Research Article: Graphene Nanoribbon Based Thermoelectrics: Controllable Self‐ Doping and Long‐Range Disorder

Date Published: March 31, 2017

Publisher: John Wiley and Sons Inc.

Author(s): Huashan Li, Jeffrey C. Grossman.


Control of both the regularity of a material ensemble and nanoscale architecture provides unique opportunities to develop novel thermoelectric applications based on 2D materials. As an example, the authors explore the electronic and thermal properties of functionalized graphene nanoribbons (GNRs) in the single‐sheet and helical architectures using multiscale simulations. The results suggest that appropriate functionalization enables precise tuning of the doping density in a planar donor/acceptor GNR ensemble without the need to introduce an explicit dopant, which is critical to the optimization of power factor. In addition, the self‐interaction between turns of a GNR may induce long‐range disorder along the helical axis, which suppresses the thermal contribution from phonons with long wavelengths, leading to anomalous length independent phonon thermal transport in the quasi‐1D system.

Partial Text

2D materials such as graphene sheets,1, 2, 3 graphene nanoribbons (GNRs),4, 5, 6, 7 molybdenum dichalcogenides,8, 9 and phosphorene (monolayer black phosphorus)10 have been computationally proposed as promising building blocks for thermoelectric (TE) materials, although their realization in experiment remains a challenge due to the extrinsic scattering sources originating from material imperfections.8, 11 In addition to the modification of intrinsic quantum confinement and anisotropy of 2D materials,10 the control over architecture may serve as an attractive means to promote device performance,1 because the all‐surface character of 2D materials offers opportunities to strengthen interfacial effects in an organized ensemble, and the flexibility of 2D structures provides a large phase space for building tailored nano‐ and mesoscale architectures.

The design of organized architectures using various types of building blocks has been shown by previous theoretical studies1, 32 to be a potential way to take advantage of the control over ensemble regularity due to the rich classes of phenomena incurred by interfaces. Following this strategy, we considered an ensemble of aligned GNRs chemically connected to each other (Figure2g–j), which effectively forms a functionalized graphene sheet with tunable energy level alignments between its 1D partitions. These particular benzene ligands are selected because they have been successfully added to the graphene surface by solution processing in recent experiments,33 and are arranged in the energetically favorable configurations suggested by previous calculations.34

In summary, the comparison of single‐sheet and helical architectures of functionalized GNRs sheds light on the potential benefits in TE applications from material architecture design: precise tuning of electronic structure and modification of vibrational channels via self‐interactions. Specifically, a type‐III energy level alignment can be established in the single‐sheet architecture to achieve controllable and homogeneous modulation ground state doping without deleterious scattering from explicit dopants, which is important for optimizing electrical conductivity and thermoelectric response. For the helix architecture, thermal conductivity can either be decreased by the long‐range disorder that suppresses the thermal contribution from long‐wavelength phonons, or increased by the additional transport paths through ligands that are close to or interconnected to each other. Although only the TE applications for GNRs with various architectures have been considered in our work, and the assumptions made in our model induce uncertainties in predictions, the ubiquitous underlying principles should be possible to be applied in other novel designs.

A combination of electronic structure calculations and the Boltzmann transport approach was employed to predict the electronic transport properties at room temperature. Standard ab initio calculations within the framework of density functional theory (DFT), implemented in the Vienna Ab Initio Simulation package (v5.3),51 were employed to calculate the atomic structure, DOS, and bandstructure. Plane‐wave and projector‐augmented‐wave type pseudopotentials52 were applied with the PBE exchange‐correlation functional.53 Since the band structure of the entire sheet near the band edge is similar to that of its GNR components, the doping density was determined by integrating the DOS from the Fermi level to the band edge of the donor/acceptor GNRs, which is justified by the matching between doping densities of the entire sheet and its components. Transport coefficients at 300 K were obtained by semiclassical Boltzmann theory with an energy dependent relaxation time1 using the Boltzmann Transport Properties package (modified from v1.2.5).54 Since acoustic phonon scattering is the dominant scattering mechanism for carriers in GNRs,35 the electron relaxation time was calculated by deformation potential theory.1 The electron–electron scattering processes, though, must be accounted for in the heat transport calculations, thus the thermal relaxation time was estimated based on a previous analysis of the reduced Wiedemann–Franz ratio.55




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