F increases, the emission of holes from trap to free states becomes easier and hence pf becomes larger. These results, consistent with our previous study,[13] imply that carrier localization is inevitable at high charge densities due to a strong correlation between holes and anions at the rubrene/ IL interface. Transport in this system involves hole transitions between free sites, between trap sites, and between traps and free sites. The system is mapped onto a two-dimensional square lattice and is treated as a bond percolation problem.[31] At equilibrium, no additional ions are present, and this lattice has M/τ nodes (per unit area). When N ions are exchanged, the lattice has M/τ – N(γ/τ) free nodes and N trap nodes. The fraction of normalized trap concentration is: ft =
n 1 ⎛γ ⎞ − n ⎜ − 1⎟ τ ⎝τ ⎠
(4)
A bond that describes the hole transport from free to free sites has the probability of bf = (1 −ft)2. Similarly, the bond fraction for the hole transport between trap sites is bt = ft2, and the bond fraction between a trap and a free site is btf = 2ft(1 −ft). The overall hole transition rate within each type of bond network is
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0.07
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Figure 3. a,b) Free hole density pf (a) and fractions of free holes and trapped holes relative to the total holes (for F = 0.1) (b), as a function of the total hole concentration p, calculated from Equation 3. The hole densities pf and p are normalized with respect to the total areal density of ions, M. In panel (a), results are shown for different F values: F = 0.1 (solid line), F = 0.01 (dashed line), F = 0.001 (dash-dotted line).
proportional to the transition rate through a single bond, the densities of holes in the network where the transition starts, and the density of available sites in the network where the transition ends. The obtained overall transition rate is subsequently transformed into an equivalent “bond strength” for the specific network. The effective hole transition rate combining all three types of bonds is calculated analytically using an effective medium approximation (EMA), which replaces the random distribution of different types of bonds by a single effective bond that is the same for the whole lattice. The macroscopic properties of the system calculated from EMA are approximately the same with the results from Monte Carlo simulation.[32,33] The details are shown in Section 3 in the Supporting Information. Once the effective transition rate wm is determined, the channel conductivity in the semiconductor is given by:[34] g bm =
e2 w kT m
(5)
The calculated channel conductivity is displayed in Figure 4 for different emission/capture ratios, F. Two pronounced peaks are clearly accounted for by the proposed theory, in good agreement with our experimental observations. The first peak is attributed to the conduction of free holes. When the magnitude of VG is small, the density of trap sites is below the percolation threshold, therefore holes can only travel in the rubrene channel via free sites. As the magnitude of VG increases, the conductivity initially increases because pf increases, and
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Figure 4. Channel conductivity (arbitrary units, evaluated in effective medium approximation) as a function of the total hole concentration p (normalized with respect to the total areal density of ions, M). The total hole density is proportional to VG in rubrene EDLTs. Two peaks in the conductivity are observed. Results are shown for different F values: F = 0.1 (solid line), F = 0.01 (dashed line), F = 0.001 (dash-dotted line).
subsequently decreases because the increasing density of traps blocks the percolation path through free sites. The second peak is contributed by the conduction of trapped holes. As the magnitude of VG further increases beyond the complete obstruction of free sites, the percolation path through trap sites starts to form and the conductivity again increases. Eventually the conductivity decreases because most of the trap sites are filled and few sites are unoccupied as needed for hole transitions. The non-zero conductivity in the region between the two peaks is due to the free-to-trap and trap-to-free transitions. However, this transition is relatively weak since the free-to-free and trapto-trap transitions correspond to resonant processes but the former processes do not. The range of the hole concentration involving the two peaks predicted by the model depends on the specific arrangement of ions (i.e., the values of τ and γ). Our model is also applicable to traps with different energetic depths, namely, either shallow or deep traps, since the conductivity peaks are qualitatively the same for different F values. It is noteworthy that the two-channel conduction is more of a strong coupling effect between the holes in the rubrene and anions in the IL, rather than being dependent on any specific properties of rubrene itself. As a result, we expect this peak behavior of conductivity to be a general phenomenon in EDLTs based on low dielectric constant and narrow bandwidth semiconductors. However, we note also that in the system explored here the areal densities of IL molecules and organic semiconductor molecules are very similar. In summary, a charge transport model is proposed to explain the experimentally observed and unusual conductivity peaks as a function of hole densities above 1013 cm−2 in IL-gated rubrene EDLTs. We attribute the results to hole conduction in a free-site channel at low hole density, and in a trap-site channel at large hole density. Charge-carrier trapping arising from the strong interaction between holes and negatively charged ions is the
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key concept for understanding the transport behavior in these unconventional transistors. The experimental and theoretical results suggest that in order to overcome the conductivity peak and further enhance the conductivity, the electrical potential landscape at the rubrene/IL interface has to be smoothed. This can possibly be achieved by the use of semiconductor crystals with larger dielectric constant, or perhaps by enlarging the anion and/or cation radius to reduce the Coulombic interaction with holes. Our work is important to the current research community exploring novel transport phenomena in organic semiconductors through electrolyte gating.
Experimental Section Crystal Growth: The source materials of rubrene were purchased from Sigma–Aldrich (sublimed grade) (Milwaukee, US). Rubrene crystals were grown by horizontal physical vapor transport.[35] Thick crystals (>10 μm in thickness) were selected for subsequent device fabrication. Device Fabrication: Air-gap polydimethylsiloxane (PDMS) (Sylgard 184, Ellsworth Adhesives) substrates with pre-patterned souce/drain/ gate contacts were fabricated using previously establish procedures.[36] The metal contacts were 3/20 nm Cr/Au (evaporation rate 0.1 nm/s) deposited in a CHA e-beam evaporator. The depth of the air-gap was 5 μm, measured by a KLA-Tencor P-16 surface profiler. Crystals were laminated across the source and drain contacts forming so-called air-gap transistors at first, and the EDLTs were fabricated by injecting a drop of ionic liquid (IL) (all in high purity grade 99.9%, purchased from EMD Chemicals, USA) into the channel and filling up the entire air-gap through capillarity. The liquids were dried before use in a vacuum oven at 70 °C for three days and were kept in a N2-filled glovebox afterwards to minimize the water contamination. Electrical Measurement: Rubrene EDLTs were characterized in a Desert Cryogenics (Lakeshore, Inc) vacuum probe station in a N2-filled glovebox with Keithley 236 and 6517 electrometers using homemade LabVIEW programs for control. In the four-probe measurement, two 10 μm-wide voltage-sensing probes were connected with high-impedance Keithley 6517 electrometers. The low-temperature measurement employed a Lakeshore 331 temperature controller. The lock-in measurement used an EG&G 7260 Lock-In Amplifier (typical AC oscillation was 100 mV). All the measurements were carried out in the dark and in vacuum at a pressure of
