AC performance of nanoelectronics: towards a ballistic THz nanotube transistor

doi:10.1016/j.sse.2004.05.044

Solid-State Electronics

Volume 48, Issues 10–11, October–November 2004, Pages 1981-1986

https://doi.org/10.1016/j.sse.2004.05.044 Get rights and content

Abstract

We present phenomenological predictions for the cutoff frequency of carbon nanotube transistors. We also present predictions of the effects parasitic capacitances on AC nanotube transistor performance. The influence of quantum capacitance, kinetic inductance, and ballistic transport on the high-frequency properties of nanotube transistors is analyzed. We discuss the challenges of impedance matching for ac nano-electronics in general, and show how integrated nanosystems can solve this challenge. Our calculations show that carbon nano-electronics may be faster than conventional Si, SiGe, GaAs, or InP semiconductor technologies. We predict a cutoff frequency of 80 GHz/L, where L is the gate length in microns, opening up the possibility of 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 f_T, 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 f_T is given by: $1 2πf_{T} =(R_{S} +R_{D})C_{gd,p} + 1 g_{m} C_{gs} +C_{gd,p} +C_{gd,p} + g_{d} g_{m} (R_{S} +R_{D}) C_{gs} +C_{gd,p} +C_{gd,p}$

Here the p subscript denotes “parasitic”. Using the experimentally measured transconductance of 10 μs, a parasitic capacitance value of 10⁻¹⁶ F, and a C_gs 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 R_Q=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, $Z_{C} =(με)^{1/2} =377 Ω$ . The ratio of Z_C/R_Q=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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AC performance of nanoelectronics: towards a ballistic THz nanotube transistor

Abstract

Introduction

Section snippets

Nanotube interconnects: quantum impedances

Active devices: nanotube transistors

Relevant frequency scales

Small-signal equivalent circuit

Cutoff frequency

Noise performance: Towards the quantum limit?

Challenges: impedance matching

Conclusions

Acknowledgements

Luttinger liquid theory as a model of the GHz electrical properties of carbon nanotubes

IEEE Trans. Nanotechnol

An RF circuit model for carbon nanotubes

IEEE Trans. Nanotechnol

Fields and waves in communications electronics

Carbon nanotubes as Schottky barrier transistors

Phys. Rev. Lett

Ballistic carbon nanotube field-effect transistors

Nature

Single-walled carbon nanotube electronics

IEEE Trans. Nanotechnol

High-K dielectrics for advanced carbon-nanotube transistors and logic gates

Nature Mater

High performance electrolyte gated carbon nanotube transisors

Nano Lett

Performance projections for ballistic carbon nanotube field-effect transistors

Appl. Phys. Lett