1. Department of Applied Physics and DIMES, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

Correspondence to: Cees Dekker¹ Correspondence and requests for materials should be addressed to C.D. (Email: dekker@qt.tn.tudelft.nl).

The samples presented in this study are fabricated as described elsewhere⁵,¹³. Figure 1a shows an atomic force microscopy (AFM) image of a single nanotube contacting three Pt electrodes (1, 2 and 3). The semiconducting Si substrate, covered with a 300-nm layer of thermally grown SiO₂, was used as a back-gate (Fig. 1b). In our electrical transport studies on single-wall nanotubes, we have measured many individual tubes (in excess of 20) and find two types of behaviour at room temperature. The metallic variety oftubes reported previously have linear current–voltage curves (I–V_bias) and show no dependence on the gate voltage (V_gate). Here we present two-probe and three-probe measurements on the second type of sample.

Figure 1: a, Tapping-mode AFM image of an individual carbon nanotube on top of three Pt electrodes.

b, Schematic side view of the TUBEFET device. A single semiconducting nanotube is contacted by two electrodes. The Si substrate, which is covered by a layer of SiO₂ 300 nm thick, acts as a back-gate. c, Suggested band diagram of the device. The nanotube with a gap of 0.6 eV is connected to the leads with Fermi energy E_F by tunnelling contacts, indicated by the black vertical bars. At A and C (see b), the valence-band edge is pinned to the Fermi energy of the leads. Owing to a difference in work function between the tube and the electrodes, the bands bend towards lower energy in between the electrodes (B). For positive V_gate the bands bend more strongly, leading to an insulating state.For negative V_gate the bands flatten, resulting in a metal-like conductance. d,Application of a bias voltage results in a suppression of the barrier.

High resolution image and legend (93K)

Figure 2 displays I–V_bias curves for the sample in Fig. 1a. At V_gate = 0, a small nonlinearity seems to be present in the I–V_bias curve. When V_gate is increased to positive values, a pronounced gap-like nonlinearity develops around V_bias = 0. The curves seem to exhibit a power-law behaviour (solid lines), that is I (V_bias), with between 1 and 12. Upon application of a negative V_gate, the I–V_bias curve becomes linear with a resistance that saturates around 1 M. This is the same resistance that we find for the metallic tubes in a similar layout. For the major part this resistance is due to the contact resistance between the tube and the electrodes¹⁴. We thus obtain a controllable semiconductor-to-metal transition in a one-dimensional system. The nonlinearity at room temperature and the asymmetric dependence of the conductance on the gate voltage polarity indicate that the nanotube of this sample is semiconducting. In the inset of Fig. 2, the conductance of the device at V_bias = 0 is plotted against V_gate. This shows that the conductance can be strongly modulated, by about six orders of magnitude on a change of 10 V in V_gate. Measurements on the electrode pair 2–3 gave similar results. This sample (Fig. 1a) is one of five samples that showed a similar behaviour. In the other samples, noise due to two-level fluctuators was often larger, especially at large applied voltages. For some samples, the I–V_bias curves were asymmetric around V_bias = 0. Although some drift occurred along the V_gate axis, the transport characteristics of the sample presented here were reproducible over a period of months.

Figure 2: Two probe I–V_bias curves for various values of the gate voltage (V_gate).

Data were taken at room temperature and in vacuum (10^-4 mbar), with the voltage applied to contacts 1 (drain) and 2 (source). A negative V_gate leads to ohmic behaviour while a positive V_gate results in a strong suppression of the current at low bias voltage and nonlinear I–V_bias curves at higher bias. Inset, conductance at V_bias = 0 as a function of V_gate. The conductance through this single molecular switch can be varied over at least six orders of magnitude and saturates at 10^-6 -1 for negative V_gate.

