# 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.