In collaboration with our colleagues from Warsaw University of Technology, we have started an operation aimed at developing Monte Carlo simulation codes for systems based on 2D materials. These materials, whose prototypical example is graphene, exhibit many extraordinary properties which can find applications in many fields, including electronics and spintronics and the emerging field of ‘valleytronics’.
The first step was to build models of electron transport in 2D materials, in particular graphene and silicene (its silicon counterpart), which are both gapless with linear dispersion near the K points minima. Piecewise analytic approximations of high energy dispersion relation, have been used, in order to make easier future implementation in device simulator. Velocity field characteristics, mobility and diffusion coefficients in the materials have been calculated. Special attention has been paid to the case of high carrier density, often overlooked in the literature, and special techniques have been developed to account for Pauli exclusion and Coulomb scattering.
In view of spintronics applications, a Monte Carlo model has been developed which describes both electron transport and spin dynamics. The originality is that Pauli principle is treated in a special way to account for both random (scattering induced) and coherent spin evolution, enabling to consider high carrier densities. Our results are consistent with experimental findings and support the idea that spin polarization may be conserved for a long time (several ns), in graphene, which is attractive for spintronic applications.
In spintronics, the spin of electrons is used to carry information. In systems such as graphene and ‘graphene-like’ 2D materials, band structure presents two valleys, not equivalent but energetically degenerate, at points K and K’. The valley index bears some similarity with the spin and this additional degree of freedom can also be used to carry information. This is the realm of an emerging discipline called valleytronics. In the next years, we plan to investigate ‘valley properties’ of graphene and other 2D materials.