A precision physical model for three terminal diffused or ion-implanted resistors

In modern CMOS and BiCMOS technologies, the diffused or ion-implanted resistors are widely used devices. One important source of errors in the accurate analog circuit simulation is the variation of resistance respect to applied voltage for diffused or ion-implanted resistors. This paper analyzes the electrical properties of the diffused resistors, and derives a closed form precision physical model for three terminal diffused resistors or ion-implanted. The voltage dependency of the resistance can be described by the depletion layer spreading into the resistor body. The back bias effect is also included in the model. The temperature model is derived from the mobility and built-in potential temperature models. The extreme cases have been studied, which sets up the minimum resistor width and maximum applied voltage of diffused or ion-implanted resistors. Good match between the modeled and experimental results is observed in the diffused resistors with n- and p-type doping.