Analytical Expression for Thermionic Transport Through Isotype Heterojunction Interfaces of Arbitrary Doping Ratio

We present 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 is equal to one. This result relies on the solution of a transcendental equation associated with the heterojunction boundary conditions by means of the Lambert W function. As done in the derivation of the standard expression, the generalization only considers thermionic emission, but the method can equally be applied for other transport mechanisms. The general result mathematically contains the expression for the current density across a metal-semiconductor Schottky contact as a limiting case, unifying the treatment of these two heterointerfaces into a single general analytical description.