AC performance of nanoelectronics: towards a ballistic THz nanotube transistor
Introduction
Nano-electronic devices fall into two classes: tunnel devices, and ballistic transport devices. In tunnel devices, single electron effects occur if the tunnel resistance is larger than h/e2≈25 kΩ. In ballistic devices with cross-sectional dimensions of order the quantum mechanical wavelength of electrons, the resistance is of order h/e2≈25 kΩ. At first glance, these high resistance values may seem to restrict the operational speed of nanoelectronics in general. However, the capacitance for these devices is also generally small, as is the typical source–drain spacing. This gives rise to very small RC times, and very short transit times, of order ps or less. Thus, the speed limit may be very large, up to the THz range.
In this paper we take a more careful look at the general arguments for the speed limits of nanoelectronic devices. We find that the coupling to the outside world will usually be slow or narrowband, but that the coupling to other nano-electronic devices can be extremely fast. A more concrete goal of this paper is to present models and performance predictions about the effects that set the speed limit in carbon nanotube transistors, which form an ideal test-bed for understanding the high-frequency properties of nano-electronics because they may behave as ideal ballistic 1d transistors.
Section snippets
Nanotube interconnects: quantum impedances
The first step towards understanding the high-frequency electronic properties of carbon nanotubes is to understand the passive, ac impedance of a 1d quantum system. We have recently proposed an effective circuit model for the ac impedance of a carbon nanotube [1], [2]. While our model was formulated for metallic nanotubes, it should be approximately correct for semiconducting nanotubes as well. In the presence of a ground plane below the nanotube or top gate above the nanotube, there is
Active devices: nanotube transistors
In this section, we extend our discussion to include active nanotube devices. A typical nanotube transistor geometry is shown in Fig. 3 below. In contrast to silicon transistors, the fundamental physical mechanism responsible for transistor action in nanotube transistors is still not completely understood. One action of the gate may be to modulate the (Schottky barrier) contact resistance [7]. Experiments also indicate that the source–drain voltage drops at least in part along the length of the
Relevant frequency scales
We begin by estimating the frequency scales for the most important processes: the RC time and the transconductance.
Small-signal equivalent circuit
In this section, we propose a small-signal equivalent circuit model based on a combination of known physics in the small signal limit and generally common behavior for all field effect type devices. Our proposed active circuit model is not rigorously justified or derived. Rather, we hope to capture the essential physics of device operation and at the same time provide simple estimates of device performance.
We show in Fig. 4 our predicted small-signal circuit model for a nanotube transistor. In
Cutoff frequency
In this section, we provide estimates of the cutoff frequency fT, a standard yardstick for transistor high-speed performance, defined as the frequency at which the current gain falls to unity [22]. Based on the circuit model in Fig. 4, it can be shown [22] that fT is given by:
Here the p subscript denotes “parasitic”. Using the experimentally measured transconductance of 10 μs, a parasitic capacitance value of 10−16 F, and a Cgs of 4
Noise performance: Towards the quantum limit?
One promising potential application is in low-noise analog microwave amplification circuits. Recent work on noise in mesoscopic systems has been extensive and has shown suppressed noise due to the Pauli exclusion principle [25]. Since electrons can travel without scattering from source to drain, and the Pauli exclusion principle suppresses the current noise, it may be possible to engineer extremely low noise microwave amplifiers using carbon nanotubes, possibly even approaching the quantum
Challenges: impedance matching
Nano-devices generally have high resistance values, of order the resistance quantum RQ=h/e2. At high frequencies, for driving circuits more the one electromagnetic wavelength away from the device, the load impedance is typically of order the characteristic impedance of free space, . The ratio of ZC/RQ=1/137 has a special significance in physics and is called the fine structure constant; it is set by only three fundamental constants of nature: e, h, and c. For electrical
Conclusions
In conclusion, we have presented phenomenological predictions for the ac performance of nanotube transistors. Based on our calculations, we predict carbon nanotube transistors may be faster than conventional semiconductor technologies. There are many challenges that must be overcome to meet this goal, which can be best be achieved by integration of nanosystems.
Acknowledgements
I wish to thank my students Shengdong Li, Zhen Yu and collaborator W.C. Tang for many useful discussions. This work was supported by the Army Research Office (award DAAD19-02-1-0387), the Office of the Naval Research (award N00014-02-1-0456), and DARPA (award N66001-03-1-8914).
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