Eric W. Beach

Mismatch characterization of a high precision resistor array test structure

In this paper we describe a 2times (2timesn) pad resistor array test structure. The structure can also be used for analog CMOS, bipolar, capacitor arrays. It provides a flexible and convenient way to study devices in an array. We will focus on various matching properties of the precision thin film resistors, specifically, between any one of the resistors with the average of the whole array, between two resistors (neighbor and far away pair), and between resistor combinations in the array. Both random and systematic mismatch properties are studied. We illustrate key factors for resistor matching from both process and layout perspectives. The principles, analyses and main conclusions apply to other active and passive devices as well. The array layout can be copied directly from and into a circuit design.

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.