NANO LETTERS
Effect of Diameter Variation in a Large Set of Carbon Nanotube Transistors
2006 Vol. 6, No. 7 1364-1368
Yu-Chih Tseng,* Kinyip Phoa, David Carlton, and Jeffrey Bokor Department of Electrical Engineering and Computer Sciences, UniVersity of California at Berkeley, Berkeley, California 94720 Received February 9, 2006; Revised Manuscript Received April 27, 2006
ABSTRACT A study involving a large number of carbon nanotube transistors reveals that the nanotube diameter and the metal contact material play key roles in determining the on- and off-state currents of these devices. The results are discussed in terms of the Schottky barrier at the metal− semiconductor junction and the variation of this barrier relative to the alignment of energy levels between the carbon nanotube and the metal.
The Schottky barrier (SB) at the contacts of a field-effect transistor (FET) using a carbon nanotube (CNT) as the channel plays a crucial role in determining the performance of the device. CNT transistors with negligible Schottky barrier height and with minimal series resistance were recently realized,1 and have performance that surpasses their silicon-based counterpart. This is largely due to the fact that the hole mobility in CNTFETs is estimated to be several thousands of cm2/(V s),1-3 about an order of magnitude higher than the state-of-the-art p-type silicon metal oxide semiconductor (MOS) transistor. The height of the SB between a CNT and its metal contact depends on several material parameters, such as the metal contact work function,4 the environment to which the device is exposed,5 and the diameter of the nanotube.6 Given the many possible sources of variation, it is desirable to study a large set of devices to obtain statistically meaningful results for how each parameter impacts upon the device characteristics. In this work, we report on a set of measurements of the electrical characteristics of several hundreds of CNT transistors. From these data, we elucidate the influence of the nanotube diameter the contact metal on the operating characteristics of a CNT transistor, both in its on- and offstate. A large array of back-gated carbon nanotube devices were fabricated using conventional microfabrication techniques as illustrated in Figure 1. Starting from a highly doped silicon substrate, a 160-nm-thick silicon dioxide layer was grown under dry conditions. The contact to the substrate was defined, followed by the growth of carbon nanotubes on lithographically defined catalyst islands using processes similar to that in ref 7. Source and drain contacts were patterned using optical lithography for all nanotube devices * To whom correspondence should be addressed. E-mail: tsengy@ eecs.berkeley.edu. 10.1021/nl060305x CCC: $33.50 Published on Web 06/29/2006
© 2006 American Chemical Society
Figure 1. Process steps for making a large number of CNT devices: (a) contact to substrate, (b) growth of nanotubes, (c) bilayer of lift-off stack, photoresist on top of PMMA, the latter of which is selectively dissolved in chlorobenzene, and (d) deposition and lift-off of metal contacts. (e) Scanning electron micrograph of an actual device. A total of 896 such devices is packed into a 1 cm2 chip.
simultaneously, in a bilayer lift-off stack. Metal contacts are then deposited using e-beam evaporation, followed by liftoff in acetone. The gate length, set by the gap between the contacts, is 2 µm. There are a total of 896 devices per 1 cm2 chip. The devices were characterized using an Electroglas
Figure 2. Examples of Id-Vg characteristics for devices with different contact metal. Ion is the current at Vg ) -15 V. Imin is the minimum point in the sweep. The diameter for all devices is 1.7 nm.
