Process variations have become a serious concern for nanometer technologies. The interconnect and device variations include inter-and intra-die variations of geometries, as well as process and electrical parameters. In this paper, pattern (i.e. density, width and space) dependent interconnect thickness and width variations are studied based on a well-designed test chip in a 90 nm technology. The parasitic resistance and capacitance variations due to the process variations are investigated, and process-variation-aware extraction techniques are proposed. In the test chip, electrical and physical measurements show strong metal thickness and width variations mainly due to chemical mechanical polishing (CMP) in nanometer technologies. The loop inductance dependence of return patterns is also validated in the test chip. The proposed new characterization methods extract interconnect RC variations as a function of metal density, width and space. Simulation results show excellent agreement between on-wafer measurements and extractions of various RC structures, including a set of metal loaded/unloaded ring oscillators in a complex wiring environment.

Models and techniques used in a switched-capacitor functional model generator are described. The simulation models described are asynchronous with respect to the clock inputs, and the proposed models are useful for achieving functional verification of chips consisting of clock generating circuitry, switched-capacitor circuits, and other analog or digital blocks. Graph-based methods are used for each clock configuration to minimize CPU requirements. Continuous feedthrough of the analog signals is adequately handled. The program MODGENSC has been developed to generate the models directly from the circuit description in SWITCAP. With this capability, full-chip mixed digital/analog simulation is achievable and the simulation time is reduced significantly.>

Recent trends in the integration of process-, device-, and circuit-modeling tools and the current rapid emergence of Unix-based computing environments of networked workstations and computer engines makes possible user-friendly, task-based CAD systems for technology optimization, characterization, and cell design. The authors discuss these trends and identify opportunities to use technology CAD tools in the development of competitive technologies and products. It is shown that the ability to provide design centering and extreme-case analysis related to process variables has been a key to aggressive design of robust IC products. This capability results from efforts in the early to mid-1980's to establish integrated modeling systems such as MECCA, the application of general-purpose optimization capabilities such as WATOPT and CENTER, and recent advances in open and powerful computing environments (principally Unix-based distributed resources).>

The approximation of MOSFET nonlinearities by use of polynomial splines was investigated for reducing both circuit model development time and model simulation cost. After a brief tutorial on spline functions, it is shown how the number of independent variables for the MOSFET simulation models in digital circuits is reduced by their use. A tableau formulation for generating splines is presented along with a storage-reduction technique for polynomial spline coefficients. Mathematical programming problems for one-, two-, and three-dimensional splines are given that result in accurate monotonic splines using few segments. Two spline segments are shown to provide sufficient accuracy in the one-dimensional case, while 4*4 and 2*5*5 segments provide sufficient accuracy in the two- and three-dimensional cases, respectively.>

A nonlinear constrained optimizer, WATOPT, targeted towards circuit applications is described. It utilizes a specially tailored quadratic program which reduces storage requirements and improves speed of computations. Three advanced designs in the frequency domain show application.

The discipline of linear graph theory, which has been applied extensively to the analysis of electrical networks, is now extended to encompass general three-dimensional isolated rigid-body systems. The graph-theoretic models of a rigid body and its relevant components are discussed elaborately to pave the way for further studies in multibody systems. Utilizing the analysis based on system topology, the mathematical model of a mechanical system is derived by means of a hybrid formulation in which Euler parameters (or normalized quaternions) are incorporated to define the orientations of rigid bodies. A single body system serves as an illustrative example.