APPLIED PHYSICS LETTERS 88, 073104 共2006兲
Gate capacitance in electrochemical transistor of single-walled carbon nanotube Hidekazu Shimotani,a兲 Takayoshi Kanbara, and Yoshihiro Iwasa Institute for Materials Research, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan and Japan Science and Technology Agency (CREST), 4-1-8, Honcho, Kawaguchi-shi, Saitama 332-0012, Japan
Kazuhito Tsukagoshi RIKEN, 2-1, Hirosawa, Wako, Saitama 351-0198, Japan
Yoshinobu Aoyagi RIKEN, 2-1, Hirosawa, Wako, Saitama 351-0198, Japan and Tokyo Institute of Technology, Yokohama 226-8502, Japan
Hiromichi Kataura National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8562, Japan
共Received 16 September 2005; accepted 14 January 2006; published online 14 February 2006兲 In the electrochemical transistor of a single-walled carbon nanotube, we introduced the fourth terminal, which works as a reference electrode. This enables accurate control of change in gate voltage, i.e., potential difference between the electrolyte and the source electrode, and quantitative analyses of the gate capacitance. We found that the geometrical capacitance, which was ignored in the conventional model, makes a crucial contribution to the device characteristics, comparable to that from the chemical capacitance. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2173626兴 Field-effect transistors 共FETs兲 of single-walled carbon nanotubes 共SWNTs兲 are of scientific and practical interest for their superior FET characteristics.1 Recently, another type of transistor using a SWNT 共Ref. 2兲 and a multiwalled carbon nanotube 共MWNT兲 共Ref. 3兲 employing electrolyte as a gate electrode has been proposed from the viewpoint of sensor applications. These transistors are called electrochemical transistors 共ECTs兲. SWNT-ECTs are also realized with a polymer electrolyte.4,5 In an ECT, a very thin 共⬃1 nm兲 electric double layer 共EDL兲 on a surface of a SWNT works as a gate capacitor instead of a thick dielectric layer in back-gated FETs. Therefore, the geometrical electrostatic capacitance 共Cgeom兲 of ECTs is much larger than that of typical back-gated FETs. The amount of the charge 共Q兲 in a ba ck-gated SWNTFET is assumed to be linearly controlled by the gate voltage 共VG兲 as ⌬Q = Cgeom⌬VG. In a SWNT-ECT, only a small VG共⬃1 V兲 can accumulate large Q due to the large Cgeom, and the Fermi energy 共EF兲 shifts notably for its mesoscopic size. The fact invalidates the simple Cgeom model, and complicates the quantitative understanding of the SWNT-ECT. To reach its thorough understanding, precise control of the voltage drop in the EDL is essential. We made four-terminal ECT devices with a reference electrode 共RE兲 for this purpose, which is similar to the configuration employed in some conducting polymer ECTs.6,7 FET devices 关Fig. 1共a兲兴 was prepared on a SiO2 共200 nm兲 / n++-Si substrate. SWNTs synthesized by a laser ablation method were dispersed in 1,2-dichloroethane with a兲
Author to whom correspondence should be addressed at: Division of Low Temperature Condensed State Physics, Institute for Materials Research, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan; electronic mail:
[email protected]
ultrasonic and dropped on the substrate. The source and drain electrodes 共Pt–Au兲 were formed on a SWNT with electronbeam lithography.8 Because a SWNT shows either semiconducting or metallic conduction depending on its chirality, semiconducting ones were sorted out from tens of devices by FET characteristics. Two devices among them are shown in this letter. The diameters of the SWNT channels of the two devices measured by an atomic force microscope were 1.3– 1.7 nm and 1.4– 2.0 nm. Inaccuracies of the diameters are due to the roughness of the substrates. This means that the devices consist of one SWNT or a bundle of a few
FIG. 1. Configurations of 共a兲 back-gate FET and 共b兲 ECT. The photograph is a scanning electron micrograph of the device showing two Pt/ Au electrodes and a SWNT. VDS: Voltage between the source and drain electrodes, ID: Current into the drain electrode, RE: Ag/ Ag+ reference electrode. CE: Pt counterelectrode.
0003-6951/2006/88共7兲/073104/3/$23.00 88, 073104-1 © 2006 American Institute of Physics Downloaded 26 Apr 2006 to 220.149.161.21. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
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FIG. 2. The conductance 共G兲 vs 共VG-Vth兲 of a metal oxide semiconductor FET 共dashed line兲 and an electrochemical transistor 共solid line兲 of a SWNT, where VG is the gate voltage and Vth is the threshold voltages of hole conductions.
