[Paper Review] Terahertz response of carbon nanotube transistors

Diego Kienle, François Léonard|ArXiv.org|Jun 16, 2009

Carbon Nanotubes in Composites3 citations

TL;DR

This paper presents a self-consistent non-equilibrium Green's function (NEGF) formalism for time-dependent quantum transport in ballistic carbon nanotube field-effect transistors (NTFETs), revealing that the dynamic conductance exhibits plasmonic resonant peaks at terahertz (THz) frequencies in the ON state due to collective electron excitations, while single-particle effects dominate in the OFF state. The nanotube kinetic inductance is shown to be essential in enabling inductive behavior in the dynamic capacitance, fundamentally distinguishing NTFETs from conventional FETs.

ABSTRACT

We present an approach for time-dependent quantum transport based on a self-consistent non-equilibrium Green function formalism. The technique is applied to a ballistic carbon nanotube transistor in the presence of a time harmonic signal at the gate. In the ON state the dynamic conductance exhibits plasmonic resonant peaks at terahertz frequencies. These vanish in the OFF state, and the dynamic conductance displays smooth oscillations, a signature of single particle quantum effects. We show that the nanotube kinetic inductance plays an essential role in the high-frequency behavior.

Motivation & Objective

• To develop a self-consistent time-dependent quantum transport framework for nanoscale devices under non-equilibrium conditions.
• To investigate the high-frequency AC response of ballistic carbon nanotube FETs (NTFETs), particularly in the terahertz regime.
• To distinguish between single-particle and collective (plasmonic) excitations in low-dimensional systems like nanotubes.
• To determine the role of kinetic inductance in shaping the dynamic capacitance and overall high-frequency behavior of NTFETs.
• To provide a theoretical foundation for designing THz detectors and emitters based on nanotube devices.

Proposed method

• A self-consistent non-equilibrium Green's function (NEGF) formalism is employed to model time-dependent quantum transport in a gated NTFET.
• The approach solves Dyson's equation for time-ordered Green's functions, incorporating a time- and space-dependent electrostatic potential from the gate.
• The dynamic conductance is calculated from the frequency-dependent particle current using the Keldysh formalism and the lesser Green's function.
• Charge density is computed from the lesser Green's function, and Poisson's equation is solved self-consistently to close the feedback loop between charge and potential.
• The dynamic capacitance is derived from the total charge response, and its frequency dependence reveals inductive behavior due to kinetic inductance.
• A classical RLC circuit model is used to extract the kinetic inductance value from the dynamic capacitance transition frequency.

Experimental results

Research questions

• RQ1 Can self-consistent quantum transport modeling distinguish plasmonic resonances from single-particle effects in carbon nanotube transistors at terahertz frequencies?
• RQ2 What is the role of nanotube kinetic inductance in determining the high-frequency impedance and capacitance behavior of NTFETs?
• RQ3 How do plasmon frequencies in gated NTFETs scale with channel length and mode number?
• RQ4 Why does the dynamic conductance exhibit divergent peaks in the ON state but smooth oscillations in the OFF state?
• RQ5 Can the NTFET be modeled as a resonant quantum cavity for terahertz plasmons?

Key findings

• In the ON state, the dynamic conductance exhibits divergent peaks at terahertz frequencies, which are identified as plasmonic resonances due to self-consistent electron-electron interactions.
• In the OFF state, the conductance shows only smooth oscillations, indicating the dominance of single-particle quantum effects without collective excitations.
• The self-consistency between charge and potential is essential for the emergence of plasmonic divergences; non-self-consistent calculations eliminate these peaks.
• The dielectric function derived from the potential response shows a zero crossing at the plasmon resonance frequency, confirming collective excitation behavior.
• Plasmon frequencies scale linearly with inverse channel length and mode number, with a plasmon velocity of 2.7×10⁶ m/s, four times the Fermi velocity.
• The real part of the dynamic capacitance transitions from capacitive to inductive behavior at approximately 8 THz, indicating a fundamental inductive contribution from nanotube kinetic inductance, with LK = 0.2 nH extracted for a 30 nm device.