Stability of a reflective coupling diode with the inclusion of thermal effects in narrow band-gap materials

Despite the difficulty in fabrication, resonant tunnelling diodes (RTD) have found a great deal of usage in the analogue, digital and mixed signal realms as a means of increasing the speed of signal processing circuitry, or in reducing the static power dissipation in the circuitry. Nevertheless, RTDs suffer from their non-planar structure. One possible solution is a planar diode, which operates via coupling of injected electron modes from an input waveguide to a corresponding output waveguide in a semiconductor hetrostructure, or a reflective coupling diode (RCD). In this paper, we investigate the role of temperature on the operation of an RCD. The resonant tunnelling diode (RTD) has been a staple of physics for many years. It has found great many uses in analogue, digital and mixed signal circuits [1]. However, the fact that the RTD must be fabricated using molecular beam epitaxy (MBE), which results in a non-planar device, leads to some drawbacks. First, the traditional RTD must be grown in layers with precise control over the application of different layers of atoms to form the device. If precise control of the location and thicknesses of atomic layers is lost, then the operation of the device could change significantly as the barriers change size and shape. These changes in the size and shape of the quantum well will accordingly alter the position and the form of the I–V characteristics. While the science of MBE has reduced the probability of losing precise control of the atoms that impinge on a given substrate to form the RTD, this has not erased the problem of melding a non-planar device into a planar integrated circuit. Therefore, efforts have been made to explore the possibility of using other quantum phenomenon to induce similar I–V characteristics as those seen in the RTD [2–6]. To this end, there has been a recent proposal of a single input, single output device fabricated in a coupled waveguide structure, the reflective coupling diode (RCD) [7]. The RCD operates based on the fact that in a coupled waveguide structure there exits highly reflective energies where the incident modes are reflected back to the input of the device, thereby producing similar I–V characteristics as that of the RTD. In this paper, we study the effects that temperature and material disorder have on the operation of the RCD. The structure under consideration is described in [7]. The simulations are performed on a discretized grid using a variation of the Usuki mode matching technique via the scattering matrix [8], using a grid spacing of 5 nm. To examine the effects of finite temperature on the system, we must include the difference between the Fermi level at the source and the Fermi level at the drain in the Landauer formula, as well as include the thermal effects on the energy of the incoming mode. To include thermal effects we now use I (Vsd) = 2e h ∫ dE · T (E) [fs(E)− fd(E − eVsd)] (1) to calculate the current at different applied biases where, in the above equation fs and fd are the values of the Fermi functions at the source contact and drain contacts, respectively. In figure 1, we plot the I–V characteristics of the RCD with the inclusion of thermal effects. In figure 1(a), we plot the I–V characteristics of the RCD with no thermal effects included and the source–drain bias varied from 0–3 mV. This causes a spatial modulation of the Fermi level in the system, which in turn, causes a modulation of the velocity of the incoming mode. In figure 1(b), we plot the I–V characteristics of the RCD with the temperature of the system set to 1 K. In figure 1(b), we note several differences from the ideal case. First, we note that magnitude of the current has been reduced. This can be explained by the fact that now, when the Landauer 0268-1242/04/040481+02$30.00 © 2004 IOP Publishing Ltd Printed in the UK S481