Anand Panyam

Routing in the Third Dimension

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Over-the-cell routing algorithms for industrial cell models

The effective utilization of over-the-cell areas for routing leads to minimization or elimination of channel areas in standard cell designs. In this paper, we present two results. Firstly, we develop a new cell model called Target Based Cell (TBC) designs. Standard cells in TBC designs have terminals in the form of vertical segments in M1 layer. The exact locations for placing interconnect contacts on the targets are determined by the routing algorithms. Cell widths in TBC designs are smaller than the widths in existing cell designs and have improved over-the-cell routing flexibility. Secondly, we develop an efficient router for TBC designs which includes two key features; an optimal O(KL) algorithm (where K, and L are number of cell rows and layout width respectively) for assigning over-the-cell area to each channel, so as to minimize total layout height, and an irregular boundary channel HV-HVH-HV router for over-the-cell and channel areas between terminal rows which optimally utilizes the over-the-cell area.<<ETX>>

Comparative analysis of new CMOS leaf cells for OTC routing

Recently four new cell models have been developed for over the cell routing. The usefulness of a cell model cannot simply be determined by utilization of OTC areas since cell widths, gate delays and layout parameters must also be considered. In this paper, we develop standard cells libraries in all the four models and compare the cell width and gate delay analysis of the cells. We also study the parameters which contribute to the variation in cell widths and gate delay between the different cell models. We show that the main parameters which contribute to the difference in cell widths in the four models are the number of terminals, intracell routing and cell functionality.<<ETX>>

Middle terminal cell models for efficient over-the-cell routing in high-performance circuits

A new class of cell models called middle terminal models (MTM) is introduced. MTM-based cells allow flexibility in the selection of terminal locations and therefore utilize the over-the-cell (OTC) area more efficiently, as compared to cells based on existing models. For MTM-based designs, two new routers, MTM+V and MTM-V are presented. The first router is suitable for processes that allow vias over-the-cell and is based on an optimal Theta (K) algorithm for terminal row selection for over-the-cell channel routing, where K is the number of cell rows. The second router is suitable for the processes which do not allow vias in over-the-cell areas. This router consists of two key steps. The first step consists of the selection of a maximum planar set of nets for routing in between the terminal rows. For the second step, an optimal algorithm is developed for planar routing between the terminal row and the cell boundary. The experimental results on the PRIMARY I benchmark show that for a two-layer model, MTM-V performs 4.20% better than the best existing routers. >

An efficient four layer over-the-cell router

Several Over-the-Cell (OTC) routing algorithms have been proposed for two and three layer processes. All the existing OTC routers assume that the terminals are laid out in a specific predetermined fashion. These restrictions on the terminals complicate the task of cell design and increase the width of the cells. In this paper, we develop a four layer OTC router which allows arbitrary terminal locations. Freed from fixed terminal placement restrictions, cell designers can aim to design with minimum width. Our router has been implemented and tested on several circuits. For most of the circuits, it obtained channel-less layouts.<<ETX>>

On Optimum Cell Models for Over-the-Cell Routing

Abst r act Over-theCell routing has led to significant improvement in the layout area in standard cell designs, and several over-the-cell routers have been developed. The effectiveness of utilization of the over-the-cell metal layers is determined by the cell model. As a result, research is focused on development of new cell models. Based o n the locations of terminals there are two classes of models in use, a class of Boundary Terminal Models ( B T M ) and a class of Center Terminal Models (CTM) . The first class performs well for the channels with large set of independent nets, on the other hand, C T M performs well for channels with large vertical constraint chains. In this paper, we present two results. First, we introduce a new class of cell model called Middle Terminal Model M T M ) that combines the advantages of

Efficient OTC routing algorithm for via-less middle terminal models

MTM-V router, an efficient router for MTM based standard cell designs when vias are not allowed over-the-cell, is presented. MTM-V router is based on two key algorithms. First, an approximation algorithm to select a planar set of nets for routing between two terminal rows of a cell row is developed. Second, an optimal algorithm for planar routing between the terminal row and the cell boundary is developed. MTM-V router has been implemented in C on a SUN SPARC-station 1+ and has been tested on several benchmarks including PRIMARY I and PRIMARY II from MCNC. MTM-V router produces smaller height layouts as compared to those produced by the routers based on the existing cell models.<<ETX>>

Optimal algorithms for planar over-the-cell routing problems

In this paper, we consider the two row maximum planar subset (TRMPS) problem in over-the-cell routing. The TRMPS problem requires selection of the maximum planar subset of nets, which can be routed between two rows of terminals in a cell row. This problem was first encountered by Gong, Liu, and Preas (1990). They stated the complexity of this problem to be unknown, and presented a min {1,k/d(S)} approximation algorithm, where k is the number of tracks available over the cell area and d(S) is the density of a solution S. We show that TRMPS problem can be solved optimally in polynomial time. We present a O(kn/sup 2/) dynamic programming algorithm for the TRMPS problem, where n is the number of nets. We also present a parallel version of our algorithm, which has a complexity of O(kn). Our algorithm can also be extended to solve the TRMPS problem, in the presence of prerouted nets, a chosen subset of nets, as well as for planar channel routing. We also apply our technique to obtain a 0.5 approximation, for over the cell routing in middle terminal model, thus improving the best known existing algorithm. The weighted version of the TRMPS problem, as well as, all the extensions can also be solved in O(kn/sup 2/) time.

Efficient over-the-cell routing algorithm for general middle terminal model

A new class of cell models called Middle Terminal Model (MTM) has been proposed. In MTM, each cell contains two rows of terminals such that two terminals in a column of a cell are equipotential. Selecting an appropriate terminal row from two terminal rows available for each cell row in a standard cell design allows allocation of more over-the-cell area to the nets in congested channels. The MTM+V router is presented. It is an efficient router for MTM based standard cell designs, when vias are allowed in over-the-cell areas. The MTM+V router is based on two key algorithms, i.e., an optimal algorithm for terminal row selection and a greedy routing algorithm for over-the-cell and channel routing.<<ETX>>

Routing Algorithms for the Advanced ThreeLayer Process

This chapter contains sections titled: Routing Algorithm for the BTM Routing Algorithms for the CTM Routing Algorithms for the MTM Routing Algorithms for the ATM Routing Algorithms for the TBC Experimental Evaluation of Routers Summary This chapter contains sections titled: Problems Bibliographic Notes