Thermal transport in low-dimensional materials

Recent years have witnessed a paradigm shift in the world of electronics. Researchers have not only continued to postpone the long dreaded end-of-Moore’s-law, but have also opened up a new world of possibilities with electronics. The future of electronics is widely anticipated to be dominated by wearable and implantable devices, the realization of which will be made possible by the discovery of new materials. Graphene and hexagonal boron nitride (hBN) are two such materials that have shown promising properties to make these devices possible. It has been shown that an energy bandgap can be opened in graphene by patterning it as a narrow ribbon, by applying an electric displacement field to a bilayer configuration, and by other means. The possibility of tuning the bandgap makes graphene an ideal channel material for future electronics. Similarly, hexagonal boron nitride (hBN) and its ribbon configurations have been shown to be excellent dielectric materials. In addition, the similarities in the atomic configurations of graphene and hBN allow them to conform extremely well to each other, achieving atomically smooth interfaces. Graphene devices on hBN substrates have been shown to have mobilities an order of magnitude larger than graphene devices fabricated on silicon dioxide. In addition to their outstanding electrical properties, graphene and hBN have been shown to have excellent thermal properties compared to their traditional counterparts (silicon and silicon dioxide, respectively). More specifically, these materials have been shown to have size dependent thermal properties which may be used to tune device performance. In this thesis, we study the thermal transport of three important classes of materials – graphene nanoribbons, hBN nanoribbons and graphene-hBN heterostructures using the phonon Boltzmann transport equation in a linearized framework. An exact solution of the Boltzmann transport equation is obtained ensuring that normal and umklapp phonon scattering processes are appropriately treated. In the first part of the thesis, we present a computational technique called method of automatic code differentiation to calculate sensitivities in nanoscale thermal transport simulations. Key phonon parameters like force constants, group velocities, the Gruneisen parameter, etc., which can be expressed as sensitivities or derivatives, are computed using this technique. The derivatives computed using this technique are exact and can be generalized to any order with minimal effort. This technique can be unintrusively integrated with existing first-principles simulation codes to obtain the sensitivities of parameters computed therein to chosen inputs. The next focus is to investigate the thermal properties of three main classes of materials – graphene nanoribbons, hBN nanoribbons,and graphene-hBN heterostructures. For nanoribbons, we consider ribbons of varying widths to investigate the transition of key thermal properties with width. The lattice structure of the ribbon structures considered is fully resolved. An efficient parallelization technique is developed to handle the large number of atoms in a unit cell. The thermal conductivity is obtained by an iterative solution of the linearized Boltzmann transport equation. For graphene and hBN ribbons, we find that the thermal conductivity increases with the ribbon width following a power-law trend. The rate of increase of thermal conductivity with width for hBN ribbons is found to be slower compared to graphene. Flexural phonons are found to contribute to the majority of heat conduction in both the materials. Frequency- and polarization-resolved transport is analyzed for ribbon of all widths. The thermal conductivity of single- and few-layer hexagonal boron nitride is also computed and compared with measured data. It is found that the thermal conductivity of hBN based nanostructures (single-layer, few-layer and ribbons) is around 6-8 times smaller than that for the corresponding graphene-based nanostructure. The effect of strain in both these materials is investigated. We find that the thermal conductivity of single-layer hBN is very sensitive to strain whereas graphene shows relatively less sensitivity for the same strains. Finally, thermal transport in graphene-hBN heterostructures is simulated. Two different structures are considered – single-layer graphene on an hBN substrate, and bilayer graphene on an hBN substrate. Substrates of different thickness are considered. Due to the weak interlayer coupling in these heterostructures, it is found that the phonon dispersion remains largely unchanged from the dispersions of the individual layers. The only difference in dispersion is noticed for flexural phonons, which are the only modes affected by interlayer coupling. The addition of an hBN layer underneath the graphene/bilayer graphene layer is found to drastically reduce the thermal conductivity of the heterostructures. This reduction is due to breakdown of the selection rule for flexural phonons which results in increased scattering channels for these phonons. The thermal conductivity gradually decreases, saturating to a bulk value with an increase in the number of hBN layers. The results presented in this thesis are expected to help guide the design of graphene/hBN based flexible electronics.