Anomalous diameter dependence of thermal transport in ultra-narrow Si nanowires

We present atomistic valence force field calculations of thermal transport in Si nanowires of diameters from 12nm down to 1nm. We show that as the diameter is reduced, the phonon density-of-states and transmission function acquire a finite value at low frequency, in contrast to approaching zero as in the bulk material. It turns out that this effect results in what Ziman described as the "problem of long longitudinal waves" [1], which states that the thermal conductivity of a material increases as its length is increased due to the vanishing scattering for long-wavelength phonons. We show that this thermal transport improvement also appears in nanowires as their diameter is decreased below D=5nm (not only as the length increases) originating from the increase in the density of the long wavevector modes. The observation is present under ballistic transport conditions, and further enhanced with the introduction of phonon-phonon scattering. Because of this, in such ultra-narrow nanowires, as the diameter is reduced, phonon transport is dominated more and more by lower energy phonons with longer mean-free paths. We show that ~80% of the heat is carried by phonons with energies less than 5meV, most with mean-free paths of several hundreds of nanometers.Comment: 7 figure

On the channel width-dependence of the thermal conductivity in ultra-narrow graphene nanoribbons

The thermal conductivity of low-dimensional materials and graphene nanoribbons, in particular, is limited by the strength of line-edge-roughness scattering. One way to characterize the roughness strength is the dependency of the thermal conductivity on the channel's width in the form Wβ. Although in the case of electronic transport, this dependency is very well studied, resulting in W 6 for nanowires and quantum wells and W 4 for nanoribbons, in the case of phonon transport it is not yet clear what this dependence is. In this work, using lattice dynamics and Non-Equilibrium Green's Function simulations, we examine the width dependence of the thermal conductivity of ultra-narrow graphene nanoribbons under the influence of line edge-roughness. We show that the exponent β is in fact not a single well-defined number, but it is different for different parts of the phonon spectrum depending on whether phonon transport is ballistic, diffusive, or localized. The exponent β takes values β < 1 for semi-ballistic phonon transport, values β ≫ 1 for sub-diffusive or localized phonons, and β = 1 only in the case where the transport is diffusive. The overall Wβ dependence of the thermal conductivity is determined by the width-dependence of the dominant phonon modes (usually the acoustic ones). We show that due to the long phonon mean-free-paths, the width-dependence of thermal conductivity becomes a channel length dependent property, because the channel length determines whether transport is ballistic, diffusive, or localized

Phonon transport simulations in low-dimensional disordered graphene nanoribbons

We investigate the thermal conductance of one-dimensional periodic width-modulated graphene nanoribbons using lattice dynamics for the phonon spectrum and the Landauer formalism for phonon transport. We conduct a full investigation considering all relevant geometrical features, i.e., the various lengths and widths of the narrow and wide regions that form the channel. In all cases that we examine, we find that width-modulation suppresses the thermal conductance at values even up to ∼70% below those of the corresponding uniform narrow nanoribbon. We show that this can be explained by the fact that the phonon spectrum of the width-modulated channels acquires less dispersive bands with lower group velocities and several narrow bandgaps, which reduce the phonon transmission function significantly. The largest degradation in thermal conductance is determined by the geometry of the narrow regions. The geometry of the wider regions also influences thermal conductance, although modestly. Our results add to the ongoing efforts in understanding the details of phonon transport at the nanoscale, and our conclusions are generic and could also apply to other one-dimensional channel materials

Use of field-effect density modulation to increase ZT for Si nanowires : a simulation study

Modulation doping is a promising means of increasing the electrical conductivity of thermoelectric (TE) materials and achieving a high figure of merit (ZT). We compared, qualitatively and quantitatively, the TE performance of a field-effect density modulated Si nanowire channel of diameter D = 12 nm with that of its doped counterpart, by use of self-consistent atomistic tight-binding simulations coupled to the Boltzmann transport equation. We describe the simulation model, and show that as a result of a large improvement in electrical conductivity, gating, rather than doping, can result in greater than three-fold improvement of the TE power factor. Despite the large increase in the electronic part of the thermal conductivity, the total thermal conductivity is still dominated by phonons. Thus, a ZT more than three-fold higher can also be achieved in the gated channel compared with the doped channel. Finally, we show that the power factor peak is obtained when the Fermi level resides ∼k B T below the band edge, as is observed for doped channels

Phonon transport effects in one-dimensional width-modulated graphene nanoribbons

We investigate the thermal conductance of one-dimensional periodic width-modulated graphene nanoribbons using lattice dynamics for the phonon spectrum and the Landauer formalism for phonon transport. We conduct a full investigation considering all relevant geometrical features, i.e., the various lengths and widths of the narrow and wide regions that form the channel. In all cases that we examine, we find that width-modulation suppresses the thermal conductance at values even up to ∼70% below those of the corresponding uniform narrow nanoribbon. We show that this can be explained by the fact that the phonon spectrum of the width-modulated channels acquires less dispersive bands with lower group velocities and several narrow bandgaps, which reduce the phonon transmission function significantly. The largest degradation in thermal conductance is determined by the geometry of the narrow regions. The geometry of the wider regions also influences thermal conductance, although modestly. Our results add to the ongoing efforts in understanding the details of phonon transport at the nanoscale, and our conclusions are generic and could also apply to other one-dimensional channel materials

Low-dimensional phonon transport effects in ultra-narrow, disordered graphene nanoribbons

We investigate the influence of low-dimensionality and disorder in phonon transport in ultra-narrow armchair graphene nanoribbons (GNRs) using non-equilibrium Greens function (NEGF) simulation techniques. We specifically focus on how different parts of the phonon spectrum are influenced by geometrical confinement and line edge roughness. With the introduction of line edge roughness, the phonon transmission is reduced, but non-uniformly throughout the spectrum. We identify four distinct behaviors within the phonon spectrum in the presence of disorder: i) the low-energy, low-wavevector acoustic branches have very long mean-free-paths and are affected the least by edge disorder, even in the case of ultra-narrow W=1nm wide GNRs; ii) energy regions that consist of a dense population of relatively flat phonon modes (including the optical branches) are also not significantly affected, except in the case of the ultranarrow W=1nm GNRs, in which case the transmission is reduced because of band mismatch along the phonon transport path; iii) quasi-acoustic bands that lie within the intermediate region of the spectrum are strongly affected by disorder as this part of the spectrum is depleted of propagating phonon modes upon both confinement and disorder especially as the channel length increases; iv) the strongest reduction in phonon transmission is observed in energy regions that are composed of a small density of phonon modes, in which case roughness can introduce transport gaps that greatly increase with channel length. We show that in GNRs of widths as small as W=3nm, under moderate roughness, both the low-energy acoustic modes and dense regions of optical modes can retain semi-ballistic transport properties, even for channel lengths up to L=1 um. Modes in the sparse regions of the spectrum fall into the localization regime even for channel lengths as short as 10s of nanometers.Comment: 45 pages, 12 figure