Process variations in advanced CMOS process nodes limit the benefits of scaling for analog designs. In the presence of increasing random intra-die variations, mismatch becomes a significant design challenge in circuits such as comparators. In this paper we describe and demonstrate the details of a statistical element selection (SES) methodology that relies on choosing a subset of selectable circuit elements (e.g., input transistors in a comparator) to achieve the desired specification (e.g., offset). Silicon results from a 65nm test chip demonstrate that SES can achieve an order of magnitude better matching than both redundancy and Pelgrom-model sizing given the same core circuit area.
I. INTRODUCTIONContinuous advancement of CMOS process technology over the past four decades has made inexpensive integrated circuit products with significant processing capabilities an everyday reality. Cost pressures have resulted in substantial integration of analog and digital blocks on the same die, forcing analog designers to adapt to processes that were built for digital systems [1,2]. As we rapidly approach the physical limits of scaling, one of the major challenges for analog circuits has been to ensure consistently high yield in the presence of increasing variability in these nanoscale CMOS processes.In this paper we explore the benefits of a statistical element selection (SES) methodology for analog circuits that is based on post-manufacturing tuning to accommodate large-scale process variations [3,4]. SES exploits inherent random variations to improve the matching of transistors and to increase yield for matching-critical circuits such as comparators. A subset of k elements is selected among an identically laid out set of N elements to provide the best matching performance. As the number of available subsets among a set of N elements increases exponentially (2 N -1), it is possible to achieve impressive matching performance with near-minimum size unit elements. The elements might be individual transistors, pairs of transistors, or passive components.We present a general methodology to determine the appropriate (N, k) numbers and the size of the unit element to ensure that a desired matching specification is met. We present measurement results from a 65nm CMOS test chip using SESbased comparators to validate the model predictions. The generalized methodology can be used for a wide variety of analog circuits-such as current sources, differential amplifiers and comparators-that rely on precise matching of components.