Epitaxial graphene growth on 3C SiC by Si sublimation in UHV

This thesis is a step forward in understanding the growth of graphene, a single layer of carbon atoms, by annealing Silicon Carbide (SiC) thin films in Ultra High Vacuum. The research lead to the discovery that the details of the transition from SiC to graphene, providing, for the first time, atomic resolution images of the different stages of the transformation and a model of the growth. The epitaxial growth of graphene developed by this study is a cost effective procedure to obtain this material directly on Si chips, a breakthrough for the future electronic industry.

Time evolution of graphene growth on SiC as a function of annealing temperature

We followed by X-ray Photoelectron Spectroscopy (XPS) the time evolution of graphene layers obtained by annealing 3C SiC(111)/Si(111) crystals at different temperatures. The intensity of the carbon signal provides a quantification of the graphene thickness as a function of the annealing time, which follows a power law with exponent 0.5. We show that a kinetic model, based on a bottom-up growth mechanism, provides a full explanation to the evolution of the graphene thickness as a function of time, allowing to calculate the effective activation energy of the process and the energy barriers, in excellent agreement with previous theoretical results. Our study provides a complete and exhaustive picture of Si diffusion into the SiC matrix, establishing the conditions for a perfect control of the graphene growth by Si sublimation.

A semi-analytical solution for multilayer diffusion in a composite medium consisting of a large number of layers

Diffusion in a composite slab consisting of a large number of layers provides an ideal prototype problem for developing and analysing two-scale modelling approaches for heterogeneous media. Numerous analytical techniques have been proposed for solving the transient diffusion equation in a one-dimensional composite slab consisting of an arbitrary number of layers. Most of these approaches, however, require the solution of a complex transcendental equation arising from a matrix determinant for the eigenvalues that is difficult to solve numerically for a large number of layers. To overcome this issue, in this paper, we present a semi-analytical method based on the Laplace transform and an orthogonal eigenfunction expansion. The proposed approach uses eigenvalues local to each layer that can be obtained either explicitly, or by solving simple transcendental equations. The semi-analytical solution is applicable to both perfect and imperfect contact at the interfaces between adjacent layers and either Dirichlet, Neumann or Robin boundary conditions at the ends of the slab. The solution approach is verified for several test cases and is shown to work well for a large number of layers. The work is concluded with an application to macroscopic modelling where the solution of a fine-scale multilayered medium consisting of two hundred layers is compared against an “up-scaled” variant of the same problem involving only ten layers.