2001X automatic probing station in ambient conditions. The characterization of all 896 devices requires approximately 3 h, with one measurement on each device. Each device fabricated using this method may contain more than one nanotube. To analyze devices with only semiconducting nanotubes, we exclude those with an on/off ratio of less than 100. Devices containing only one nanotube, determined from the scanning electron micrograph (SEM) image of each device, were randomly selected for diameter measurement. The diameter is measured using tapping mode atomic force microscopy (AFM, Digital Instruments 3000) and is taken as the height of the nanotube relative to the substrate, averaged over a length of several hundred nanometers. The 1-sigma uncertainty in each measurement is estimated to be 0.2 nm and corresponds well to the rms roughness of the oxide substrate itself, indicating that the precision of the measurement is probably limited by the substrate roughness. Two parameters from the gate voltage dependence of each device were extracted. As shown in Figure 2, we define the on-state current Ion as the current reached at Vg ) -15 V and Imin as the minimum current reached in the entire range of Vg (-15 V to +15 V). We also define Imin as the “offstate” current. This differs from the usual definition in device applications, where the off-state is at Vg ) 0. However, it is necessary for comparison between the devices used presently, since the threshold voltage of each device is not well controlled. By plotting Ion vs Imin (Figure 3), for devices with three types of metal contacts, the following is revealed: For devices with Pd contacts, Imin is distributed across a wider range (variation of 104) than Ion (variation of 102). In addition, there exists a correlation between Ion and Imin. The correlation between Ion and Imin changes with the contact metal, becoming stronger for devices with Cu and Ti contacts. We propose that the variation in Ion and Imin observed among these devices can be explained by the variation in the nanotube diameter. By the use of a simple, unpinned model between the metal contact and the semiconducting nanotube,8 devices with Pd contacts are expected to have the valence band edge closely aligned to, or even above, the Nano Lett., Vol. 6, No. 7, 2006
Figure 3. Ion vs Imin for the three sets of devices. All devices have the ratio Ion/Imin greater than 100: Pd, 209 devices; Cu, 232 devices; Ti, 138 devices.
contact metal’s Fermi level (about 5 eV below the vacuum level, Evac6). Indeed, for a nanotube of 1.5 to 2 nm in diameter, we can calculate the valence band edge Evac - Ev to be at about 5 eV, using eq 1, where EM (between 4.7 eV9 to 4.8 eV10) is the mid-gap energy of the CNT relative to Evac and the band gap Eg is calculated as 0.84 eV/d (nm).11,12 Evac - Ev ) Eg/2 + EM (eV)
(1)
The barrier for hole conduction in the on-state is low and becomes significant only for very small diameters. We note that the work function of Pd in ambient needs to be more precisely known to determine the diameter at which the hole barrier height falls to zero. The work function of Pd depends strongly on its surface orientation, and polycrystalline Pd has a work function of 5.12 eV,13 which should give a Schottky-barrier-free device even at a diameter of 1 nm, if the unpinned model is used and good coupling with metal is assumed.6 The details of the Pd-CNT contact merit further studies to determine the SB height accurately. In the offstate, however, a barrier exists for both holes and electrons. With a sufficiently high barrier, conduction of holes is mainly limited by thermionic emission over the potential barrier in the bulk of the nanotube, whereas the conduction of electrons proceeds by both thermionic emission, as well as tunneling through the electron barrier at the drain side. Consequently, the off-state current is very sensitive to the change in band gap energy Eg. For devices with Cu and Ti contacts, the Fermi level of the metal is deeper inside the band gap, resulting in a substantial barrier for the conduction of holes in the on-state. In the off-state, a barrier is present for each type of carrier. The consequence is that both Ion and Imin are sensitive to the change in band gap of the nanotube. To verify the above hypothesis, we correlate the diameter of several devices directly to their on- and off-state current. The devices chosen for this purpose have only one nanotube per device. Figure 4 shows the dependence of the on- and off-state currents on diameter for all three contact metals. Both Ion and Imin increase strongly with diameter. We also note the considerable scatter in Figure 4 that is not explained by a measurement error in the diameter. Other variations also contribute to the variation in Ion and Imin. Possible causes 1365
Figure 4. Dependence of on- and off-state current on diameter: (a) on-state current vs diameter and (b) off-state current vs diameter for the same set of devices. Vd ) -2 V for Cu and Ti devices. Vd ) -3 V for Pd devices.
include the variation in contact work functions due to exposure to air and the presence of defects along the nanotube that leads to degraded device mobility.14 For devices with Pd contacts, Ion varies over a smaller range than Imin. The on- and off-state currents of the devices with Cu and Ti contacts, on the other hand, vary across equal orders of magnitudes, resulting in the strong correlation between Ion and Imin seen in Figure 3. The on-current in Figure 4a is defined as the current at Vgs - Vt ) -7 v, to account for variations in the threshold voltage. The results in Figure 4 also imply that the nanotube with the largest diameter will conduct the most current in the on-state and the off-state in a device with multiple nanotubes. The inclusion of devices with multiple nanotubes does not change significantly the interpretation drawn from Figure 3, since we can essentially ignore the smaller diameter nanotubes in a multitube device. SEM images of all 209 devices with Pd contacts reveal that 95% of the devices contain three or less nanotubes. The large minimum current for some devices in Figure 3 should originate mostly from the leakage of a single large diameter tube, rather than parallel conduction from many smaller ones. A simple model for conduction in the off-state is to include only thermionic emission of the carriers. Such a mechanism would lead to an exponential dependence of Imin on the barrier height. Direct tunneling may be relatively unimportant due to the large gate oxide thickness.6 We shall also neglect contributions from band-to-band tunneling. More studies are needed to verify the contribution from each mechanism. Simplistically, as the diameter increases, the narrowing in 1366
Figure 5. Off-state current as a function of the band gap energy: (a) Pd contact, (b) Cu contacts, and (c) Ti Contacts. The slope is obtained from the best linear fit to the graph.
