Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering, Phys. Rev. B (2009) -Editors' Suggestion . 1 arXiv:0812.0518 [cond-mat.mtrl-sci] Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering, Phys. Rev. B (2009) -Editors' Suggestion .2 AbstractWe investigated theoretically the phonon thermal conductivity of single layer graphene. The phonon dispersion for all polarizations and crystallographic directions in graphene lattice was obtained using the valence-force field method. The three-phonon Umklapp processes were treated exactly using an accurate phonon dispersion and Brillouin zone, and accouting for all phonon relaxation channels allowed by the momentum and energy conservation laws. The uniqueness of graphene was reflected in the two-dimensional phonon density of states and restrictions on the phonon Umklapp scattering phase-space. The phonon scattering on defects and graphene edges has been also included in the model. The calculations were performed for the Gruneisen parameter, which was determined from the ab initio theory as a function of the phonon wave vector and polarization branch, and for a range of values from experiments. It was found that the near room-temperature thermal conductivity of single layer graphene, calculated with a realistic Gruneisen parameter, is in the range ~ 2000 -5000 W/mK depending on the defect concentration and roughness of the edges. Owing to the long phonon mean free path the graphene edges produce strong effect on thermal conductivity even at room temperature. The obtained results are in good agreement with the recent measurements of the thermal conductivity of suspended graphene.

We investigated the thermal conductivity K of graphene ribbons and graphite slabs as the function of their lateral dimensions. Our theoretical model considered the anharmonic three-phonon processes to the second-order and included the angle-dependent phonon scattering from the ribbon edges. It was found that the long mean free path of the longwavelength acoustic phonons in graphene can lead to an unusual non-monotonic dependence of the thermal conductivity on the length L of a ribbon. The effect is pronounced for the ribbons with the smooth edges (specularity parameter p>0.5). Our results also suggest that -contrary to what was previously thought -the bulk-like 3D phonons in graphite can make a rather substantial contribution to its in-plane thermal conductivity. The Umklapp-limited thermal conductivity of graphite slabs scales, for L below ~ 10 m, as log(L) while for larger L, the thermal conductivity approaches a finite value following the dependence K 0 -A×L -1/2 , where K 0 and A are parameters independent of the length. Our theoretical results clarify the scaling of the phonon thermal conductivity with the lateral sizes in graphene and graphite. The revealed anomalous dependence K(L) for the micrometer-size graphene ribbons can account for some of the discrepancy in reported experimental data for graphene.

The authors theoretically investigated the electron mobility in the nanometer thickness AlN / GaN / AlN heterostructures limited by the polar optical and confined acoustic phonons. The proposed model accurately takes into account dispersion of the optical and acoustic phonons in such heterostructures as well as inelasticity of the electron scattering on both optical and acoustic phonons. It has been shown that the intersubband electronic transitions play an important role in limiting the electron mobility when the energy separation between one of the size-quantized excited electron subbands and the Fermi energy becomes comparable to the optical or confined acoustic phonon energy. The latter results in the nonmonotonic oscillatory dependence of the electron mobility on the thickness of the GaN conduction channel layer. The predicted effect is observable at room temperature and over a wide range of carrier densities. The described mechanism can be used for fine tuning the confined electron and phonon states in the nanoscale heterostructures made of different material systems in order to achieve performance enhancement of the nanoscale electronic devices.

We have studied the electron mobility in the AlN/GaN/AlN heterostructures with the nanometer scale thickness by taking into account multiple quantized electron subbands and the confined optical phonon dispersion. It was shown that the inter-subband electronic transitions play an important role in limiting the electron mobility in the heterostructures when the energy separation between one of the size-quantized excited electron subbands and the Fermi energy becomes comparable to the optical phonon energy. The latter leads to the oscillatory dependence of the electron mobility on the thickness of the heterostructure conduction channel layer. This effect is observable at room temperature and over a wide range of the carrier densities. The developed formalism and calculation procedure are readily applicable to other material systems. The described effect can be used for fine-tuning the confined electron and phonon states in the nanoscale heterostructures in order to achieve performance enhancement of the nanoscale electronic and optoelectronic devices.