A detailed examination of polysilicon resistivity incorporating the grain size distribution

TL;DR

This paper introduces a two-dimensional resistivity model for polysilicon that incorporates grain size distribution, revealing significant impacts of grain size variation on resistivity and improving the accuracy of electrical property characterization.

Contribution

The authors developed a Voronoi-based resistor network model that integrates grain size distribution into resistivity calculations, enhancing existing models with a novel two-dimensional approach.

Findings

Wider grain size distributions reduce resistivity by over 50%.

Larger grains lead to fewer grain boundaries and barriers.

Resistivity decreases from 11 kΩ·cm to 4.5 kΩ·cm for 175 nm grains.

Abstract

Current transport in polysilicon is a complicated process with many factors to consider. The inhomogeneous nature of polysilicon with its differently shaped and sized grains is one such consideration. We have developed a method that enhances existing resistivity models with a two-dimensional extension that incorporates the grain size distribution using a Voronoi-based resistor network. We obtain grain size distributions both from our growth simulations (700 K, 800 K, and 900 K) and experimental analysis. Applying our method, we investigate the effect that variation in grain size produces with cases of different average grain sizes (2 nm to 3 $\mu$m). For example, the resistivity of polysilicon with an average grain size of 175 nm drops from 11 k$\Omega$ $\cdot$ cm to 4.5 k$\Omega$ $\cdot$ cm when compared to conventional one-dimensional modeling. Our study highlights the strong effect of grain size variation on resistivity, revealing that wider distributions result in significant resistivity reductions of up to more than 50%. Due to the larger grains present with a grain size distribution, current transport encounters fewer grain boundaries while the average grain size remains the same resulting in fewer barriers along the current transport path. Incorporating the grain structure into the resistivity modeling facilitates a more detailed and comprehensive characterization of the electrical properties of polysilicon.