Atomic and Electronic Structure of Multilayer Graphene on a Monolayer Hexagonal Boron Nitride

ABSTRACTThe atomic and electronic structures of multilayer graphene on a monolayer boron nitride (MLBN) have been investigated by using the pseudopotential method and the local density approximation (LDA) of the density functional theory (DFT). We show that the LDA energy band gap can be tuned in the range 41-278 meV for a multilayer graphene by using MLBN as a substrate. The dispersion of the π/π* bands slightly away from the K point is linear with the electron speed of 0.9×106 and 0.93×106 for graphene (MLG)/MLBN and ABA trilayer graphene (TLG)/MLBN systems, respectively. This behaviour becomes quadratic with a relative effective mass of 0.0021 for the bilayer graphene (BLG)/MLBN system. The calculated binding energies are in the range of 10-43 meV per C atom.

Energy Band Gap Modification of Graphene Deposited on a Multilayer Hexagonal Boron Nitride Substrate

ABSTRACTThe equilibrium geometry and electronic structure of graphene deposited on a multilayer hexagonal boron nitride (h-BN) substrate has been investigated using the density functional and pseudopotential theories. We found that the energy band gap for the interface between a monolayer graphene (MLG) and a monolayer BN (MLBN) lies between 47 and 62 meV, depending on the relative orientations of the layers. In the most energetically stable configuration the binding energy is found to be approximately 40 meV per C atom. Slightly away from the Dirac point, the dispersion curve is linear, with the electron speed almost identical to that for isolated graphene. The dispersion relation becomes reasonably quadratic for the interface between MLG and 4-layer-BN, with a relative effective mass of 0.0047. While the MLG/MLBN superlattice is metallic, the thinnest armchair nanoribbon of MLG/MLBN interface is semiconducting with a gap of 1.84 eV.

VERY LONG DECAY TIME FOR ELECTRON VELOCITY DISTRIBUTION IN SEMICONDUCTORS, AND CONSEQUENT 1/f NOISE

The Boltzmann equation with electron-electron (e − e) interactions has been reduced to a Fokker-Planck equation (e − e FP ) in a previuos paper. In steady-state conditions, its solution q0(v) (where v is the electron speed) depends on the square of the acceleration a = eE/m. If we introduce the nonrenormalized zero-point field (ZPF) of QED, i.e., the one considered in stochastic electrodynamics, so that [Formula: see text], then q0(v) becomes similar to the Fermi-Dirac equation, and the two collision frequencies ν1(v) and ν2(v) appearing in the e − e FP become both proportional to 1/v in a small δv interval. The condition ν1(v) ∝ ν2(v) ∝ 1/v is at the threshold of the runaways. In the same δv range, the time-dependent solution q0(v,τ) of the e − e FP decays no longer exponentially but according to a power law ∝ τ− ɛ where 0.004 < ɛ < 0.006, until τ → ∞. That extremely long memory of a fluctuation implies the same dependence τ − ɛ for the conductance correlation function, hence a corresponding power-spectral noise S(f) ∝ fɛ−1 where f is the frequency. That behaviour is maintained even for a small sample because the back diffusion velocity of the electrons in the effective range δv, where they are in runaway conditions, is much larger than the drift velocity.