Geert Brocks

Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations

We determine the electronic structure of a graphene sheet on top of a lattice-matched hexagonal boron nitride (h-BN) substrate using ab initio density functional calculations. The most stable configuration has one carbon atom on top of a boron atom, the other centered above a BN ring. The resulting inequivalence of the two carbon sites leads to the opening of a gap of 53 meV at the Dirac points of graphene and to finite masses for the Dirac fermions. Alternative orientations of the graphene sheet on the BN substrate generate similar band gaps and masses. The band gap induced by the BN surface can greatly improve room temperature pinch-off characteristics of graphene-based field effect transistors.

First-principles study of the interaction and charge transfer between graphene and metals

Measuring the transport of electrons through a graphene sheet necessarily involves contacting it with metal electrodes. We study the adsorption of graphene on metal substrates using first-principles calculations at the level of density-functional theory. The bonding of graphene to Al, Ag, Cu, Au, and Pt (111) surfaces is so weak that its unique “ultrarelativistic” electronic structure is preserved. The interaction does, however, lead to a charge transfer that shifts the Fermi level by up to 0.5 eV with respect to the conical points. The crossover from p-type to n-type doping occurs for a metal with a work function ~5.4 eV, a value much larger than the work function of free-standing graphene, 4.5 eV. We develop a simple analytical model that describes the Fermi-level shift in graphene in terms of the metal substrate work function. Graphene interacts with and binds more strongly to Co, Ni, Pd, and Ti. This chemisorption involves hybridization between graphene pz states and metal d states that opens a band gap in graphene, and reduces its work function considerably. The supported graphene is effectively n-type doped because in a current-in-plane device geometry the work-function lowering will lead to electrons being transferred to the unsupported part of the graphene sheet.

Theoretical prediction of perfect spin filtering at interfaces between close-packed surfaces of Ni or Co and graphite or graphene

The in-plane lattice constants of close-packed planes of fcc and hcp Ni and Co match that of graphite almost perfectly so that they share a common two-dimensional reciprocal space. Their electronic structures are such that they overlap in this reciprocal space for one spin direction only allowing us to predict perfect spin filtering for interfaces between graphite and (111) fcc or (0001) hcp Ni or Co. First-principles calculations of the scattering matrix show that the spin filtering is quite insensitive to amounts of interface roughness and disorder which drastically influence the spin-filtering properties of conventional magnetic tunnel junctions or interfaces between transition metals and semiconductors. When a single graphene sheet is adsorbed on these open d-shell transition-metal surfaces, its characteristic electronic structure, with topological singularities at the K points in the two-dimensional Brillouin zone, is destroyed by the chemical bonding. Because graphene bonds only weakly to Cu which has no states at the Fermi energy at the K point for either spin, the electronic structure of graphene can be restored by dusting Ni or Co with one or a few monolayers of Cu while still preserving the ideal spin-injection property.

Work functions of self-assembled monolayers on metal surfaces by first-principles calculations

Using first-principles calculations we show that the work function of noble metals can be decreased or increased by up to 2 eV upon the adsorption of self-assembled monolayers of organic molecules. We identify the contributions to these changes for several (fluorinated) thiolate molecules adsorbed on Ag(111), Au(111), and Pt(111) surfaces. The work function of the clean metal surfaces increases in this order, but adsorption of the monolayers reverses the order completely. Bonds between the thiolate molecules and the metal surfaces generate an interface dipole, whose size is a function of the metal, but it is relatively independent of the molecules. The molecular and bond dipoles can then be added to determine the overall work function

Germanene: the germanium analogue of graphene

Recently, several research groups have reported the growth of germanene, a new member of the graphene family. Germanene is in many aspects very similar to graphene, but in contrast to the planar graphene lattice, the germanene honeycomb lattice is buckled and composed of two vertically displaced sub-lattices. Density functional theory calculations have revealed that free-standing germanene is a 2D Dirac fermion system, i.e. the electrons behave as massless relativistic particles that are described by the Dirac equation, which is the relativistic variant of the Schrödinger equation. Germanene is a very appealing 2D material. The spin-orbit gap in germanene (~24 meV) is much larger than in graphene (<0.05 meV), which makes germanene the ideal candidate to exhibit the quantum spin Hall effect at experimentally accessible temperatures. Additionally, the germanene lattice offers the possibility to open a band gap via for instance an externally applied electrical field, adsorption of foreign atoms or coupling with a substrate. This opening of the band gap paves the way to the realization of germanene based field-effect devices. In this topical review we will (1) address the various methods to synthesize germanene (2) provide a brief overview of the key results that have been obtained by density functional theory calculations and (3) discuss the potential of germanene for future applications as well for fundamentally oriented studies.

