Linear Response of Bound Electrons to a Quasi-Static Oscillating Field in GaN Nanowire Structures

There is a growing body of literature that recognizes the importance of nanostructured semiconductor materials. Their potential novel properties arise when the physical dimensions of the structure reach the nanometer scale. In particular, one-dimensional systems made of wide-bandgap semiconducting ordered alloys such as GaN have attracted significant interest due to their remarkable properties for electronics, optics, and photonics. In this work, we studied the problem of charge trapping around individual infinite metallic nanowires, with a two-dimensional numerical approach combining Schrödinger’s and Poisson’s equations. The effect of wire radius and distance between wires were first investigated in detail. We then emphasize the finding that under different applied voltages, the system exhibits a potential to respond to an electromagnetic radiation in a tunable way. This effect is stronger for smaller systems. However, for a given system size, we found out that the energy values as well as the energy steps are larger for both thick and narrow wires due to the quantum confinement of electrons, with a minimum energy observed for a radius of about 10% of the system dimension. We also investigated the linear response of bound electrons around an isolated wire exposed to a quasi-static oscillating electric field. To this purpose, we defined the average charge radius as the integral of the product of the wave function squared by the position operator over the surface of a square cell. Our results show that the wave functions can be grouped into different classes. Inside a class, the average radii have almost the same value for all wave functions and the energy values depend in a quadratic manner on the order of the eigen wave function. Due to the relatively large cell size and to the almost unimpeded motion of the electrons around the metal wires, the nanostructures proposed in work are expected to exhibit a large electrical polarizability. Our results confirm this assertion and our numerical formalism allowed us to determine the linear response, or polarizability, in representative systems. To this perspective, the transition probabilities between different energy levels, as well as the oscillator strengths are important quantities to consider. The systems proposed in this work could be of great practical interest. Indeed, the energy of excitation between two different classes of levels is in the range of 10 meV, or a few tens of meV at most. This corresponds to photon frequencies in the THz range, where emitters and detectors are not numerous. A possible application as radiation detector could use the modification of the in-plane electrical conductivity brought by an electromagnetic wave. Indeed, the overlap between wave functions on neighboring sites depends on the electron state of excitation which is changed by the incident wave. Another possible process is the ionization of the bound states which could induce a capacitive current in the central wire