This paper introduces an approach to manufacture a small multiplexer with dense field-effect transistors. First, a framework of two-level current-mode logic gates was designed for the transistors. The logic gates are organized heterogeneously with a substrate, epitaxial layers and buffer layer. Considering the different properties of materials in the framework, the density of transistors was improved by annealing dopant and/or radiation defects, thus reducing the size of the multiplexer. In addition, the mismatch-induced stress was alleviated through ion implantation. Next, an analytical approach was developed to analyze the mass and heat transport in the heterogenous framework during the production of integrated circuits, in the presence of mismatch-induced stress. The proposed method makes it possible to capture both nonlinear variations of parameters in space and time through the production process.