Abstract: We developed a variational approach to investigate the ground state energy and the extend of the wavefunction of a neutral donor located near a semiconductor surface in the presence of scanning tunneling microscope (STM) metallic tip. We apply the effective mass approximation and use a variational wavefunction that takes into account the influence of all image charges that arise due to the presence of a metallic tip. The behavior of the ground state energy when the tip approaches the semiconductor surface is investigated.

Abstract: The ground state energy and the extent of the wavefunction of a negatively charged donor (D − ) located near a semiconductormetal or a semiconductordielectric interface are obtained. We apply the effective mass approximation and use a variational two-electron wavefunction that takes into account the influence of all image charges that arise due to the presence of the interface, as well as the correlation between the two electrons bound to the donor. For a semiconductormetal interface, the D − binding energy is enhanced for donor positions d > 1.5aB (aB is the effective Bohr radius) due to the additional attraction of the electrons with their images. When the donor approaches the interface (i.e. d < 1.5aB) the D − binding energy drops and eventually it becomes unbound. For a semiconductordielectric (or a semiconductorvacuum) interface the D − binding energy is reduced for any donor position as compared to the bulk case and the system becomes rapidly unbound when the donor approaches the interface.

Abstract: It is known that a perpendicular electric field applied to multilayers of graphene modifies the electronic structure near the K point and may induce an energy gap in the electronic spectrum which is tunable by the gate voltage. Here we consider a system of graphene multilayers in the presence of a positively charged top and a negatively charged back gate to control independently the density of electrons on the graphene layers and the Fermi energy of the system. The band structure of three- and four-layer graphene systems in the presence of the top and back gates is obtained using a tight-binding approach. A self-consistent Hartree approximation is used to calculate the induced charges on the different graphene layers. We predict that for opposite and equal charges on the top and bottom layers an energy gap is opened at the Fermi level. For an even number of layers this gap is larger than in the case of an odd number of graphene layers. We find that the circular asymmetry of the spectrum, which is a consequence of the trigonal warping, changes the size of the induced electronic gap, even when the total density of the induced electrons on the graphene layers is low.

Abstract: The lowest energy electronic states of a donor located near a semiconductor-insulator-metal interface are investigated within the effective mass approach. The effect of the finite thickness of the insulator between the semiconductor and the metallic gate on the energy levels is studied. The lowest energy states are obtained through a variational approach, which takes into account the influence of all image charges that arise due to the presence of the metallic and the dielectric interfaces. We compare our results with a numerical exact calculation using the finite element technique.