Analytical Modelling of Isotype Heterojunctions

Abstract

<p>An <em>isotype heterojunction</em> is a junction between two layers of dissimilar semiconductors both of which are doped either n-type or p-type. These semiconductor structures are found in a variety of optoelectronic devices, such as solar cells, semiconductor lasers, and detectors. Motivated by the structure of third generation inorganic solar cells, this thesis concentrates on the analytical modelling of isotype heterojunctions and its application to the design optimization of these devices. The main development of this work is the introduction of an analytical expression for the current density across an isotype heterojunction valid for arbitrary doping concentration ratios. This result generalizes the standard expression found in the literature, which is limited by the assumption that the doping concentration ratio between the two sides of the heterojunction is equal to one. The generalization is developed by employing the Lambert W function in the solution of the electrostatic boundary condition associated with the heterojunction interface. As done in the derivation of the standard expression found in the literature, the generalization only considers thermionic emission, but the same method can readily be applied for other transport mechanisms. A key feature of this generalized result is that it mathematically contains the expression for the current density across a metal-semiconductor Schottky contact as a limiting case, thereby unifying the treatment of these two heterointerfaces into a single general analytical description. This latter find is particularly significant from a theoretical perspective, considering that the two heterointerfaces are traditionally described as separate topics in the presentation of semiconductor device theory.</p>