19-02-2013, 12:35 PM
AC PERFORMANCE OF NANO ELECTRONIC
AC PERFORMANCE.docx (Size: 1.4 MB / Downloads: 38)
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 kX. In ballistic devices with cross-sectional dimensions of order the quantum
mechanical wavelength of electrons, the resistance is of order h=e2 _ 25 kX. 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 highfrequency properties of nano-electronics because they may behave as ideal ballistic 1d transistors.
What is nano technology?
Nanotechnology is basically a material science. Richard .P. Feynman is the father of Nanotechnology. Nanoelectronics is nanotechnology applied in the context of electronic components and circuits. Ordinary transistors don’t fall under nanoelectronics even though they have size less than 100nm.
NANOTUBES INTERCONNECTS:QUANTAM IMPANDANCES
The first step towards understanding the high-frequencyelectronic 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 .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 electrostatic capacitance between the nanotube and the metal. Due to the quantum properties of 1d systems, however, there are two additional components
to the ac impedance: the quantum capacitance and the kinetic inductance. Thus, the equivalent circuit of ananotube consists of three distributed circuit elements, which we summarize in Figs. 1 and 2
Band structure, spin degeneracy
A carbon nanotube, because of its band structure, has two propagating channels. In addition, the electronscan be spin up or spin down. Hence, there are four
channels in the Landauer–B€uttiker formalism. Taking this into account, in Ref. we show that the circuit model of Fig. 1 is still valid as an effective circuit model for the charged mode if LK is replaced by LK=4 and CQ is replaced by 4CQ. Thus, the ac impedance of a nanotube consists of significant capacitive and inductive elements in addition to the real resistance which must be considered in any future nano-electronics system architecture.
SMALL-SINGNAL 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 the following sections we discuss each of the important components.
Gate–source capacitance
The capacitance of a passive nanotube in the presence of a gate was discussed extensively in the first section; this can be used as an estimate of the gate–source capacitance Cgs in active mode; shown in Fi. This capacitance includes the geometrical capacitance
Transconductance
While the transconductance is the most critical parameter, the underlying mechanism is the least understood. In order to predict device high-frequency performance, we use experimental data from dc measurements as our guide. We show in Table 1 data from various research groups measured to date. Transconductances up to 20 lS have been measured , using an
aqueous gate geometry. A transconductance of 60 lS was recently predicted by simulation.
Drain resistance
In Fig. 4, gd represents the output impedance of the device, if it does not appear as an ideal current source. In Table 1 , we present some representative values from the literature which we have determined from the published source–drain I–V
curves.
Series resistance
In most conventional transistors the series resistance consists of the metallization layer and the ohmic contact resistance. We argue that, in nanotube transistors, the intrinsic contact resistance will be of order the resistance quantum because of the 1d nature of the system. We
elaborate. At dc, the lowest value of resistance possible for a carbon nanotube is h=4e2. This is because there are four channels for conductance in the Landauer–B€uttiker formalism, each contributing h=e2 to the conductance. To date very little experimental work has been done to
measure the ac impedance of ballistic systems . From a theoretical point of view, B€uttiker and Christen have carefully analyzed the case of a capacitive contact to a ballistic conductor (in his case a 2DEG without scattering) in contact with one dc electrical lead through a quantum point contact. They find that the ac impedance from gate to lead includes a real