SWNTs, considering the typical diameter of SWNTs prepared by laser ablation 共1.4 nm兲. The device was then immersed in 0.1 M propylene carbonate solution of LiClO4 in an electrochemical cell 关Fig. 1共b兲兴 with a Pt counterelectrode 共CE兲 and a Ag/ Ag+ RE共0.01 M AgNO3 / 0.1 M NBu4ClO4 / CH3CN, BAS Inc.兲 for ECT measurements. The electrostatic potential 共兲 of the source and drain electrode with respect to the RE was controlled by a potentiostat. VG of an ECT, which is the voltage drop at the EDL gate capacitor, is precisely controlled by as ⌬VG = −⌬ using the RE, otherwise ⌬VG cannot be controlled, because the partition of into the voltage drop at the CE and the source and drain electrodes is not measurable. The conductance 共G兲 of the SWNT was measured at various from slopes of ID − VDS 关see definitions in Fig. 1共b兲兴 curves 共−50 mV艋 VDS 艋 50 mV兲 to eliminate influences from residual current. The average potential of the source and drain electrode was kept at during the ID − VDS measurements. All ECT measurements were done at room temperature under N2 flow. G in back-gated FET and ECT modes are plotted in Fig. 2 for an identical SWNT against VG − Vth, where Vth is the threshold voltage. The transconductance of the back-gated FET and ECT at VDS = 50 mV were 1.1⫻ 10−9 S and 5.4 ⫻ 10−7 S, respectively. Figure 2 clearly demonstrates the excellent gate coupling in the SWNT-ECT, being consistent with the multiwalled carbon nonotube-ECT.3 Cgeom of an EDL is approximated by that of the Helmholtz layer when the electrolyte concentration is high and the present experiments satisfies the criterion.9 The thickness of the Helmholtz layer, which is the summation of the van der Waals radius of a carbon atom in the SWNT and the radius of a solvated ion in the electrolyte, was assumed to be 1 nm. The ratio of the capacitor thicknesses to that in the FET configuration 共1:200兲 is in the same order as that of the transconductance. Figures 3共a兲 and 3共b兲 display ECT characteristics of the two different devices for one cycle of scan. Differently from Fig. 2, the horizontal axis is not VG but . Therefore, holes and electrons are accumulated in the right and left hand of the plot, respectively. The contribution from a residual current to G was estimated as 共dIC / d兲 / 共−2兲, where IC is a current into the CE, assuming the residual currents from the
FIG. 3. 共a兲 and 共b兲 Conductance 共G兲 vs average potential of the source and drain electrodes 共兲 with respect to the Ag/ Ag+ RE. The results of two different devices were plotted. The closed triangles show points where the first valence and conduction subbands start contributing to the current. The open triangles show the onset of the current through the second valence subband. The dashed lines are a guide for the eyes. 共c兲 DOS 关N共E兲兴 of a SWNT is plotted against energy 共E兲. The closed triangles show the edge of the first valence and conduction bands. The open triangle shows the edge of the second valence subband.
source and drain electrode were comparable with each other, and the contribution was less than 80 nS. In the direction of hole doping, a two-stepped behavior was observed in both devices: G took off at ⬃ 0 V, saturated at 0.4– 0.6 V, and increased again at ⬃0.8 V. This is attributable to a consequence of the one-dimensional conductance in a SWNT, where the product of the density of states 共DOS兲 and the Fermi velocity in a subband is constant. Therefore, step-wise increases of G versus VG in a SWNT are expected, as the number of subbands contributing to the conduction increases by VG.10 Similar G-VG behavior was reported Appenzeller et al.11 on SWNT-FETs with a rather thin 共5 nm兲 gate dielectric layer. In mesoscopic devices with large Cgeom, researchers have often approached from the other limit, where directly controls EF in semiconductors as ⌬ = ⌬EF rather than Q. Actually, previous papers on ECT of carbon nanotubes assumed this limit.2,3 According to this model, the voltage difference between the filled and open triangles in Figs. 3共a兲 and 3共b兲 共0.7– 0.8 V兲 corresponds to the energy separation between the first and second valence subbands. For a direct comparison between ECT characteristics and band structures of SWNTs, we show in Fig. 3共c兲 a universal DOS 共Ref. 12兲 of a SWNT of 1.4 nm in diameter employing the nearestneighboring interaction of 2.7 eV. The difference of , where the first and second valence subbands start contributing to the current, is considerably larger than the energy difference of the corresponding subband edges 共0.2– 0.3 eV for a SWNT of 1.3– 2.0 nm in diameter兲.13 This discrepancy in-
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FIG. 4. 共a兲 The potential drop by the geometric capacitance 共Vchem兲 and by the chemical capacitance 共Vgeom兲 plotted against the gate voltage 共VG兲. Vchem and Vgeom are plotted by a dashed line and a solid line, respectively. 共b兲The universal DOS of the first and second valence subband of a SWNT of 1.4 nm in diameter. The closed and open triangles in 共a兲 indicate the points where EF reaches the first and second valence subbands shown in 共b兲, respectively.
