Self-consistent statistical model for current transport in polycrystalline semiconductors

Transport in novel materials, specifically those scaled up to wafer sizes, will be dominated by thermionic emission over charged, randomly oriented grain boundaries. However, the challenges presented by random dopant fluctuation in lightly and moderately doped nano-crystalline materials are yet to be addressed. Here, we present a self-consistent model to describe the transport in polycrystalline materials with medium doping levels, where conductivity is governed by thermionic emission over low and wide barriers. We show that random doping fluctuations contribute to a higher material resistivity, which is explained through a non-linear potential drop over the depletion regions on both sides of the boundary. This leads to a decrease in the exponential slope at the onset of conductivity, down to values of ∼exp⁡(−2.4kT)−1, as well as to asymmetry in the current–voltage characteristics. We demonstrate that the model can be scaled up to several grains and their boundaries, by using commercially available circuit simulators, where non-linearity is realized through look-up tables. We find that an increase in resistivity of up to 18% compared to the nominal, uniformly doped material can be explained simply by the introduction of random dopant fluctuations.