Mark Lundstrom

Ballistic carbon nanotube field-effect transistors

A common feature of the single-walled carbon-nanotube field-effect transistors fabricated to date has been the presence of a Schottky barrier at the nanotube–metal junctions. These energy barriers severely limit transistor conductance in the ‘ON’ state, and reduce the current delivery capability—a key determinant of device performance. Here we show that contacting semiconducting single-walled nanotubes by palladium, a noble metal with high work function and good wetting interactions with nanotubes, greatly reduces or eliminates the barriers for transport through the valence band of nanotubes. In situ modification of the electrode work function by hydrogen is carried out to shed light on the nature of the contacts. With Pd contacts, the ‘ON’ states of semiconducting nanotubes can behave like ohmically contacted ballistic metallic tubes, exhibiting room-temperature conductance near the ballistic transport limit of 4e2/h (refs 4–6), high current-carrying capability (∼25 µA per tube), and Fabry–Perot interferences at low temperatures. Under high voltage operation, the current saturation appears to be set by backscattering of the charge carriers by optical phonons. High-performance ballistic nanotube field-effect transistors with zero or slightly negative Schottky barriers are thus realized.

Theory of ballistic nanotransistors

Numerical simulations are used to guide the development of a simple analytical theory for ballistic field-effect transistors. When two-dimensional (2-D) electrostatic effects are small (and when the insulator capacitance is much less than the semiconductor (quantum) capacitance), the model reduces to Natoris theory of the ballistic MOSFET. The model also treats 2-D electrostatics and the quantum capacitance limit where the semiconductor quantum capacitance is much less than the insulator capacitance. This new model provides insights into the performance of MOSFETs near the scaling limit and a unified framework for assessing and comparing a variety of novel transistors.

Elementary scattering theory of the Si MOSFET

A simple one-flux scattering theory of the silicon MOSFET is introduced. Current-voltage (I-V) characteristics are expressed in terms of scattering parameters rather than a mobility. For long-channel transistors, the results reduce to conventional drift-diffusion theory, but they also apply to devices in which the channel length is comparable to or even shorter than the mean-free-path. The results indicate that for very short channels the transconductance is limited by carrier injection from the source. The theory also indicates that evaluation of the drain current in short-channel MOSFETs is a near-equilibrium transport problem, even though the channel electric field is large in magnitude and varies rapidly in space.

Self-Aligned Ballistic Molecular Transistors and Electrically Parallel Nanotube Arrays

Carbon nanotube field-effect transistors with structures and properties near the scaling limit with short (down to 50 nm) channels, self-aligned geometries, palladium electrodes with low contact resistance, and high-K dielectric gate insulators are realized. Electrical transport in these miniature transistors is nearly ballistic up to high biases at both room and low temperatures. Atomic-layer-deposited (ALD) high-K films interact with nanotube sidewalls via van der Waals interactions without causing weak localization at 4 K. New fundamental understanding of ballistic transport, optical phonon scattering, and potential interfacial scattering mechanisms in nanotubes is obtained. Also, parallel arrays of such molecular transistors are enabled to deliver macroscopic currents-an important milestone for future circuit applications.

High-Field Quasiballistic Transport in Short Carbon Nanotubes

Single walled carbon nanotubes with Pd Ohmic contacts and lengths ranging from several microns down to 10 nm are investigated by electron transport experiments and theory. The mean-free path (MFP) for acoustic phonon scattering is estimated to be l(ap) approximately 300 nm, and that for optical phonon scattering is l(op) approximately 15 nm. Transport through very short (approximately 10 nm) nanotubes is free of significant acoustic and optical phonon scattering and thus ballistic and quasiballistic at the low- and high-bias voltage limits, respectively. High currents of up to 70 microA can flow through a short nanotube. Possible mechanisms for the eventual electrical breakdown of short nanotubes at high fields are discussed. The results presented here have important implications to high performance nanotube transistors and interconnects.

Sub-10 nm carbon nanotube transistor.

This first demonstration of CNT transistors with channel lengths down to 9 nm shows substantially better scaling behavior than theoretically expected. Numerical simulations suggest that a possible explanation for the surprisingly good performance is a result of the gate modulating both the charge in the channel and in the contact regions. The unprecedented performance should ignite exciting new research into improving the purity and placement of nanotubes, as well as optimizing CNT transistor structure and integration. Results from aggressively scaling these molecular-channel transistors exhibit their strong suitability for a low-voltage, high-performance logic technology.

Simulating Quantum Transport in Nanoscale Transistors: Real versus Mode-Space Approaches

In this article, we present a computationally efficient, two-dimensional quantum mechanical simulation scheme for modeling electron transport in thin body, fully depleted, n-channel, silicon-on-insulator transistors in the ballistic limit. The proposed simulation scheme, which solves the nonequilibrium Green’s function equations self-consistently with Poisson’s equation, is based on an expansion of the active device Hamiltonian in decoupled mode space. Simulation results from this method are benchmarked against solutions from a rigorous two-dimensional discretization of the device Hamiltonian in real space. While doing so, the inherent approximations, regime of validity and the computational efficiency of the mode-space solution are highlighted and discussed. Additionally, quantum boundary conditions are rigorously derived and the effects of strong off-equilibrium transport are examined. This article shows that the decoupled mode-space solution is an efficient and accurate simulation method for modeling e...

A Three-Dimensional quantum simulation of Silicon nanowire transistors with the effective mass approximation

The silicon nanowire transistor (SNWT) is a promising device structure for future integrated circuits, and simulations will be important for understanding its device physics and assessing its ultimate performance limits. In this work, we present a three-dimensional (3D) quantum mechanical simulation approach to treat various SNWTs within the effective-mass approximation. We begin by assuming ballistic transport, which gives the upper performance limit of the devices. The use of a mode space approach (either coupled or uncoupled) produces high computational efficiency that makes our 3D quantum simulator practical for extensive device simulation and design. Scattering in SNWTs is then treated by a simple model that uses so-called Buttiker probes, which was previously used in metal-oxide-semiconductor field effect transistor simulations. Using this simple approach, the effects of scattering on both internal device characteristics and terminal currents can be examined, which enables our simulator to be used f...

A numerical study of scaling issues for Schottky-barrier carbon nanotube transistors

We performed a comprehensive scaling study of Schottky-barrier (SB) carbon nanotube transistors using self-consistent, atomistic scale simulations. We restrict our attention to SB carbon nanotube field-effect transistors (FETs) whose metal source-drain is attached to an intrinsic carbon nanotube channel. Ambipolar conduction is found to be an important factor that must be carefully considered in device design, especially when the gate oxide is thin. The channel length scaling limit imposed by source-drain tunneling is found to be between 5 nm and 10 nm, depending on the off-current specification. Using a large diameter tube increases the on-current, but it also increases the leakage current. Our study of gate dielectric scaling shows that the charge on the nanotube can play an important role above threshold.

Performance Projections for Ballistic Carbon Nanotube Field-Effect Transistors

The performance limits of carbon nanotube field-effect transistors (CNTFETs) are examined theoretically by extending a one-dimensional treatment used for silicon metal–oxide–semiconductor field-effect transistors (MOSFETs). Compared to ballistic MOSFETs, ballistic CNTFETs show similar I–V characteristics but the channel conductance is quantized. For low-voltage, digital applications, the CNTFET with a planar gate geometry provides an on-current that is comparable to that expected for a ballistic MOSFET. Significantly better performance, however, could be achieved with high gate capacitance structures. Because the computed performance limits greatly exceed the performance of recently reported CNTFETs, there is considerable opportunity for progress in device performance.