Low-dimensional phonon transport effects in ultranarrow disordered graphene nanoribbons

Abstract

We investigate the influence of low-dimensionality and disorder in phonon transport in ultra-narrow armchair graphene nanoribbons (GNRs) using non-equilibrium Green's function (NEGF) simulation techniques. We specifically focus on how different parts of the phonon spectrum are influenced by geometrical confinement and line edge roughness. Under ballistic conditions, phonons throughout the entire phonon energy spectrum contribute to thermal transport. With the introduction of line edge roughness, the phonon transmission is reduced, but in a manner which is significantly non-uniform 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 ultra-narrow 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 (resulting in sparse E(q) phononic bandstructure), 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 2 L=1μm. These modes tend to completely dominate thermal transport. Modes in the sparse regions of the spectrum, however, tend to fall into the localization regime, even for channel lengths as short as 10s of nanometers, despite their relatively high phonon group velocities.

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

“…The amplitude of the thermal conductance, however, is slightly higher compared to that in AGNRs because, as we explain in Ref. [12], the dispersions in ZGNRs are more dispersive. With regards to the effect of distortion and non-perfect periodicity, which would be the more realistic scenario, Blandre et al [33] considers width-modulated Si nanowires with amorphous outer shell regions of similar diameters as the GNR widths we consider.…”

“…The amplitude of the thermal conductance, however, is slightly higher compared to that in AGNRs because as we explain in Ref. [12] the dispersions in ZGNRs are more dispersive (dashed-green lines are for the ZGNRs, same data lines the green lines as in Fig. 7 and Fig.…”

“…We mention here that 'transport' bandgaps appear even in uniform channels in the presence of surface roughness, which creates band mismatch and propagating modes cannot survive, and similarly they also reduce thermal conductance [12,52]. That however, originates from disorder, whereas the bandgaps under width-modulation are actual bandstructure modifications.…”

“…Examples of these features include that: i) the thermal conductivity could deviate from Fourier's law [1][2][3][4][5], ii) a crossover is observed from ballistic into diffusive transport regimes [6,7], or from nanoto macro-scale behaviors [8,9], iii) the thermal conductivity could even increase under channel width confinement [10,11], iv) band mismatch under extreme confinement could result to phonon localization and 'effective transmission bandgaps' [12], v) heat transport could be below the Casimir or the amorphous limits, and many more [13,14]. Several interesting device concepts have also emerged recently in the area of phononics, which attempt to use heat to perform transistor action [15], create heat rectifiers [16], engineer the sound velocities and phonon dispersions, etc.…”

Phonon transport simulations in low-dimensional, disordered graphene nanoribbons

“…is the second derivative of the potential energy (U ) after atoms 'i' and 'j' are slightly displaced along the m-axis and For setting up the dynamical matrix component between the i th and the j th carbon atoms, which are the N th nearestneighbors of each other, we use the force constant method (FCM), involving interactions up to the fourth nearestneighbor [54,55]. The force constant tensor is given by:…”