Three-dimensional analysis of the geometrical rectifying properties of metal-vacuum-metal junctions and extension for energy conversion

We study the rectification properties of geometrically asymmetric metal-vacuum-metal junctions. In particular, we focus on systems in which the cathode metal supports a hemispherical protrusion. By using a transfer-matrix methodology to take account of three-dimensional aspects of the problem, we compute the forward and backward currents that flow in this device when it is subject to positive or negative external biases. These currents enable the calculation of the rectification properties of the device in the limit of quasistatic fields. We also determine the power this device could provide to an external load. We study in detail how these properties depend (i) on the magnitude of the bias established between the two metallic electrodes, (ii) on the separation between the two electrodes, (iii) on differences in the work function of the two metals, (iv) on differences in the temperature of the two metals, and (v) on the height of the protrusion. These calculations provide quantitative results for the use of these junctions as an energy converter and the efficiency with which the energy of incident radiation is being converted into a dc current and delivered to an external load.