Physical model for the resistivity and temperature coefficient of resistivity in heavily doped polysilicon

One of the key benefits of using polysilicon as the material for resistors and piezoresistors is that the temperature coefficient of resistivity (TCR) can be tailored to be negative, zero, or positive by adjusting the doping concentration. This paper focuses on optimization of the boron doping of low-pressure chemical vapor deposited polysilicon resistors for obtaining near-zero TCR and development of a physical model that explains quantitatively all the results obtained in the optimization experiments encompassing the doping concentration ranges that show negative, near-zero, and positive TCR values in the polysilicon resistors. The proposed model considers single-crystal silicon grain in equilibrium with amorphous silicon grain boundary. The grain boundary carrier concentration is calculated considering exponential band tails in the density of states for amorphous silicon in the grain boundaries. Comparison of the results from the model shows excellent agreement with the measured values of resistivity as well as TCR for heavily doped polysilicon. It is shown that the trap density for holes in the grain boundary increases as the square root of the doping concentration, which is consistent with the defect compensation model of doping in the amorphous silicon grain boundaries.