Modeling and optimization of monolithic polycrystalline silicon resistors

The processing parameters of monolithic polycrystalline silicon resistors are examined, and the effect of grain size on the sensitivity of polysilicon resistivity versus doping concentration is studied theoretically and experimentally. Because existing models for polysilicon do not accurately predict resistivity dependence on doping concentration as grain size increases above 600 Å, a modified trapping model for polysilicon with different grain sizes and under various applied biases is introduced. Good agreement between theory and experiments demonstrates that an increase in grain size from 230 to 1220 Å drastically reduces the sensitivity of polysilicon resistivity to doping levels by two orders of magnitude. Such an increase is achieved by modifications of the integrated-circuit processes. Design criteria for the optimization of monolithic polysilicon resistors have also been established based on resistivity control, thermal properties, and device geometry.