The effects of propagational factors on quantum wires in close parallel proximity

Abstract

Recent advances in semiconductor technology have made it possible to produce devices of such small size that electronic conduction through these devices is dominated by the quantum properties of the electron. The fact that an electron travelling through such a device is unaffected by scattering and is able to retain coherence, has received some attention in recent literature [1-3]. The ability to guide an electron wave in quantum wires has in particular opened up opportunities for device applications which are based on the wave nature of the electron. In this paper we wish to investigate the propagation of an electron wave along the length of two coupled quantum wires. We assume that the wires are sufficiently long and straight, and that they run parallel to each other. These assumptions allow the neglect of the end effects of the wires on the electronic motion and offer considerable simplicity in the calculations. The quantum nature of the wires arises due to smallness of the cross sectional area of the wires which is usually of the order of 100 Angstroms in length in any direction. The wires are defined in terms of two quantum wells such that the electron motion is restricted in the direction transverse to the length of the wire and is unrestricted along its length. We assume that the wires are sufficiently close to each other that an electron wave introduced in one of the wires is able to tunnel itself into the other. The wave could in fact oscillate back and forth between the wires. The frequency of osxillations will depend on the width and depth of the quantum wells and the distance separating the wires. In addition to these parameters, the frequency is also affected by the effective mass of the electron if it is different within and outside the wires [4-5], a situation which can frequently arise. In this situation we will show that the motion of the electrons in the parallel and perpendicular directions become coupled and that the frequency of oscillations of the electron wave depends on the motion of the wave'parallei to the wire. It is the main aim of this paper to investigate the effect of the changes in the electron effective mass on the frequency. In addition we wish to obtain the dependence of the frequency on the distance between the wires, and the potential depths and width of the quantum wells.