the band gap is distributed evenly between the conduction and valence band. The barrier heights for electrons Φe and holes Φh are then linearly related to half of the band gap. Using an expression for parabolic bands, Imin depends on the barrier heights as Imin ) AT2 exp(-qΦe/kT) + BT2 exp(-qΦh/kT)
(2)
where the prefactors A and B are proportional to the effective mass and inversely to the diameter. For the range of diameters (1-4 nm) considered here, the variation in the effective mass changes Imin by a factor of 4 at most, which is relatively minor compared with the effect of the variation in barrier height (6 orders of magnitude). Imin should change by one decade for each 60 meV change in the barrier height. For each 60 meV change in barrier height, a 120 meV change Nano Lett., Vol. 6, No. 7, 2006
Figure 6. Measurement under varying temperature for a different set of devices (Pd contacts): (a) Imin vs band gap Eg, as calculated using (1) and (b) Ion vs diameter. Vds ) -1 V for both cases.
in the band gap is then required. Figure 5a shows that devices with Pd contacts roughly follow this trend, whereas devices with Cu and Ti seem to deviate from it, possibly due to significant contribution from tunneling, since the barrier height for the electrons at the drain is smaller. Improved measurements of the diameter should reduce the amount of scatter and elucidate further on the mechanism involved. Low-temperature measurements (Figure 6) show that there is indeed a large thermal component in the minimum current Imin. We also note that, for Pd-contacted devices, the onstate current drops sharply upon cooling when d < 1.5 nm, indicating that an SB starts to develop around that diameter, consistent with the observation in ref 6. Ion of device A in Figure 6b drops unexpectedly with temperature, possibly due to an on-tube defect that changes the band structure locally. There is a possibility that the nanotubes with relatively large diameter may be double-walled or even multiwalled. Assuming that all shells are semiconducting, the leakage current through the outer, larger diameter shell of the DWNT or MWNT should dominate. If a DWNT has an inner shell of 1.5 nm, then the outer shell has a diameter of 2.18 nm, using an intershell distance of 0.34 nm.15 Using our simplistic model for leakage current, the outer shell would conduct 28 times more current in the off-state than the inner shell. In addition, the coupling of the contact to the inner shell is generally weaker. The leakage current of the devices in Figure 4 is much lower than what would be expected from a metallic nanotube (∼10 µA). As such, if the nanotubes in Nano Lett., Vol. 6, No. 7, 2006
Figure 7. Distribution of the currents at a large gate bias: (a) current at Vg ) -15 V and (b) current at Vg ) +15 V. At Vg ) +15 V, Pd- and Cu-contacted devices with Imin > 1 nA are relatively large in diameter (>1.6 nm). Vd ) -2 V for all devices.
question have multiple walls, then either they have no metallic shell or the contact to these is extremely poor. Further influence of the contact metal work function is demonstrated in Figure 7, where a distribution in the current at each extreme of the range of Vg is plotted. We observe that the average current at Vg ) -15 V is, in general, anticorrelated with the average current at Vg ) +15 V. Ti, having the lowest average at Vg ) -15 V, has the highest average at Vg ) +15 V, given the same range of nanotube diameter. Although exposure to oxygen can significantly increase the work function of Ti and Cu,16 the distributions in Figure 6 suggest that Ti remains the metal with the lowest work function under the measurement conditions. As such, Ti-contacted devices have the highest barrier for hole transport but the lowest for electrons. For integrated circuit applications, a large-diameter nanotube with an appropriate metal contact is desirable for its low contact resistance and enhanced mobility.17,18 However, the off-current Imin associated with such devices will invariably be higher, due to enhanced thermionic emission and ambipolar conduction. The results presented here indicate that, for very small diameter nanotubes (