Nonlinear screening of charges induced in graphene by metal contacts

To understand the band bending caused by metal contacts, we study the potential and charge density induced in graphene in response to contact with a metal strip. We find that the screening is weak by comparison with a normal metal as a consequence of the ultrarelativistic nature of the electron spectrum near the Fermi energy. The induced potential decays with the distance from the metal contact as x−1/2 and x−1 for undoped and doped graphene, respectively, breaking its spatial homogeneity. In the contact region, the metal contact can give rise to the formation of a p-p′, n-n′, and p-n junction (or with additional gating or impurity doping, even a p-n-p′ junction) that contributes to the overall resistance of the graphene sample, destroying its electron-hole symmetry. Using the work functions of metal-covered graphene recently calculated by Khomyakov et al. [Phys. Rev. B 79, 195425 (2009)], we predict the boundary potential and junction type for different metal contacts.

Electrostatic Doping of Graphene through Ultrathin Hexagonal Boron Nitride Films

When combined with graphene, hexagonal boron nitride (h-BN) is an ideal substrate and gate dielectric with which to build metal|h-BN|graphene field-effect devices. We use first-principles density functional theory (DFT) calculations for Cu|h-BN|graphene stacks to study how the graphene doping depends on the thickness of the h-BN layer and on a potential difference applied between Cu and graphene. We develop an analytical model that describes the doping very well, allowing us to identify the key parameters that govern the device behavior. A predicted intrinsic doping of graphene is particularly prominent for ultrathin h-BN layers and should be observable in experiment. It is dominated by novel interface terms that we evaluate from DFT calculations for the individual materials and for interfaces between h-BN and Cu or graphene.

Controlling the Schottky barrier at MoS 2/metal contacts by inserting a BN monolayer

Making a metal contact to the two-dimensional semiconductor MoS 2 without creating a Schottky barrier is a challenge. Using density functional calculations we show that, although the Schottky barrier for electrons obeys the Schottky-Mott rule for high work function (≳4.7 eV) metals, the Fermi level is pinned at 0.1–0.3 eV below the conduction band edge of MoS 2 for low work function metals, due to the metal-MoS 2 interaction. Inserting a boron nitride (BN) monolayer between the metal and the MoS 2 disrupts this interaction, and restores the MoS 2 electronic structure. Moreover, a BN layer decreases the metal work function of Co and Ni by ∼2 eV, and enables a lineup of the Fermi level with the MoS 2 conduction band. Surface modification by adsorbing a single BN layer is a practical method to attain vanishing Schottky barrier heights.

DFT study of planar boron sheets: a new template for hydrogen storage

We study the hydrogen storage properties of planar boron sheets and compare them to those of graphene. The binding of molecular hydrogen to the boron sheet (0.05 eV) is stronger than that to graphene. We find that dispersion of alkali metal (AM = Li, Na, and K) atoms onto the boron sheet markedly increases hydrogen binding energies and storage capacities. The unique structure of the boron sheet presents a template for creating a stable lattice of strongly bonded metal atoms with a large nearest neighbor distance. In contrast, AM atoms dispersed on graphene tend to cluster to form a bulk metal. In particular, the boron−Li system is found to be a good candidate for hydrogen storage purposes. In the fully loaded case, this compound can contain up to 10.7 wt % molecular hydrogen with an average binding energy of 0.15 eV/H2.

Electronic Correlations in Oligo-acene and -Thiopene Organic Molecular Crystals

From first-principles calculations we determine the Coulomb interaction between two holes on oligo-acene and -thiophene molecules in a crystal, as a function of the oligomer length. The electronic polarization of the molecules that surround the charged oligomer reduces the bare Coulomb repulsion between the holes by approximately a factor of 2. The effects of relaxing the molecular geometry in the presence of holes is found to be significantly smaller. In all cases the effective hole-hole repulsion is much larger than the valence bandwidth, which implies that at high doping levels the properties of these organic semiconductors are determined by electron-electron correlations.