Simple Analytical Model of the Thermal Resistance of Resistors in Integrated Circuits

The value of resistors generally changes with electrical current. For precision analog circuit layout, it is important to predict those resistance variations. For that purpose, we derive for the first time a simple analytic 3-D model to describe thermal resistance and self-heating, which we show as the dominant contribution to resistor nonlinearity for a wide range of resistors. The model shows good agreement with numerical simulations. Measured voltage coefficients of metal and polysilicon resistors can be fit to the model over a wide range of geometries. Finally, we show how thermal resistance can be reduced by placing metal bar structures underneath the resistor and apply the model to quantify the improvement.