dicates that the model is insufficient for a quantitative description of the SWNT-ECT. For full understanding of the characteristics of the ECTs, their capacitance needs to be considered in more detail. The gate capacitance of the SWNT-ECTs should be considered as a series of Cgeom and chemical capacitance 共Cchem兲. Cchem is defined by dQ / d共EF / e兲,14 and the total −1 −1 −1 capacitance 共Ctot兲 is derived from Ctot = Cgeom + Cchem . The applied voltage between the electrolyte and the source and drain electrodes 共VG兲 is divided into Vchem and Vgeom, where dVchem = dQ / Cchem and dVgeom = dQ / Cgeom. Considering the definition of Cchem , dEF = edVchem is derived. In the following, we estimated the contribution of Cgeom and Cchem for quantitative explanation of the ECT characteristics. The Cgeom was derived as the following equation considering the SWNT and the outer Helmholtz plane forming the EDL as two coaxial cylinders:Cgeom = 20 / ln关共d + 2t兲2兴, where 0 and are the electric constant in a vacuum and the dielectric constant of propylene carbonate in the Helmholtz layer, respectively. The diameter of SWNT 共d兲 and the thickness of the Helmholtz layer 共t兲 were as sumed to be 1.4 nm and 1 nm, respectively, as mentioned above. If of bulk propylene carbonate 共64.92兲 is employed, Cgeom becomes much larger than Cchem. Consequently, Vchem approximates VG, which means e⌬共=−e⌬VG兲 ⬃ ⌬EF. The previous works on carbon nanotube ECTs employed this assumption.2,3 However, of solvent in a Helmholtz layer is generally smaller than that in a bulk state. For instance, of water 共78.3兲 is reduced to 5–10 in a Helmholtz layer.15 Therefore, the above assumption should not be employed, but a reduced must be considered. Indeed, the experimental results are well explained employing one-fifth of the dielectric constant of the bulk propylene carbonate as , which gives Cgeom = 0.03 共electron/ V atom兲, as described below. The calculated partition of VG into Vgeom and Vchem was plotted against VG in Fig. 4, where VG = 0 was set to the SWNT charge neutrality point. Q共Vchem兲 was derived from universal DOS 关D共E兲兴 of a SWNT of 1.4 nm in diameter, and Fermi–Dirac distribution at T = 290 K as follows:
Vgeom共Vchem兲 = Q共Vchem兲 / Cgeom and VG共Vchem兲 = Vchem + Vgeom共Vchem兲. Figure 4 shows that employing the reduced by onefifth, EF shift, which is equal to eVchem shift, from the first 共closed triangle兲 to second 共open triangle兲 subband edge requires the change of VG by −0.74 V, i.e., the change of by 0.74 V. This value well reproduces the experimental results in Figs. 3共a兲 and 3共b兲, where the required changes of are 0.7 V and 0.8 V, respectively. Because of uncertainty of the diameters of the SWNTs, was in fact estimated between one-fifth and one-twelfth of bulk propylene carbonate. It should be noted that the comparable magnitude of Vchem and Vgeom shows that neither Cgeom nor Cchem is negligible to analyze ECTs. Additionally, the Schottky barrier must be considered. Although the two capacitances are considered, the gap between the valence- and conduction-band conduction is larger than 0.69 V, expected from Fig. 3共c兲. This is probably due to the Schottky barrier at the junction of the Pt/ Au electrodes and the SWNT. Appenzeller et al.11 reported that the Schottky barrier prevents a current flow even though EF reaches a subband edge of a SWNT. In conclusion, we have controlled the EF in SWNT-ECT devices from the first conduction subband to the second valence subband, demonstrating that the ECT accumulates charges more effectively than the back-gated FET. Using a RE, we succeeded in the experimental determination and quantitative explanation of the difference between the potentials needed for EF to reach the first and second valence subband. It was clarified that the Cgeom, which was ignored in the conventional model, makes a crucial contribution to the device characteristics, comparable to that from the Cchem. This work was partly supported by Tohoku University Materials Research Center under the program of 21st century COE. 1
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