The influence of electron-electron scattering on the distribution function and transport characteristics of intrinsic monolayer graphene is investigated via an ensemble Monte Carlo simulation. Due to the linear dispersion relation in the vicinity of the Dirac points, it is found that pair-wise collisions in graphene do not conserve the ensemble average velocity in contrast to conventional semiconductors with parabolic energy bands. Numerical results indicate that electron-electron scattering can lead to a decrease in the low field mobility by more than 80 % for moderate electron densities. At high densities, the impact gradually diminishes due to increased degeneracy.Since graphene was first realized experimentally in 2004, 1 it has attracted significant interest due to its unique electronic properties. At low electron energies near the inequivalent Dirac points, there is no gap between the valence and conduction bands and the dispersion of the energy bands is linear. 2 Extremely high electrical mobilities have been reported in suspended graphene, exceeding 10 5 cm 2 /Vs near room temperature, 3 suggesting potential applications to ultrahigh frequency electronic devices. 4 The carrier density, which is controlled by the gate voltage, can be expected to vary by orders of magnitude. An interesting consequence of the linear energy dispersion is that the ensemble average velocity is not necessarily conserved upon an electronelectron (e-e) scattering event. Accordingly, inter-carrier collisions deserve careful consideration in the determination of the transport properties.Das Sarma et al. 5 found the inelastic e-e scattering rate and mean free path in graphene through the analysis of the quasiparticle self-energies. The scattering rate, calculated for electron densities from 1−10×10 12 cm −2 , was found to be of the same order of magnitude for electronphonon scattering rates evaluated in the deformation potential approximation (DPA). 6 Several authors have considered the electronic transport properties of graphene based on approaches such as the Monte Carlo simulation (see, for example, Ref. 7); however, the effects of e-e scattering have yet to be addressed to the best of our knowledge. In the present study, we examine the influence of this interaction mechanism in intrinsic monolayer graphene at room temperature. A full-band ensemble Monte Carlo method is used for accurate analysis of the distribution function as well as its macroscopic manifestations, particularly, the electron low-field mobilities and drift velocities.In both bulk and two-dimensional (2D) conventional semiconducting systems, e-e scattering has been well studied as is documented in the literature. 8 During an e-e scattering event, both the energy and momentum are conserved. In a parabolic band structure, common in conventional semiconductors, momentum conservation directly leads to the conservation of velocity. This can be readily shown by multiplying the momentum conservation equation by /m, which givesIt is then clear that, in a material with a p...

Density functional perturbation theory is used to analyze electron-phonon interaction in bilayer graphene. The results show that phonon scattering in bilayer graphene bears more resemblance with bulk graphite than monolayer graphene. In particular, electron-phonon scattering in the lowest conduction band is dominated by six lowest (acoustic and acoustic-like) phonon branches with only minor contributions from optical modes. The total scattering rate at low/moderate electron energies can be described by a simple two-phonon model in the deformation potential approximation with effective constants D ac ≈ 15 eV and D op ≈ 2.8 × 10 8 eV/cm for acoustic and optical phonons, respectively. With much enhanced acoustic phonon scattering, the low field mobility of bilayer graphene is expected to be significantly smaller than that of monolayer graphene.

Electron transport in bilayer graphene is studied by using a first-principles analysis and the Monte Carlo simulation under conditions relevant to potential applications. While the intrinsic properties are found to be much less desirable in bilayer than in monolayer graphene, with significantly reduced mobilities and saturation velocities, the calculation also reveals a dominant influence of extrinsic factors such as the substrate and impurities. Accordingly, the difference between two graphene forms is more muted in realistic settings, although the velocity-field characteristics remain substantially lower in the bilayer. When bilayer graphene is subject to an interlayer bias, the resulting changes in the energy dispersion lead to stronger electron scattering at the bottom of the conduction band. The mobility decreases significantly with the size of the generated band gap, whereas the saturation velocity remains largely unaffected.

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Decimal reduction times (D-values) were determined for Salmonella enterica serotypes, Listeria monocytogenes, and Staphylococcus aureus in two high solids egg mixes designated A and B (water activity [a(w)] = 0.76 and 0.82; solids = 53.12 and 52.63%; pH = 5.09 and 5.29; viscosity = 183 and 119 centipoise/s, respectively) using a low-volume (0.06 ml) sealed glass capillary tube procedure. For Salmonella, D-values ranged from 0.035 (70 degrees C) to 0.193 min (64 degrees C) in product A and from 0.048 to 0.193 min in product B. For Listeria, D-values ranged from 0.133 (70 degrees C) to 0.440 min (64 degrees C) in product A and from 0.074 to 0.364 min in product B. For Staphylococcus, D-values ranged from 0.332 (70 degrees C) to 1.304 min (64 degrees C) in product A and from 0.428 to 1.768 min in product B. For Listeria, the D-values of all heating temperatures were significantly higher (P < 0.01) in product A than in product B. The similar trend was also observed for Salmonella and Staphylococcus but only at 66 degrees C for Salmonella and 64 degrees C for Staphylococcus. Greater temperature dependence was observed for Salmonella inactivation in the low a(w) and low pH product (A), while the product (B) with the higher a(w) and pH had greater temperature dependence for Listeria. Compared across both egg mixes and all heating temperatures, the Staphylococcus strains were from 6.2 to 11.7 times more heat resistant than S. enterica serotypes and from 2.2 to 7.5 times more heat resistant than L. monocytogenes.