• René Petersen
4. term, Nanotechnology, Master (Master Programme)
Excitonic binding energies in graphene antidot lattices are calculated using the Wannier model with the effective mass approximation. The screening is determined by solving the Poisson equation for the two interface system air-graphene-SiO2 and calculating the dielectric function of the graphene layer itself by employing a two band model of gapped graphene. An expression for the binding energy which depends on the thickness of the graphene layer is obtained and it is found that the exciton binding energy is almost independent of the layer thickness. Choosing the graphene lattice constant a_cc=1.42 Å as the layer thickness it is found that the binding energies are reduced by a factor of approximately 2.6 compared to a much simpler model used earlier.Furthermore, exciton binding energies are calculated using the Wannier model with linear bands. This is more appropriate to graphene. It is found that the linear band model increases the binding energy and thereby makes the electron and the hole more tightly bound. In some cases the binding energy diverges which is probably due to limitations in the variational approach used.In addition, antidot lattices in which the holes are placed in a rectangular lattice are investigated and compared to the hexagonal antidot lattices. It is found that the presence of a gap is highly dependent on the details of the structure and that only structures for which the unit cell width obeys the rule L_y=3+2n (n=1,2...), with the width measured in the armchair direction, have an appreciable band gap. Furthermore, in the case of hexagonal lattices the gap is always located at the gamma point in the Brillouin zone, however, for different rectangular lattices the gap moves around the Brillouin zone and might even be located between two high symmetry points.
LanguageEnglish
Publication date2009
Number of pages62
Publishing institutionAalborg Universitet, Institut for fysik og nanoteknologi
ID: 17778912