An extension of the Canessa and Nguyen binary model for the nonlinear current-voltage (I-V) characteristics of polycrystalline semiconductors, based on the electrical properties of individual grains, is presented. Simple analytical models for the nonuniform distribution of barrier heights at grain boundaries are assumed. The set of nonlinear Kirchhoff equations, that determine the macroscopic current across the specimen, and the nonlinearity coefficient α are solved numerically. The applied voltage dependence of the barrier height models gives α values reaching ≈ 50, indicating high nonlinearity as required by potential commercial applications. © Tübi̇tak.