Wave Propagation and Oscillations in a Semiconductor Nanostructure

A semiconductor superlattice (SL) is a succession of alternating layers of two different semiconductors. They are grown by depositing alternatively a few monolayers of (for example) GaAs and AlAs on top of a common substrate. After growth, mesas of cylindrical shape are cut and contact layers are attached to the top and bottom of the superlattice. Typical dimensions are: 40 to 50 for the number of SL periods, 120 microns for the mesa diameter, 9 nanometers wide GaAs layer and 4 nanometers wide AlAs layer for each period of the superlattice (Kastrup et al., 1997). The contact layers are usually heavily doped (to produce extra electrons or holes) and the super-lattice in between may or may not be doped. Under proper specifications and bias, a device such as described here may produce time-dependent oscillations on a wide temperature range including room temperature. Thus a superlattice can be used as a high-speed oscillator in the communications industry. We shall describe and analyze here a simple model of the mechanism responsible for the self-sustained oscillations of the electric current through a doped superlattice. The case of an undoped superlattice subject to laser illumination will not be considered here, although it is also of great interest for applications (see (Bonilla et al., 1994) for a simple model and its analysis).