Effect of a perpendicular magnetic field on the shallow donor states near a semiconductor-metal interface

We investigate the influence of an external perpendicular magnetic field on the lowest-energy states of an electron bound to a donor which is located near a semiconductor-metal interface. The problem is treated within the effective mass approach and the lowest-energy states are obtained through (1) the “numerically exact” finite element method, and (2) a variational approach using a trial wave function where all image charges that emerge due to the presence of the metallic gate are taken into account. The trial wave functions are constructed such that they reduce to an exponential behavior for sufficiently small magnetic fields and become Gaussian for intermediate and large magnetic fields. The average electron-donor distance can be controlled by the external magnetic field. We find that the size of the 2pz state depends strongly on the magnetic field when the donor is close to the interface, showing a nonmonotonic behavior, in contrast with the ground and the other excited states.