Exciton Ionization, Franz-Keldysh and Stark Effects in Carbon Nanotubes

We calculate the optical properties of carbon nanotubes in an external static electric field directed along the tube axis. We predict strong Franz-Keldysh oscillations in the first and second band-to-band absorption peaks, quadratic Stark effect of the first two excitons, and the field dependence of the bound exciton ionization rate for a wide range of tube chiralities. We find that the phonon assisted mechanism dominates the dissociation rate in electro-optical devices due to the hot optical phonons. We predict a quadratic dependence of the Sommerfeld factor on the electric field and its increase up to 2000% at the critical field of the full exciton dissociation.Comment: 12 pages, 5 figures, Nano Letters (2007

Mobility in semiconducting carbon nanotubes at finite carrier density

Carbon nanotube field-effect transistors operate over a wide range of electron or hole density, controlled by the gate voltage. Here we calculate the mobility in semiconducting nanotubes as a function of carrier density and electric field, for different tube diameters and temperature. The low-field mobility is a non-monotonic function of carrier density, and varies by as much as a factor of 4 at room temperature. At low density, with increasing field the drift velocity reaches a maximum and then exhibits negative differential mobility, due to the non-parabolicity of the bandstructure. At a critical density $\rho_c\sim$ 0.35-0.5 electrons/nm, the drift velocity saturates at around one third of the Fermi velocity. Above $\rho_c$, the velocity increases with field strength with no apparent saturation.Comment: 5 pages, 4 figure

Radiative Lifetime of Excitons in Carbon Nanotubes

We calculate the radiative lifetime and energy bandstructure of excitons in semiconducting carbon nanotubes, within a tight-binding approach. In the limit of rapid interband thermalization, the radiative decay rate is maximized at intermediate temperatures, decreasing at low temperature because the lowest-energy excitons are optically forbidden. The intrinsic phonons cannot scatter excitons between optically active and forbidden bands, so sample-dependent extrinsic effects that break the symmetries can play a central role. We calculate the diameter-dependent energy splittings between singlet and triplet excitons of different symmetries, and the resulting dependence of radiative lifetime on temperature and tube diameter.Comment: 4 pages, 3 figure

Relaxation of Optically Excited Carriers in Graphene

We explore the relaxation of photo-excited graphene by solving a transient Boltzmann transport equation with electron-phonon (e-ph) and electron-electron (e-e) scattering. Simulations show that when the excited carriers are relaxed by e-ph scattering only, a population inversion can be achieved at energies determined by the photon energy. However, e-e scattering quickly thermalizes the carrier energy distributions washing out the negative optical conductivity peaks. The relaxation rates and carrier multiplication effects are presented as a function of photon energy and dielectric constant.Comment: 4 pages, 4 figure

Inelastic Scattering and Current Saturation in Graphene

We present a study of transport in graphene devices on polar insulating substrates by solving the Bolzmann transport equation in the presence of graphene phonon, surface polar phonon, and Coulomb charged impurity scattering. The value of the saturated velocity shows very weak dependence on the carrier density, the nature of the insulating substrate, and the low-field mobility, varied by the charged impurity concentration. The saturated velocity of 4 - 8 x 10^7 cm/s calculated at room temperature is significantly larger than reported experimental values. The discrepancy is due to the self-heating effect which lowers substantially the value of the saturated velocity. We predict that by reducing the insulator oxide thickness, which limits the thermal conductance, the saturated currents can be significantly enhanced. We also calculate the surface polar phonon contribution to the low-field mobility as a function of carrier density, temperature, and distance from the substrate.Comment: 8 pages 9 figure