High resolution image and legend (21K)

In the energy diagrams of Fig. 1c and 1d we attempt to model the electronic structure and functioning of the TUBEFET (single carbon nanotube field-effect transistor) device. The charge carriers flow through the part of the tube that is on top of the source (A), on the SiO₂ surface (B), and on the drain electrode (C) (see also Fig. 1b). Semiconducting tubes with a 1.4 nm diameter have a bandgap of 0.6 eV (refs 15,16,17). As for a traditional semiconductor–metal interface, a difference in work function will result in bending of the bands of the semiconductor¹⁸. The work function of Pt is 5.7 eV, whereas the work function of carbon nanotubes is near 4.5 eV. Owing to this difference, a local polarization layer will develop on the electrode–nanotube interface until the nanotube valence band edge aligns with the Fermi level of the metal electrode. Such pinning of the valence band edge to the Fermi level of the electrode was observed in scanning tunnelling spectroscopy experiments of semiconducting nanotubes on Au(111) (ref. 16). Away from the electrodes, the bands bend to lower energy (Fig. 1c, segment B). A gate voltage will not have a strong effect on the nanotube at position A and C owing to the screening of the nearby metallic leads and the capacitive coupling between the tube and theleads. In segment B, however, the electric field of the gate electrode will couple to the tube. For negative V_gate this will lead to an accumulation of holes and an increasing conductance, whereas for a positive V_gate the holes are depleted, yielding a lower conductance (Fig. 1c). Cooling the sample to 160 K, the metallic saturation resistance (V_gate < -3 V) increases from 1 to 4 M. For a metallic tube we find the same room temperature resistance of 1 M and a similar dependence on temperature. This result supports the band diagram proposed above (Fig. 1c) because our model predicts that in segments A and C the tube should be metal-like owing to the pinning of the valence band edge. If, as an alternative model, there were an induced Schottky barrier¹⁸ inside the tube at A and C, the device would exhibit a much stronger temperature dependence.

The suggested band structure of this device (Fig. 1c) is similar to that of a traditional semiconductor device, the so-called 'barrier injection transit time' (BARITT) diode¹⁸. This device consists of a semiconductor connected to two metal contacts, that is, two Schottky-type diodes connected back to back. Although we do not yet have a detailed understanding of the functioning of the TUBEFET, we shall attempt to give a qualitative description by using the well-known BARITT model. In both devices holes have tobe transported over the barrier induced by the band bending (insegment B; Fig. 1c). When a bias is applied to a BARITT diode (Fig. 1d) an asymmetric space charge distribution results, because the barrier at the positive contact prevents holes from entering, whereas at the negative contact holes exit from the semiconductor, leaving a large space charge concentration. This leads to an asymmetry in electric field profile and correspondingly yields an unequal voltage drop over the right and left part of the device. When the electric field reaches through the entire device, current is able to flow.

We have performed current-bias transport measurements on the sample of Fig. 1a in a three-point configuration. We now can divide the sample into two segments: one between electrode pair 1–2 and one between pair 2–3. With the current source connected to electrode 3 and electrode 1 grounded, we can measure separately the voltage drops over these two tube segments. The total voltage over pair 1–3 is also measured, with electrode 2 left floating. The result for V_gate = 2 V is displayed in Fig. 3a. Again we observe gap-like features in the I–V curve. The voltages over the two segments indeed add up to the total voltage drop over the device. However, the voltage drop seems to be different for both segments, with most of the voltage dropping over segment 2–3 at negative bias. This is in agreement with the above described mechanism for a BARITT-like diode because at negative bias the potential of electrode 3 is lower than that of electrode 1, resulting in more space charge and thus a larger voltage drop near contact 3. For positive bias, electrode 1 has the lowest potential, yielding a larger voltage drop at electrode 1. This is indeed observed in the measurements. A different voltage division is observed when the same measurement is performed at a larger positive V_gate (Fig. 3b). The space-charge profile is now rather symmetric, as can be concluded from the almost equal voltage drop over segments 1-2 and 2-3. At large positive V_gate, more holes are depleted from the tube, leaving less room for an asymmetric space charge profile. With fewer free charges in the tube, it behaves more like an insulator and the dominant charge build-up is in the electrodes, resulting in equal voltage drops over the two segments. This trend is indicated in the inset of Fig. 3a, where the voltage over the two segments at -4 nA and +4 nA is plotted as a percentage of the total voltage (1–3) against V_gate.

