Prediction for Distribution of Interconnects in Nano-Systems

Interconnect density prediction is important to investigate the future of giga-scale integration [1]. Nowadays IC designers confront Very Deep Submicron (VDSM) and nano-scale challenges and opportunities. International Technology Roadmap for Semiconductor (ITRS) reports a total wire length of thousands of meters for a die of only 2×2 mm2! Technology Scaling deepens the effects of parasitics and increases the density of interconnects [2]. To describe the behavior of interconnects in such all-wire SoC or NoC the congestion of interconnects should be defined [3]. One quantity that describes this congestion is Interconnect Density Function (IDF) [4]. For a given interconnect length of L, Interconnect Density Function (IDF(L)) is defined as the number of interconnects per unit length of die. The larger value for IDF means the more congestion for interconnects. Other quantity is Interconnect Pattern Density (IPD). IPD(L) is the fractional area occupied by interconnects on a certain area (window) of a die. Prediction here means that IDF and IPD can be calculated before the layout stage [5]. This prediction is useful in the design flow of Wireless Sensor Networks (WSN), Lab on Chips, processors, FPGAs, Retina Chips and many other VDSM and nano-scale designs. Then it is possible to predict power, delay and crosstalk in early stages of chip design [6]. In the past, some works have been performed toward IDF prediction. However, each of them suffers of limitations. For instance in [1] there is limited information on IDF distribution; in [2] the interconnect length is constant. In [4] and [6] there is no information on the distribution of IDF and also the average distance between two adjacent gates (so called Gate Pitch) is constant. This work predicts IDF to overcome some mentioned drawbacks of previous works. It basically uses a Bernoulli probability distribution and Rent’s Rule for interconnects. Although we may choose different distributions such as Poison, Binomial and so on, a simple math suggests that assumptions we make for the distribution calculations, are best fitted to Bernoulli function.