Measuring and Tailoring the Structure of Two-Dimensional Materials by Transmission Electron Microscopy

As the critical dimensions of electronic devices decrease in size, the nanoscale structure becomes important for the electronic properties. Two-dimensional (2D) materials, with a thickness down to one atom, are very affected by disorder. Any type of disorder in graphene, including lattice disorder, roughness, and stress, contributes to charge carrier scattering and limits the carrier mobility. The current de-facto standard for making high quality graphene devices is by hexagonal boron nitride (hBN) encapsulation, which plays the role of a dielectric providing perfect protection from the environment and flattening the graphene. However, such encapsulated samples are commonly placed on silicon oxide substrates which are non-planar surfaces that induce roughness. Another source of carrier scattering, edge roughness, is detrimental for the carrier mobility of nanostructured graphene devices. The minimisation of these sources of scattering is, therefore, important for industrial applications as well as fundamental scientific purposes.
Transmission electron microscopy (TEM) is an excellent tool for structural characterisation of 2D materials because of its sub-angstrom resolution, and potential for adding stimuli like heat, electrical biasing, and studying the interaction with gas molecules. In this project, TEM has been used to measure the structure and also to physically pattern graphene on the nanoscale.
First, the design, fabrication and characterisation of TEM sample carriers for simultaneous in-situ heating and electrical biasing of 2D materials is presented. Chips with platinum heaters on a free-standing silicon nitride membrane were fabricated. The chips were capable of heating to 350 °C consistently for at least 24 hours, and displayed a maximum temperature of 749 °C. The best performing chips were found to be those with larger silicon nitride membranes, and the failure mechanism was related to the stability of the membranes. Patterning graphene with low edge roughness is necessary to avoid charge carrier mobility degradation in graphene devices. Crystallographic etching of graphene by oxygen is a viable route towards low edge roughness patterning and was investigated in an environmental TEM. The edge roughness was found to be dependent on the oxygen pressure, where lower pressures lead to hexagonally shaped holes in graphene with armchair-oriented edges, while higher pressures lead to irregularly shaped holes. Furthermore, the etch rate was found to increase with pressure, electron beam current density, and temperature. The high resolution of the TEM also allowed to study the discrete nature of the etching process at low pressures, where the instantaneous etch rates can be described by the Poisson distribution.
Finally, the roughness of suspended graphene, suspended graphene/hBN heterostructures, and hBN/graphene/hBN heterostructures were investigated by an electron diffraction technique in the TEM. This method enables to measure the roughness of graphene at a higher resolution than scanning probe techniques, which suffer from noise at the low levels of roughness investigated here, and also measure the roughness of graphene embedded in hBN. The root mean square roughness of suspended bare graphene was measured to a value of 114 pm, and decreased to a value of 21 pm and 12 pm for hBN supported graphene and hBN encapsulated graphene, respectively. Simulations support the notion that hBN encapsulated graphene should display lower roughness than hBN supported graphene due to a localisation of flexural phonons in the hBN layers.