Figure 3: Three-probe I_bias–V curves for two gate voltages.

The current is biased over the two outer contacts 1 and 3. The voltage drop is measured over contact pairs 1–2 (), 2–3 () and 1–3 () (right inset). At low V_gate (a), the voltage drop over 1–2 is not the same as for 2–3, whereas for larger V_gate (b), the two voltages are identical. Left inset, voltages over pairs 1–2 and 2–3 as a percentage of the total voltage (1–3), both for negative bias (open symbols) and for positive bias (solid symbols). The observed behaviour is in agreement with the proposed band diagram of the device (Fig. 1).

High resolution image and legend (20K)

Screening in truly one-dimensional conductors is expected to be different from that in a three-dimensional system. It is therefore of interest to deduce the typical length over which the bands are bent along the nanotube axis. From our data we can make a rough estimate of this value. Fig. 2 shows that at V_gate = 0 the tube is almost in the metallic state, and that the Fermi energy must therefore be close to the valence band edge throughout the device. If the band-bending length were short (400 nm), the Fermi level in the nanotube segments away from the electrodes would be located in the middle of the gap between conduction and valence band, and hole transport would be very hard because of the appreciable (0.3 eV) barrier. If the band-bending length were very large (400 nm), however, no significant band bending would occur and the tube would respond similarly to a metallic tube. A negative gate voltage would thus have no effect. What we observe experimentally is something in between, and we thus conclude that, without applied electric fields, the band-bending length is roughly of the order of the distance between the electrodes, which is 400 nm.

The gain of the TUBEFET device can be estimated by considering the voltage over the device at a certain current. Going from +4 V to +6 V in V_gate, for example, results in a maximum change in voltage over the device of 0.7 V (Fig. 2), which yields a gain of 0.35. The simplest way to improve this value in the current device geometry would be to decrease the SiO₂ layer thickness. Currently this is 300 nm but it could be reduced to 5 nm (ref. 19), resulting in a gain of order 1 or higher. Other geometries that further increase the capacitance between the gate and the tube might also be possible. Considering the ultimate speed of the device, we calculate a ballistic traversal time of 10^-13 s (or 10 THz) for 100 nm length of tube and a Fermi velocity for electrons in carbon nanotubes of 8 10⁵ m s^-1 (ref. 15). Another limitation to the device speed is the RC (resistance–capacitance) time. From Coulomb blockade measurements at low temperatures⁵ we deduce that the total capacitance of a piece of nanotube 100 nm long in a similar device geometry is of order 10^-18 F. With an 'on' resistance of 1 M, this gives a frequency limit of 0.1 THz. At present the device resistance is dominated by the contact resistance¹⁴. If low-ohmic contacts can be realized, the two-probe resistance is expected to reach the lower quantum limit of about 6 k, which would allow a maximum frequency of order 10 THz.

The fabrication of the TUBEFET, the single-molecule field-effect transistor described here, is relatively straightforward, and integration of multiple devices into a circuit may eventually be possible by using molecular self-assembly techniques²⁰. Potential applications may therefore be possible, particularly as the device operates at room temperature and high switching speeds, and improved voltage gains seem possible.

In discussions of the fundamental limits of integrated circuit dimensions, warnings are often expressed that at some point radically new device structures should be used because of dominant quantum mechanical effects. Such new device concepts have been explored in the fields of mesoscopic physics and in molecular electronics. It is quite striking that it seems possible to describe qualitatively the ultra-small TUBEFET device, which is based on a single nanotube molecule, by the same semiclassical models that are used for devices in today's computer industry.

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Acknowledgements

We thank R. E. Smalley and co-workers for the supply of the indispensable single-wall carbon nanotubes; A. Bezryadin, C. J. P. M. Harmans and P. Hadley for discussions; A. van den Enden for technical assistance. The work was supported by the Dutch Foundation for Fundamental Research on Matter (FOM).