## First principles investigations of electronic structure and transport properties of graphitic structures and single molecular junctions

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##### Authors

Owens, Jonathan R.

##### Issue Date

2014-12

##### Type

Electronic thesis

Thesis

Thesis

##### Language

ENG

##### Keywords

Physics

##### Alternative Title

##### Abstract

The first two projects pertain to nitrogen doping in graphene nanoribbons (GNRs). We study nitrogen doping in two different schema: concentration-based (Nx$-doped) and structural based (N2AA-doped).

The next problem studied pertains to observed switching in an experimentally-measured IV curve, this time of a longer zinc porphyrin molecule, still within a gold nano-gap. The switching behavior is observed only at 300K, not at 4.2K. The temperature-dependance of this problem renders our previous toolset of DFT calculations void; DFT is a ground-state theory. Instead, we employ a density functional-based tight-binding (DFTB) approach in a molecular dynamics simulation. Basically, the structural configuration evaluated at each time step is based on a tight-binding electronic structure calculation, instead of a typical MD force field. Trajectories are presented at varying temperatures and electric field strengths. Indeed, we observe a conformation of the porphyrin molecule between two configurations of the dihedral angle of the central nitrogen ring, Â±15Â° at 300K, but not 4.2K. These confirmations are equally likely, i.e., the structure assumes these configurations an equal number of teams, meaning the average structure has an angle of 0Â°. After computing the DOS of all three aforementioned configurations (0Â° and Â±15Â°), we indeed see a difference between the DOS curves at Â±15Â° (which are equal) and at 0Â°.

The first observation we want to explain is the asymmetric nature of the experimental IV curve for this porphyrin system, where the IV curve is skewed heavily to the negative bias region. Using a plane-wave DFT calculation, we present the density of states of the porphyrin molecule (both in the presence and absence of the electrodes) and indeed see highly delocalized states (as confirmed by site-projection of the DOS) only in the negative bias region, meaning that the channels with high transmission probability reside there, in agreement with experimental observation.

We next venture to explain different observed properties of the IV curves of single molecule nano-junctions. Specifically, these systems consist of a zinc-porphyrin molecule coupled between two gold electrodes, i.e., a nano-gap.

We move on to studying an entirely different class of structures carbon Schwarzites, and in particular, the carbon gyroid. This is a highly symmetric structure (space group #230), the generation of which is nontrivial. So we first discuss our technique to generate the structures, then present a systematic study of the energetics, electronic properties, and topology of all 13 structures we found. Notable features include the presence of occupied and unoccupied Dirac cones, both metallic and semi-conducting behavior, and various carbon ring sizes, i.e., Gaussian curvature.

We conclude by presenting the theory of neutron scattering using phonon spectra and compute the neutron scattering spectra on an isolated 2,4-diidothiophene molecule. Comparing our spectrum with an experimentally observed neutron scattering spectrum of the same molecule reveals very close agreement between theory and experiment, laying the foundation for structural identification via neutron scattering calculations.

The N2AA-doped GNR study was inspired by experimental observation of an atomically precise nitrogen doping scheme in bulk graphene. Experimental STM images, combined with simulated STM images, revealed that the majority (80%) of doping sites consist of nitrogen atoms on neighboring sites of the same sublattice (A) in graphene, hence N2AA doping. We examine this doping scheme applied to zigzag and armchair GNRs under different orientations of the dopants. We present spin-resolved charge densities, energetics, transport, DOS, and simulated STM images for all four systems studied. Our results show the possibility of spin-filtered devices and the STM images provide an aid in helping experimentalist identify the dopant patterns, if these GNRs are fabricated.

Concentration based doping is explored in the context of experimental measurements of IV curves on GNRs with differing dopant concentrations. These results show a shift towards semi-conducting behavior with an increase in dopant concentration. We combine first principles calculations (DFT) and transport calculations in the Landauer formalism to compute the density-of-states (DOS) and transport curves for various dopant concentrations (0.46%, 1.39%, 1.89%, and 2.31%), which corroborate the experimental observations.

In this work, we first present two powerful methods for understanding the electronic, structural, conducting, and energetic properties of nano-materials: density functional theory (DFT) and quantum transport. The basics of the theory and background of both methods are discussed thoroughly. After establishing a firm foundation, we turn our attention to using these tools to solve practical problems, often in collaboration with experimental colleagues.

The next problem studied pertains to observed switching in an experimentally-measured IV curve, this time of a longer zinc porphyrin molecule, still within a gold nano-gap. The switching behavior is observed only at 300K, not at 4.2K. The temperature-dependance of this problem renders our previous toolset of DFT calculations void; DFT is a ground-state theory. Instead, we employ a density functional-based tight-binding (DFTB) approach in a molecular dynamics simulation. Basically, the structural configuration evaluated at each time step is based on a tight-binding electronic structure calculation, instead of a typical MD force field. Trajectories are presented at varying temperatures and electric field strengths. Indeed, we observe a conformation of the porphyrin molecule between two configurations of the dihedral angle of the central nitrogen ring, Â±15Â° at 300K, but not 4.2K. These confirmations are equally likely, i.e., the structure assumes these configurations an equal number of teams, meaning the average structure has an angle of 0Â°. After computing the DOS of all three aforementioned configurations (0Â° and Â±15Â°), we indeed see a difference between the DOS curves at Â±15Â° (which are equal) and at 0Â°.

The first observation we want to explain is the asymmetric nature of the experimental IV curve for this porphyrin system, where the IV curve is skewed heavily to the negative bias region. Using a plane-wave DFT calculation, we present the density of states of the porphyrin molecule (both in the presence and absence of the electrodes) and indeed see highly delocalized states (as confirmed by site-projection of the DOS) only in the negative bias region, meaning that the channels with high transmission probability reside there, in agreement with experimental observation.

We next venture to explain different observed properties of the IV curves of single molecule nano-junctions. Specifically, these systems consist of a zinc-porphyrin molecule coupled between two gold electrodes, i.e., a nano-gap.

We move on to studying an entirely different class of structures carbon Schwarzites, and in particular, the carbon gyroid. This is a highly symmetric structure (space group #230), the generation of which is nontrivial. So we first discuss our technique to generate the structures, then present a systematic study of the energetics, electronic properties, and topology of all 13 structures we found. Notable features include the presence of occupied and unoccupied Dirac cones, both metallic and semi-conducting behavior, and various carbon ring sizes, i.e., Gaussian curvature.

We conclude by presenting the theory of neutron scattering using phonon spectra and compute the neutron scattering spectra on an isolated 2,4-diidothiophene molecule. Comparing our spectrum with an experimentally observed neutron scattering spectrum of the same molecule reveals very close agreement between theory and experiment, laying the foundation for structural identification via neutron scattering calculations.

The N2AA-doped GNR study was inspired by experimental observation of an atomically precise nitrogen doping scheme in bulk graphene. Experimental STM images, combined with simulated STM images, revealed that the majority (80%) of doping sites consist of nitrogen atoms on neighboring sites of the same sublattice (A) in graphene, hence N2AA doping. We examine this doping scheme applied to zigzag and armchair GNRs under different orientations of the dopants. We present spin-resolved charge densities, energetics, transport, DOS, and simulated STM images for all four systems studied. Our results show the possibility of spin-filtered devices and the STM images provide an aid in helping experimentalist identify the dopant patterns, if these GNRs are fabricated.

Concentration based doping is explored in the context of experimental measurements of IV curves on GNRs with differing dopant concentrations. These results show a shift towards semi-conducting behavior with an increase in dopant concentration. We combine first principles calculations (DFT) and transport calculations in the Landauer formalism to compute the density-of-states (DOS) and transport curves for various dopant concentrations (0.46%, 1.39%, 1.89%, and 2.31%), which corroborate the experimental observations.

In this work, we first present two powerful methods for understanding the electronic, structural, conducting, and energetic properties of nano-materials: density functional theory (DFT) and quantum transport. The basics of the theory and background of both methods are discussed thoroughly. After establishing a firm foundation, we turn our attention to using these tools to solve practical problems, often in collaboration with experimental colleagues.

##### Description

December 2014

School of Science

School of Science

##### Full Citation

##### Publisher

Rensselaer Polytechnic Institute, Troy, NY